Abstract

Typically, photonic waveguides designed for nonlinear frequency conversion rely on intuitive and established principles, including index guiding and bandgap engineering, and are based on simple shapes with high degrees of symmetry. We show that recently developed inverse-design techniques can be applied to discover new kinds of microstructured fibers and metasurfaces designed to achieve large nonlinear frequency-conversion efficiencies. As a proof of principle, we demonstrate complex, wavelength-scale chalcogenide glass fibers and gallium phosphide three-dimensional metasurfaces exhibiting some of the largest nonlinear conversion efficiencies predicted thus far, e.g., lowering the power requirement for third-harmonic generation by 104 and enhancing second-harmonic generation conversion efficiency by 107. Such enhancements arise because, in addition to enabling a great degree of tunability in the choice of design wavelengths, these optimization tools ensure both frequency- and phase-matching in addition to large nonlinear overlap factors.

© 2018 Chinese Laser Press

Full Article  |  PDF Article

Corrections

12 March 2019: A correction was made to the funding section.


OSA Recommended Articles
Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization

Zin Lin, Xiangdong Liang, Marko Lončar, Steven G. Johnson, and Alejandro W. Rodriguez
Optica 3(3) 233-238 (2016)

Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion

Zin Lin, Marko Lončar, and Alejandro W. Rodriguez
Opt. Lett. 42(14) 2818-2821 (2017)

Enhanced nonlinear optics in photonic-crystal microcavities

Jorge Bravo-Abad, Alejandro Rodriguez, Peter Bermel, Steven G. Johnson, John D. Joannopoulos, and Marin Soljačić
Opt. Express 15(24) 16161-16176 (2007)

References

  • View by:
  • |
  • |
  • |

  1. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
    [Crossref]
  2. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. 22, 1341–1343 (1997).
    [Crossref]
  3. T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).
    [Crossref]
  4. P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31, 71–73 (2006).
    [Crossref]
  5. K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
    [Crossref]
  6. R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).
  7. A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
    [Crossref]
  8. S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
    [Crossref]
  9. S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
    [Crossref]
  10. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
    [Crossref]
  11. M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today 47, 25–32 (1994).
    [Crossref]
  12. M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004).
    [Crossref]
  13. Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
    [Crossref]
  14. L.-A. Wu, M. Xiao, and H. J. Kimble, “Squeezed states of light from an optical parametric oscillator,” J. Opt. Soc. Am. B 4, 1465–1476 (1987).
    [Crossref]
  15. C. Simonneau, J. P. Debray, J. C. Harmand, P. Vidaković, D. J. Lovering, and J. A. Levenson, “Second-harmonic generation in a doubly resonant semiconductor microcavity,” Opt. Lett. 22, 1775–1777 (1997).
    [Crossref]
  16. R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117–122 (1994).
  17. K. Koch and G. T. Moore, “Singly resonant cavity-enhanced frequency tripling,” J. Opt. Soc. Am. B 16, 448–459 (1999).
    [Crossref]
  18. M. Liscidini and L. A. Andreani, “Highly efficient second-harmonic generation in doubly resonant planar microcavities,” Appl. Phys. Lett. 85, 1883–1885 (2004).
    [Crossref]
  19. K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
    [Crossref]
  20. D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
    [Crossref]
  21. Z. Lin, T. Alcorn, M. Loncar, S. Johnson, and A. Rodriguez, “High-efficiency degenerate four wave-mixing in triply,” Phys. Rev. A 89, 053839 (2014).
    [Crossref]
  22. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012).
    [Crossref]
  23. Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators,” Opt. Express 20, 7526–7543 (2012).
    [Crossref]
  24. K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
    [Crossref]
  25. S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).
    [Crossref]
  26. A. Rodriguez, M. Soljačić, J. D. Joannopulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
    [Crossref]
  27. Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
    [Crossref]
  28. Z. Lin, M. Lončar, and A. W. Rodriguez, “Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion,” arXiv:1701.05628 (2017).
  29. L. Goldberg and D. A. V. Kliner, “Tunable UV generation at 286 nm by frequency tripling of a high-power mode-locked semiconductor laser,” Opt. Lett. 20, 1640–1642 (1995).
    [Crossref]
  30. Y. Yelin and D. Silberberg, “Laser scanning third-harmonic-generation microscopy in biology,” Opt. Express 5, 169–175 (1999).
    [Crossref]
  31. P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
    [Crossref]
  32. D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
    [Crossref]
  33. K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 98, 263113 (2011).
    [Crossref]
  34. S. Buckley, M. Radulaski, K. Biermann, and J. Vuckovic, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” arXiv:1308.6051v1 (2013).
  35. D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
    [Crossref]
  36. R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).
  37. M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, “Colloquium: nonlinear metamaterials,” Rev. Mod. Phys. 86, 1093–1123 (2014).
    [Crossref]
  38. S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett. 104, 131104 (2014).
    [Crossref]
  39. J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
    [Crossref]
  40. O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
    [Crossref]
  41. K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
    [Crossref]
  42. Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
    [Crossref]
  43. N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).
    [Crossref]
  44. J. Butet, P.-F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9, 10545–10562 (2015).
    [Crossref]
  45. A. Bétourné, Y. Quiquempois, G. Bouwmans, and M. Douay, “Design of a photonic crystal fiber for phase-matched frequency doubling or tripling,” Opt. Express 16, 14255–14262 (2008).
    [Crossref]
  46. F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1158–1160 (2001).
    [Crossref]
  47. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
    [Crossref]
  48. G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
    [Crossref]
  49. S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
    [Crossref]
  50. O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
    [Crossref]
  51. M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
    [Crossref]
  52. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).
  53. S. Molesky, Z. Lin, A. Piggot, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Outlook for inverse design in nanophotonics,” arXiv:1801.06715 (2018).
  54. W. J. Kim and J. D. O’Brien, “Optimization of a two-dimensional photonic-crystal waveguide branch by simulated annealing and the finite-element method,” J. Opt. Soc. Am. B 21, 289–295 (2004).
    [Crossref]
  55. B. S. Darki and N. Granpayeh, “Improving the performance of a photonic crystal ring-resonator-based channel drop filter using particle swarm optimization method,” Opt. Commun. 283, 4099–4103 (2010).
    [Crossref]
  56. M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2014).
    [Crossref]
  57. A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
    [Crossref]
  58. J. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
    [Crossref]
  59. N. Aage, E. Andreassen, B. S. Lazarov, and O. Sigmund, “Giga-voxel computational morphogenesis for structural design,” Nature 550, 84–86 (2017).
    [Crossref]
  60. X. Liang and S. G. Johnson, “Formulation for scalable optimization of microcavities via the frequency-averaged local density of states,” Opt. Express 21, 30812–30841 (2013).
    [Crossref]
  61. D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21, 14223–14243 (2013).
    [Crossref]
  62. A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
    [Crossref]
  63. H. Men, K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson, “Robust topology optimization of three-dimensional photonic-crystal band-gap structures,” arXiv:1405.4350 (2014).
  64. A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
    [Crossref]
  65. B. Shen, P. Wang, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
    [Crossref]
  66. G. Strang, Computational Science and Engineering (Wellesley-Cambridge, 2007), Vol. 791.
  67. J. D. Deaton and R. V. Grandhi, “A survey of structural and multidisciplinary continuum topology optimization: post 2000,” Struct. Multidiscip. Optim. 49, 1–38 (2014).
    [Crossref]
  68. M. P. Bendsøe, O. Sigmund, M. P. Bendsøe, and O. Sigmund, Topology Optimization by Distribution of Isotropic Material (Springer, 2004).
  69. M. Y. Wang, X. Wang, and D. Guo, “A level set method for structural topology optimization,” Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003).
    [Crossref]
  70. J. Haslinger and R. A. Mäkinen, Introduction to Shape Optimization: Theory, Approximation, and Computation (SIAM, 2003).
  71. K. Svanberg, “A class of globally convergent optimization methods based on conservative convex separable approximations,” SIAM J. Optim. 12, 555–573 (2002).
    [Crossref]
  72. F. Wang and O. Sigmund, “Optimization of photonic crystal cavities,” in International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) (IEEE, 2017), pp. 39–40.
  73. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  74. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).
  75. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
    [Crossref]
  76. X. Feng, T. Monro, P. Petropoulos, V. Finazzi, and D. Hewak, “Solid microstructured optical fiber,” Opt. Express 11, 2225–2230 (2003).
    [Crossref]
  77. V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13, 6798–6806 (2005).
    [Crossref]
  78. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2012), Vol. 222.
  79. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
    [Crossref]
  80. L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118, 243904 (2017).
    [Crossref]
  81. S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photon. 3, 117–123 (2015).
    [Crossref]
  82. A. Krasnok, M. Tymchenko, and A. Alù, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” arXiv:1706.07563 (2017).
  83. W. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
    [Crossref]
  84. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coefficients,” J. Opt. Soc. Am. B 14, 2268–2294 (1997).
    [Crossref]

