Abstract

Highly efficient second harmonic generation (SHG) bridging the mid-infrared (IR) and near-IR wavelengths in a coupled hyperbolic metamaterial waveguide with a nonlinear-polymer-filled nanoscale slot is theoretically investigated. By engineering the geometrical parameters, the collinear phase matching condition is satisfied between the even hybrid modes at the fundamental frequency (3,100 nm) and the second harmonic (1,550 nm). Two modes manifest the great field overlap and the significant field enhancement in the nonlinear integration area (i.e. the slot), which leads to extreme large nonlinear coupling coefficient. For a low pumping power of 100 mW, the device length is as short as 2.19 µm and the normalized conversion efficiency comes up to more than 6.37 × 105 W−1cm−2 which outperforms that of the plasmonic-based structures. Moreover, the efficient SHG can be achieved with great phase matching tolerance, i.e., a small theoretical fabrication-error sensitivity to filling ratio and a broad pump bandwidth in a compact device length of 2.19 µm using 100 mW pump. The proposed scheme links the mature near-IR devices to the mid-IR regime and have a great potential for integrated chip-scale all-optical signal processes.

© 2015 Optical Society of America

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References

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D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
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2013 (4)

2012 (7)

S. B. Hasan, C. Rockstuhl, T. Pertsch, and F. Lederer, “Second-order nonlinear frequency conversion processes in plasmonic slot waveguides,” J. Opt. Soc. Am. B 29(7), 1606–1611 (2012).
[Crossref]

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[Crossref]

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H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012).
[Crossref]

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[Crossref]

Y. He, S. He, and X. Yang, “Optical field enhancement in nanoscale slot waveguides of hyperbolic metamaterials,” Opt. Lett. 37(14), 2907–2909 (2012).
[Crossref] [PubMed]

2011 (4)

Y. Bian, Z. Zheng, Y. Liu, J. Liu, J. Zhu, and T. Zhou, “Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement,” Opt. Express 19(23), 22417–22422 (2011).
[Crossref] [PubMed]

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[Crossref] [PubMed]

F. F. Lu, T. Li, X. P. Hu, Q. Q. Cheng, S. N. Zhu, and Y. Y. Zhu, “Efficient second-harmonic generation in nonlinear plasmonic waveguide,” Opt. Lett. 36(17), 3371–3373 (2011).
[PubMed]

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[Crossref] [PubMed]

2010 (4)

B. Jalali, “Silicon photonics: Nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
[Crossref]

E.-K. Tien, Y. Huang, S. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010).
[Crossref] [PubMed]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

Z.- Wu, X.- Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.- Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

2009 (3)

2007 (2)

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

2006 (1)

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

2003 (1)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

2002 (1)

1985 (1)

V. Agranovich and V. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun. 55(1), 85–90 (1985).
[Crossref]

1972 (1)

P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Agranovich, V.

V. Agranovich and V. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun. 55(1), 85–90 (1985).
[Crossref]

Alic, N.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

Baets, R.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6(10), 667–671 (2012).
[Crossref]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Bian, Y.

Boggio, J. M. C.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

Boltasseva, A.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Boyraz, O.

Brongersma, M. L.

W. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[Crossref] [PubMed]

Buchwald, W. R.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

Cai, W.

W. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[Crossref] [PubMed]

Cassan, E.

Cheng, Q. Q.

Christy, R.-W.

P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Davoyan, A. R.

Derose, C.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

Drachev, V. P.

Emelett, S. J.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

Enami, Y.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Fan, S.

Fejer, M. M.

Fujimura, M.

Fullerton, E. E.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

Gao, D.

Gao, J.

Gao, S.

Gosztola, D. J.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

Grange, R.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 1–6 (2012).

Green, W. M. J.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6(10), 667–671 (2012).
[Crossref]

Greenlee, C.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Hasan, S. B.

He, S.

He, Y.

Hendren, W.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

Hu, W.

Z.- Wu, X.- Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.- Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Hu, X.-

Z.- Wu, X.- Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.- Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Hu, X. P.

Huang, Y.

