Abstract

We design an AlGaAs-based terahertz photonic crystal waveguide (PCW) to achieve terahertz-wave difference frequency generation (DFG) from near-infrared light sources. The PCW structure provides a tight confinement of terahertz-wave field, resulting in a good mode field overlap of three waves. The unique phase matching condition between two pump waves and terahertz Bloch wave can be satisfied through choosing appropriate waveguide parameters and pump wavelengths. With the coupled-mode equations derived from modal theory for describing the light propagation, we simulate the continuous terahertz DFG process, and a high power-normalized conversion efficiency of 0.7632 × 10<sup>-4</sup> W<sup>-1</sup> for 3 THz generation is obtained.

© 2012 IEEE

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  1. M. Tonouchi, "Cutting-edge terahertz technology," Nature Photon. 1, 97-105 (2007).
  2. B. Williams, "Terahertz quantum-cascade lasers," Nature Photon. 1, 517-525 (2007).
  3. S. Takigawa, S. Noda, "Mode analysis of two-dimensional photonic crystal terahertz lasers with gain/loss dispersion characteristics," J. Opt. Soc. Amer. B 27, 2556-2567 (2010).
  4. M. van Exter, D. Grischkowsky, "Characterization of an optoelectronic terahertz beam system," IEEE Trans. Microw. Theory Tech. 38, 1684-1691 (1990).
  5. E. Petersen, W. Shi, A. Chavez-Pirson, N. Peyghambarian, A. Cooney, "Efficient parametric terahertz generation in quasi-phase-matched GaP through cavity enhanced difference-frequency generation," Appl. Phys. Lett. 98, 121119-1-121119-3 (2011).
  6. Q. Wu, M. Litz, X. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68, 2924-2926 (1996).
  7. Y. Takushima, S. Shin, Y. C. Chung, "Design of a LiNbO3 ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration," Opt. Exp. 15, 14783-14792 (2007).
  8. Y. Huang, T. Wang, Y. Lin, C. Lee, M. Chuang, Y. Lin, F. Lin, "Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide," Opt. Exp. 19, 24577-24582 (2011).
  9. K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, K. Kawase, "Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation," Opt. Exp. 17, 6676-6681 (2009).
  10. Y. H. Avetisyan, "Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique," Opt. Lett. 35, 2508-2510 (2010).
  11. C. Staus, T. Kuech, L. McCaughan, "Continuously phase-matched terahertz difference frequency generation in an embedded-waveguide structure supporting only fundamental modes," Opt. Exp. 16, 13296-13303 (2008).
  12. C. M. Staus, T. F. Kuech, L. McCaughan, "AlxGa1-xAs nested waveguide heterostructures for continuously phase-matched terahertz difference frequency generation," Opt. Exp. 18, 2332-2338 (2010).
  13. M. Schall, H. Helm, S. Keiding, "Far infrared properties of electro-optic crystals measured by THz time-domain spectroscopy," Int. J. Infrared Millimeter Waves 20, 595-604 (1999).
  14. N. E. Yu, C. Kang, H. K. Yoo, C. Jung, Y. L. Lee, C.-S. Kee, D.-K. Ko, J. Lee, K. Kitamura, S. Takekawa, "Simultaneous forward and backward terahertz generations in periodically poled stoichiometric LiTaO3 crystal using femtosecond pulses," Appl. Phys. Lett. 93, 041104-1-041104-3 (2008).
  15. S. Adachi, Properties of Aluminium Gallium Arsenide (Inst. Eng. Technol., 1993).
  16. M. Brozel, G. Stillman, Properties of Gallium Arsenide (Inst. Eng. Technol., 1996).
  17. A. Marandi, T. Darcie, P. So, "Design of a continuous-wave tunable terahertz source using waveguide-phase-matched GaAs," Opt. Exp. 16, 10427-10433 (2008).
  18. T. Baba, "Slow light in photonic crystals," Nature Photon. 2, 465-473 (2008).
  19. H. Chen, J. Su, J. Wang, X. Zhao, "Optically-controlled high-speed terahertz wave modulator based on nonlinear photonic crystals," Opt. Exp. 19, 3599-3603 (2011).