2017 (3)

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

N. Aage, E. Andreassen, B. S. Lazarov, and O. Sigmund, “Giga-voxel computational morphogenesis for structural design,” Nature 550, 84–86 (2017).
[Crossref]

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118, 243904 (2017).
[Crossref]

2016 (2)

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

2015 (10)

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).
[Crossref]

J. Butet, P.-F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9, 10545–10562 (2015).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photon. 3, 117–123 (2015).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

B. Shen, P. Wang, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

2014 (9)

J. D. Deaton and R. V. Grandhi, “A survey of structural and multidisciplinary continuum topology optimization: post 2000,” Struct. Multidiscip. Optim. 49, 1–38 (2014).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).
[Crossref]

M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, “Colloquium: nonlinear metamaterials,” Rev. Mod. Phys. 86, 1093–1123 (2014).
[Crossref]

S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett. 104, 131104 (2014).
[Crossref]

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2014).
[Crossref]

Z. Lin, T. Alcorn, M. Loncar, S. Johnson, and A. Rodriguez, “High-efficiency degenerate four wave-mixing in triply,” Phys. Rev. A 89, 053839 (2014).
[Crossref]

2013 (2)

2012 (3)

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators,” Opt. Express 20, 7526–7543 (2012).
[Crossref]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012).
[Crossref]

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

2011 (4)

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
[Crossref]

D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
[Crossref]

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 98, 263113 (2011).
[Crossref]

J. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[Crossref]

2010 (5)

B. S. Darki and N. Granpayeh, “Improving the performance of a photonic crystal ring-resonator-based channel drop filter using particle swarm optimization method,” Opt. Commun. 283, 4099–4103 (2010).
[Crossref]

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[Crossref]

D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

2009 (2)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (4)

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31, 71–73 (2006).
[Crossref]

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[Crossref]

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[Crossref]