Iorsh, I.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Irudayaraj, J. M. K.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Jacob, Z.

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

Jalali, B.

B. Jalali, “Silicon photonics: Nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
[Crossref]

Jen, A.-Y.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Johnson, P. B.

P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kalyoncu, S. K.

Kan, J. J.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

Kildishev, A. V.

Kim, T.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Kivshar, Y. S.

Kravtsov, V.

V. Agranovich and V. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun. 55(1), 85–90 (1985).
[Crossref]

Kretzschmar, I.

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

Krishnamoorthy, H. N. S.

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

Kurz, J. R.

Kuyken, B.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6(10), 667–671 (2012).
[Crossref]

Lederer, F.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Li, T.

Liu, J.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Y. Bian, Z. Zheng, Y. Liu, J. Liu, J. Zhu, and T. Zhou, “Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement,” Opt. Express 19(23), 22417–22422 (2011).
[Crossref] [PubMed]

Liu, X.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6(10), 667–671 (2012).
[Crossref]

Liu, Y.

Liu, Z.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Loychik, C.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Lu, D.

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

Lu, F. F.

Lu, Y.-

Z.- Wu, X.- Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.- Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Luo, J.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Mathine, D.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Menon, V. M.

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

Mookherjea, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

Moro, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

Naik, G. V.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Narimanov, E.

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

Norwood, R.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Osgood, R. M.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6(10), 667–671 (2012).
[Crossref]

Parameswaran, K. R.

Park, J. S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

Pertsch, T.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 1–6 (2012).

S. B. Hasan, C. Rockstuhl, T. Pertsch, and F. Lederer, “Second-order nonlinear frequency conversion processes in plasmonic slot waveguides,” J. Opt. Soc. Am. B 29(7), 1606–1611 (2012).
[Crossref]

Peyghambarian, N.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Podolskiy, V. A.

V. P. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic metamaterials: new physics behind a classical problem,” Opt. Express 21(12), 15048–15064 (2013).
[Crossref] [PubMed]

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

Pollard, R.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

Qian, F.

Radic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

Rho, J.

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012).
[Crossref]

Richter, J.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 1–6 (2012).

Rockstuhl, C.

Roelkens, G.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6(10), 667–671 (2012).
[Crossref]

Roussev, R. V.

Route, R. K.

Ruan, Z.

Saber, S. M.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Saha, B.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Sands, T. D.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Shadrivov, I. V.

Shalaev, V. M.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Smith, D. R.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Song, Q.

Soref, R. A.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

Stach, E. A.

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Steinbrück, A.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 1–6 (2012).

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Tian, Y.

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

Tien, E.-K.

Tünnermann, A.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 1–6 (2012).

Vasudev, A. P.

W. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[Crossref] [PubMed]

Veronis, G.

Vodopyanov, K. L.

Wiederrecht, G. P.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

Wu, Z.-

Z.- Wu, X.- Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.- Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Wurtz, G. A.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Xu, F.

Z.- Wu, X.- Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.- Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Yang, X.

Yao, J.

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012).
[Crossref]

Yin, X.

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012).
[Crossref]

Yu, Z.-y.

Z.- Wu, X.- Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.- Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Zayats, A. V.

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

Zhang, J.

Zhang, X.

Zhao, X.

Zheng, Z.

Zhou, T.

Zhu, J.

Zhu, S. N.

Zhu, Y. Y.

Zlatanovic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Nanotechnol. (2)

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

Nat. Photonics (6)

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[Crossref]

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6(10), 667–671 (2012).
[Crossref]

B. Jalali, “Silicon photonics: Nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
[Crossref]

Y. Enami, C. Derose, D. Mathine, C. Loychik, C. Greenlee, R. Norwood, T. Kim, J. Luo, Y. Tian, A.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012).
[Crossref]

Opt. Express (7)

Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, “Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides,” Opt. Express 17(16), 13502–13515 (2009).
[Crossref] [PubMed]

Y. Bian, Z. Zheng, X. Zhao, J. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express 17(23), 21320–21325 (2009).
[Crossref] [PubMed]

