Abstract

Novel multi-tasking geometric phase metasurfaces were incorporated into a modified degenerate cavity laser as an output coupler to efficiently generate spin-dependent twisted light beams of different topologies. Multiple harmonic scalar vortex laser beams were formed by replacing the laser output coupler with a shared-aperture metasurface. A variety of distinct wave functions were obtained with an interleaving approach – random interspersing of geometric phase profiles within shared-aperture metasurfaces. Utilizing the interleaved metasurfaces, we generated vectorial vortices by coherently superposing of scalar vortices with opposite topological charges and spin states. We also generated multiple partially coherent vortices by incorporating harmonic response metasurfaces. The incorporation of the metasurface platforms into a laser cavity opens a pathway to novel types of nanophotonic functionalities and enhanced light-matter interactions, offering exciting new opportunities for light manipulation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (9)

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, “Photonic spin-controlled multifunctional shared-aperture antenna array,” Science 352(6290), 1202–1206 (2016).
[Crossref] [PubMed]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital Angular Momentum Microlaser,” Science 353(6298), 464–467 (2016).
[Crossref] [PubMed]

L. Xu, D. Chen, T. Itoh, J. L. Reno, and B. S. Williams, “Focusing metasurface quantum-cascade laser with a near diffraction-limited beam,” Opt. Express 24(21), 24117–24128 (2016).
[Crossref] [PubMed]

Z. J. Wong, Y. Xu, J. Kim, K. O’Brien, Y. Wang, L. Feng, and X. Zhang, “Lasing and anti-lasing in a single cavity,” Nat. Photonics 7(10), 796–801 (2016).
[Crossref]

S. Knitter, C. Liu, B. Redding, M. K. Khokha, M. A. Choma, and H. Cao, “Coherence switching of a degenerate VECSEL for multimodality imaging,” Optica 3(4), 403 (2016).
[Crossref]

Q. Wang, E. T. F. Rogers, B. Gholipour, C. Wang, G. Yuan, J. Teng, and N. I. Zheludev, “Optically reconfigurable metasurfaces and photonic devices based on phase change materials,” Nat. Photonics 10(1), 60–65 (2016).
[Crossref]

M. P. Backlund, A. Arbabi, P. N. Petrov, E. Arbabi, S. Saurabh, A. Faraon, and W. E. Moerner, “Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask,” Nat. Photonics 10(7), 459–462 (2016).
[Crossref] [PubMed]

B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, A. Forbes, and G. A. Swartzlander, “Digital generation of partially coherent vortex beams,” Opt. Lett. 41(15), 3471–3474 (2016).
[Crossref] [PubMed]

2015 (11)

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (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(4), 379–383 (2015).
[Crossref] [PubMed]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
[Crossref] [PubMed]

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photonics Rev. 9(2), 195–213 (2015).
[Crossref]

R. Chriki, M. Nixon, V. Pal, C. Tradonsky, G. Barach, A. A. Friesem, and N. Davidson, “Manipulating the spatial coherence of a laser source,” Opt. Express 23(10), 12989–12997 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

Y. Ye, Z. J. Wong, X. Lu, X. Ni, H. Zhu, X. Chen, Y. Wang, and X. Zhang, “Monolayer excitonic laser,” Nat. Photonics 9(11), 733–737 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

2014 (3)

J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning Light on the Nanoscale,” Nano Lett. 14(5), 2726–2729 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

2013 (6)

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110(18), 184102 (2013).
[Crossref] [PubMed]

M. Nixon, B. Redding, A. A. Friesem, H. Cao, and N. Davidson, “Efficient method for controlling the spatial coherence of a laser,” Opt. Lett. 38(19), 3858–3861 (2013).
[Crossref] [PubMed]

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett. 38(4), 513–515 (2013).
[Crossref] [PubMed]

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3(1), 2155 (2013).
[Crossref] [PubMed]

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7(11), 919–924 (2013).
[Crossref]

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

2012 (4)

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

H. Husu, R. Siikanen, J. Mäkitalo, J. Lehtolahti, J. Laukkanen, M. Kuittinen, and M. Kauranen, “Metamaterials with tailored nonlinear optical response,” Nano Lett. 12(2), 673–677 (2012).
[Crossref] [PubMed]

