Abstract

The time-domain beam propagation method (TD-BPM) has been implemented and analyzed using several iterative numerical techniques to model the propagation of ultra short pulses in optical structures. The methods depend on one-way non-paraxial time domain propagation that use Pade approximant formulation. Several numerical tests showed that the iterative TD-BPM techniques are very stable and converge using few iterations. From accuracy assessment compared to the FDTD, it has been observed that the longitudinal and the temporal steps sizes can be a number of orders of magnitude larger than the FDTD step sizes with little percentage difference. Computer performance analysis showed the TD-BPM is well suited for long dielectric structures interaction of short and ultra short pulse propagation.

© 2011 IEEE

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  1. P. Vasa, C. Ropers, R. Pomraenke, C. Lieau, "Ultra-fast nano-optics," Laser & Photon Rev. 3, 483-507 (2009).
  2. G. Steinmeyer, "A review of ultrafast optics and optoelectronics: Review article," J. Opt. Aperture Appl. Opt. 5, R1-R15 (2003).
  3. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
  4. A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).
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  7. S. Ju, K. Jung, H. Kim, "Investigation on the characteristics of the envelope FDTD based on the alternating direction implicit scheme," IEEE Microw. Wireless Compon. Lett. 13, 414-416 (200).
  8. H. Rao, R. Scarmozzino, R. M. Osgood, "An improved ADI-FDTD method and its application to photonic simulations," IEEE Photon. Technol. Lett. 14, 477-479 (2002).
  9. S. G. García, T. W. Lee, S. C. Hagness, "On the accuracy of the ADI-FDTD method," IEEE Antennas Wireless Propag. Lett. 1, 31-34 (2002).
  10. Q. Liu, Z. Chen, W. Yin, "An arbitrary-order LOD-FDTD method and its stability and numerical dispersion," IEEE Trans. Antennas Propag. 57, 2409-2417 (2009).
  11. F. Zheng, Z. Chen, "Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method," IEEE Trans. Microw. Theory Tech. 49, 1006-1009 (2001).
  12. J. Shibayama, A. Nomura, R. Ando, J. Yamauchi, H. Nakano, "A frequency dependent LOD-FDTD Method and its application to the analyses of plasmonic waveguide devices," IEEE J. Quantum Electron. 46, 40-49 (2010).
  13. K. Y. Jung, F. L. Teixeira, S. G. Garcia, R. Lee, "On numerical artifacts of the complex envelope ADI-FDTD method," IEEE Trans. Antennas Propag. 57, 491-498 (2009).
  14. J. Shibayama, M. Muraki, R. Takahashi, J. Yamauchi, H. Nakano, "Performance evaluation of several implicit FDTD methods for optical waveguide analysis," J. Lightw. Technol. 24, 2465-2471 (2006).
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  16. H. M. Masoudi, M. A. AlSunaidi, J. M. Arnold, "Time-domain finite-difference beam propagation method," IEEE Photon. Technol. Lett. 11, 1274-1276 (1999).
  17. H. M. Masoudi, M. A. AlSunaidi, J. M. Arnold, "Efficient time-domain beam propagation method for modeling integrated optical devices," J. Lightw. Technol. 19, 759-771 (2001).
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  19. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
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2010 (1)

J. Shibayama, A. Nomura, R. Ando, J. Yamauchi, H. Nakano, "A frequency dependent LOD-FDTD Method and its application to the analyses of plasmonic waveguide devices," IEEE J. Quantum Electron. 46, 40-49 (2010).

2009 (3)

K. Y. Jung, F. L. Teixeira, S. G. Garcia, R. Lee, "On numerical artifacts of the complex envelope ADI-FDTD method," IEEE Trans. Antennas Propag. 57, 491-498 (2009).

P. Vasa, C. Ropers, R. Pomraenke, C. Lieau, "Ultra-fast nano-optics," Laser & Photon Rev. 3, 483-507 (2009).

Q. Liu, Z. Chen, W. Yin, "An arbitrary-order LOD-FDTD method and its stability and numerical dispersion," IEEE Trans. Antennas Propag. 57, 2409-2417 (2009).

2007 (1)

H. M. Masoudi, "A novel nonparaxial time-domain beam-propagation method for modeling ultrashort pulses in optical structures," J. Lightw. Technol 25, 3174-3185 (2007).

2006 (1)

J. Shibayama, M. Muraki, R. Takahashi, J. Yamauchi, H. Nakano, "Performance evaluation of several implicit FDTD methods for optical waveguide analysis," J. Lightw. Technol. 24, 2465-2471 (2006).

2005 (1)

J. N. Shibayama, M. Muraki, J. Yamauchi, H. Nakano, "Comparative study of several time-domain methods for optical waveguide analyses," J. Lightw. Technol. 23, 2285-2293 (2005).

2003 (1)

G. Steinmeyer, "A review of ultrafast optics and optoelectronics: Review article," J. Opt. Aperture Appl. Opt. 5, R1-R15 (2003).

2002 (2)

H. Rao, R. Scarmozzino, R. M. Osgood, "An improved ADI-FDTD method and its application to photonic simulations," IEEE Photon. Technol. Lett. 14, 477-479 (2002).

S. G. García, T. W. Lee, S. C. Hagness, "On the accuracy of the ADI-FDTD method," IEEE Antennas Wireless Propag. Lett. 1, 31-34 (2002).

2001 (2)

F. Zheng, Z. Chen, "Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method," IEEE Trans. Microw. Theory Tech. 49, 1006-1009 (2001).

