R. Letizia, S. S. A. Obayya, "Efficient multiresolution time domain analysis of arbitrarly shaped
photonic devices," IET Optoelecton. 2, 241-253 (2008).

H. Satoh, N. Yoshida, S. Kitayama, S. Konaka, "Analysis of 2-D frequency converter utilizing compound nonlinear
photonic-crystal structure by condensed node spatial network method," IEEE Trans. Microw. Theory Tech. 54, 210-215 (2006).

C. M. Reinke, A. Jafarpour, B. Momeni, M. Soltani, S. Khorasani, A. Adibi, Y. Xu, R. K. Lee, "Nonlinear finite-difference time-domain method for the simulation of
anisotropic, $\chi^{(2)}$, and $\chi^{(3)}$ optical effects," J. Lightw. Technol. 24, 624-635 (2006).

F. Dell'Anno, S. De Siena, F. Illuminati, "Multiphoton quantum optics and quantum state engineering," Phys. Rep. 428, 53-168 (2006).

A. Di Falco, C. Conti, G. Assanto, "Quadratic phase macthing in slot waveguides," Opt. Lett. 31, 3146-3148 (2006).

X. Yu, L. Scaccabarozzi, A. C. Lin, M. M. Fejer, J. S. Harris, "Growth of GaAs with orientation-patterned structures for nonlinear optics," J. Cryst. Grow. 301–302, 163-167 (2006).

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simonovskii, X. Yu, J. S. Harris, D. Bliss, D. Weyburne, "Optical parametric generation of a mid-IR continuum in
orientation-patterned GaAs," Opt. Lett. 31, 71-73 (2006).

Y. Wang, T. Wang, J. Liu, "Waveguide modes in coupled-resonator optical waveguides," Phys. Lett. A 353, 101-104 (2006).

G. McConnell, A. Ferguson, "Simultaneous stimulated Raman scattering and second harmonic generation in
periodically poled lithium niobate," Opt. Exp. 13, 2099-2104 (2005).

C. J. Jin, N. P. Johnson, H. M. H. Chong, A. S. Jugessur, S. Day, D. Gallagher, R. M. De La Rue, "Transmission of photonic crystal-resonator waveguide (PhCCRW) structure
enhanced via mode matching," Opt. Exp. 13, 2295-2302 (2005).

Z. Xu, J. Wang, Q. He, L. Cao, P. Su, G. Jin, "Optical filter based on contra-directional waveguide coupling in a 2D
photonic crystal with square lattice of dielectric rods," Opt. Exp. 13, 5608-5613 (2005).

H. Yanming, G. G. King, P. K. Cheo, "Second-harmonic generation using a high-energy and tunable Q-switched
multicore fiber laser," IEEE Photon. Tech. Lett. 16, 2224-2226 (2004).

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, C. De Angelis, "Time-domain BPM for ultrashort pulse propagation in nonlinear multilayers," IEEE Photon. Technol. Lett. 16, 2054-2056 (2004).

S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, "Nonlinear frequency conversion in semiconductor optical waveguides using
birefringent, modal and quasi-phase-matching techniques," J. Opt. A: Pure Appl. Opt. 6, 569-584 (2004).

V. F. Rodriguez-Esquerre, M. Koshiba, H. Figueroa, "Finite-element time-domain analysis of 2-D photonic crystal resonant
cavities," IEEE Photon. Technol, Lett. 16, 816-818 (2004).

M. Soltani, A. Haque, B. Momeni, A. Adibi, Y. Xu, R. K. Lee, "Designing complex optical filters using photonic crystal microcavities," Proc. SPIE 5000, 257 (2003).

S. Ashihara, T. Shimura, K. Kuroda, "Group-velocity matched second-harmonic generation in tilted
quasi-phase-matched gratings," J. Opt. Soc. B 20, 853-856 (2003).

C. Seassal, Y. Desieres, X. Letartre, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, T. Benyattou, "Optical coupling between a two-dimensional photonic crystal-based
microcavity and single-line defect waveguide on InP membranesk," IEEE J. Quantum Electron. 38, 811-815 (2002).

S. Mookherjea, A. Yariv, "Coupled resonator optical waveguide," IEEE J. Sel. Topics Quant. Electron. 8, 448-456 (2002).

H. Satoh, N. Yoshida, Y. Miyanaga, "Analysis of fundamental property of 2D photonic crystal optical waveguide
with various medium conditions by condensed node spatial network," Electron. Commun. Japan 85, 210-20 (2002).