Y. Yang, M. Mazilu, and K. Dholakia, “Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions,” Opt. Lett. 37(23), 4949–4951 (2012).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2011 (1)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

2009 (2)

A. A. Ishaaya, N. Davidson, and A. A. Friesem, “Passive Laser Beam Combining With Intracavity Interferometric Combiners,” IEEE J. Sel. Top. Quantum Electron. 15(2), 301–311 (2009).
[Crossref]

I. E. Lager, C. Trampuz, M. Simeoni, and L. P. Ligthart, “Interleaved Array Antennas for FMCW Radar Applications,” IEEE Trans. Antenn. Propag. 57(8), 2486–2490 (2009).
[Crossref]

2008 (1)

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref] [PubMed]

2007 (1)

G. A. Swartzlander and R. I. Hernandez-Aranda, “Optical Rankine vortex and anomalous circulation of light,” Phys. Rev. Lett. 99(16), 163901 (2007).
[Crossref] [PubMed]

2006 (3)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Manipulation of the Pancharatnam phase in vectorial vortices,” Opt. Express 14(10), 4208–4220 (2006).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, “Passive intra-cavity phase locking of laser channels,” Opt. Commun. 263(1), 60–64 (2006).
[Crossref]

2005 (1)

R. L. Haupt, “Interleaved thinned linear arrays,” IEEE Trans. Antenn. Propag. 53(9), 2858–2864 (2005).
[Crossref]

2004 (1)

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander., “Spatial correlation singularity of a vortex field,” Phys. Rev. Lett. 92(14), 143905 (2004).
[Crossref] [PubMed]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

2002 (2)

2001 (3)

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam-Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26(18), 1424–1426 (2001).
[Crossref] [PubMed]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
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M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
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2000 (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
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1998 (2)

P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Blazed binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings,” Opt. Lett. 23(14), 1081–1083 (1998).
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F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, “Analytical derivation of the optimum triplicator,” Opt. Commun. 157(1-6), 13–16 (1998).
[Crossref]

1997 (1)

1987 (1)

M. V. Berry, “The Adiabatic Phase and Pancharatnam’s Phase for Polarized Light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
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1974 (1)

J. Wynne, “Generation of the rotationally symmetric TE01 and TM01 from a wavelength-tunable laser,” IEEE J. Quantum Electron. 10, 125–127 (1974).
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1971 (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
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Ahmed, N.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
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Albrektsen, O.

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3(1), 2155 (2013).
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Allen, L.

Arbabi, A.

M. P. Backlund, A. Arbabi, P. N. Petrov, E. Arbabi, S. Saurabh, A. Faraon, and W. E. Moerner, “Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask,” Nat. Photonics 10(7), 459–462 (2016).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Arbabi, E.

M. P. Backlund, A. Arbabi, P. N. Petrov, E. Arbabi, S. Saurabh, A. Faraon, and W. E. Moerner, “Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask,” Nat. Photonics 10(7), 459–462 (2016).
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Astilean, S.

Backlund, M. P.

M. P. Backlund, A. Arbabi, P. N. Petrov, E. Arbabi, S. Saurabh, A. Faraon, and W. E. Moerner, “Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask,” Nat. Photonics 10(7), 459–462 (2016).
[Crossref] [PubMed]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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Barach, G.

Berry, M. V.

M. V. Berry, “The Adiabatic Phase and Pancharatnam’s Phase for Polarized Light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
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Biener, G.

Bliokh, K. Y.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
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K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
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K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
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Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
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Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
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Bomzon, Z.

Borghi, R.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, “Analytical derivation of the optimum triplicator,” Opt. Commun. 157(1-6), 13–16 (1998).
[Crossref]

Bozhevolnyi, S. I.

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3(1), 2155 (2013).
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A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett. 38(4), 513–515 (2013).
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K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
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Bromberg, Y.

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7(11), 919–924 (2013).
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Brongersma, M. L.

