Abstract

We study second harmonic generation in a 2-D photonic crystal with the pump field tuned at the Dirac point of the structure. The simultaneous generation of both forward and backward phase-matched second harmonic is achieved by exploiting a peculiar regime in which the interacting waves have zero phase velocity in the lattice. This regime can be attained even when strong material dispersion is present and therefore lends itself well to be implemented in semiconductor-based frequency conversion devices. A comparison between this method and the quasi-phase-matching technique is also presented.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
    [CrossRef]
  2. J. A. Giordmaine, “Mixing of Light Beams in Crystals,” Phys. Rev. Lett. 8(1), 19–20 (1962).
    [CrossRef]
  3. P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
    [CrossRef]
  4. M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
    [CrossRef]
  5. G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Scalora, “Large Enhancement of Interface Second-Harmonic Generation Near the Zero-n Gap of a Negative-Index Bragg Grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 036603 (2006).
    [CrossRef] [PubMed]
  6. G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-Harmonic Generation at Angular Incidence in a Negative-Positive Index Photonic Band-Gap Structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026608 (2006).
    [CrossRef] [PubMed]
  7. M. A. Vincenti, D. de Ceglia, J. W. Haus, M. Scalora, “Harmonic generation in multiresonant plasma films,” Phys. Rev. A 88(4), 043812 (2013).
    [CrossRef]
  8. D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
    [CrossRef]
  9. H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
    [CrossRef] [PubMed]
  10. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
    [CrossRef] [PubMed]
  11. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
    [CrossRef] [PubMed]
  12. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light. (Princeton University, 1995).
  13. J. M. Lourtioz, H. Benisty, V. Berger, J.-M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals, (Springer, 2005).
  14. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  15. N. Bloembergen, A. J. Sieveres, “Nonlinear Optical Properties of Periodic Laminar Structures,” Appl. Phys. Lett. 17(11), 483–486 (1970).
    [CrossRef]
  16. C. L. Tang, P. P. Bey, “Phase Matching in Second-Harmonic Generation Using Artificial Periodic Structures,” IEEE J. Quantum Electron. 9(1), 9–17 (1973).
    [CrossRef]
  17. J. P. van der Ziel, M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs-Al0.3Ga0.7As structures,” Appl. Phys. Lett. 28(8), 437–439 (1976).
    [CrossRef]
  18. C. M. Bowden, A. M. Zheltikov, “Nonlinear Optics of Photonic Crystals,” J. Opt. Soc. Am. B 19(9), 2046–2048 (2002).
    [CrossRef]
  19. E. Centeno, “Second-harmonic superprism effect in photonic crystals,” Opt. Lett. 30(9), 1054–1056 (2005).
    [CrossRef] [PubMed]
  20. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
    [CrossRef] [PubMed]
  21. A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
    [CrossRef]
  22. F. D. M. Haldane, S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
    [CrossRef] [PubMed]
  23. S. Raghu, F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
    [CrossRef]
  24. R. A. Sepkhanov, Ya. B. Bazaliy, C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
    [CrossRef]
  25. X. Zhang, “Observing Zitterbewegung for Photons near the Dirac Point of a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
    [CrossRef] [PubMed]
  26. M. Diem, T. Koschny, C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
    [CrossRef]
  27. X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
    [CrossRef] [PubMed]
  28. K. Sakoda, “Double Dirac cones in triangular-lattice metamaterials,” Opt. Express 20(9), 9925–9939 (2012).
    [CrossRef] [PubMed]
  29. G. D’Aguanno, N. Mattiucci, C. Conti, M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B 87(8), 085135 (2013).
    [CrossRef]
  30. N. Mattiucci, M. J. Bloemer, G. D’Aguanno, “All-optical bistability and switching near the Dirac point of a 2-D photonic crystal,” Opt. Express 21(10), 11862–11868 (2013).
    [CrossRef] [PubMed]
  31. Handbook of Optical Constants of Solids, E. D. Palik ed. (Academic Inc., 1991).
  32. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13(5), 1024–1035 (1996).
    [CrossRef]
  33. B. Gralak, S. Enoch, G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17(6), 1012–1020 (2000).
    [CrossRef] [PubMed]
  34. G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111–2121 (2002).
    [CrossRef]
  35. N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, “Coherence Length during a SH Generation Process in Nonlinear, One-Dimensional, Finite, Multilayered Structures,” J. Opt. Soc. Am. B 24, 877–886 (2007).
    [CrossRef]

