Abstract

Gradient metasurfaces have recently been demonstrated to provide control of the phase of scattered fields over subwavelength scales, enabling a broad range of linear optical components in a flat, ultrathin, integrable platform. Additionally, the development of nonlinear metasurfaces has disrupted conventional nonlinear optical device design by relaxing phase matching constraints, reducing size and dimensionality, and providing record values of localized nonlinear responses. However, extending the “flat optics” paradigm to the nonlinear case faces important challenges, since we are required to simultaneously achieve efficient frequency conversion and sub-diffractive phase control. Here, we experimentally demonstrate continuous phase control of the giant nonlinear second harmonic optical response from metasurfaces tied to intersubband transitions in semiconductor multi-quantum wells, establishing an exciting path toward realizing the vision of flat, nonlinear optics.

© 2016 Optical Society of America

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References

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2015 (6)

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]

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, 607–612 (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]

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]

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

J. S. Gomez-Diaz, M. Tymchenko, J. Lee, M. A. Belkin, and A. Alù, “Nonlinear Processes in multi-quantum-well plasmonic metasurfaces: electromagnetic response, saturation effects, limits and potentials,” Phys. Rev. B 92, 125429 (2015).
[Crossref]

2014 (2)

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

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

2013 (2)

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

2012 (2)

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108, 263905 (2012).
[Crossref]

2011 (2)

A. Rose and D. R. Smith, “Overcoming phase mismatch in nonlinear metamaterials [Invited],” Opt. Mater. Express 1, 1232–1243 (2011).
[Crossref]

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, 333–337 (2011).
[Crossref]

2009 (1)

2008 (1)

J. B. Pendry, “Time reversal and negative refraction,” Science 322, 71–73 (2008).
[Crossref]

2006 (1)

2002 (1)

1996 (1)

A. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum optical engineering of nonlinearities,” Science 271, 168–173 (1996).
[Crossref]

1987 (1)

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[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, 333–337 (2011).
[Crossref]

Alu, A.

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

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]

J. S. Gomez-Diaz, M. Tymchenko, J. Lee, M. A. Belkin, and A. Alù, “Nonlinear Processes in multi-quantum-well plasmonic metasurfaces: electromagnetic response, saturation effects, limits and potentials,” Phys. Rev. B 92, 125429 (2015).
[Crossref]

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

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108, 263905 (2012).
[Crossref]

Amann, M.

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

Amann, M.-C.

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

Argyropoulos, C.

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

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108, 263905 (2012).
[Crossref]

Avayu, O.

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

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. S. Gomez-Diaz, M. Tymchenko, J. Lee, M. A. Belkin, and A. Alù, “Nonlinear Processes in multi-quantum-well plasmonic metasurfaces: electromagnetic response, saturation effects, limits and potentials,” Phys. Rev. B 92, 125429 (2015).
[Crossref]

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

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

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]

Berger, V.

A. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum optical engineering of nonlinearities,” Science 271, 168–173 (1996).
[Crossref]

Berry, M. V.

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[Crossref]

Biener, G.

Boehm, G.

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

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

Bois, P.

A. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum optical engineering of nonlinearities,” Science 271, 168–173 (1996).
[Crossref]

Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Bomzon, Z.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2008).

Brener, I.

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]

Brueck, S. R. J.

Busch, K.

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]

Capasso, F.

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

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, 333–337 (2011).
[Crossref]

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, 607–612 (2015).
[Crossref]

Chen, P. Y.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108, 263905 (2012).
[Crossref]

Chen, P.-Y.

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

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, 607–612 (2015).
[Crossref]

D’Aguanno, G.

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108, 263905 (2012).
[Crossref]

Demmerle, F.

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

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

Ellenbogen, T.

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).

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, 427 (2012).
[Crossref]

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Fan, W.

Feth, N.

Fiore, A.

A. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum optical engineering of nonlinearities,” Science 271, 168–173 (1996).
[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, 333–337 (2011).
[Crossref]

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, 333–337 (2011).
[Crossref]

Gieseler, J.

Gomez-Diaz, J. S.

