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).

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).

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,
"Al_{x}Ga_{1-x}As 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).

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).

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 LiTaO_{3}
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).

Y. Takushima, S. Shin, Y. C. Chung, "Design of a
LiNbO_{3} 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).

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

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-Al_{2}O_{3} 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).

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

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).

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

C. Xu, H. Okayama, K. Shinozaki, K. Watanabe, M.
Kawahara, "Wavelength conversions 1.5 µm by difference frequency generation
in periodically domain-inverted LiNbO_{3} channel waveguides," Appl. Phys. Lett.
63, 1170-1172 (1993).

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

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).

M. Afromowitz, "Refractive index of
Ga_{1-x}Al_{x}As," Solid State Commun. 15, 59-63 (1974).

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).

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).

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

C. Xu, H. Okayama, K. Shinozaki, K. Watanabe, M.
Kawahara, "Wavelength conversions 1.5 µm by difference frequency generation
in periodically domain-inverted LiNbO_{3} 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 LiTaO_{3}
crystal using femtosecond pulses," Appl. Phys. Lett. 93, 041104-1-041104-3
(2008).

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-Al_{2}O_{3} nonlinear waveguides
measured using femtosecond pulses," IEEE J. Quantum Electron. 39, 478-486
(2003).

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).

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

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).

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

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).

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).

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).

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).

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

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).

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).

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,
"Al_{x}Ga_{1-x}As nested waveguide heterostructures for continuously
phase-matched terahertz difference frequency generation," Opt. Exp. 18, 2332-2338
(2010).

Y. Takushima, S. Shin, Y. C. Chung, "Design of a
LiNbO_{3} 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).

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).

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).

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).

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).

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).

M. Afromowitz, "Refractive index of
Ga_{1-x}Al_{x}As," Solid State Commun. 15, 59-63 (1974).

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).