2013 (5)

M. A. Vincenti, D. de Ceglia, J. W. Haus, M. Scalora, “Harmonic generation in multiresonant plasma films,” Phys. Rev. A 88(4), 043812 (2013).
[CrossRef]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[CrossRef]

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, C. Conti, M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B 87(8), 085135 (2013).
[CrossRef]

N. Mattiucci, M. J. Bloemer, G. D’Aguanno, “All-optical bistability and switching near the Dirac point of a 2-D photonic crystal,” Opt. Express 21(10), 11862–11868 (2013).
[CrossRef] [PubMed]

2012 (1)

2011 (1)

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

2010 (1)

M. Diem, T. Koschny, C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[CrossRef]

2009 (1)

A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

2008 (3)

F. D. M. Haldane, S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[CrossRef] [PubMed]

S. Raghu, F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[CrossRef]

X. Zhang, “Observing Zitterbewegung for Photons near the Dirac Point of a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[CrossRef] [PubMed]

2007 (2)

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, “Coherence Length during a SH Generation Process in Nonlinear, One-Dimensional, Finite, Multilayered Structures,” J. Opt. Soc. Am. B 24, 877–886 (2007).
[CrossRef]

R. A. Sepkhanov, Ya. B. Bazaliy, C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[CrossRef]

2006 (2)

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Scalora, “Large Enhancement of Interface Second-Harmonic Generation Near the Zero-n Gap of a Negative-Index Bragg Grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 036603 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-Harmonic Generation at Angular Incidence in a Negative-Positive Index Photonic Band-Gap Structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026608 (2006).
[CrossRef] [PubMed]

2005 (2)

E. Centeno, “Second-harmonic superprism effect in photonic crystals,” Opt. Lett. 30(9), 1054–1056 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

2002 (2)

2000 (1)

1996 (1)

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

1976 (1)

J. P. van der Ziel, M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs-Al0.3Ga0.7As structures,” Appl. Phys. Lett. 28(8), 437–439 (1976).
[CrossRef]

1973 (1)

C. L. Tang, P. P. Bey, “Phase Matching in Second-Harmonic Generation Using Artificial Periodic Structures,” IEEE J. Quantum Electron. 9(1), 9–17 (1973).
[CrossRef]

1970 (1)

N. Bloembergen, A. J. Sieveres, “Nonlinear Optical Properties of Periodic Laminar Structures,” Appl. Phys. Lett. 17(11), 483–486 (1970).
[CrossRef]

1962 (2)

J. A. Giordmaine, “Mixing of Light Beams in Crystals,” Phys. Rev. Lett. 8(1), 19–20 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[CrossRef]

Bazaliy, Ya. B.

R. A. Sepkhanov, Ya. B. Bazaliy, C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[CrossRef]

Beenakker, C. W. J.

R. A. Sepkhanov, Ya. B. Bazaliy, C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[CrossRef]

Bertolotti, M.

Bey, P. P.

C. L. Tang, P. P. Bey, “Phase Matching in Second-Harmonic Generation Using Artificial Periodic Structures,” IEEE J. Quantum Electron. 9(1), 9–17 (1973).
[CrossRef]

Bloembergen, N.

N. Bloembergen, A. J. Sieveres, “Nonlinear Optical Properties of Periodic Laminar Structures,” Appl. Phys. Lett. 17(11), 483–486 (1970).
[CrossRef]

Bloemer, M. J.