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, “Photonic spin-controlled multifunctional shared-aperture antenna array,” Science 352(6290), 1202–1206 (2016).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
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A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photonics Rev. 9(2), 195–213 (2015).
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Campione, S.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
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Cao, H.

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
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J. Sun, X. Wang, T. Xu, Z. A. Kudyshev, A. N. Cartwright, and N. M. Litchinitser, “Spinning Light on the Nanoscale,” Nano Lett. 14(5), 2726–2729 (2014).
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Chavel, P.

Cheah, K. W.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
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Chen, D.

Chen, S.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14(6), 607–612 (2015).
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Chen, X.

Y. Ye, Z. J. Wong, X. Lu, X. Ni, H. Zhu, X. Chen, Y. Wang, and X. Zhang, “Monolayer excitonic laser,” Nat. Photonics 9(11), 733–737 (2015).
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Choma, M. A.

Chong, K. E.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

Chriki, R.

Cincotti, G.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, “Analytical derivation of the optimum triplicator,” Opt. Commun. 157(1-6), 13–16 (1998).
[Crossref]

Dammann, H.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Davidson, N.

R. Chriki, M. Nixon, V. Pal, C. Tradonsky, G. Barach, A. A. Friesem, and N. Davidson, “Manipulating the spatial coherence of a laser source,” Opt. Express 23(10), 12989–12997 (2015).
[Crossref] [PubMed]

M. Nixon, B. Redding, A. A. Friesem, H. Cao, and N. Davidson, “Efficient method for controlling the spatial coherence of a laser,” Opt. Lett. 38(19), 3858–3861 (2013).
[Crossref] [PubMed]

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110(18), 184102 (2013).
[Crossref] [PubMed]

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7(11), 919–924 (2013).
[Crossref]

A. A. Ishaaya, N. Davidson, and A. A. Friesem, “Passive Laser Beam Combining With Intracavity Interferometric Combiners,” IEEE J. Sel. Top. Quantum Electron. 15(2), 301–311 (2009).
[Crossref]

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, “Passive intra-cavity phase locking of laser channels,” Opt. Commun. 263(1), 60–64 (2006).
[Crossref]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[Crossref]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[Crossref]

Davoyan, A. R.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Decker, M.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

Dholakia, K.

Di Fabrizio, E.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, “Analytical derivation of the optimum triplicator,” Opt. Commun. 157(1-6), 13–16 (1998).
[Crossref]

Dolinar, S.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Dominguez, J.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
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Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper Focus for a Radially Polarized Light Beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
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Dudley, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Ekhouse, V.

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, “Passive intra-cavity phase locking of laser channels,” Opt. Commun. 263(1), 60–64 (2006).
[Crossref]

Ellenbogen, T.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
[Crossref]

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband Light Bending with Plasmonic Nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Engheta, N.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Faraon, A.

M. P. Backlund, A. Arbabi, P. N. Petrov, E. Arbabi, S. Saurabh, A. Faraon, and W. E. Moerner, “Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask,” Nat. Photonics 10(7), 459–462 (2016).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Fazal, I. M.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Feng, L.

Z. J. Wong, Y. Xu, J. Kim, K. O’Brien, Y. Wang, L. Feng, and X. Zhang, “Lasing and anti-lasing in a single cavity,” Nat. Photonics 7(10), 796–801 (2016).
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P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital Angular Momentum Microlaser,” Science 353(6298), 464–467 (2016).
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Forbes, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, A. Forbes, and G. A. Swartzlander, “Digital generation of partially coherent vortex beams,” Opt. Lett. 41(15), 3471–3474 (2016).
[Crossref] [PubMed]

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Friesem, A. A.

