Abstract

A two-dimensional (2-D) finite-difference time-domain (FDTD) code for the study of nonlinear optical phenomena, in which both the slowly varying and the rapidly varying components of the electromagnetic fields are considered, has been developed. The algorithm solves vectorial Maxwell's equations for all field components and uses the nonlinear constitutive relation in matrix form as the equations required to describe the nonlinear system. The stability of the code is discussed and its effectiveness is demonstrated through the simulations of self-phase modulation (SPM) and second-harmonic generation (SHG). The authors also show that the combination of nonlinear effects with PCs can result in a significant improvement in device size and integrability, using the example of a Mach-Zehnder interferometer (MZI).

© 2006 IEEE

PDF Article

References

  • View by:
  • |

  1. R. W. Boyd, Nonlinear Optics, San Diego, CA: Academic, 1992.
  2. Y. S. Kivshar and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Boston, MA: Academic, 2003.
  3. C. Flytzanis and J. L. Oudar, Nonlinear Optics: Materials and Devices, Berlin: Springer-Verlag, 1986.
  4. D. L. Mills, Nonlinear Optics, 2nd ed. Berlin: Springer-Verlag, 1998.
  5. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos and L. A. Kolodziejski, "Guided modes in photonic crystal slabs", Phys. Rev. B, Condens. Matter, vol. 60, no. 8, pp. 5751-5758, Aug. 1999.
  6. M. Qiu, K. Azizi, A. Karlsson, M. Swillo and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals", Phys. Rev. B, Condens. Matter, vol. 64, no. 15, pp. 155113-155117, Oct. 2001.
  7. S. Boscolo, C. Conti, M. Midrio and C. G. Someda, "Numerical analysis of propagation and impedance matching in 2D photonic crystal waveguides with finite length", J. Lightw. Technol., vol. 20, no. 2, pp. 304-310, Feb. 2002.
  8. P. Lalanne, "Electromagnetic analysis of photonic crystal waveguides operating above the light cone", IEEE J. Quantum Electron., vol. 38, no. 7, pp. 800-804, Jul. 2002.
  9. T. Sondergaard, J. Arentoft and M. Kristensen, "Theoretical analysis of finite-height semiconductor-on-insulator-based planar photonic crystal waveguides", J. Lightw. Technol., vol. 20, no. 8, pp. 1619-1626, Aug. 2002.
  10. E. Lidorikis, M. L. Povinelli, S. G. Johnson and J. D. Joannopoulos, "Polarization-independent linear waveguides in 3D photonic crystals", Phys. Rev. Lett., vol. 91, no. 2, pp. 23902-23905, Jul. 2003.
  11. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics", Phys. Rev. Lett., vol. 58, no. 20, pp. 2059-2062, May 1987.
  12. S. John, "Strong localization of photons in certain disordered dielectric superlattices", Phys. Rev. Lett., vol. 58, no. 23, pp. 2486-2489, Jun. 1987.
  13. K. M. Ho, C. T. Chan and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures", Phys. Rev. Lett., vol. 65, no. 25, pp. 3152-3155, Dec. 1990.
  14. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array", Phys. Rev. Lett., vol. 68, no. 13, pp. 2023-2026, Mar. 1992.
  15. K. W. K. Shung and Y. C. Tsai, "Surface effects and band measurements in photonic crystals", Phys. Rev. B, vol. 48, no. 15, pp. 1265-11269, Oct. 1993.
  16. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides", Phys. Rev. Lett., vol. 77, no. 18, pp. 3787-3790, Oct. 1996.
  17. M. Loncar, M. Hochberg, A. Scherer and Q. Yueming, "High quality factors and room-temperature lasing in a modified single-defect photonic crystal cavity", Opt. Lett., vol. 29, no. 7, pp. 721-723, Apr. 2004.
  18. H. Takano, Y. Akahane, T. Asano and S. Noda, "In-plane-type channel drop filter in a two-dimensional photonic crystal slab", Appl. Phys. Lett., vol. 84, no. 13, pp. 2226-2228, Mar. 2004.