N. Mattiucci, M. J. Bloemer, G. D’Aguanno, “All-optical bistability and switching near the Dirac point of a 2-D photonic crystal,” Opt. Express 21(10), 11862–11868 (2013).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, C. Conti, M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B 87(8), 085135 (2013).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, “Coherence Length during a SH Generation Process in Nonlinear, One-Dimensional, Finite, Multilayered Structures,” J. Opt. Soc. Am. B 24, 877–886 (2007).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Scalora, “Large Enhancement of Interface Second-Harmonic Generation Near the Zero-n Gap of a Negative-Index Bragg Grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 036603 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-Harmonic Generation at Angular Incidence in a Negative-Positive Index Photonic Band-Gap Structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026608 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111–2121 (2002).
[CrossRef]

Bowden, C. M.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Campione, S.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[CrossRef]

Capolino, F.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[CrossRef]

Centeno, E.

Centini, M.

Chan, C. T.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Conti, C.

G. D’Aguanno, N. Mattiucci, C. Conti, M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B 87(8), 085135 (2013).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, N. Mattiucci, C. Conti, M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B 87(8), 085135 (2013).
[CrossRef]

N. Mattiucci, M. J. Bloemer, G. D’Aguanno, “All-optical bistability and switching near the Dirac point of a 2-D photonic crystal,” Opt. Express 21(10), 11862–11868 (2013).
[CrossRef] [PubMed]

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, “Coherence Length during a SH Generation Process in Nonlinear, One-Dimensional, Finite, Multilayered Structures,” J. Opt. Soc. Am. B 24, 877–886 (2007).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-Harmonic Generation at Angular Incidence in a Negative-Positive Index Photonic Band-Gap Structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026608 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Scalora, “Large Enhancement of Interface Second-Harmonic Generation Near the Zero-n Gap of a Negative-Index Bragg Grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 036603 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111–2121 (2002).
[CrossRef]

de Ceglia, D.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[CrossRef]

M. A. Vincenti, D. de Ceglia, J. W. Haus, M. Scalora, “Harmonic generation in multiresonant plasma films,” Phys. Rev. A 88(4), 043812 (2013).
[CrossRef]

Diem, M.

M. Diem, T. Koschny, C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Enoch, S.

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[CrossRef]

Geim, A. K.

A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Giordmaine, J. A.

J. A. Giordmaine, “Mixing of Light Beams in Crystals,” Phys. Rev. Lett. 8(1), 19–20 (1962).
[CrossRef]

Gralak, B.

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Guinea, F.

A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Haldane, F. D. M.

F. D. M. Haldane, S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[CrossRef] [PubMed]

S. Raghu, F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[CrossRef]

Hang, Z. H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Haus, J. W.

M. A. Vincenti, D. de Ceglia, J. W. Haus, M. Scalora, “Harmonic generation in multiresonant plasma films,” Phys. Rev. A 88(4), 043812 (2013).
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[CrossRef]

Huang, X.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Ilegems, M.

J. P. van der Ziel, M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs-Al0.3Ga0.7As structures,” Appl. Phys. Lett. 28(8), 437–439 (1976).
[CrossRef]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Koschny, T.

M. Diem, T. Koschny, C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[CrossRef]

Lai, Y.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Li, L.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

Mattiucci, N.

G. D’Aguanno, N. Mattiucci, C. Conti, M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B 87(8), 085135 (2013).
[CrossRef]

N. Mattiucci, M. J. Bloemer, G. D’Aguanno, “All-optical bistability and switching near the Dirac point of a 2-D photonic crystal,” Opt. Express 21(10), 11862–11868 (2013).
[CrossRef] [PubMed]

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, “Coherence Length during a SH Generation Process in Nonlinear, One-Dimensional, Finite, Multilayered Structures,” J. Opt. Soc. Am. B 24, 877–886 (2007).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Scalora, “Large Enhancement of Interface Second-Harmonic Generation Near the Zero-n Gap of a Negative-Index Bragg Grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 036603 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-Harmonic Generation at Angular Incidence in a Negative-Positive Index Photonic Band-Gap Structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026608 (2006).
[CrossRef] [PubMed]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Neto, A. H.

A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

Novoselov, K. S.