Y. Bian, Z. Zheng, Y. Liu, J. Liu, J. Zhu, and T. Zhou, “Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement,” Opt. Express 19(23), 22417–22422 (2011).
[Crossref] [PubMed]

V. P. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic metamaterials: new physics behind a classical problem,” Opt. Express 21(12), 15048–15064 (2013).
[Crossref] [PubMed]

J. Zhang, E. Cassan, D. Gao, and X. Zhang, “Highly efficient phase-matched second harmonic generation using an asymmetric plasmonic slot waveguide configuration in hybrid polymer-silicon photonics,” Opt. Express 21(12), 14876–14887 (2013).
[Crossref] [PubMed]

E.-K. Tien, Y. Huang, S. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010).
[Crossref] [PubMed]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Quadratic phase matching in nonlinear plasmonic nanoscale waveguides,” Opt. Express 17(22), 20063–20068 (2009).
[Crossref] [PubMed]

Opt. Lett. (4)

Phys. Rev. B (2)

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[Crossref]

Z.- Wu, X.- Hu, Z.-y. Yu, W. Hu, F. Xu, and Y.- Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Phys. Rev. Lett. (1)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Plasmonics (1)

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 1–6 (2012).

Proc. Natl. Acad. Sci. U.S.A. (1)

G. V. Naik, B. Saha, J. Liu, S. M. Saber, E. A. Stach, J. M. K. Irudayaraj, T. D. Sands, V. M. Shalaev, and A. Boltasseva, “Epitaxial superlattices with titanium nitride as a plasmonic component for optical hyperbolic metamaterials,” Proc. Natl. Acad. Sci. U.S.A. 111(21), 7546–7551 (2014).
[Crossref] [PubMed]

Science (3)

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

W. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[Crossref] [PubMed]

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[Crossref]

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R. W. Boyd, Nonlinear Optics (Elsevier Science, 2008).

M. Ebrahim-Zadeh and I. T. Sorokina, Mid-infrared Coherent Sources and Applications (Springer, 2008).

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Figures (6)

Fig. 1
Fig. 1 Schematic of the proposed waveguide with a nonlinear-polymer-filled nanoscale slot.
Fig. 2
Fig. 2 The Ey profiles of (a) EHM(1,2) at 3,100 nm, (b) EHM(1,1) at 1,550 nm with fr = 0.57 using the effective medium approximation.
Fig. 3
Fig. 3 The effective index Re(neff) as a function of the filling ratio fr using the effective medium approximation.
Fig. 4
Fig. 4 Optical powers of the FF and SH waves as a function of the propagation distance pumped by (a) 1W and (b) 100mW.
Fig. 5
Fig. 5 The (a) maximum of SH power max(PSH), normalized conversion efficiency η, (b) peak position Lp and peak efficiency ηp as a function of the input pumping power PFF.
Fig. 6
Fig. 6 The phase mismatch as functions of (a) filling ratio fr and (b) wavelength of the FF.

Equations (9)

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ε x = ε z = f r ε Ag +(1 f r ) ε Ge ε y = ε Ag ε Ge f r ε Ge +(1 f r ) ε Ag .
ε Ag (ω)= ε ω p 2 / ( ω 2 +iωγ),
ε Ge =9.28156+6.72880 λ 2 /( λ 2 0.44105)+0.21307 λ 2 /( λ 2 3870.1).
e(x,y,z)=A(z)E(x,y)exp[(β+ i*α /2 )z],
κ 1 = ε 0 [ χ (2) : E SH (x,y) E FF * (x,y) E ' FF (x,y)]dxdy κ 2 = ε 0 [ χ (2) : E FF (x,y) E FF (x,y) E ' SH (x,y)]dxdy,
A FF z = α FF 2 A FF +i ω 4 κ 1 A FF * A SH exp(iΔβz) A SH z = α SH 2 A SH +i ω 4 κ 2 * A FF A FF exp(iΔβz).
η= P SH ( L P ) P FF (0) 2 L p 2 ,
η p = P SH ( L P ) P FF (0) ,
| Δβ |<Δ β c 2π /L ,

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