  19. S. F. Mingaleev and Y. S. Kivshar, "Nonlinear transmission and light localization in photonic crystal waveguides", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 9, pp. 2241-2249, Sep. 2002.
  20. J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton, NJ: Princeton Univ. Press, 1995.
  21. E. Yablonovitch, "Photonic crystals", J. Mod. Opt., vol. 41, no. 2, pp. 173-194, 1994.
  22. S. John and M. Florescu, "Photonic bandgap materials: Towards an all-optical micro-transistor", J. Opt., A Pure Appl. Opt., vol. 3, no. 6, pp. S103-S120, 2001.
  23. S. Fan and J. D. Joannopoulos, "Photonic crystals: Towards large-scale integration of optical and optoelectronic circuits", Opt. Photon. News, vol. 11, no. 10, pp. 28-33, 2000.
  24. J. Martorell, "Parametric nonlinear interaction in centrosymmetric three-dimensional photonic crystals", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 9, pp. 2075-2082, Sep. 2002.
  25. Y. Xu, R. K. Lee and A. Yariv, "Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide", J. Opt. Soc. Amer. B, Opt. Phys., vol. 17, no. 3, pp. 387-400, Mar. 2000.
  26. Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. Mériadec and A. Levenson, "\chi(2) semiconductor photonic crystals", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 9, pp. 2094-2101, Sep. 2002.
  27. M. D. Rahn, A. M. Fox, M. S. Skolnick and T. F. Krauss, "Propagation of ultrashort nonlinear pulses through two-dimensional AlGaAs high-contrast photonic crystal waveguides", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 4, pp. 716-721, Apr. 2002.
  28. M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos and Y. Fink, "Optical bistability in axially modulated OmniGuide fibers", Opt. Lett., vol. 28, no. 7, pp. 516-518, Apr. 2003.
  29. M. Soljacic, C. Luo, J. D. Joannopoulos and S. Fan, "Nonlinear photonic crystal microdevices for optical integration", Opt. Lett., vol. 28, no. 8, pp. 637-639, Apr. 2003.
  30. A. Babin and A. Figotin, "Nonlinear photonic crystals-I: Quadratic nonlinearity", Waves Random Media, vol. 11, no. 2, pp. R31-R102, 2001.
  31. A. Babin and A. Figotin, "Nonlinear photonic crystals-II: Interaction classification for quadratic nonlinearities", Waves Random Media, vol. 12, no. 4, pp. R25-R52, 2002.
  32. A. Babin and A. Figotin, "Nonlinear photonic crystals-III: Cubic nonlinearity", Waves Random Media, vol. 13, no. 4, pp. R41-R69, 2003.
  33. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 9, pp. 2052-2059, Sep. 2002.
  34. D. Mihalache, F. Lederer and D. M. Baboiu, "Two-parameter family of exact solutions of the nonlinear Schrodinger equation describing optical-soliton propagation", Phys. Rev. A, vol. 47, no. 4, pp. 3285-3290, Apr. 1993.
  35. E. L. Dawes and J. H. Marburger, "Computer studies in self-focusing", Phys. Rev., vol. 179, no. 3, pp. 862-868, Mar. 1969.
  36. R. G. Beausoleil, W. J. Munro and T. P. Spiller, "Applications of coherent population transfer to quantum information processing", J. Modern Opt., vol. 51, no. 11, pp. 1559-1601, Nov. 2004.
  37. G. Fibich, B. Ilan and S. Tsynkov, "Backscattering and nonparaxiality arrest collapse of damped nonlinear waves", SIAM J. Appl. Math., vol. 63, no. 1, pp. 1718-1736, Feb. 2003.
  38. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media", IEEE Trans. Antennas Propag., vol. AP-14, no. 3, pp. 302-307, May 1966.
  39. D. M. Sullivan, "Nonlinear FDTD formulations using Z transforms", IEEE Trans. Microw. Theory Tech., vol. 43, no. 3, pp. 676-682, Mar. 1995.
  40. H.-H. Lee, K.-M. Chae, S.-Y. Yim and S.-H. Park, "Finite-difference time-domain analysis of self-focusing in a nonlinear Kerr film", Opt. Express, vol. 12, no. 12, pp. 2603-2609, Jun. 2004.
  41. M. Bahl, N.-C. Panoiu and R. M. Osgood Jr., "Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects", Phys. Rev. B, vol. 67, no. 5, pp. 56604-1-56604-9, May 2003.