  20. J. Li, J. He, Z. Hong, "Terahertz wave switch based on silicon photonic crystals," Appl. Opt. 46, 5034-5037 (2007).
  21. Y. Zhang, Y. Zhang, B. Li, "Highly-efficient directional emission from photonic crystal waveguides for coupling of freely propagated terahertz waves into Si slab waveguides," Opt. Exp. 15, 9281-9286 (2007).
  22. H. Kurt, D. Citrin, "Photonic crystals for biochemical sensing in the terahertz region," Appl. Phys. Lett. 87, 041108-1-041108-3 (2005).
  23. C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, K. Staliunas, "Second-harmonic generation of narrow beams in subdiffractive photonic crystals," Phys. Rev. A 78, 053818-1-053818-4 (2008).
  24. R. Iliew, C. Etrich, T. Pertsch, F. Lederer, "Slow-light enhanced collinear second-harmonic generation in two-dimensional photonic crystals," Phys. Rev. B 77, 115124-1-115124-9 (2008).
  25. B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O'Faolain, T. Krauss, "Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides," Nature Photon. 3, 206-210 (2009).
  26. C. Monat, C. Grillet, B. Corcoran, D. J. Moss, B. J. Eggleton, T. P. White, T. F. Krauss, "Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics," Opt. Exp. 18, 6831-6840 (2010).
  27. T. Chen, J. Sun, L. Li, J. Tang, Y. Zhou, "Design of a photonic crystal waveguide for terahertz-wave difference frequency generation," IEEE Photon. Technol. Lett. 24, 921-923 (2012).
  28. C. Xu, H. Okayama, K. Shinozaki, K. Watanabe, M. Kawahara, "Wavelength conversions 1.5 µm by difference frequency generation in periodically domain-inverted LiNbO3 channel waveguides," Appl. Phys. Lett. 63, 1170-1172 (1993).
  29. A. Mock, L. Lu, J. O'Brien, "Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides," Phys. Rev. B 81, 155115-1-155115-11 (2010).
  30. R. Iliew, C. Etrich, T. Pertsch, F. Lederer, Y. Kivshar, "Huge enhancement of backward second-harmonic generation with slow light in photonic crystals," Phys. Rev. A 81, 023820-1-023820-10 (2010).
  31. A. Snyder, J. Love, Optical Waveguide Theory (Springer, 1983).
  32. D. Michaelis, U. Peschel, C. Wächter, A. Bräuer, "Reciprocity theorem and perturbation theory for photonic crystal waveguides," Phys. Rev. E 68, 065601-1-065601-4 (2003).
  33. S. Johnson, J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Exp. 8, 173-190 (2001).
  34. E. Centeno, C. Ciracì, "Theory of backward second-harmonic localization in nonlinear left-handed media," Phys. Rev. B 78, 235101-1-235101-8 (2008).
  35. M. Afromowitz, "Refractive index of Ga1-xAlxAs," Solid State Commun. 15, 59-63 (1974).
  36. A. Fallahkhair, K. Li, T. Murphy, "Vector finite difference modesolver for anisotropic dielectric waveguides," J. Lightw. Technol. 26, 1423-1431 (2008).
  37. S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, V. Berger, "Influence of scattering and two-photon absorption on the optical loss in GaAs-Al2O3 nonlinear waveguides measured using femtosecond pulses," IEEE J. Quantum Electron. 39, 478-486 (2003).
  38. H. Ishikawa, T. Kondo, "Birefringent phase matching in thin rectangular high-index-contrast waveguides," Appl. Phys. Exp. 2, 042202-1-042202-3 (2009).
  39. T. Kim, T. Matsushita, T. Kondo, "Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides," Appl. Phys. Exp. 4, 082201-1-082201-3 (2011).
  40. E. Kapon, R. Bhat, "Low-loss single-mode GaAs/AlGaAs optical waveguides grown by organometallic vapor phase epitaxy," Appl. Phys. Lett. 50, 1628-1630 (1987).
  41. J. Shin, Y.-C. Chang, N. Dagli, "Propagation loss study of very compact GaAs/AlGaAs substrate removed waveguides," Opt. Exp. 17, 3390-3395 (2009).
  42. L. OFaolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, T. F. Krauss, "Loss engineered slow light waveguides," Opt. Exp. 18, 27627-27638 (2010).