A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

O’Brien, K.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[CrossRef] [PubMed]

Peres, N. M. R.

A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[CrossRef]

Raghu, S.

F. D. M. Haldane, S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[CrossRef] [PubMed]

S. Raghu, F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[CrossRef]

Sakoda, K.

Salandrino, A.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[CrossRef] [PubMed]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

Scalora, M.

M. A. Vincenti, D. de Ceglia, J. W. Haus, M. Scalora, “Harmonic generation in multiresonant plasma films,” Phys. Rev. A 88(4), 043812 (2013).
[CrossRef]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[CrossRef]

N. Mattiucci, G. D’Aguanno, M. Scalora, M. J. Bloemer, “Coherence Length during a SH Generation Process in Nonlinear, One-Dimensional, Finite, Multilayered Structures,” J. Opt. Soc. Am. B 24, 877–886 (2007).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-Harmonic Generation at Angular Incidence in a Negative-Positive Index Photonic Band-Gap Structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026608 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Scalora, “Large Enhancement of Interface Second-Harmonic Generation Near the Zero-n Gap of a Negative-Index Bragg Grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 036603 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multilayered structures,” J. Opt. Soc. Am. B 19(9), 2111–2121 (2002).
[CrossRef]

Sepkhanov, R. A.

R. A. Sepkhanov, Ya. B. Bazaliy, C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[CrossRef]

Sibilia, C.

Sieveres, A. J.

N. Bloembergen, A. J. Sieveres, “Nonlinear Optical Properties of Periodic Laminar Structures,” Appl. Phys. Lett. 17(11), 483–486 (1970).
[CrossRef]

Soukoulis, C. M.

M. Diem, T. Koschny, C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[CrossRef]

Suchowski, H.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[CrossRef] [PubMed]

Tang, C. L.

C. L. Tang, P. P. Bey, “Phase Matching in Second-Harmonic Generation Using Artificial Periodic Structures,” IEEE J. Quantum Electron. 9(1), 9–17 (1973).
[CrossRef]

Tayeb, G.

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

van der Ziel, J. P.

J. P. van der Ziel, M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs-Al0.3Ga0.7As structures,” Appl. Phys. Lett. 28(8), 437–439 (1976).
[CrossRef]

Vincenti, M. A.

M. A. Vincenti, D. de Ceglia, J. W. Haus, M. Scalora, “Harmonic generation in multiresonant plasma films,” Phys. Rev. A 88(4), 043812 (2013).
[CrossRef]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[CrossRef]

Wong, Z. J.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Yin, X.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[CrossRef] [PubMed]

Zhang, X.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[CrossRef] [PubMed]

X. Zhang, “Observing Zitterbewegung for Photons near the Dirac Point of a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[CrossRef] [PubMed]

Zheltikov, A. M.

Zheng, H.

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

N. Bloembergen, A. J. Sieveres, “Nonlinear Optical Properties of Periodic Laminar Structures,” Appl. Phys. Lett. 17(11), 483–486 (1970).
[CrossRef]

J. P. van der Ziel, M. Ilegems, “Optical second harmonic generation in periodic multilayer GaAs-Al0.3Ga0.7As structures,” Appl. Phys. Lett. 28(8), 437–439 (1976).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. L. Tang, P. P. Bey, “Phase Matching in Second-Harmonic Generation Using Artificial Periodic Structures,” IEEE J. Quantum Electron. 9(1), 9–17 (1973).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

Nat. Mater. (1)

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Nature (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (3)

M. A. Vincenti, D. de Ceglia, J. W. Haus, M. Scalora, “Harmonic generation in multiresonant plasma films,” Phys. Rev. A 88(4), 043812 (2013).
[CrossRef]

S. Raghu, F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[CrossRef]

R. A. Sepkhanov, Ya. B. Bazaliy, C. W. J. Beenakker, “Extremal transmission at the Dirac point of a photonic band structure,” Phys. Rev. A 75(6), 063813 (2007).
[CrossRef]

Phys. Rev. B (2)

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[CrossRef]