  42. M. A. Alsunaidi, H. M. Masoudi and J. M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in nonlinear optical structures", IEEE Photon. Technol. Lett., vol. 12, no. 4, pp. 396-397, Apr. 2000.
  43. A. Di Falco, C. Conti and G. Assanto, "Terahertz Pulse Generation via Optical Rectification in Photonic Crystal Microcavities", 2005.
  44. C. Conti, A. Di Falco and G. Assanto, "Frequency generation within the forbidden band gap: All optical Rabi-like splitting in photonic crystals and microcavities", Phys. Rev. E, vol. 70, no. 6, pp. 66614-1-66614-5, Dec. 2004.
  45. C. Conti, A. Di Falco and G. Assanto, "Optical parametric oscillations in isotropic photonic crystals", Opt. Express, vol. 12, no. 5, pp. 823-828, Mar. 2004.
  46. C. Conti, A. Di Falco and G. Assanto, "Controlled transmission in the forbidden photonic bandgap via transient nonlinear states", Opt. Lett., vol. 29, no. 24, pp. 2902-2904, Oct. 2004.
  47. A. Di Falco, "Wavelength shifting in photonic bandgap microcavities with isotropic media", Appl. Phys. Lett., vol. 85, no. 20, pp. 4585-4587, Nov. 2004.
  48. P. Tran, "Optical switching with a nonlinear photonic crystal: A numerical study", Opt. Lett., vol. 21, no. 15, pp. 1138-1140, Aug. 1996.
  49. P. Tran, "Optical limiting and switching of short pulses by use of a nonlinear photonic bandgap structure with a defect", J. Opt. Soc. Amer. B, Opt. Phys., vol. 14, no. 10, pp. 2589-2595, Oct. 1997.
  50. S. Visnovsky, R. Lopusnik, M. Bauer, J. Bok, J. Fassbender and B. Hillebrands, "Magnetooptic ellipsometry in multilayers at arbitrary magnetization", Opt. Express, vol. 9, no. 3, pp. 121-135, Jul. 2001.
  51. R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics", IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 364-374, Mar. 1997.
  52. A. Taflove and S. C. Hagness, Computation Electrodynamics: The Finite-Difference Time-Domain Method, Norwood, MA: Artech House, 2000.
  53. C. T. Chan, Q. L. Yu and K. M. Ho, "Order-N spectral method for electromagnetic waves", Phys. Rev. B, vol. 51, no. 23, pp. 16635-16642, Jun. 1995.
  54. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Comput. Phys., vol. 114, no. 2, pp. 185-200, Oct. 1994.
  55. L.-X. Chen and D. Kim, "A bistable switching of two-dimensional photonic crystal with Kerr point defect", Opt. Commun., vol. 218, no. 1-3, pp. 19-26, Mar. 2003.
  56. A. C. Cangellaris, "Numerical stability and numerical dispersion of a compact 2-D/FDTD method used for the dispersion analysis of waveguides", IEEE Microw. Guided Wave Lett., vol. 3, no. 1, pp. 3-5, Jan. 1993.
  57. R. F. Remis, "On the stability of the finite-difference time-domain method", J. Comput. Phys., vol. 163, no. 1, pp. 249-261, Sep. 2000.
  58. Y. Amnon and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation, New York: Wiley, 1984.
  59. V. Van and S. K. Chaudhuri, "A hybrid implicit-explicit FDTD scheme for nonlinear optical waveguide modeling", IEEE Microw. Theory Tech., vol. 47, no. 5, pp. 540-545, May 1999.
  60. D. E. Merewether, R. Fisher and F. W. Smith, "On implementing a numeric Huygen's source scheme in a finite difference program to illuminate scattering bodies", IEEE Trans. Nucl. Sci., vol. NS-27, no. 6, pp. 1829-1833, Dec. 1980.
  61. T. Baba and T. Iwai, "Enhancement of third order nonlinearity calculated for two-dimensional photonic crystal", Jpn. J. Appl. Phys., vol. 42, no. 4A, pp. 1603-1608, Apr. 2003.
  62. A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv and A. Scherer, "Role of distributed Bragg reflection in photonic-crystal optical waveguides", Phys. Rev. B, vol. 64, no. 4, p. 041102, Jul. 2001.
  63. A. Adibi, Y. Xu, R. K. Lee, A. Yariv and A. Scherer, "Guiding mechanisms in dielectric-core photonic-crystal optical waveguides", Phys. Rev. B, vol. 64, no. 3, p. 033308, Jul. 2001.