2012

T. Chen, J. Sun, L. Li, J. Tang, Y. Zhou, "Design of a photonic crystal waveguide for terahertz-wave difference frequency generation," IEEE Photon. Technol. Lett. 24, 921-923 (2012).

2011

E. Petersen, W. Shi, A. Chavez-Pirson, N. Peyghambarian, A. Cooney, "Efficient parametric terahertz generation in quasi-phase-matched GaP through cavity enhanced difference-frequency generation," Appl. Phys. Lett. 98, 121119-1-121119-3 (2011).

Y. Huang, T. Wang, Y. Lin, C. Lee, M. Chuang, Y. Lin, F. Lin, "Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide," Opt. Exp. 19, 24577-24582 (2011).

H. Chen, J. Su, J. Wang, X. Zhao, "Optically-controlled high-speed terahertz wave modulator based on nonlinear photonic crystals," Opt. Exp. 19, 3599-3603 (2011).

T. Kim, T. Matsushita, T. Kondo, "Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides," Appl. Phys. Exp. 4, 082201-1-082201-3 (2011).

2010

C. Monat, C. Grillet, B. Corcoran, D. J. Moss, B. J. Eggleton, T. P. White, T. F. Krauss, "Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics," Opt. Exp. 18, 6831-6840 (2010).

L. OFaolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, T. F. Krauss, "Loss engineered slow light waveguides," Opt. Exp. 18, 27627-27638 (2010).

Y. H. Avetisyan, "Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique," Opt. Lett. 35, 2508-2510 (2010).

C. M. Staus, T. F. Kuech, L. McCaughan, "AlxGa1-xAs nested waveguide heterostructures for continuously phase-matched terahertz difference frequency generation," Opt. Exp. 18, 2332-2338 (2010).

S. Takigawa, S. Noda, "Mode analysis of two-dimensional photonic crystal terahertz lasers with gain/loss dispersion characteristics," J. Opt. Soc. Amer. B 27, 2556-2567 (2010).

A. Mock, L. Lu, J. O'Brien, "Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides," Phys. Rev. B 81, 155115-1-155115-11 (2010).

R. Iliew, C. Etrich, T. Pertsch, F. Lederer, Y. Kivshar, "Huge enhancement of backward second-harmonic generation with slow light in photonic crystals," Phys. Rev. A 81, 023820-1-023820-10 (2010).

2009

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O'Faolain, T. Krauss, "Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides," Nature Photon. 3, 206-210 (2009).

K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, K. Kawase, "Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation," Opt. Exp. 17, 6676-6681 (2009).

J. Shin, Y.-C. Chang, N. Dagli, "Propagation loss study of very compact GaAs/AlGaAs substrate removed waveguides," Opt. Exp. 17, 3390-3395 (2009).

H. Ishikawa, T. Kondo, "Birefringent phase matching in thin rectangular high-index-contrast waveguides," Appl. Phys. Exp. 2, 042202-1-042202-3 (2009).

2008

C. Staus, T. Kuech, L. McCaughan, "Continuously phase-matched terahertz difference frequency generation in an embedded-waveguide structure supporting only fundamental modes," Opt. Exp. 16, 13296-13303 (2008).

N. E. Yu, C. Kang, H. K. Yoo, C. Jung, Y. L. Lee, C.-S. Kee, D.-K. Ko, J. Lee, K. Kitamura, S. Takekawa, "Simultaneous forward and backward terahertz generations in periodically poled stoichiometric LiTaO3 crystal using femtosecond pulses," Appl. Phys. Lett. 93, 041104-1-041104-3 (2008).