2005 (2)

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13, 6798–6806 (2005).
[Crossref]

2004 (3)

W. J. Kim and J. D. O’Brien, “Optimization of a two-dimensional photonic-crystal waveguide branch by simulated annealing and the finite-element method,” J. Opt. Soc. Am. B 21, 289–295 (2004).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004).
[Crossref]

M. Liscidini and L. A. Andreani, “Highly efficient second-harmonic generation in doubly resonant planar microcavities,” Appl. Phys. Lett. 85, 1883–1885 (2004).
[Crossref]

2003 (2)

X. Feng, T. Monro, P. Petropoulos, V. Finazzi, and D. Hewak, “Solid microstructured optical fiber,” Opt. Express 11, 2225–2230 (2003).
[Crossref]

M. Y. Wang, X. Wang, and D. Guo, “A level set method for structural topology optimization,” Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003).
[Crossref]

2002 (3)

K. Svanberg, “A class of globally convergent optimization methods based on conservative convex separable approximations,” SIAM J. Optim. 12, 555–573 (2002).
[Crossref]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[Crossref]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

2001 (1)

1999 (2)

1997 (3)

1995 (1)

1994 (3)

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today 47, 25–32 (1994).
[Crossref]

R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117–122 (1994).

1989 (1)

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[Crossref]

1987 (1)

1982 (1)

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).
[Crossref]

1965 (1)

W. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[Crossref]

Aage, N.

N. Aage, E. Andreassen, B. S. Lazarov, and O. Sigmund, “Giga-voxel computational morphogenesis for structural design,” Nature 550, 84–86 (2017).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2012), Vol. 222.

Ahmad, R.

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Albrecht, R.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Alcorn, T.

Z. Lin, T. Alcorn, M. Loncar, S. Johnson, and A. Rodriguez, “High-efficiency degenerate four wave-mixing in triply,” Phys. Rev. A 89, 053839 (2014).
[Crossref]

Alibart, O.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Allerman, A. A.

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

Alu, A.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Alù, A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

A. Krasnok, M. Tymchenko, and A. Alù, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” arXiv:1706.07563 (2017).

Amann, M.-C.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Andersen, U. L.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Anderson, E.

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Andreani, L. A.

M. Liscidini and L. A. Andreani, “Highly efficient second-harmonic generation in doubly resonant planar microcavities,” Appl. Phys. Lett. 85, 1883–1885 (2004).
[Crossref]

Andreassen, E.

N. Aage, E. Andreassen, B. S. Lazarov, and O. Sigmund, “Giga-voxel computational morphogenesis for structural design,” Nature 550, 84–86 (2017).
[Crossref]

Arbore, M. A.

Arend, C.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Argyropoulos, C.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Arriaga, J.

Avayu, O.

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118, 243904 (2017).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photon. 3, 117–123 (2015).
[Crossref]

Babinec, T. M.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

Baldi, P.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Becher, C.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Belkin, M. A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Bendsøe, M. P.

M. P. Bendsøe, O. Sigmund, M. P. Bendsøe, and O. Sigmund, Topology Optimization by Distribution of Isotropic Material (Springer, 2004).

M. P. Bendsøe, O. Sigmund, M. P. Bendsøe, and O. Sigmund, Topology Optimization by Distribution of Isotropic Material (Springer, 2004).

Benoit, G.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[Crossref]

Benz, A.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett. 104, 131104 (2014).
[Crossref]

Bétourné, A.

Bi, Z.-F.

Biermann, K.

S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).
[Crossref]

S. Buckley, M. Radulaski, K. Biermann, and J. Vuckovic, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” arXiv:1308.6051v1 (2013).

Bliss, D.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31, 71–73 (2006).
[Crossref]

Boehm, G.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Bond, W.

W. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[Crossref]

Borrelli, N. F.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[Crossref]

Boulesbaa, A.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Bouwmans, G.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Brener, I.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett. 104, 131104 (2014).
[Crossref]

Brevet, P.-F.

J. Butet, P.-F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9, 10545–10562 (2015).
[Crossref]

Briggs, D. P.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Buckley, S.

S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).
[Crossref]

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 98, 263113 (2011).
[Crossref]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
[Crossref]

S. Buckley, M. Radulaski, K. Biermann, and J. Vuckovic, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” arXiv:1308.6051v1 (2013).

Butet, J.

J. Butet, P.-F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9, 10545–10562 (2015).
[Crossref]

Campione, S.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett. 104, 131104 (2014).
[Crossref]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Capolino, F.

S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett. 104, 131104 (2014).
[Crossref]

Chen, C. K.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).
[Crossref]

Chen, L.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[Crossref]

Chen, P.-Y.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Chou, M. H.

Corcoran, B.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Darki, B. S.

B. S. Darki and N. Granpayeh, “Improving the performance of a photonic crystal ring-resonator-based channel drop filter using particle swarm optimization method,” Opt. Commun. 283, 4099–4103 (2010).
[Crossref]

Deaton, J. D.

J. D. Deaton and R. V. Grandhi, “A survey of structural and multidisciplinary continuum topology optimization: post 2000,” Struct. Multidiscip. Optim. 49, 1–38 (2014).
[Crossref]

Debray, J. P.

DeLong, K. W.

Demmerle, F.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Douay, M.

Duchesne, D.

Dumbaugh, W. H.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[Crossref]

Dumeige, Y.

Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[Crossref]

Eggleton, B. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Ellenbogen, T.