Other (63)

R. W. Boyd, Nonlinear Optics, San Diego, CA: Academic, 1992.

Y. S. Kivshar and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Boston, MA: Academic, 2003.

C. Flytzanis and J. L. Oudar, Nonlinear Optics: Materials and Devices, Berlin: Springer-Verlag, 1986.

D. L. Mills, Nonlinear Optics, 2nd ed. Berlin: Springer-Verlag, 1998.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos and L. A. Kolodziejski, "Guided modes in photonic crystal slabs", Phys. Rev. B, Condens. Matter, vol. 60, no. 8, pp. 5751-5758, Aug. 1999.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals", Phys. Rev. B, Condens. Matter, vol. 64, no. 15, pp. 155113-155117, Oct. 2001.

S. Boscolo, C. Conti, M. Midrio and C. G. Someda, "Numerical analysis of propagation and impedance matching in 2D photonic crystal waveguides with finite length", J. Lightw. Technol., vol. 20, no. 2, pp. 304-310, Feb. 2002.

P. Lalanne, "Electromagnetic analysis of photonic crystal waveguides operating above the light cone", IEEE J. Quantum Electron., vol. 38, no. 7, pp. 800-804, Jul. 2002.

T. Sondergaard, J. Arentoft and M. Kristensen, "Theoretical analysis of finite-height semiconductor-on-insulator-based planar photonic crystal waveguides", J. Lightw. Technol., vol. 20, no. 8, pp. 1619-1626, Aug. 2002.

E. Lidorikis, M. L. Povinelli, S. G. Johnson and J. D. Joannopoulos, "Polarization-independent linear waveguides in 3D photonic crystals", Phys. Rev. Lett., vol. 91, no. 2, pp. 23902-23905, Jul. 2003.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics", Phys. Rev. Lett., vol. 58, no. 20, pp. 2059-2062, May 1987.

S. John, "Strong localization of photons in certain disordered dielectric superlattices", Phys. Rev. Lett., vol. 58, no. 23, pp. 2486-2489, Jun. 1987.

K. M. Ho, C. T. Chan and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures", Phys. Rev. Lett., vol. 65, no. 25, pp. 3152-3155, Dec. 1990.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe and J. D. Joannopoulos, "Measurement of photonic band structure in a two-dimensional periodic dielectric array", Phys. Rev. Lett., vol. 68, no. 13, pp. 2023-2026, Mar. 1992.

K. W. K. Shung and Y. C. Tsai, "Surface effects and band measurements in photonic crystals", Phys. Rev. B, vol. 48, no. 15, pp. 1265-11269, Oct. 1993.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides", Phys. Rev. Lett., vol. 77, no. 18, pp. 3787-3790, Oct. 1996.

M. Loncar, M. Hochberg, A. Scherer and Q. Yueming, "High quality factors and room-temperature lasing in a modified single-defect photonic crystal cavity", Opt. Lett., vol. 29, no. 7, pp. 721-723, Apr. 2004.

H. Takano, Y. Akahane, T. Asano and S. Noda, "In-plane-type channel drop filter in a two-dimensional photonic crystal slab", Appl. Phys. Lett., vol. 84, no. 13, pp. 2226-2228, Mar. 2004.

S. F. Mingaleev and Y. S. Kivshar, "Nonlinear transmission and light localization in photonic crystal waveguides", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 9, pp. 2241-2249, Sep. 2002.

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

E. Yablonovitch, "Photonic crystals", J. Mod. Opt., vol. 41, no. 2, pp. 173-194, 1994.

S. John and M. Florescu, "Photonic bandgap materials: Towards an all-optical micro-transistor", J. Opt., A Pure Appl. Opt., vol. 3, no. 6, pp. S103-S120, 2001.

