Abstract

Efficient nonlinear frequency conversion requires a phase matching condition to be satisfied. We analyze the dispersion of the modes of hyperbolic wire metamaterials and demonstrate that phase matching at infrared wavelengths can be achieved with a variety of constituent materials, such as GaAs, in which phase matching cannot easily be achieved by conventional means. Our finding promises access to many materials with attractive nonlinear properties.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Metal selection for wire array metamaterials for infrared frequencies

Juliano G. Hayashi, Simon Fleming, Boris T. Kuhlmey, and Alexander Argyros
Opt. Express 23(23) 29867-29881 (2015)

Highly efficient second harmonic generation in hyperbolic metamaterial slot waveguides with large phase matching tolerance

Yu Sun, Zheng Zheng, Jiangtao Cheng, Guodong Sun, and Guofu Qiao
Opt. Express 23(5) 6370-6378 (2015)

Low-frequency nonlocal and hyperbolic modes in corrugated wire metamaterials

Bo Fan, Dmitry Filonov, Pavel Ginzburg, and Viktor A. Podolskiy
Opt. Express 26(13) 17541-17548 (2018)

References

  • View by:
  • |
  • |
  • |

  1. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003), Ch. 2.
  2. P. E. Powers, Fundamentals of Nonlinear Optics (CRC Press, 2011), Ch. 5.
  3. V. Berger, A. Fiore, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998).
    [Crossref]
  4. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
    [Crossref]
  5. M. J. Steel and C. M. de Sterke, “Second-harmonic generation in second-harmonic fiber Bragg gratings,” Appl. Opt. 35(18), 3211–3222 (1996).
    [Crossref] [PubMed]
  6. M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
    [Crossref] [PubMed]
  7. J. Torres, G. Vecchi, D. Coquillat, M. A. Malvezzi, R. Legros, J. P. Lascaray, D. Peyrade, Y. Chen, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, and R. M. De La Rue, “Enhancement of second harmonic generation in one-dimensional and two-dimensional epitaxial GaN-based photonic crystals,” in Photonic Crystal Materials and Nanostructures, R. M. DeLaRue, P. Viktorovitch, C. M. S. Torres, and M. Midrio, eds. (SPIE, 2004), pp. 240–249.
  8. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
    [Crossref]
  9. C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24(31), 4229–4248 (2012).
    [Crossref] [PubMed]
  10. I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 23(3), 529–534 (2006).
    [Crossref]
  11. Z. Kudyshev, I. Gabitov, and A. Maimistov, “Effect of phase mismatch on second-harmonic generation in negative-index materials,” Phys. Rev. A 87(6), 063840 (2013).
    [Crossref]
  12. O. Sydoruk, V. Kalinin, and E. Shamonina, “Parametric amplification of magnetoinductive waves supported by metamaterial arrays,” Phys. Status Solidi 244(4), 1176–1180 (2007).
    [Crossref]
  13. A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A 84(1), 013823 (2011).
    [Crossref]
  14. A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. 107(6), 063902 (2011).
    [Crossref] [PubMed]
  15. C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
    [Crossref] [PubMed]
  16. M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ϵ-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006).
    [Crossref] [PubMed]
  17. M. G. Silveirinha, “Effective medium response of metallic arrays with Kerr-type dielectric host,” Phys. Rev. E 87, 165127 (2013).
  18. S. M. Wang, S. Y. Mu, C. Zhu, Y. X. Gong, P. Xu, H. Liu, T. Li, S. N. Zhu, and X. Zhang, “Hong-Ou-Mandel interference mediated by the magnetic plasmon waves in a three-dimensional optical metamaterial,” Opt. Express 20(5), 5213–5218 (2012).
    [Crossref] [PubMed]
  19. 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]
  20. C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
    [Crossref]
  21. J. G. Hayashi, S. Fleming, B. T. Kuhlmey, and A. Argyros, “Metal selection for wire array metamaterials for infrared frequencies,” Opt. Express 23(23), 29867–29881 (2015).
    [Crossref]
  22. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
  23. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
    [Crossref]
  24. B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express 18(8), 7770–7781 (2010).
    [Crossref] [PubMed]

2015 (3)

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

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]

J. G. Hayashi, S. Fleming, B. T. Kuhlmey, and A. Argyros, “Metal selection for wire array metamaterials for infrared frequencies,” Opt. Express 23(23), 29867–29881 (2015).
[Crossref]

2013 (2)

M. G. Silveirinha, “Effective medium response of metallic arrays with Kerr-type dielectric host,” Phys. Rev. E 87, 165127 (2013).