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118, 243904 (2017).
[Crossref]

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photon. 3, 117–123 (2015).
[Crossref]

Elser, D.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Engeness, T.

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Fedrizzi, A.

D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref]

Fejer, M. M.

Feng, X.

Feron, P.

Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[Crossref]

Fiedler, K.

R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117–122 (1994).

Finazzi, V.

Fink, Y.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[Crossref]

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Fraser, S. E.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[Crossref]

Freund, R. M.

H. Men, K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson, “Robust topology optimization of three-dimensional photonic-crystal band-gap structures,” arXiv:1405.4350 (2014).

Fürst, J. U.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Gabrielli, L. H.

Galvanauskas, A.

Geohegan, D.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Gisin, N.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Goldberg, L.

Gomez-Diaz, J. S.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

Gondarenko, A.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[Crossref]

Grandhi, R. V.

J. D. Deaton and R. V. Grandhi, “A survey of structural and multidisciplinary continuum topology optimization: post 2000,” Struct. Multidiscip. Optim. 49, 1–38 (2014).
[Crossref]

Granpayeh, N.

B. S. Darki and N. Granpayeh, “Improving the performance of a photonic crystal ring-resonator-based channel drop filter using particle swarm optimization method,” Opt. Commun. 283, 4099–4103 (2010).
[Crossref]

Grillet, C.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Grubsky, V.

Guo, D.

M. Y. Wang, X. Wang, and D. Guo, “A level set method for structural topology optimization,” Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

Halder, M.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Hall, D. W.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[Crossref]

Hamel, D. R.

D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref]

Harmand, J. C.

Harris, J. S.

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31, 71–73 (2006).
[Crossref]

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

Hart, S. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[Crossref]

Harter, D.

Hashemi, H.

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators,” Opt. Express 20, 7526–7543 (2012).
[Crossref]

D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
[Crossref]

Haslinger, J.

J. Haslinger and R. A. Mäkinen, Introduction to Shape Optimization: Theory, Approximation, and Computation (SIAM, 2003).

Hatami, F.

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 98, 263113 (2011).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
[Crossref]

Heinz, T. F.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).
[Crossref]

Hendler, N.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).
[Crossref]

Hepp, C.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Hewak, D.

Hunter, J.

Hurlbut, W. C.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

Ibanescu, M.

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Ito, R.

Jennewein, T.

D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref]

Jensen, J.

J. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[Crossref]

Jetter, M.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Jin, W.

S. Molesky, Z. Lin, A. Piggot, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Outlook for inverse design in nanophotonics,” arXiv:1801.06715 (2018).

Joannopoulos, J. D.

D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004).
[Crossref]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Joannopulos, J. D.

Johnson, S.

Z. Lin, T. Alcorn, M. Loncar, S. Johnson, and A. Rodriguez, “High-efficiency degenerate four wave-mixing in triply,” Phys. Rev. A 89, 053839 (2014).
[Crossref]

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Johnson, S. G.

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

X. Liang and S. G. Johnson, “Formulation for scalable optimization of microcavities via the frequency-averaged local density of states,” Opt. Express 21, 30812–30841 (2013).
[Crossref]

D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21, 14223–14243 (2013).
[Crossref]

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators,” Opt. Express 20, 7526–7543 (2012).
[Crossref]

D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
[Crossref]

A. Rodriguez, M. Soljačić, J. D. Joannopulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

H. Men, K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson, “Robust topology optimization of three-dimensional photonic-crystal band-gap structures,” arXiv:1405.4350 (2014).

Kadlec, E. A.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

Kante, B.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

Keeler, G. A.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Keren-Zur, S.

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118, 243904 (2017).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photon. 3, 117–123 (2015).
[Crossref]

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).
[Crossref]

Keßler, C. A.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Kettler, J.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Kiesel, N.

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

Kim, W. J.

Kimble, H. J.

King, W.

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Kitamoto, A.

Kivshar, Y. S.

M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, “Colloquium: nonlinear metamaterials,” Rev. Mod. Phys. 86, 1093–1123 (2014).
[Crossref]

Klem, J. F.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

Kliner, D. A. V.

Knight, J. C.

Koch, K.

Kondo, T.

Kozlov, V. G.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

Krasnok, A.

A. Krasnok, M. Tymchenko, and A. Alù, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” arXiv:1706.07563 (2017).

Krauss, T. F.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Kravchenko, I. I.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Krischek, R.

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

Kuo, P. S.

Kurz, P.

R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117–122 (1994).

Lagoudakis, K. G.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

Lapine, M.

M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, “Colloquium: nonlinear metamaterials,” Rev. Mod. Phys. 86, 1093–1123 (2014).
[Crossref]

Lassen, M.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Lazarov, B. S.

N. Aage, E. Andreassen, B. S. Lazarov, and O. Sigmund, “Giga-voxel computational morphogenesis for structural design,” Nature 550, 84–86 (2017).
[Crossref]

Lee, J.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Lee, K. Y. K.

H. Men, K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson, “Robust topology optimization of three-dimensional photonic-crystal band-gap structures,” arXiv:1405.4350 (2014).

Lee, Y.-S.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

Lenhard, A.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Leuchs, G.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Levenson, J. A.

Li, G.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

Liang, X.

Lin, Z.

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

Z. Lin, T. Alcorn, M. Loncar, S. Johnson, and A. Rodriguez, “High-efficiency degenerate four wave-mixing in triply,” Phys. Rev. A 89, 053839 (2014).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
[Crossref]

S. Molesky, Z. Lin, A. Piggot, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Outlook for inverse design in nanophotonics,” arXiv:1801.06715 (2018).