J. S. Gomez-Diaz, M. Tymchenko, J. Lee, M. A. Belkin, and A. Alù, “Nonlinear Processes in multi-quantum-well plasmonic metasurfaces: electromagnetic response, saturation effects, limits and potentials,” Phys. Rev. B 92, 125429 (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]

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

Grbic, A.

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

Hasman, E.

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]

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]

Kats, M. A.

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, 333–337 (2011).
[Crossref]

Keren-Zur, S.

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).

Kildishev, A. V.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Kleiner, V.

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]

Lee, J.

J. S. Gomez-Diaz, M. Tymchenko, J. Lee, M. A. Belkin, and A. Alù, “Nonlinear Processes in multi-quantum-well plasmonic metasurfaces: electromagnetic response, saturation effects, limits and potentials,” Phys. Rev. B 92, 125429 (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]

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

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

Li, G.

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, 607–612 (2015).
[Crossref]

Linden, S.

Liu, 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]

Lu, F.

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

Luk, T. S.

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Michaeli, L.

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

Monticone, F.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108, 263905 (2012).
[Crossref]

Nagle, J.

A. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum optical engineering of nonlinearities,” Science 271, 168–173 (1996).
[Crossref]

Ni, X.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Niegemann, J.

Niesler, F. B. P.

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]

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

Osgood, R. M.

Panoiu, N. C.

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J. B. Pendry, “Time reversal and negative refraction,” Science 322, 71–73 (2008).
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Pfeiffer, C.

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
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Pholchai, N.

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, 607–612 (2015).
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Pun, E. Y. B.

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, 607–612 (2015).
[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]

Reineke, B.

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, 607–612 (2015).
[Crossref]

Rose, A.

Rosencher, A. E.

A. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum optical engineering of nonlinearities,” Science 271, 168–173 (1996).
[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]

Shalaev, V. M.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[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).
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Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, 2002).

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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).
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Smith, D. R.

Tetienne, J.-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, 333–337 (2011).
[Crossref]

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J. S. Gomez-Diaz, M. Tymchenko, J. Lee, M. A. Belkin, and A. Alù, “Nonlinear Processes in multi-quantum-well plasmonic metasurfaces: electromagnetic response, saturation effects, limits and potentials,” Phys. Rev. B 92, 125429 (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]

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

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

Vinter, B.

A. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum optical engineering of nonlinearities,” Science 271, 168–173 (1996).
[Crossref]

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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]

Wong, P. W. H.

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, 607–612 (2015).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

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, 333–337 (2011).
[Crossref]

Zentgraf, T.

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, 607–612 (2015).
[Crossref]

Zhang, 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, 607–612 (2015).
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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).

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M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[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. (2)

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, 607–612 (2015).
[Crossref]

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

Nat. Photonics (1)

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]

Nature (1)

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

Opt. Express (1)

Opt. Lett. (2)

Opt. Mater. Express (1)

Phys. Rev. B (1)

J. S. Gomez-Diaz, M. Tymchenko, J. Lee, M. A. Belkin, and A. Alù, “Nonlinear Processes in multi-quantum-well plasmonic metasurfaces: electromagnetic response, saturation effects, limits and potentials,” Phys. Rev. B 92, 125429 (2015).
[Crossref]

Phys. Rev. Lett. (4)

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]

C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108, 263905 (2012).
[Crossref]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: Tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

Science (4)

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, 333–337 (2011).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

J. B. Pendry, “Time reversal and negative refraction,” Science 322, 71–73 (2008).
[Crossref]

A. E. Rosencher, A. Fiore, B. Vinter, V. Berger, P. Bois, and J. Nagle, “Quantum optical engineering of nonlinearities,” Science 271, 168–173 (1996).
[Crossref]

Other (4)

J. Lee, N. Nookala, J. S. Gomez-Diaz, M. Tymchenko, F. Demmerle, G. Boehm, M. Amann, A. Alu, and M. A. Belkin, “Ultrathin second-harmonic metasurfaces with record-high nonlinear optical response,” Adv. Opt. Mater. (2016).

