Abstract

In this paper, a new 2-D frequency converter based on second harmonic generation (SHG) in GaAs photonic crystal waveguides is proposed. The input waveguide, where the second order nonlinear process takes place, is coupled to a secondary waveguide that is designed to allow only SH propagation. A row of photonic crystal microcavity resonators is then placed parallel to the waveguides in order to assist the field coupling. By tuning the resonance of the microcavities at second harmonic wave, the waveguides-microcavities arrangement showed good enhancement of conversion efficiency and selectivity. The performance of the proposed frequency converter has been analyzed by using multiresolution time domain (MRTD) scheme developed for nonlinear problems in conjunction with uniaxial perfectly matched layer (UPML) boundary conditions that rigorously truncate the computational window.

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  38. M. Krumpholz, L. P. B. Katehi, "MRTD: New time domain schemes based on multiresolution analysis," IEEE Trans. Microwave Theory Tech. 44, 555-571 (1996).
  39. 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).
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  44. 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).
  45. Y. Wang, T. Wang, J. Liu, "Waveguide modes in coupled-resonator optical waveguides," Phys. Lett. A 353, 101-104 (2006).
  46. 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).
  47. 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).
  48. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, H. A. Haus, "Channel drop tunneling trough localized states," Phys. Rev. Lett. 80, 960-963 (1998).
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  50. Y. Xu, Y. Li, R. K. Lee, A. Yariv, "Scattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E 62, 7389-7404 (2000).
  51. 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).

2008

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

2006

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).

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).

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).

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

2005

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).

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).

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).

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).

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).

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. 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).

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).

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).

2001

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

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

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

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).

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).

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).

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).

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).

1998

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

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).

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

1996

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).

1995

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).

1994

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).

1993

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).

Appl. Phys. Lett.

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).

Electron. Commun. Japan

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).

Electron. Lett.

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

IEEE J. Lightw. Technol.

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).

IEEE J. Quant. Electron.

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).

IEEE J. Quantum Electron.

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).

IEEE J. Sel. Topics Quant. Electron.

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

IEEE Photon. Tech. Lett.

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).

IEEE Photon. Technol, Lett.

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).

IEEE Photon. Technol. Lett.

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).

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).

IEEE Trans. Antennas Propagat.

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).

IEEE Trans. Microw. Theory Tech.

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).

IEEE Trans. Microwave Theory Tech.

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

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

IET Optoelecton.

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

J. Appl. Phys.

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).

J. Cryst. Grow.

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).

J. Lightw. Technol.

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).

J. Opt. A: Pure Appl. Opt.

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).

J. Opt. Soc. Amer. B

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).

J. Opt. Soc. B

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).

JETP Lett.

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).

Opt. Exp.

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