S. Fan and J. D. Joannopoulos, "Photonic crystals: Towards large-scale integration of optical and optoelectronic circuits", Opt. Photon. News, vol. 11, no. 10, pp. 28-33, 2000.

J. Martorell, "Parametric nonlinear interaction in centrosymmetric three-dimensional photonic crystals", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 9, pp. 2075-2082, Sep. 2002.

Y. Xu, R. K. Lee and A. Yariv, "Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide", J. Opt. Soc. Amer. B, Opt. Phys., vol. 17, no. 3, pp. 387-400, Mar. 2000.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. Mériadec and A. Levenson, "\chi(2) semiconductor photonic crystals", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 9, pp. 2094-2101, Sep. 2002.

M. D. Rahn, A. M. Fox, M. S. Skolnick and T. F. Krauss, "Propagation of ultrashort nonlinear pulses through two-dimensional AlGaAs high-contrast photonic crystal waveguides", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 4, pp. 716-721, Apr. 2002.

M. Soljacic, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos and Y. Fink, "Optical bistability in axially modulated OmniGuide fibers", Opt. Lett., vol. 28, no. 7, pp. 516-518, Apr. 2003.

M. Soljacic, C. Luo, J. D. Joannopoulos and S. Fan, "Nonlinear photonic crystal microdevices for optical integration", Opt. Lett., vol. 28, no. 8, pp. 637-639, Apr. 2003.

A. Babin and A. Figotin, "Nonlinear photonic crystals-I: Quadratic nonlinearity", Waves Random Media, vol. 11, no. 2, pp. R31-R102, 2001.

A. Babin and A. Figotin, "Nonlinear photonic crystals-II: Interaction classification for quadratic nonlinearities", Waves Random Media, vol. 12, no. 4, pp. R25-R52, 2002.

A. Babin and A. Figotin, "Nonlinear photonic crystals-III: Cubic nonlinearity", Waves Random Media, vol. 13, no. 4, pp. R41-R69, 2003.

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 9, pp. 2052-2059, Sep. 2002.

D. Mihalache, F. Lederer and D. M. Baboiu, "Two-parameter family of exact solutions of the nonlinear Schrodinger equation describing optical-soliton propagation", Phys. Rev. A, vol. 47, no. 4, pp. 3285-3290, Apr. 1993.

E. L. Dawes and J. H. Marburger, "Computer studies in self-focusing", Phys. Rev., vol. 179, no. 3, pp. 862-868, Mar. 1969.

R. G. Beausoleil, W. J. Munro and T. P. Spiller, "Applications of coherent population transfer to quantum information processing", J. Modern Opt., vol. 51, no. 11, pp. 1559-1601, Nov. 2004.

G. Fibich, B. Ilan and S. Tsynkov, "Backscattering and nonparaxiality arrest collapse of damped nonlinear waves", SIAM J. Appl. Math., vol. 63, no. 1, pp. 1718-1736, Feb. 2003.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media", IEEE Trans. Antennas Propag., vol. AP-14, no. 3, pp. 302-307, May 1966.

D. M. Sullivan, "Nonlinear FDTD formulations using Z transforms", IEEE Trans. Microw. Theory Tech., vol. 43, no. 3, pp. 676-682, Mar. 1995.

H.-H. Lee, K.-M. Chae, S.-Y. Yim and S.-H. Park, "Finite-difference time-domain analysis of self-focusing in a nonlinear Kerr film", Opt. Express, vol. 12, no. 12, pp. 2603-2609, Jun. 2004.

M. Bahl, N.-C. Panoiu and R. M. Osgood Jr., "Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects", Phys. Rev. B, vol. 67, no. 5, pp. 56604-1-56604-9, May 2003.

M. A. Alsunaidi, H. M. Masoudi and J. M. Arnold, "A time-domain algorithm for the analysis of second-harmonic generation in nonlinear optical structures", IEEE Photon. Technol. Lett., vol. 12, no. 4, pp. 396-397, Apr. 2000.