R. W. Boyd, Nonlinear Optics (Academic, 2008).

E. Almeida, G. Shalem, and Y. Prior, “Nonlinear phase control and anomalous phase matching in plasmonic metasurfaces,” http://arxiv.org/abs/1505.05618 .

Y. R. Shen, The Principles of Nonlinear Optics (Wiley-Interscience, 2002).

Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1.

Nonlinear metasurface structure. (a) Conduction band diagram of one period of an In 0.53 Ga 0.47 As / Al 0.48 In 0.52 As quantum well structure designed for giant nonlinear SHG response. Shown are the square of the electron subband wavefunctions and the intersubband transition energies and dipole moments. The layer sequence in nm is 2.5/6.2/1.4/2.4/2.5, where Al 0.48 In 0.52 As barriers are shown in bold, and the first 1.5 nm of the first 2.5 nm-barrier and the last 1.5 nm of the last 2.5 nm-barrier are n-doped to 6 × 10 18    cm 3 . (b) Second-order nonlinear susceptibility for SHG in MQW structure in (a) as a function of the pump frequency. (c)  1800    nm × 1800    nm unit cell of the metasurface with the key dimensions given in nm.

Fig. 2.
Fig. 2.

(a) Simulated normalized E z field distribution in MQW layer of proposed SRR structures. The SRRs are doubly resonant at the FF and SH. They are seen responding to x -polarized light at the FF, and y -polarized at the SH. (b) Experimental absorption spectrum of fabricated SRR structures, demonstrating resonance at FF and SH as described. (c) Optical setup for second harmonic power characterization. Linearly polarized light from a tunable QCL at wavenumber 1015    cm 1 passes through a QWP and is converted to RCP light, followed by long-pass filter to block thee SH from the laser, and is focused onto an array of un-rotated SRRs by a numerical aperture 0.5 collimating lens. The generated second harmonic reflects off the beam splitter and is converted to linearly polarized light after passing through another QWP. RCP and LCP SH light is discriminated by the linear polarizer, and the resulting beam is focused onto a liquid-nitrogen cooled InSb detector after passing through an SP to block out FF reflection from the pump. (d) SH peak power (left axis) or peak intensity (right axis) as a function of the FF peak power squared (bottom axis) or peak intensity squared (top axis). Inset: Scanning electron microscope (SEM) image of fabricated SRR structure.

Fig. 3.
Fig. 3.

Phase gradient nonlinear metasurface. (a) Schematic of metasurface unit cell, with cartoon depiction of RCP incident FF light converting to RCP and LCP SH beams. (b)–(f) SEMs of fabricated gradient SRR arrays, with differing angular rotational steps. Five samples with angular steps Δ φ of 10, 15, 20, 24, and 30 deg were fabricated and tested.

Fig. 4.
Fig. 4.

Phase-gradient nonlinear metasurface characterization. (a) Optical setup for large angle nonlinear beam steering measurement. Linearly polarized light from a continuous-wave CO 2 laser at 1015    cm 1 passes through a QWP to convert to RCP light, followed by a mechanical chopper, and then a ZnSe lens with a 6 in. (15.24 cm)focal length to focus on the sample. The SH beam is generated toward an angle θ , and passes through an SP to remove FF light and through a QWP/linear polarizer to select the LCP or RCP components. The signal is finally detected by an InSb photodetector with approximately 900    μm × 900    μm sensor size positioned 30 cm away from the sample. (b) Optical setup for small angle NL beam steering measurement. The setup is largely the same as in (a), save for the inclusion of a beam splitter to reflect collimated SH light to the polarization control optics and InSb detector. The angular resolution is determined via detection in the plane transverse to the beam’s direction. (c) Far field profiles of RCP SH output from phase-gradient metasurfaces with Δ φ of 10, 15, 20, 24, and 30 deg. (d) Same as (c), but for LCP SH output.

Equations (1)

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χ i j k ( 2 ) = χ MQW , z z z ( 2 ) [ UC ξ i 2 ω ( x , y , z ) ξ j ω ( x , y , z ) ξ k ω ( x , y , z ) d V V ] ,

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