Z. Kudyshev, I. Gabitov, and A. Maimistov, “Effect of phase mismatch on second-harmonic generation in negative-index materials,” Phys. Rev. A 87(6), 063840 (2013).
[Crossref]

2012 (3)

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24(31), 4229–4248 (2012).
[Crossref] [PubMed]

S. M. Wang, S. Y. Mu, C. Zhu, Y. X. Gong, P. Xu, H. Liu, T. Li, S. N. Zhu, and X. Zhang, “Hong-Ou-Mandel interference mediated by the magnetic plasmon waves in a three-dimensional optical metamaterial,” Opt. Express 20(5), 5213–5218 (2012).
[Crossref] [PubMed]

C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

2011 (2)

A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A 84(1), 013823 (2011).
[Crossref]

A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. 107(6), 063902 (2011).
[Crossref] [PubMed]

2010 (1)

2007 (1)

O. Sydoruk, V. Kalinin, and E. Shamonina, “Parametric amplification of magnetoinductive waves supported by metamaterial arrays,” Phys. Status Solidi 244(4), 1176–1180 (2007).
[Crossref]

2006 (2)

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 23(3), 529–534 (2006).
[Crossref]

M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ϵ-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006).
[Crossref] [PubMed]

1999 (1)

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

1998 (1)

V. Berger, A. Fiore, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998).
[Crossref]

1997 (1)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

1996 (1)

1994 (1)

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Argyros, A.

Atrashchenko, A. V.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24(31), 4229–4248 (2012).
[Crossref] [PubMed]

Belov, P. A.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24(31), 4229–4248 (2012).
[Crossref] [PubMed]

Berger, V.

V. Berger, A. Fiore, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998).
[Crossref]

Bertolotti, M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Bloemer, M. J.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Bowden, C. M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Bravetti, P.

V. Berger, A. Fiore, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998).
[Crossref]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Centini, M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Corcoran, B.

Cortes, C.

C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

D’Aguanno, G.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

de Sterke, C. M.

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

M. J. Steel and C. M. de Sterke, “Second-harmonic generation in second-harmonic fiber Bragg gratings,” Appl. Opt. 35(18), 3211–3222 (1996).
[Crossref] [PubMed]

DeLong, K. W.

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Duncan, C.

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

Eggleton, B. J.

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Fiore, A.

V. Berger, A. Fiore, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998).
[Crossref]

Fleming, S.

Gabitov, I.

Z. Kudyshev, I. Gabitov, and A. Maimistov, “Effect of phase mismatch on second-harmonic generation in negative-index materials,” Phys. Rev. A 87(6), 063840 (2013).
[Crossref]

Gong, Y. X.

Grillet, C.

Haus, J. W.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Hayashi, J. G.

Huang, D.

A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. 107(6), 063902 (2011).
[Crossref] [PubMed]

Hunter, J.

Jacob, Z.

C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Kalinin, V.

O. Sydoruk, V. Kalinin, and E. Shamonina, “Parametric amplification of magnetoinductive waves supported by metamaterial arrays,” Phys. Status Solidi 244(4), 1176–1180 (2007).
[Crossref]

Kante, B.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Kivshar, Y. S.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24(31), 4229–4248 (2012).
[Crossref] [PubMed]

Kivshar, Yu. S.

Krauss, T. F.

Kudyshev, Z.

Z. Kudyshev, I. Gabitov, and A. Maimistov, “Effect of phase mismatch on second-harmonic generation in negative-index materials,” Phys. Rev. A 87(6), 063840 (2013).
[Crossref]

Kuhlmey, B. T.