A. Di Falco, C. Conti and G. Assanto, "Terahertz Pulse Generation via Optical Rectification in Photonic Crystal Microcavities", 2005.

C. Conti, A. Di Falco and G. Assanto, "Frequency generation within the forbidden band gap: All optical Rabi-like splitting in photonic crystals and microcavities", Phys. Rev. E, vol. 70, no. 6, pp. 66614-1-66614-5, Dec. 2004.

C. Conti, A. Di Falco and G. Assanto, "Optical parametric oscillations in isotropic photonic crystals", Opt. Express, vol. 12, no. 5, pp. 823-828, Mar. 2004.

C. Conti, A. Di Falco and G. Assanto, "Controlled transmission in the forbidden photonic bandgap via transient nonlinear states", Opt. Lett., vol. 29, no. 24, pp. 2902-2904, Oct. 2004.

A. Di Falco, "Wavelength shifting in photonic bandgap microcavities with isotropic media", Appl. Phys. Lett., vol. 85, no. 20, pp. 4585-4587, Nov. 2004.

P. Tran, "Optical switching with a nonlinear photonic crystal: A numerical study", Opt. Lett., vol. 21, no. 15, pp. 1138-1140, Aug. 1996.

P. Tran, "Optical limiting and switching of short pulses by use of a nonlinear photonic bandgap structure with a defect", J. Opt. Soc. Amer. B, Opt. Phys., vol. 14, no. 10, pp. 2589-2595, Oct. 1997.

S. Visnovsky, R. Lopusnik, M. Bauer, J. Bok, J. Fassbender and B. Hillebrands, "Magnetooptic ellipsometry in multilayers at arbitrary magnetization", Opt. Express, vol. 9, no. 3, pp. 121-135, Jul. 2001.

R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics", IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 364-374, Mar. 1997.

A. Taflove and S. C. Hagness, Computation Electrodynamics: The Finite-Difference Time-Domain Method, Norwood, MA: Artech House, 2000.

C. T. Chan, Q. L. Yu and K. M. Ho, "Order-N spectral method for electromagnetic waves", Phys. Rev. B, vol. 51, no. 23, pp. 16635-16642, Jun. 1995.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Comput. Phys., vol. 114, no. 2, pp. 185-200, Oct. 1994.

L.-X. Chen and D. Kim, "A bistable switching of two-dimensional photonic crystal with Kerr point defect", Opt. Commun., vol. 218, no. 1-3, pp. 19-26, Mar. 2003.

A. C. Cangellaris, "Numerical stability and numerical dispersion of a compact 2-D/FDTD method used for the dispersion analysis of waveguides", IEEE Microw. Guided Wave Lett., vol. 3, no. 1, pp. 3-5, Jan. 1993.

R. F. Remis, "On the stability of the finite-difference time-domain method", J. Comput. Phys., vol. 163, no. 1, pp. 249-261, Sep. 2000.

Y. Amnon and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation, New York: Wiley, 1984.

V. Van and S. K. Chaudhuri, "A hybrid implicit-explicit FDTD scheme for nonlinear optical waveguide modeling", IEEE Microw. Theory Tech., vol. 47, no. 5, pp. 540-545, May 1999.

D. E. Merewether, R. Fisher and F. W. Smith, "On implementing a numeric Huygen's source scheme in a finite difference program to illuminate scattering bodies", IEEE Trans. Nucl. Sci., vol. NS-27, no. 6, pp. 1829-1833, Dec. 1980.

T. Baba and T. Iwai, "Enhancement of third order nonlinearity calculated for two-dimensional photonic crystal", Jpn. J. Appl. Phys., vol. 42, no. 4A, pp. 1603-1608, Apr. 2003.

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv and A. Scherer, "Role of distributed Bragg reflection in photonic-crystal optical waveguides", Phys. Rev. B, vol. 64, no. 4, p. 041102, Jul. 2001.

A. Adibi, Y. Xu, R. K. Lee, A. Yariv and A. Scherer, "Guiding mechanisms in dielectric-core photonic-crystal optical waveguides", Phys. Rev. B, vol. 64, no. 3, p. 033308, Jul. 2001.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.