F. Ranieri, Y. Dumeige, A. Levenson, X. Letartre, "Nonlinear decoupled FDTD code: Phasematching in 2D defective photonic
crystal," Electron. Lett. 38, 1704-1706 (2002).

B. Shi, Z. M. Jiang, X. F. Zhou, X. Wang, "A two-dimensional nonlinear photonic crystal for strong second harmonic
generation," J. Appl. Phys. 91, 6769-6771 (2002).

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, T. Tanaka, "Channel drop filter using a single defect in a 2-D photonic crystal slab
waveguide," IEEE J. Lightw. Technol. 20, 845 (2002).

T. Dogaru, L. Carin, "Multiresolution time-domain using CDF biorthogonal wavelets," IEEE Trans. Microwave Theory Tech. 49, 685-691 (2001).

T. Yasui, M. Koshiba, "Three-dimensional vector beam-propagation method for second harmonic
generation analysis," J. Lightw. Technol. 19, 780-785 (2001).

T. Dolgova, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, S. Nakabayashi, "Giant second-harmonic generation in coupled microcavities based on porous
silicon photonic crystals," JETP Lett. 73, 8-12 (2001).

M. Baylindir, B. Temelkuran, E. Ozbay, "Propagation of photons by hopping: A waveguiding mechanism through
localized coupled cavities in three-dimensional photonic crystals," Phys. Rev. B 61, 856-858 (2000).

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, "Waveguiding in planar photonic crystals," Appl. Phys. Lett. 77, 4281-4292 (2000).

F. A. Katsriku, B. M. A. Rahman, K. T. V. Grattan, "Finite-element analysis of second-harmonic generation in AlGaAs waveguides," IEEE J. Quant. Electron. 36, 282-289 (2000).

Y. Xu, R. K. Lee, A. Yariv, "Propagation and second harmonic generation of electromagnetic waves in a
coupled-resonator optical waveguide," J. Opt. Soc. Amer. B 17, 387-400 (2000).

Y. Xu, Y. Li, R. K. Lee, A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62, 7389-7404 (2000).

M. A. Alsunaidi, H. M. Masoudi, J. M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in
nonlinear optical structures," IEEE Photon. Technol. Lett. 12, 395-397 (2000).

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quant. Electron. 35, 1322-1332 (1999).

A. Yariv, Y. Xu, R. K. Lee, A. Scherer, "Coupled-resonator optical waveguide: A proposal and analysis," Opt. Lett. 24, 711-713 (1999).

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. Z. Zhang, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, H. A. Haus, "Channel drop tunneling trough localized states," Phys. Rev. Lett. 80, 960-963 (1998).

R. M. Joseph, A. Taflove, "FDTD Maxwell's Equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propagat. 45, 364-375 (1997).

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

S. D. Gedney, "An anisotropic perfectly matched layer absorbing media for the truncation
of FDTD lattice," IEEE Trans. Antennas Propagat. 44, 1630-1639 (1996).

M. Krumpholz, L. P. B. Katehi, "MRTD: New time domain schemes based on multiresolution analysis," IEEE Trans. Microwave Theory Tech. 44, 555-571 (1996).

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling
efficiency," Phys. Rev. B, Condens. Matter 54, 7837-7842 (1996).

H. M. Masoudi, J. M. Arnold, "Modeling second-order nonlinear effects in optical waveguides using a
parallel-processing beam propagation method," IEEE J. Quant. Electron. 31, 2107-2113 (1995).

M. L. Bortz, S. J. Field, M. M. Fejer, D. W. Nam, R. G. Waarts, D. F. Welch, "Noncritical quasi-phase-matched second harmonic generation in an annealed
proton-exchanged ${\hbox {LiNbO}}_{3}$ waveguide," IEEE J. Quant. Electron. 30, 2953-2960 (1994).

P. S. Weitzman, U. Österberg, "A modified beam propagation method to model second harmonic generation in
optical fibers," IEEE J. Quant. Electron. 29, 1437-1443 (1993).

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer, T. P. Pearsall, "Waveguiding in planar photonic crystals," Appl. Phys. Lett. 77, 4281-4292 (2000).

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. Z. Zhang, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).

H. Satoh, N. Yoshida, Y. Miyanaga, "Analysis of fundamental property of 2D photonic crystal optical waveguide
with various medium conditions by condensed node spatial network," Electron. Commun. Japan 85, 210-20 (2002).

F. Ranieri, Y. Dumeige, A. Levenson, X. Letartre, "Nonlinear decoupled FDTD code: Phasematching in 2D defective photonic
crystal," Electron. Lett. 38, 1704-1706 (2002).