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

J. G. Hayashi, S. Fleming, B. T. Kuhlmey, and A. Argyros, “Metal selection for wire array metamaterials for infrared frequencies,” Opt. Express 23(23), 29867–29881 (2015).
[Crossref]

Lapine, M.

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

Li, T.

Liu, H.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Maimistov, A.

Z. Kudyshev, I. Gabitov, and A. Maimistov, “Effect of phase mismatch on second-harmonic generation in negative-index materials,” Phys. Rev. A 87(6), 063840 (2013).
[Crossref]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Molesky, S.

C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Monat, C.

Moss, D. J.

Mu, S. Y.

Nagle, J.

V. Berger, A. Fiore, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998).
[Crossref]

Nefedov, I.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Newman, W.

C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

O’Brien, K.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

O’Faolain, L.

Palomba, S.

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

Pelusi, M.

Perret, L.

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

Rho, J.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Rose, A.

A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. 107(6), 063902 (2011).
[Crossref] [PubMed]

A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A 84(1), 013823 (2011).
[Crossref]

Rosencher, E.

V. Berger, A. Fiore, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998).
[Crossref]

Salandrino, A.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Scalora, M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Shadrivov, I. V.

Shamonina, E.

O. Sydoruk, V. Kalinin, and E. Shamonina, “Parametric amplification of magnetoinductive waves supported by metamaterial arrays,” Phys. Status Solidi 244(4), 1176–1180 (2007).
[Crossref]

Sibilia, C.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Silveirinha, M. G.

M. G. Silveirinha, “Effective medium response of metallic arrays with Kerr-type dielectric host,” Phys. Rev. E 87, 165127 (2013).

M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ϵ-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006).
[Crossref] [PubMed]

Simovski, C. R.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24(31), 4229–4248 (2012).
[Crossref] [PubMed]

Smith, D. R.

A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A 84(1), 013823 (2011).
[Crossref]

A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. 107(6), 063902 (2011).
[Crossref] [PubMed]

Steel, M. J.

Suchowski, H.

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]

Sydoruk, O.

O. Sydoruk, V. Kalinin, and E. Shamonina, “Parametric amplification of magnetoinductive waves supported by metamaterial arrays,” Phys. Status Solidi 244(4), 1176–1180 (2007).
[Crossref]

Trebino, R.

Viswanathan, R.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Wang, S. M.

White, T. P.

White, W. E.

Xu, P.

Yin, X.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Zhang, X.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

S. M. Wang, S. Y. Mu, C. Zhu, Y. X. Gong, P. Xu, H. Liu, T. Li, S. N. Zhu, and X. Zhang, “Hong-Ou-Mandel interference mediated by the magnetic plasmon waves in a three-dimensional optical metamaterial,” Opt. Express 20(5), 5213–5218 (2012).
[Crossref] [PubMed]

Zharov, A. A.

Zhu, C.

Zhu, S. N.

Adv. Mater. (1)

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24(31), 4229–4248 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

J. Opt. (1)

C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

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

Nat. Mater. (1)

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]

Nature (1)

V. Berger, A. Fiore, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391(6666), 463–466 (1998).
[Crossref]

Opt. Express (3)

Phys. Rev. A (3)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56(4), 3166–3174 (1997).
[Crossref]

Z. Kudyshev, I. Gabitov, and A. Maimistov, “Effect of phase mismatch on second-harmonic generation in negative-index materials,” Phys. Rev. A 87(6), 063840 (2013).
[Crossref]

A. Rose and D. R. Smith, “Broadly tunable quasi-phase-matching in nonlinear metamaterials,” Phys. Rev. A 84(1), 013823 (2011).
[Crossref]

Phys. Rev. E (1)

M. G. Silveirinha, “Effective medium response of metallic arrays with Kerr-type dielectric host,” Phys. Rev. E 87, 165127 (2013).