Z. Lin, M. Lončar, and A. W. Rodriguez, “Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion,” arXiv:1701.05628 (2017).

Lipson, H.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[Crossref]

Lipson, M.

D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21, 14223–14243 (2013).
[Crossref]

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[Crossref]

Liscidini, M.

M. Liscidini and L. A. Andreani, “Highly efficient second-harmonic generation in doubly resonant planar microcavities,” Appl. Phys. Lett. 85, 1883–1885 (2004).
[Crossref]

Liu, D.

Liu, S.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

Loncar, M.

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

Z. Lin, T. Alcorn, M. Loncar, S. Johnson, and A. Rodriguez, “High-efficiency degenerate four wave-mixing in triply,” Phys. Rev. A 89, 053839 (2014).
[Crossref]

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators,” Opt. Express 20, 7526–7543 (2012).
[Crossref]

Z. Lin, M. Lončar, and A. W. Rodriguez, “Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion,” arXiv:1701.05628 (2017).

Lovering, D. J.

Lu, F.

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

Lu, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

Luk, T. S.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

Lynch, C.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

Ma, X.

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

Mäkinen, R. A.

J. Haslinger and R. A. Mäkinen, Introduction to Shape Optimization: Theory, Approximation, and Computation (SIAM, 2003).

Maloney, J.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[Crossref]

Marquardt, C.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Martin, O. J.

J. Butet, P.-F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9, 10545–10562 (2015).
[Crossref]

Masselink, W. T.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Men, H.

H. Men, K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson, “Robust topology optimization of three-dimensional photonic-crystal band-gap structures,” arXiv:1405.4350 (2014).

Menon, R.

B. Shen, P. Wang, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

Michaeli, L.

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118, 243904 (2017).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photon. 3, 117–123 (2015).
[Crossref]

Michelberger, P.

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

Michler, P.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Minkov, M.

M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2014).
[Crossref]

Mlynek, J.

R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117–122 (1994).

Molesky, S.

S. Molesky, Z. Lin, A. Piggot, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Outlook for inverse design in nanophotonics,” arXiv:1801.06715 (2018).

Monat, C.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Monro, T.

Moore, G. T.

Moores, M. D.

Moss, D. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Newhouse, M. A.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[Crossref]

Nookala, N.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

O’Brien, J. D.

O’Brien, K.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

O’Faolain, L.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Omenetto, F. G.

Ozawa, A.

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

Pantazis, P.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[Crossref]

Paschotta, R.

R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117–122 (1994).

Peake, G. M.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Peraire, J.

H. Men, K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson, “Robust topology optimization of three-dimensional photonic-crystal band-gap structures,” arXiv:1405.4350 (2014).

Pernice, W. H. P.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012).
[Crossref]

Pertsch, T.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Petropoulos, P.

Petykiewicz, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).
[Crossref]

Piggot, A.

S. Molesky, Z. Lin, A. Piggot, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Outlook for inverse design in nanophotonics,” arXiv:1801.06715 (2018).

Piggott, A. Y.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

Preble, S.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[Crossref]

Pressman, L.

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Puretzky, A.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Quiquempois, Y.

Radulaski, M.

S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).
[Crossref]

S. Buckley, M. Radulaski, K. Biermann, and J. Vuckovic, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” arXiv:1308.6051v1 (2013).

Ramelow, S.

D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref]

Ramirez, D.

D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
[Crossref]

Ravikumar, A. P.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

Reno, J.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Resch, K. J.

D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref]

Rho, J.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

Ricard, D.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).
[Crossref]

Rivoire, K.

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
[Crossref]

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 98, 263113 (2011).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
[Crossref]

Robinson, J.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[Crossref]

Rodriguez, A.

Z. Lin, T. Alcorn, M. Loncar, S. Johnson, and A. Rodriguez, “High-efficiency degenerate four wave-mixing in triply,” Phys. Rev. A 89, 053839 (2014).
[Crossref]

A. Rodriguez, M. Soljačić, J. D. Joannopulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
[Crossref]

Rodriguez, A. W.

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators,” Opt. Express 20, 7526–7543 (2012).
[Crossref]

D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
[Crossref]

S. Molesky, Z. Lin, A. Piggot, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Outlook for inverse design in nanophotonics,” arXiv:1801.06715 (2018).

Z. Lin, M. Lončar, and A. W. Rodriguez, “Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion,” arXiv:1701.05628 (2017).

Russell, P. St. J.

Salandrino, A.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

Saravi, S.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Savchenko, A.

Savona, V.

M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2014).
[Crossref]

Schuck, C.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012).
[Crossref]

Schulz, W.-M.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Segal, N.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).
[Crossref]

Setzpfandt, F.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Shadrivov, I. V.

M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, “Colloquium: nonlinear metamaterials,” Rev. Mod. Phys. 86, 1093–1123 (2014).
[Crossref]

Shaner, E. A.

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

Shen, B.

B. Shen, P. Wang, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

Shen, Y. R.

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).
[Crossref]

Shirane, M.

Shoji, I.

Sigmund, O.

N. Aage, E. Andreassen, B. S. Lazarov, and O. Sigmund, “Giga-voxel computational morphogenesis for structural design,” Nature 550, 84–86 (2017).
[Crossref]

J. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[Crossref]

M. P. Bendsøe, O. Sigmund, M. P. Bendsøe, and O. Sigmund, Topology Optimization by Distribution of Isotropic Material (Springer, 2004).

