Abstract

A combination of a higher order accurate FDTD algorithm, a decoupling procedure, and a moving computational window is presented for the solution of the phase-sensitive second harmonic generation problem. The requirement that the spatial step size in the propagation direction be a small fraction of the wavelength is significantly relaxed using the proposed efficient FDTD schemes. It has been shown that these fully explicit schemes deliver convergence of the solution using significantly less computation time and less memory requirement as compared to the standard FDTD scheme.

© 2009 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. R. Ziolkowski, "The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulation," IEEE Trans. Antennas Propagat. 45, 375-391 (1997).
  2. R. Ziolkowski, J. Judkins, "Application of the nonlinear finite-difference time-domain (NL-FDTD) method to pulse propagation in nonlinear media: Self-focusing and linear-nonlinear interfaces," Radio Sci. 28, 901-911 (1993).
  3. A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  4. M. A. Alsunaidi, H. M. Masoudi, J. M. Arnold, "A time-domain algorithm for second harmonic generation in nonlinear optical structures," IEEE Photon. Technol. Lett. 12, 395-397 (2000).
  5. P. Goorjian, A. Taflove, R. Joseph, C. Hagness, "Computational modeling of femtosecond optical solitons from Maxwell's equations," IEEE J. Quant. Electron. 28, 2416-2422 (1992).
  6. K. Hwang, J. Ihm, "A stable fourth-order FDTD method for modeling electrically long dielectric waveguides," J. Lightw. Technol. 24, 1048-1056 (2006).
  7. K. Shlager, J. Schneider, "Comparison of dispersion properties of several low-dispersion finite-difference time-domain algorithms," IEEE Trans. Antennas Propagat. 51, 642-653 (2003).
  8. R. Joseph, A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propagat. 45, 364-374 (1997).
  9. T. Lee, S. C. Hagness, "Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials," J. Opt. Soc. Amer. B. 21, 330-342 (2004).
  10. 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. Tech. 24, 624-634 (2006).
  11. M. Fejer, G. Magel, D. Jundt, R. Byer, "Quasi-phase matched second harmonic generation: Tuning and tolerance," IEEE J. Quant. Electron. 28, 2631-2635 (1992).
  12. E. Sidick, A. Knosen, A. Dienes, "Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses," J. Opt. Soc. Amer. B 12, 1704-1712 (1995).
  13. K. M. Furati, M. A. Alsunaidi, H. M. Masoudi, "An explicit finite difference scheme for wave propagation in nonlinear optical structures," Appl. Math. Lett. 14, 297-302 (2001).
  14. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 1984).

2006

K. Hwang, J. Ihm, "A stable fourth-order FDTD method for modeling electrically long dielectric waveguides," J. Lightw. Technol. 24, 1048-1056 (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. Tech. 24, 624-634 (2006).

2004

T. Lee, S. C. Hagness, "Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials," J. Opt. Soc. Amer. B. 21, 330-342 (2004).

2003

K. Shlager, J. Schneider, "Comparison of dispersion properties of several low-dispersion finite-difference time-domain algorithms," IEEE Trans. Antennas Propagat. 51, 642-653 (2003).

2001

K. M. Furati, M. A. Alsunaidi, H. M. Masoudi, "An explicit finite difference scheme for wave propagation in nonlinear optical structures," Appl. Math. Lett. 14, 297-302 (2001).

2000

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

1997

R. Ziolkowski, "The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulation," IEEE Trans. Antennas Propagat. 45, 375-391 (1997).

R. Joseph, A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propagat. 45, 364-374 (1997).

1995

E. Sidick, A. Knosen, A. Dienes, "Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses," J. Opt. Soc. Amer. B 12, 1704-1712 (1995).

1993

R. Ziolkowski, J. Judkins, "Application of the nonlinear finite-difference time-domain (NL-FDTD) method to pulse propagation in nonlinear media: Self-focusing and linear-nonlinear interfaces," Radio Sci. 28, 901-911 (1993).

1992

P. Goorjian, A. Taflove, R. Joseph, C. Hagness, "Computational modeling of femtosecond optical solitons from Maxwell's equations," IEEE J. Quant. Electron. 28, 2416-2422 (1992).

M. Fejer, G. Magel, D. Jundt, R. Byer, "Quasi-phase matched second harmonic generation: Tuning and tolerance," IEEE J. Quant. Electron. 28, 2631-2635 (1992).

Appl. Math. Lett.

K. M. Furati, M. A. Alsunaidi, H. M. Masoudi, "An explicit finite difference scheme for wave propagation in nonlinear optical structures," Appl. Math. Lett. 14, 297-302 (2001).

IEEE J. Quant. Electron.

M. Fejer, G. Magel, D. Jundt, R. Byer, "Quasi-phase matched second harmonic generation: Tuning and tolerance," IEEE J. Quant. Electron. 28, 2631-2635 (1992).

P. Goorjian, A. Taflove, R. Joseph, C. Hagness, "Computational modeling of femtosecond optical solitons from Maxwell's equations," IEEE J. Quant. Electron. 28, 2416-2422 (1992).

IEEE Photon. Technol. Lett.

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

IEEE Trans. Antennas Propagat.

K. Shlager, J. Schneider, "Comparison of dispersion properties of several low-dispersion finite-difference time-domain algorithms," IEEE Trans. Antennas Propagat. 51, 642-653 (2003).

R. Joseph, A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propagat. 45, 364-374 (1997).

R. Ziolkowski, "The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulation," IEEE Trans. Antennas Propagat. 45, 375-391 (1997).

J Lightw. Tech.

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. Tech. 24, 624-634 (2006).

J. Lightw. Technol.

K. Hwang, J. Ihm, "A stable fourth-order FDTD method for modeling electrically long dielectric waveguides," J. Lightw. Technol. 24, 1048-1056 (2006).

J. Opt. Soc. Amer. B

E. Sidick, A. Knosen, A. Dienes, "Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses," J. Opt. Soc. Amer. B 12, 1704-1712 (1995).

J. Opt. Soc. Amer. B.

T. Lee, S. C. Hagness, "Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials," J. Opt. Soc. Amer. B. 21, 330-342 (2004).

Radio Sci.

R. Ziolkowski, J. Judkins, "Application of the nonlinear finite-difference time-domain (NL-FDTD) method to pulse propagation in nonlinear media: Self-focusing and linear-nonlinear interfaces," Radio Sci. 28, 901-911 (1993).

Other

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Cited By

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

Alert me when this article is cited.