G. D’Aguanno, N. Mattiucci, C. Conti, M. J. Bloemer, “Field localization and enhancement near the Dirac point of a finite defectless photonic crystal,” Phys. Rev. B 87(8), 085135 (2013).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Scalora, “Large Enhancement of Interface Second-Harmonic Generation Near the Zero-n Gap of a Negative-Index Bragg Grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(3), 036603 (2006).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, M. J. Bloemer, “Second-Harmonic Generation at Angular Incidence in a Negative-Positive Index Photonic Band-Gap Structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(2), 026608 (2006).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, “Generation of Optical Harmonics,” Phys. Rev. Lett. 7(4), 118–119 (1961).
[CrossRef]

J. A. Giordmaine, “Mixing of Light Beams in Crystals,” Phys. Rev. Lett. 8(1), 19–20 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of Dispersion and Focusing on the Production of Optical Harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

X. Zhang, “Observing Zitterbewegung for Photons near the Dirac Point of a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett. 100(11), 113903 (2008).
[CrossRef] [PubMed]

F. D. M. Haldane, S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[CrossRef] [PubMed]

Physica B (1)

M. Diem, T. Koschny, C. M. Soukoulis, “Transmission in the vicinity of the Dirac point in hexagonal photonic crystals,” Physica B 405(14), 2990–2995 (2010).
[CrossRef]

Rev. Mod. Phys. (1)

A. H. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Science (1)

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[CrossRef] [PubMed]

Other (4)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Molding the Flow of Light. (Princeton University, 1995).

J. M. Lourtioz, H. Benisty, V. Berger, J.-M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals, (Springer, 2005).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Handbook of Optical Constants of Solids, E. D. Palik ed. (Academic Inc., 1991).

Supplementary Material (1)

» Media 1: MOV (10076 KB)     

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 (7)

Fig. 1
Fig. 1

2-D PC consisting of a square array (period a) of square dielectric columns of side d. The structure possesses a finite number of rows N along the z-direction and a total length L = Na. We suppose that the columns are made of a quadratic material with a generic quadratic coefficient d(2). The pump field is a plane electromagnetic wave with the electric field parallel to the axis of the columns and is incident on the structure with its k-vector in the (x,z) plane (in-plane coupling) forming an angle ϑ with respect to the z-direction.

Fig. 2
Fig. 2

Photonic band structure of the infinitely periodic square lattice of columns. The normal incidence transmittance (in red) of a finite N = 10 period structure is superimposed along the ΓX direction (kx = 0, 0≤kz≤π/a). The angular transmittance of the same structure is superimposed along the XM direction (0≤kx≤π/a, kz = π/a). The two green dots indicate respectively the tuning of the FF pump field at the Dirac point and the tuning of the generated SH field. Both the FF and SH are tuned on the Γ point. This condition ensures the Bloch vector of both waves to be zero modulus one of the reciprocal lattice vectors.

Fig. 3
Fig. 3

Tuning conditions for the FF and SH indicated on the dispersion of the infinitely periodic lattice (a) and (c), and on the transmittance of the finite 10-period structure (b) and (d).

Fig. 4
Fig. 4

Schematic sketch of the three cases considered for the calculation of the SH conversion efficiency.

Fig. 5
Fig. 5

Conversion efficiency vs. L/a. The main figure shows the oscillations over few elementary cells. The ancillary figure reports the conversion efficiency up to 150 elementary cells. The conversion efficiency scales as L2 for both the QPM and the PC. In this case the comparison is drawn with the QPM for the forward generated SH.

Fig. 6
Fig. 6

Conversion efficiency vs. L/a. In this case the comparison is with the QPM for the backward generated SH.

Fig. 7
Fig. 7

Snapshot of the FF pump field (upper figure) tuned at the Dirac point and the SH generated field (lower figure) for the 10-period structure. For an animation showing the time evolution see Media 1. The center of both figures reports a magnification of the field localization over one line of columns along the z-axis.

Equations (1)

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

K β ( 2ω )2 K β ( ω )= G ,

Metrics