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ϵ-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(44 Pt B), 4891–4898 (1999).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

A. Rose, D. Huang, and D. R. Smith, “Controlling the second harmonic in a phase-matched negative-index metamaterial,” Phys. Rev. Lett. 107(6), 063902 (2011).
[Crossref] [PubMed]

Phys. Status Solidi (1)

O. Sydoruk, V. Kalinin, and E. Shamonina, “Parametric amplification of magnetoinductive waves supported by metamaterial arrays,” Phys. Status Solidi 244(4), 1176–1180 (2007).
[Crossref]

Sci. Rep. (1)

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. T. Kuhlmey, and C. M. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

Other (4)

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

J. Torres, G. Vecchi, D. Coquillat, M. A. Malvezzi, R. Legros, J. P. Lascaray, D. Peyrade, Y. Chen, M. Le Vassor d’Yerville, E. Centeno, D. Cassagne, J. P. Albert, and R. M. De La Rue, “Enhancement of second harmonic generation in one-dimensional and two-dimensional epitaxial GaN-based photonic crystals,” in Photonic Crystal Materials and Nanostructures, R. M. DeLaRue, P. Viktorovitch, C. M. S. Torres, and M. Midrio, eds. (SPIE, 2004), pp. 240–249.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003), Ch. 2.

P. E. Powers, Fundamentals of Nonlinear Optics (CRC Press, 2011), Ch. 5.

Cited By

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

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 (a) Schematic of wire media; (b) isofrequency surfaces of (i) TE (ordinary) mode (ii) First extraordinary (TM) mode (iii) Second extraordinary mode (quasi-TEM).
Fig. 2
Fig. 2 (a) Phase diagram for a GaAs and gold wire medium from Eq. (4), showing the low-frequency (light blue) and high-frequency (dark blue) regimes versus wavelength and fill fraction fV, for a structure with a = 150 nm, r = 20 nm, i.e., fV = 5.6%. (b)-(d) Dispersion relations of modes corresponding to the points indicated in (a), which refer to the three different frequency regimes. (b) λ = 1.55 μm (high frequency); (c) λ = 2.3 μm (intermediate frequency); (d) λ = 3.1 μm (low frequency). Dotted black curve: TE mode, red curve: TM mode, blue curve: second TM mode which is SPP like in (b) and quasi-TEM like in (c), (d).
Fig. 3
Fig. 3 Typical isofrequency contours for the four cases of FF (in red) and SH (in blue) from Table 1. Extraordinary and ordinary waves are indicated by solid and dashed curves, respectively. Phase matching solution is guaranteed to exist in cases (A) and (C). In case (B) a phase matching solution is not guaranteed. Phase matching is impossible in case (D).
Fig. 4
Fig. 4 Isofrequency contours calculated by FEM (dots) compared with an effective medium approach (dashed curves) for gold wires in GaAs with a = 150 nm, r = 20 nm, with FF λ = 3.1 μm. Phase matching solutions for (a) FF TEM and SH TE (b) FF TEM and SH TM are circled.

Tables (1)

Tables Icon

Table 1 The four possible combinations of modes for FF and SH for SHG in wire media, assuming the FF is in the low-frequency regime.

Equations (7)

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

ε xx = ε yy =1+2 [ ε m + ε h ( ε m ε h ) f V 1 ] 1 ,
ε zz =1+ [ ε h ( ε m ε h ) f V β 2 k z 2 β p 2 ] 1 ,
( β p a ) 2 2π ln( a 2πr )+0.5275 .
( k z ( 1,2 ) ) 2 = 1 2 { ε xx ( β 2 k x 2 )+( β 2 + β c 2 β p 2 ) ± [ ε xx ( β 2 k x 2 )( β 2 + β c 2 β p 2 ) ] 2 +4 ε xx β p 2 k x 2 },
c 0 ( 1,2 ) = 1 2 { ( ε xx +1 ) β 2 +( β c 2 β p 2 )±| ( ε xx 1 ) β 2 ( β c 2 β p 2 ) | },
c x ( 1,2 ) = 1 2 ε xx { 1± ( ε xx 1 ) β 2 ( β c 2 + β p 2 ) | ( ε xx 1 ) β 2 ( β c 2 β p 2 ) | }.
ε xx ( 2ω ) ε h ( 2ω )> ε xx ( ω ) ε h ( ω ).

Metrics