M. P. Bendsøe, O. Sigmund, M. P. Bendsøe, and O. Sigmund, Topology Optimization by Distribution of Isotropic Material (Springer, 2004).

F. Wang and O. Sigmund, “Optimization of photonic crystal cavities,” in International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) (IEEE, 2017), pp. 39–40.

Silberberg, D.

Simanovskii, D. M.

Simonneau, C.

Sinclair, M. B.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett. 104, 131104 (2014).
[Crossref]

Skorobogatly, M.

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Solijacic, M.

D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
[Crossref]

Soljacic, M.

A. Rodriguez, M. Soljačić, J. D. Joannopulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004).
[Crossref]

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Song, A. Y.

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

Staude, I.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Strang, G.

G. Strang, Computational Science and Engineering (Wellesley-Cambridge, 2007), Vol. 791.

Strekalov, D. V.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Suchowski, H.

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118, 243904 (2017).
[Crossref]

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

Svanberg, K.

K. Svanberg, “A class of globally convergent optimization methods based on conservative convex separable approximations,” SIAM J. Optim. 12, 555–573 (2002).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

Tang, H. X.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012).
[Crossref]

Tanzilli, S.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Taylor, A. J.

Temelkuran, B.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[Crossref]

Tittel, W.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Trebino, R.

Tymchenko, M.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

A. Krasnok, M. Tymchenko, and A. Alù, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” arXiv:1706.07563 (2017).

Udem, T.

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

Valentine, J.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

Vidakovic, P.

Vodopyanov, K. L.

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31, 71–73 (2006).
[Crossref]

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

Vuckovic, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).
[Crossref]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
[Crossref]

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 98, 263113 (2011).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
[Crossref]

S. Buckley, M. Radulaski, K. Biermann, and J. Vuckovic, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” arXiv:1308.6051v1 (2013).

S. Molesky, Z. Lin, A. Piggot, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Outlook for inverse design in nanophotonics,” arXiv:1801.06715 (2018).

Wadsworth, W. J.

Wang, F.

F. Wang and O. Sigmund, “Optimization of photonic crystal cavities,” in International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) (IEEE, 2017), pp. 39–40.

Wang, K.-M.

Wang, M. Y.

M. Y. Wang, X. Wang, and D. Guo, “A level set method for structural topology optimization,” Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003).
[Crossref]

Wang, P.

B. Shen, P. Wang, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

Wang, W.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Wang, X.

M. Y. Wang, X. Wang, and D. Guo, “A level set method for structural topology optimization,” Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003).
[Crossref]

Weidman, D. L.

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[Crossref]

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

Weinfurter, H.

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

Weisberg, O.

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

Wendt, J. R.

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

Weyburne, D.

White, T. P.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

White, W. E.

Wieczorek, W.

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Wolf, O.

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

Wu, D.

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[Crossref]

Wu, L.-A.

Xiao, M.

Xiong, C.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012).
[Crossref]

Yang, Y.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Yelin, Y.

Yin, X.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Yu, X.

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31, 71–73 (2006).
[Crossref]

Zaske, S.

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

Zbinden, H.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Zeilinger, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

Zentgraf, T.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

Zhang, J. L.

Zhang, S.

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

Zhang, X.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

ACS Nano (1)

J. Butet, P.-F. Brevet, and O. J. Martin, “Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications,” ACS Nano 9, 10545–10562 (2015).
[Crossref]

ACS Photon. (1)

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear beam shaping with plasmonic metasurfaces,” ACS Photon. 3, 117–123 (2015).
[Crossref]

Appl. Phys. Lett. (9)

S. Campione, A. Benz, M. B. Sinclair, F. Capolino, and I. Brener, “Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells,” Appl. Phys. Lett. 104, 131104 (2014).
[Crossref]

O. Wolf, A. A. Allerman, X. Ma, J. R. Wendt, A. Y. Song, E. A. Shaner, and I. Brener, “Enhanced optical nonlinearities in the near-infrared using III-nitride heterostructures coupled to metamaterials,” Appl. Phys. Lett. 107, 151108 (2015).
[Crossref]

K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y.-S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[Crossref]

M. Liscidini and L. A. Andreani, “Highly efficient second-harmonic generation in doubly resonant planar microcavities,” Appl. Phys. Lett. 85, 1883–1885 (2004).
[Crossref]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
[Crossref]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012).
[Crossref]

R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117–122 (1994).

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 98, 263113 (2011).
[Crossref]

D. W. Hall, M. A. Newhouse, N. F. Borrelli, W. H. Dumbaugh, and D. L. Weidman, “Nonlinear optical susceptibilities of high-index glasses,” Appl. Phys. Lett. 54, 1293–1295 (1989).
[Crossref]

Comput. Methods Appl. Mech. Eng. (1)

M. Y. Wang, X. Wang, and D. Guo, “A level set method for structural topology optimization,” Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003).
[Crossref]

J. Appl. Phys. (1)

W. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[Crossref]

J. Opt. Soc. Am. B (5)

Laser Photon. Rev. (1)

J. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[Crossref]

Nano Lett. (2)

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly enhanced second-harmonic generation using III--V semiconductor all-dielectric metasurfaces,” Nano Lett. 16, 5426–5432 (2016).
[Crossref]

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15, 7388–7393 (2015).
[Crossref]

Nat. Commun. (1)

O. Wolf, S. Campione, A. Benz, A. P. Ravikumar, S. Liu, T. S. Luk, E. A. Kadlec, E. A. Shaner, J. F. Klem, M. B. Sinclair, and I. Brener, “Phased-array sources based on nonlinear metamaterial nanocavities,” Nat. Commun. 6, 7667 (2015).
[Crossref]

Nat. Mater. (3)

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14, 379–383 (2015).
[Crossref]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Nat. Photonics (5)

R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nat. Photonics 4, 170–173 (2010).