A. Marandi, T. Darcie, P. So, "Design of a continuous-wave tunable terahertz source using waveguide-phase-matched GaAs," Opt. Exp. 16, 10427-10433 (2008).

T. Baba, "Slow light in photonic crystals," Nature Photon. 2, 465-473 (2008).

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, K. Staliunas, "Second-harmonic generation of narrow beams in subdiffractive photonic crystals," Phys. Rev. A 78, 053818-1-053818-4 (2008).

R. Iliew, C. Etrich, T. Pertsch, F. Lederer, "Slow-light enhanced collinear second-harmonic generation in two-dimensional photonic crystals," Phys. Rev. B 77, 115124-1-115124-9 (2008).

E. Centeno, C. Ciracì, "Theory of backward second-harmonic localization in nonlinear left-handed media," Phys. Rev. B 78, 235101-1-235101-8 (2008).

A. Fallahkhair, K. Li, T. Murphy, "Vector finite difference modesolver for anisotropic dielectric waveguides," J. Lightw. Technol. 26, 1423-1431 (2008).

2007

Y. Takushima, S. Shin, Y. C. Chung, "Design of a LiNbO3 ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration," Opt. Exp. 15, 14783-14792 (2007).

J. Li, J. He, Z. Hong, "Terahertz wave switch based on silicon photonic crystals," Appl. Opt. 46, 5034-5037 (2007).

Y. Zhang, Y. Zhang, B. Li, "Highly-efficient directional emission from photonic crystal waveguides for coupling of freely propagated terahertz waves into Si slab waveguides," Opt. Exp. 15, 9281-9286 (2007).

M. Tonouchi, "Cutting-edge terahertz technology," Nature Photon. 1, 97-105 (2007).

B. Williams, "Terahertz quantum-cascade lasers," Nature Photon. 1, 517-525 (2007).

2005

H. Kurt, D. Citrin, "Photonic crystals for biochemical sensing in the terahertz region," Appl. Phys. Lett. 87, 041108-1-041108-3 (2005).

2003

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, V. Berger, "Influence of scattering and two-photon absorption on the optical loss in GaAs-Al2O3 nonlinear waveguides measured using femtosecond pulses," IEEE J. Quantum Electron. 39, 478-486 (2003).

D. Michaelis, U. Peschel, C. Wächter, A. Bräuer, "Reciprocity theorem and perturbation theory for photonic crystal waveguides," Phys. Rev. E 68, 065601-1-065601-4 (2003).

2001

S. Johnson, J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Exp. 8, 173-190 (2001).

1999

M. Schall, H. Helm, S. Keiding, "Far infrared properties of electro-optic crystals measured by THz time-domain spectroscopy," Int. J. Infrared Millimeter Waves 20, 595-604 (1999).

1996

Q. Wu, M. Litz, X. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68, 2924-2926 (1996).

1993

C. Xu, H. Okayama, K. Shinozaki, K. Watanabe, M. Kawahara, "Wavelength conversions 1.5 µm by difference frequency generation in periodically domain-inverted LiNbO3 channel waveguides," Appl. Phys. Lett. 63, 1170-1172 (1993).

1990

M. van Exter, D. Grischkowsky, "Characterization of an optoelectronic terahertz beam system," IEEE Trans. Microw. Theory Tech. 38, 1684-1691 (1990).

1987

E. Kapon, R. Bhat, "Low-loss single-mode GaAs/AlGaAs optical waveguides grown by organometallic vapor phase epitaxy," Appl. Phys. Lett. 50, 1628-1630 (1987).

1974

M. Afromowitz, "Refractive index of Ga1-xAlxAs," Solid State Commun. 15, 59-63 (1974).

Appl. Opt.

Appl. Phys. Exp.

H. Ishikawa, T. Kondo, "Birefringent phase matching in thin rectangular high-index-contrast waveguides," Appl. Phys. Exp. 2, 042202-1-042202-3 (2009).