H. M. Masoudi, M. A. AlSunaidi, J. M. Arnold, "Efficient time-domain beam propagation method for modeling integrated optical devices," J. Lightw. Technol. 19, 759-771 (2001).

2000 (2)

D. Yevick, D. J. Thomson, "Complex Padé approximants for wide-angle acoustic propagators," J. Acoust. Soc. Amer. 108, 2784-2790 (2000).

H. Rao, M. J. Steel, R. Scarmozzino, R. M. Osgood, Jr."Complex propagators for evanescent waves in bidirectional beam propagation method," J. Lightw. Technol. 18, 1155-1160 (2000).

1999 (1)

H. M. Masoudi, M. A. AlSunaidi, J. M. Arnold, "Time-domain finite-difference beam propagation method," IEEE Photon. Technol. Lett. 11, 1274-1276 (1999).

1997 (1)

F. A. Milinazzo, C. A. Zala, G. H. Brooke, "Rational square-root approximations for parabolic equation algorithms," J. Acoust. Soc. Amer. 101, 760-766 (1997).

1989 (1)

M. D. Collins, "Applications and time-domain solution of higher-order parabolic equations in underwater acoustics," J. Acoust. Soc. Amer. 86, 1097-1102 (1989).

1966 (1)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

IEEE Antennas Wireless Propag. Lett. (1)

S. G. García, T. W. Lee, S. C. Hagness, "On the accuracy of the ADI-FDTD method," IEEE Antennas Wireless Propag. Lett. 1, 31-34 (2002).

IEEE J. Quantum Electron. (1)

J. Shibayama, A. Nomura, R. Ando, J. Yamauchi, H. Nakano, "A frequency dependent LOD-FDTD Method and its application to the analyses of plasmonic waveguide devices," IEEE J. Quantum Electron. 46, 40-49 (2010).

IEEE Microw. Wireless Compon. Lett. (1)

S. Ju, K. Jung, H. Kim, "Investigation on the characteristics of the envelope FDTD based on the alternating direction implicit scheme," IEEE Microw. Wireless Compon. Lett. 13, 414-416 (200).

IEEE Photon. Technol. Lett. (2)

H. Rao, R. Scarmozzino, R. M. Osgood, "An improved ADI-FDTD method and its application to photonic simulations," IEEE Photon. Technol. Lett. 14, 477-479 (2002).

H. M. Masoudi, M. A. AlSunaidi, J. M. Arnold, "Time-domain finite-difference beam propagation method," IEEE Photon. Technol. Lett. 11, 1274-1276 (1999).

IEEE Trans. Antennas Propag. (3)

Q. Liu, Z. Chen, W. Yin, "An arbitrary-order LOD-FDTD method and its stability and numerical dispersion," IEEE Trans. Antennas Propag. 57, 2409-2417 (2009).

K. Y. Jung, F. L. Teixeira, S. G. Garcia, R. Lee, "On numerical artifacts of the complex envelope ADI-FDTD method," IEEE Trans. Antennas Propag. 57, 491-498 (2009).

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

IEEE Trans. Microw. Theory Tech. (1)

F. Zheng, Z. Chen, "Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method," IEEE Trans. Microw. Theory Tech. 49, 1006-1009 (2001).

J. Acoust. Soc. Amer. (3)

F. A. Milinazzo, C. A. Zala, G. H. Brooke, "Rational square-root approximations for parabolic equation algorithms," J. Acoust. Soc. Amer. 101, 760-766 (1997).

D. Yevick, D. J. Thomson, "Complex Padé approximants for wide-angle acoustic propagators," J. Acoust. Soc. Amer. 108, 2784-2790 (2000).

M. D. Collins, "Applications and time-domain solution of higher-order parabolic equations in underwater acoustics," J. Acoust. Soc. Amer. 86, 1097-1102 (1989).

J. Lightw. Technol (1)

H. M. Masoudi, "A novel nonparaxial time-domain beam-propagation method for modeling ultrashort pulses in optical structures," J. Lightw. Technol 25, 3174-3185 (2007).

J. Lightw. Technol. (4)

H. Rao, M. J. Steel, R. Scarmozzino, R. M. Osgood, Jr."Complex propagators for evanescent waves in bidirectional beam propagation method," J. Lightw. Technol. 18, 1155-1160 (2000).

H. M. Masoudi, M. A. AlSunaidi, J. M. Arnold, "Efficient time-domain beam propagation method for modeling integrated optical devices," J. Lightw. Technol. 19, 759-771 (2001).

J. Shibayama, M. Muraki, R. Takahashi, J. Yamauchi, H. Nakano, "Performance evaluation of several implicit FDTD methods for optical waveguide analysis," J. Lightw. Technol. 24, 2465-2471 (2006).

J. N. Shibayama, M. Muraki, J. Yamauchi, H. Nakano, "Comparative study of several time-domain methods for optical waveguide analyses," J. Lightw. Technol. 23, 2285-2293 (2005).

J. Opt. Aperture Appl. Opt. (1)

G. Steinmeyer, "A review of ultrafast optics and optoelectronics: Review article," J. Opt. Aperture Appl. Opt. 5, R1-R15 (2003).

Laser & Photon Rev. (1)

P. Vasa, C. Ropers, R. Pomraenke, C. Lieau, "Ultra-fast nano-optics," Laser & Photon Rev. 3, 483-507 (2009).

Other (5)

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

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE Press, 2000).

R. Mittra, Y. Liu, X. Yang, Y. Wenhua, Electromagnetic Simulation Techniques Based on the FDTD Method (Wiley, 2009).

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).

Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, 2003).

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