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9, 180–184 (2015).
[Crossref]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vuckovic, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

B. Shen, P. Wang, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

Nat. Rev. Mater. (1)

G. Li, S. Zhang, and T. Zentgraf, “Nonlinear photonic metasurfaces,” Nat. Rev. Mater. 2, 17010 (2017).
[Crossref]

Nature (5)

J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G. Boehm, M.-C. Amann, A. Alu, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511, 65–69 (2014).
[Crossref]

N. Aage, E. Andreassen, B. S. Lazarov, and O. Sigmund, “Giga-voxel computational morphogenesis for structural design,” Nature 550, 84–86 (2017).
[Crossref]

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, “Direct generation of photon triplets using cascaded photon-pair sources,” Nature 466, 601–603 (2010).
[Crossref]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002).
[Crossref]

Opt. Commun. (1)

B. S. Darki and N. Granpayeh, “Improving the performance of a photonic crystal ring-resonator-based channel drop filter using particle swarm optimization method,” Opt. Commun. 283, 4099–4103 (2010).
[Crossref]

Opt. Express (10)

A. Bétourné, Y. Quiquempois, G. Bouwmans, and M. Douay, “Design of a photonic crystal fiber for phase-matched frequency doubling or tripling,” Opt. Express 16, 14255–14262 (2008).
[Crossref]

X. Liang and S. G. Johnson, “Formulation for scalable optimization of microcavities via the frequency-averaged local density of states,” Opt. Express 21, 30812–30841 (2013).
[Crossref]

D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express 21, 14223–14243 (2013).
[Crossref]

Y. Yelin and D. Silberberg, “Laser scanning third-harmonic-generation microscopy in biology,” Opt. Express 5, 169–175 (1999).
[Crossref]

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ(2) microring resonators,” Opt. Express 20, 7526–7543 (2012).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
[Crossref]

S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).
[Crossref]

A. Rodriguez, M. Soljačić, J. D. Joannopulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
[Crossref]

X. Feng, T. Monro, P. Petropoulos, V. Finazzi, and D. Hewak, “Solid microstructured optical fiber,” Opt. Express 11, 2225–2230 (2003).
[Crossref]

V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13, 6798–6806 (2005).
[Crossref]

Opt. Lett. (5)

Optica (1)

Phys. Rev. A (3)

Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[Crossref]

D. Ramirez, A. W. Rodriguez, H. Hashemi, J. D. Joannopoulos, M. Solijacic, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant nonlinear Kerr cavities,” Phys. Rev. A 83, 033834 (2011).
[Crossref]

Z. Lin, T. Alcorn, M. Loncar, S. Johnson, and A. Rodriguez, “High-efficiency degenerate four wave-mixing in triply,” Phys. Rev. A 89, 053839 (2014).
[Crossref]

Phys. Rev. Lett. (7)

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).
[Crossref]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref]

S. Zaske, A. Lenhard, C. A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, and C. Becher, “Visible-to-telecom quantum frequency conversion of light from a single quantum emitter,” Phys. Rev. Lett. 109, 147404 (2012).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear pancharatnam-berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[Crossref]

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear surface lattice resonance in plasmonic nanoparticle arrays,” Phys. Rev. Lett. 118, 243904 (2017).
[Crossref]

Phys. Today (1)

M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today 47, 25–32 (1994).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

P. Pantazis, J. Maloney, D. Wu, and S. E. Fraser, “Second harmonic generating (SHG) nanoprobes for in vivo imaging,” Proc. Natl. Acad. Sci. USA 107, 14535–14540 (2010).
[Crossref]

Rev. Mod. Phys. (1)

M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, “Colloquium: nonlinear metamaterials,” Rev. Mod. Phys. 86, 1093–1123 (2014).
[Crossref]

Sci. Rep. (2)

A. Y. Piggott, J. Lu, T. M. Babinec, K. G. Lagoudakis, J. Petykiewicz, and J. Vuckovic, “Inverse design and implementation of a wavelength demultiplexing grating coupler,” Sci. Rep. 4, 7210 (2014).
[Crossref]

M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2014).
[Crossref]

SIAM J. Optim. (1)

K. Svanberg, “A class of globally convergent optimization methods based on conservative convex separable approximations,” SIAM J. Optim. 12, 555–573 (2002).
[Crossref]

Struct. Multidiscip. Optim. (1)

J. D. Deaton and R. V. Grandhi, “A survey of structural and multidisciplinary continuum topology optimization: post 2000,” Struct. Multidiscip. Optim. 49, 1–38 (2014).
[Crossref]

Other (14)

M. P. Bendsøe, O. Sigmund, M. P. Bendsøe, and O. Sigmund, Topology Optimization by Distribution of Isotropic Material (Springer, 2004).