T. Kim, T. Matsushita, T. Kondo, "Phase-matched second-harmonic generation in thin rectangular high-index-contrast AlGaAs waveguides," Appl. Phys. Exp. 4, 082201-1-082201-3 (2011).

Appl. Phys. Lett.

E. Kapon, R. Bhat, "Low-loss single-mode GaAs/AlGaAs optical waveguides grown by organometallic vapor phase epitaxy," Appl. Phys. Lett. 50, 1628-1630 (1987).

C. Xu, H. Okayama, K. Shinozaki, K. Watanabe, M. Kawahara, "Wavelength conversions 1.5 µm by difference frequency generation in periodically domain-inverted LiNbO3 channel waveguides," Appl. Phys. Lett. 63, 1170-1172 (1993).

E. Petersen, W. Shi, A. Chavez-Pirson, N. Peyghambarian, A. Cooney, "Efficient parametric terahertz generation in quasi-phase-matched GaP through cavity enhanced difference-frequency generation," Appl. Phys. Lett. 98, 121119-1-121119-3 (2011).

Q. Wu, M. Litz, X. Zhang, "Broadband detection capability of ZnTe electro-optic field detectors," Appl. Phys. Lett. 68, 2924-2926 (1996).

N. E. Yu, C. Kang, H. K. Yoo, C. Jung, Y. L. Lee, C.-S. Kee, D.-K. Ko, J. Lee, K. Kitamura, S. Takekawa, "Simultaneous forward and backward terahertz generations in periodically poled stoichiometric LiTaO3 crystal using femtosecond pulses," Appl. Phys. Lett. 93, 041104-1-041104-3 (2008).

H. Kurt, D. Citrin, "Photonic crystals for biochemical sensing in the terahertz region," Appl. Phys. Lett. 87, 041108-1-041108-3 (2005).

IEEE J. Quantum Electron.

S. Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, V. Berger, "Influence of scattering and two-photon absorption on the optical loss in GaAs-Al2O3 nonlinear waveguides measured using femtosecond pulses," IEEE J. Quantum Electron. 39, 478-486 (2003).

IEEE Photon. Technol. Lett.

T. Chen, J. Sun, L. Li, J. Tang, Y. Zhou, "Design of a photonic crystal waveguide for terahertz-wave difference frequency generation," IEEE Photon. Technol. Lett. 24, 921-923 (2012).

IEEE Trans. Microw. Theory Tech.

M. van Exter, D. Grischkowsky, "Characterization of an optoelectronic terahertz beam system," IEEE Trans. Microw. Theory Tech. 38, 1684-1691 (1990).

Int. J. Infrared Millimeter Waves

M. Schall, H. Helm, S. Keiding, "Far infrared properties of electro-optic crystals measured by THz time-domain spectroscopy," Int. J. Infrared Millimeter Waves 20, 595-604 (1999).

J. Lightw. Technol.

A. Fallahkhair, K. Li, T. Murphy, "Vector finite difference modesolver for anisotropic dielectric waveguides," J. Lightw. Technol. 26, 1423-1431 (2008).

J. Opt. Soc. Amer. B

S. Takigawa, S. Noda, "Mode analysis of two-dimensional photonic crystal terahertz lasers with gain/loss dispersion characteristics," J. Opt. Soc. Amer. B 27, 2556-2567 (2010).

Nature Photon.

M. Tonouchi, "Cutting-edge terahertz technology," Nature Photon. 1, 97-105 (2007).

B. Williams, "Terahertz quantum-cascade lasers," Nature Photon. 1, 517-525 (2007).

T. Baba, "Slow light in photonic crystals," Nature Photon. 2, 465-473 (2008).

B. Corcoran, C. Monat, C. Grillet, D. Moss, B. Eggleton, T. White, L. O'Faolain, T. Krauss, "Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides," Nature Photon. 3, 206-210 (2009).

Opt. Exp.

C. Monat, C. Grillet, B. Corcoran, D. J. Moss, B. J. Eggleton, T. P. White, T. F. Krauss, "Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics," Opt. Exp. 18, 6831-6840 (2010).