R. Chriki, M. Nixon, V. Pal, C. Tradonsky, G. Barach, A. A. Friesem, and N. Davidson, “Manipulating the spatial coherence of a laser source,” Opt. Express 23(10), 12989–12997 (2015).
[Crossref] [PubMed]

M. Nixon, B. Redding, A. A. Friesem, H. Cao, and N. Davidson, “Efficient method for controlling the spatial coherence of a laser,” Opt. Lett. 38(19), 3858–3861 (2013).
[Crossref] [PubMed]

M. Nixon, O. Katz, E. Small, Y. Bromberg, A. A. Friesem, Y. Silberberg, and N. Davidson, “Real-time wavefront shaping through scattering media by all-optical feedback,” Nat. Photonics 7(11), 919–924 (2013).
[Crossref]

M. Nixon, E. Ronen, A. A. Friesem, and N. Davidson, “Observing geometric frustration with thousands of coupled lasers,” Phys. Rev. Lett. 110(18), 184102 (2013).
[Crossref] [PubMed]

A. A. Ishaaya, N. Davidson, and A. A. Friesem, “Passive Laser Beam Combining With Intracavity Interferometric Combiners,” IEEE J. Sel. Top. Quantum Electron. 15(2), 301–311 (2009).
[Crossref]

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, “Passive intra-cavity phase locking of laser channels,” Opt. Commun. 263(1), 60–64 (2006).
[Crossref]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[Crossref]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[Crossref]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gentili, M.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, “Analytical derivation of the optimum triplicator,” Opt. Commun. 157(1-6), 13–16 (1998).
[Crossref]

Gholipour, B.

Q. Wang, E. T. F. Rogers, B. Gholipour, C. Wang, G. Yuan, J. Teng, and N. I. Zheludev, “Optically reconfigurable metasurfaces and photonic devices based on phase change materials,” Nat. Photonics 10(1), 60–65 (2016).
[Crossref]

Gori, F.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, “Analytical derivation of the optimum triplicator,” Opt. Commun. 157(1-6), 13–16 (1998).
[Crossref]

Gorodetski, Y.

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref] [PubMed]

Görtler, K.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Hasman, E.

E. Maguid, I. Yulevich, D. Veksler, V. Kleiner, M. L. Brongersma, and E. Hasman, “Photonic spin-controlled multifunctional shared-aperture antenna array,” Science 352(6290), 1202–1206 (2016).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref] [PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Manipulation of the Pancharatnam phase in vectorial vortices,” Opt. Express 14(10), 4208–4220 (2006).
[Crossref] [PubMed]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
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G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam-Berry phase optical elements,” Opt. Lett. 27(21), 1875–1877 (2002).
[Crossref] [PubMed]

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam-Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26(18), 1424–1426 (2001).
[Crossref] [PubMed]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Transverse mode shaping and selection in laser resonators,” Prog. Opt. 42, 325–386 (2001).
[Crossref]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[Crossref]

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R. L. Haupt, “Interleaved thinned linear arrays,” IEEE Trans. Antenn. Propag. 53(9), 2858–2864 (2005).
[Crossref]

Hendler, N.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
[Crossref]

Hernandez-Aranda, R. I.

B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, A. Forbes, and G. A. Swartzlander, “Digital generation of partially coherent vortex beams,” Opt. Lett. 41(15), 3471–3474 (2016).
[Crossref] [PubMed]

G. A. Swartzlander and R. I. Hernandez-Aranda, “Optical Rankine vortex and anomalous circulation of light,” Phys. Rev. Lett. 99(16), 163901 (2007).
[Crossref] [PubMed]

Hnatovsky, C.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8(11), 846–850 (2014).
[Crossref]

Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Huang, H.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Husu, H.

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Figures (9)