J. Haslinger and R. A. Mäkinen, Introduction to Shape Optimization: Theory, Approximation, and Computation (SIAM, 2003).

F. Wang and O. Sigmund, “Optimization of photonic crystal cavities,” in International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) (IEEE, 2017), pp. 39–40.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

H. Men, K. Y. K. Lee, R. M. Freund, J. Peraire, and S. G. Johnson, “Robust topology optimization of three-dimensional photonic-crystal band-gap structures,” arXiv:1405.4350 (2014).

G. Strang, Computational Science and Engineering (Wellesley-Cambridge, 2007), Vol. 791.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

S. Molesky, Z. Lin, A. Piggot, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Outlook for inverse design in nanophotonics,” arXiv:1801.06715 (2018).

R. Ahmad, M. Soljacic, M. Ibanescu, T. Engeness, M. Skorobogatly, S. Johnson, O. Weisberg, Y. Fink, L. Pressman, W. King, E. Anderson, and J. D. Joannopoulos, “High index-contrast fiber waveguides and applications,” U.S. patent6,788,864 B2 (April 12, 2004).

S. Buckley, M. Radulaski, K. Biermann, and J. Vuckovic, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” arXiv:1308.6051v1 (2013).

Z. Lin, M. Lončar, and A. W. Rodriguez, “Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion,” arXiv:1701.05628 (2017).

A. Krasnok, M. Tymchenko, and A. Alù, “Nonlinear metasurfaces: a paradigm shift in nonlinear optics,” arXiv:1706.07563 (2017).

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2012), Vol. 222.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Schematic illustration of third-harmonic generation and second-harmonic generation processes in inverse-designed microstructured fibers and metasurfaces, respectively.
Fig. 2.
Fig. 2. Dispersion relations (solid line) and radiative lifetimes Q (dashed line) versus propagation wavenumber k of TM 01 fundamental ω 1 (red) and third-harmonic ω 3 (blue) modes in a chalcogenide/PES fiber optimized to achieve frequency matching ω 3 = 3 ω 1 and large nonlinear overlaps at k opt = 1.4 ( 2 π / λ ) . The shaded area in gray indicates regions lying below the chalcogenide light cone. The top insets show the fiber cross section overlaid with corresponding power densities at ω 1 (left) and ω 3 (right).
Fig. 3.
Fig. 3. Nonlinear overlap factor | β 3 | 2 corresponding to fundamental and third-harmonic modes in fibers that have been optimized to ensure phase-matched modes ( k 3 = 3 k opt ) at various fundamental-mode propagation wavenumbers k opt , for both TE 01 (blue) and TM 01 (red) polarizations, by the application of either topology (circles or squares) or shape (triangles) optimization. The gray-shaded area denotes the regime of guided modes below the chalcogenide lightline. For comparison, also shown is | β 3 | 2 (black cross) of a standard plain fiber manually designed for operation at ω 1 = 0.914 ( 2 π c / λ ) and k 1 = 0.992 ( 2 π / λ ) [77]. Shown as insets are fiber cross sections along with power densities of fundamental modes optimized at four different k opt = { 0.1 , 1.4 , 1.7 , 2.0 } ( 2 π / λ ) for both TE 01 (upper insets) and TM 01 (lower insets), with (i)–(iii) obtained via topology optimization and (iv) via shape optimization.
Fig. 4.
Fig. 4. (a) Schematic illustration of second-harmonic generation in a square-lattice metasurface of finite thickness t and period Λ × Λ . Shown to the right are dielectric profiles and mode profiles | E | 2 corresponding to two inverse-designed metasurfaces, both over single unit cells and z = 0 cross sections. The structures are optimized to ensure frequency and phase matching for light incident at (i) an angle θ = 3 ° or (ii) normal incidence. Dark (white) represents gallium phosphide (vacuum) regions. (b) Convergence of the objective function with respect to iteration number, leading to structure (ii).

Tables (1)

Tables Icon

Table 1. Representative Second-Harmonic Generation FOMs for Both Hand- and Inverse-Designed Metasurfaces, Including χ ( 2 ) , Fundamental Wavelength λ 1 , and Conversion Efficiency η per Unit Cella

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

max / min f ( ϵ ¯ α ) ,
g ( ϵ ¯ α ) 0 ,
0 ϵ ¯ α 1 ,
× 1 μ × E ϵ ( r ) ω 2 E = i ω J ,
max ϵ ¯ f ( ϵ ¯ ; ω n ) = Re [ J ( Ω ) * · E ( Ω ) d r ] , M ( ϵ ¯ , ω n ) E n = i ω n J n , J n = e ^ n ν δ ( r r ) , M ( ϵ ¯ , Ω ) E ( Ω ) = i Ω J ( Ω ) , J ( Ω ) = ϵ ¯ n E n ν | c n | ( * ) e ^ i , M ( ϵ ¯ , ω ) = × 1 μ × ϵ ( r ) ω 2 ,
β 3 = χ ( 3 ) ( E 1 * · E 3 ) ( E 1 * · E 1 * ) d S ( Re [ 1 2 ( E 1 * × H 1 ) · z ^ d S ] ) 3 Re [ 1 2 ( E 3 * × H 3 ) · z ^ d S ] ,
η = P 2 P 1 2 = Q 1 4 Q 2 2 Q 1 , rad 2 Q 2 , rad | β 2 | 2 λ 1 π ϵ 0 c ,
β 2 = d V χ ( 2 ) E 2 * · E 1 2 ( d V ϵ 1 | E 1 | 2 ) ( d V ϵ 2 | E 2 | 2 ) .

Metrics