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, T. Tanaka, "Channel drop filter using a single defect in a 2-D photonic crystal slab
waveguide," IEEE J. Lightw. Technol. 20, 845 (2002).

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quant. Electron. 35, 1322-1332 (1999).

M. L. Bortz, S. J. Field, M. M. Fejer, D. W. Nam, R. G. Waarts, D. F. Welch, "Noncritical quasi-phase-matched second harmonic generation in an annealed
proton-exchanged ${\hbox {LiNbO}}_{3}$ waveguide," IEEE J. Quant. Electron. 30, 2953-2960 (1994).

H. M. Masoudi, J. M. Arnold, "Modeling second-order nonlinear effects in optical waveguides using a
parallel-processing beam propagation method," IEEE J. Quant. Electron. 31, 2107-2113 (1995).

F. A. Katsriku, B. M. A. Rahman, K. T. V. Grattan, "Finite-element analysis of second-harmonic generation in AlGaAs waveguides," IEEE J. Quant. Electron. 36, 282-289 (2000).

P. S. Weitzman, U. Österberg, "A modified beam propagation method to model second harmonic generation in
optical fibers," IEEE J. Quant. Electron. 29, 1437-1443 (1993).

C. Seassal, Y. Desieres, X. Letartre, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, T. Benyattou, "Optical coupling between a two-dimensional photonic crystal-based
microcavity and single-line defect waveguide on InP membranesk," IEEE J. Quantum Electron. 38, 811-815 (2002).

S. Mookherjea, A. Yariv, "Coupled resonator optical waveguide," IEEE J. Sel. Topics Quant. Electron. 8, 448-456 (2002).

H. Yanming, G. G. King, P. K. Cheo, "Second-harmonic generation using a high-energy and tunable Q-switched
multicore fiber laser," IEEE Photon. Tech. Lett. 16, 2224-2226 (2004).

V. F. Rodriguez-Esquerre, M. Koshiba, H. Figueroa, "Finite-element time-domain analysis of 2-D photonic crystal resonant
cavities," IEEE Photon. Technol, Lett. 16, 816-818 (2004).

A. Locatelli, F. M. Pigozzo, D. Modotto, A. D. Capobianco, C. De Angelis, "Time-domain BPM for ultrashort pulse propagation in nonlinear multilayers," IEEE Photon. Technol. Lett. 16, 2054-2056 (2004).

M. A. Alsunaidi, H. M. Masoudi, J. M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in
nonlinear optical structures," IEEE Photon. Technol. Lett. 12, 395-397 (2000).

R. M. Joseph, A. Taflove, "FDTD Maxwell's Equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propagat. 45, 364-375 (1997).

S. D. Gedney, "An anisotropic perfectly matched layer absorbing media for the truncation
of FDTD lattice," IEEE Trans. Antennas Propagat. 44, 1630-1639 (1996).

H. Satoh, N. Yoshida, S. Kitayama, S. Konaka, "Analysis of 2-D frequency converter utilizing compound nonlinear
photonic-crystal structure by condensed node spatial network method," IEEE Trans. Microw. Theory Tech. 54, 210-215 (2006).

T. Dogaru, L. Carin, "Multiresolution time-domain using CDF biorthogonal wavelets," IEEE Trans. Microwave Theory Tech. 49, 685-691 (2001).

M. Krumpholz, L. P. B. Katehi, "MRTD: New time domain schemes based on multiresolution analysis," IEEE Trans. Microwave Theory Tech. 44, 555-571 (1996).

R. Letizia, S. S. A. Obayya, "Efficient multiresolution time domain analysis of arbitrarly shaped
photonic devices," IET Optoelecton. 2, 241-253 (2008).

B. Shi, Z. M. Jiang, X. F. Zhou, X. Wang, "A two-dimensional nonlinear photonic crystal for strong second harmonic
generation," J. Appl. Phys. 91, 6769-6771 (2002).

X. Yu, L. Scaccabarozzi, A. C. Lin, M. M. Fejer, J. S. Harris, "Growth of GaAs with orientation-patterned structures for nonlinear optics," J. Cryst. Grow. 301–302, 163-167 (2006).

T. Yasui, M. Koshiba, "Three-dimensional vector beam-propagation method for second harmonic
generation analysis," J. Lightw. Technol. 19, 780-785 (2001).