Fig. 1
Fig. 1 Schematic of an intra-cavity multifunctional GPM and the spin-dependent (σ ± ) output beams of wavefronts with OAM. (a) Limited strength of light-matter interaction results in low conversion efficiency η1 when used outside a laser cavity. (b) After incorporation inside a laser cavity the effective efficiency rises to ηeff≈1. (c) Illustration of twisted laser beams of opposite helicities and OAMs (red and blue helix) emerging from the output coupler GPM; OAM values are of l = −1,-2 for σ+ and l = 1, 2 for σ-.
Fig. 2
Fig. 2 Spin-controlled OAM output beams generated by intra-cavity GPM. (a) Scanning electron microscope image of the fabricated HR-GPM composed of gap-plasmon nanoantennas (inset). (b) Schematic of a twisted modified degenerate cavity laser. The output coupler of the standard cavity is replaced with a GPM, which is used to manipulate the properties of the laser output. The sign of the circular polarization of the mode that builds up inside the cavity is controlled with a polarizer (pol), a Faraday rotator (FR) and a quarter wave plate (QWP). Since the phase function of the GPM is spin-dependent, the output is switched between right and left channels by changing the orientation of the QWP. (c-f) Measured OAM outputs at the left (σ+) and right (σ-) channels of the twisted MDC laser with two orientations of the QWP(σ ± ). Red and blue squares correspond to helicity (σ+ or σ-, respectively) of the buildup mode polarization inside the laser cavity. (g, h) Self interference pattern of the output beam at the left and right channels, obtained with a Mach-Zehnder interferometer; the forks indicate OAM of l = −1 in the left channel, and OAM of l = + 1 in the right channel, as expected. (i-l) Measured multiple harmonic helical output beams, generated by placing a spin-dependent HR-GPM of OAM with l = ± 1, ± 2, ± 3.
Fig. 3
Fig. 3 Generation of partially coherent vortex beams. (a) The experimental setup of a wavefront folding interferometer for spatial coherence measurement; RAP – right angle prism (acts as a Dove prism); BS – beam splitter. Insets depict the intensity distribution of a partially coherent vortex beam generated by a GPM of l = 1 (lower inset, laser output), and the corresponding interference pattern (upper inset). (b) The resultant experimental spatial coherence function. Inset depicts the corresponding calculated coherence function. (c) Experimental intensity distribution of the laser output of multiple partially coherent harmonic vortex beams and (d) the corresponding calculation. (e) Cross sections of the experimental (red line) and calculated (black) intensity distributions of partially coherent vortices, and for fully coherent vortices (blue, taken from Fig. 2(i)).
Fig. 4
Fig. 4 Interleaved GPM concept. (a-c) Sub-array structures of 2θ(x, y) = kx + (a) 2θ(x, y) = -kx + (b) and the resultant interleaved GPM (c) for the generation of a radial vortex beam; k = (2π/λ)sin(10), λ = 1064 nm. The inset depicts the orientation angle θ. (d-e) The corresponding sparse geometric phase profiles for illumination with σ+ (d) and σ- (e), and the resultant interleaved geometric phase under linear polarization illumination (f); the color bar denotes the geometric phase from 0 to 2π.
Fig. 5
Fig. 5 Vectorial vortex output beams with different topologies. (a-c) Illustrations of the twisted output beams emerging from the intra-cavity GPM and the far-field measurements of radial polarization (a), azimuthal polarization (b), and vectorial vortex of winding number l = 2 (c), generated by a coherent superposition of wavefronts with opposite OAMs (red and blue helixes) and helicities σ+ (red arrow) and σ- (blue arrow); schematic (a) and SEM images (b, c) of the corresponding GPMs. Experimental polarization distributions were obtained by placing an external linear polarizer at eight different orientations, where the white arrows denote the space-variant polarization. Upper insets show the polarization vector fields of the output beams that were derived from the measurement of the Stokes parameters.
Fig. 6
Fig. 6 Modified degenerate cavity (MDC) laser arrangements. The number of lasing modes is controlled by changing the size of an intra-cavity pinhole aperture.
Fig. 7
Fig. 7 Intracavity GPM and external GPM elements. (a) Experimental intensity distributions of the multi-tasking elements, when placed inside (top) and outside (bottom) a laser cavity. (b) Experimental output power as a function of output coupler transmittance. The total conversion efficiency of the GPM element was designed to match the optimum transmittance of the laser, around 12%. Due to fabrication and technical issues, the actual total conversion efficiency of the elements was 10%, closely matching the optimum output coupler transmittance.
Fig. 8
Fig. 8 Spatial coherence for a vortex beam using a GPM of a single OAM of = 1. (a) Calculated and measured intensity distributions at the output from the wavefront folding interferometer. (b) The calculated and measured amplitude and phase of the complex coherence factor (spatial coherence). The experimental results are in good agreement with calculated results.
Fig. 9
Fig. 9 Polarization analysis of the detected transformation from vectorial to scalar vortex. The numbers above each measurement denote the angular orientations of the linear polarizer.

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