S. Johnson, J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Exp. 8, 173-190 (2001).

J. Shin, Y.-C. Chang, N. Dagli, "Propagation loss study of very compact GaAs/AlGaAs substrate removed waveguides," Opt. Exp. 17, 3390-3395 (2009).

L. OFaolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, T. F. Krauss, "Loss engineered slow light waveguides," Opt. Exp. 18, 27627-27638 (2010).

H. Chen, J. Su, J. Wang, X. Zhao, "Optically-controlled high-speed terahertz wave modulator based on nonlinear photonic crystals," Opt. Exp. 19, 3599-3603 (2011).

Y. Zhang, Y. Zhang, B. Li, "Highly-efficient directional emission from photonic crystal waveguides for coupling of freely propagated terahertz waves into Si slab waveguides," Opt. Exp. 15, 9281-9286 (2007).

A. Marandi, T. Darcie, P. So, "Design of a continuous-wave tunable terahertz source using waveguide-phase-matched GaAs," Opt. Exp. 16, 10427-10433 (2008).

Y. Takushima, S. Shin, Y. C. Chung, "Design of a LiNbO3 ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration," Opt. Exp. 15, 14783-14792 (2007).

Y. Huang, T. Wang, Y. Lin, C. Lee, M. Chuang, Y. Lin, F. Lin, "Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide," Opt. Exp. 19, 24577-24582 (2011).

K. Suizu, K. Koketsu, T. Shibuya, T. Tsutsui, T. Akiba, K. Kawase, "Extremely frequency-widened terahertz wave generation using Cherenkov-type radiation," Opt. Exp. 17, 6676-6681 (2009).

C. Staus, T. Kuech, L. McCaughan, "Continuously phase-matched terahertz difference frequency generation in an embedded-waveguide structure supporting only fundamental modes," Opt. Exp. 16, 13296-13303 (2008).

C. M. Staus, T. F. Kuech, L. McCaughan, "AlxGa1-xAs nested waveguide heterostructures for continuously phase-matched terahertz difference frequency generation," Opt. Exp. 18, 2332-2338 (2010).

Opt. Lett.

Phys. Rev. A

C. Nistor, C. Cojocaru, Y. Loiko, J. Trull, R. Herrero, K. Staliunas, "Second-harmonic generation of narrow beams in subdiffractive photonic crystals," Phys. Rev. A 78, 053818-1-053818-4 (2008).

R. Iliew, C. Etrich, T. Pertsch, F. Lederer, Y. Kivshar, "Huge enhancement of backward second-harmonic generation with slow light in photonic crystals," Phys. Rev. A 81, 023820-1-023820-10 (2010).

Phys. Rev. B

A. Mock, L. Lu, J. O'Brien, "Space group theory and Fourier space analysis of two-dimensional photonic crystal waveguides," Phys. Rev. B 81, 155115-1-155115-11 (2010).

E. Centeno, C. Ciracì, "Theory of backward second-harmonic localization in nonlinear left-handed media," Phys. Rev. B 78, 235101-1-235101-8 (2008).

R. Iliew, C. Etrich, T. Pertsch, F. Lederer, "Slow-light enhanced collinear second-harmonic generation in two-dimensional photonic crystals," Phys. Rev. B 77, 115124-1-115124-9 (2008).

Phys. Rev. E

D. Michaelis, U. Peschel, C. Wächter, A. Bräuer, "Reciprocity theorem and perturbation theory for photonic crystal waveguides," Phys. Rev. E 68, 065601-1-065601-4 (2003).

Solid State Commun.

M. Afromowitz, "Refractive index of Ga1-xAlxAs," Solid State Commun. 15, 59-63 (1974).

Other

A. Snyder, J. Love, Optical Waveguide Theory (Springer, 1983).

S. Adachi, Properties of Aluminium Gallium Arsenide (Inst. Eng. Technol., 1993).

M. Brozel, G. Stillman, Properties of Gallium Arsenide (Inst. Eng. Technol., 1996).

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