C. M. Reinke, A. Jafarpour, B. Momeni, M. Soltani, S. Khorasani, A. Adibi, Y. Xu, R. K. Lee, "Nonlinear finite-difference time-domain method for the simulation of
anisotropic, $\chi^{(2)}$, and $\chi^{(3)}$ optical effects," J. Lightw. Technol. 24, 624-635 (2006).

S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, "Nonlinear frequency conversion in semiconductor optical waveguides using
birefringent, modal and quasi-phase-matching techniques," J. Opt. A: Pure Appl. Opt. 6, 569-584 (2004).

Y. Xu, R. K. Lee, A. Yariv, "Propagation and second harmonic generation of electromagnetic waves in a
coupled-resonator optical waveguide," J. Opt. Soc. Amer. B 17, 387-400 (2000).

S. Ashihara, T. Shimura, K. Kuroda, "Group-velocity matched second-harmonic generation in tilted
quasi-phase-matched gratings," J. Opt. Soc. B 20, 853-856 (2003).

T. Dolgova, M. G. Martemyanov, A. A. Fedyanin, O. A. Aktsipetrov, G. Marowsky, S. Nakabayashi, "Giant second-harmonic generation in coupled microcavities based on porous
silicon photonic crystals," JETP Lett. 73, 8-12 (2001).

G. McConnell, A. Ferguson, "Simultaneous stimulated Raman scattering and second harmonic generation in
periodically poled lithium niobate," Opt. Exp. 13, 2099-2104 (2005).

C. J. Jin, N. P. Johnson, H. M. H. Chong, A. S. Jugessur, S. Day, D. Gallagher, R. M. De La Rue, "Transmission of photonic crystal-resonator waveguide (PhCCRW) structure
enhanced via mode matching," Opt. Exp. 13, 2295-2302 (2005).

Z. Xu, J. Wang, Q. He, L. Cao, P. Su, G. Jin, "Optical filter based on contra-directional waveguide coupling in a 2D
photonic crystal with square lattice of dielectric rods," Opt. Exp. 13, 5608-5613 (2005).

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simonovskii, X. Yu, J. S. Harris, D. Bliss, D. Weyburne, "Optical parametric generation of a mid-IR continuum in
orientation-patterned GaAs," Opt. Lett. 31, 71-73 (2006).

A. Yariv, Y. Xu, R. K. Lee, A. Scherer, "Coupled-resonator optical waveguide: A proposal and analysis," Opt. Lett. 24, 711-713 (1999).

A. Di Falco, C. Conti, G. Assanto, "Quadratic phase macthing in slot waveguides," Opt. Lett. 31, 3146-3148 (2006).

Y. Wang, T. Wang, J. Liu, "Waveguide modes in coupled-resonator optical waveguides," Phys. Lett. A 353, 101-104 (2006).

F. Dell'Anno, S. De Siena, F. Illuminati, "Multiphoton quantum optics and quantum state engineering," Phys. Rep. 428, 53-168 (2006).

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

M. Baylindir, B. Temelkuran, E. Ozbay, "Propagation of photons by hopping: A waveguiding mechanism through
localized coupled cavities in three-dimensional photonic crystals," Phys. Rev. B 61, 856-858 (2000).

P. R. Villeneuve, S. Fan, J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling
efficiency," Phys. Rev. B, Condens. Matter 54, 7837-7842 (1996).

Y. Xu, Y. Li, R. K. Lee, A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62, 7389-7404 (2000).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, H. A. Haus, "Channel drop tunneling trough localized states," Phys. Rev. Lett. 80, 960-963 (1998).

M. Soltani, A. Haque, B. Momeni, A. Adibi, Y. Xu, R. K. Lee, "Designing complex optical filters using photonic crystal microcavities," Proc. SPIE 5000, 257 (2003).

H. M. van Driel, "Nonlinear optics in photonic crystals," Proc. 15th Int. Conf. Transparent Optical Networks (2003) pp. 56-59.

A. R. Cowan, J. F. Young, "Second harmonic generation in planar photonic crystal waveguides," Proc. Quantum Electronics and Laser Science Conf. (2001) pp. 44-45.

K. Inoue, M. Sasada, N. Kawai, J. Kawamata, "Phase-matched second-harmonic generation in a two-dimensional photonic
crystal," Proc. Quantum Electronics and Laser Science Conf. (2000) pp. 7-12.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).

A. Yariv, Quantum Electronics (Wiley, 1989).

T. M. Liu, C. T. Lu, C. K. Sun, "2-GHz-repetition rate resonant cavity for the enhancement of second
harmonic generation," Proc. Laser and Electro-Optics Conf. (2004) pp. 2.

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