Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials

Journal of the Optical Society of America B: Optical Physics

Volumn 21, Issue 2, 2004, Pages 330-342

  Lee, Tae Woo ^a   Hagness, Susan C ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BENCHMARKING; COMPUTER SIMULATION; FINITE ELEMENT METHOD; HARMONIC ANALYSIS; MAXWELL EQUATIONS; NONLINEAR OPTICS; SECOND HARMONIC GENERATION; TIME DOMAIN ANALYSIS; VOLUMETRIC ANALYSIS; WAVE PROPAGATION;

COURANT STABILITY CONDITION; MATERIAL DISPERSION; NONLINEAR GRATINGS; NONLINEAR MATERIALS; PHASE VELOCITIES;

OPTICAL WAVEGUIDES;

EID: 1342286740     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.21.000330     Document Type: Article

References (36)

1. 3 waveguides," IEEE Photon. Technol. Lett. 11, 653-655 (1999).
2. Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, and W. Sohler, "All-optical integrated Mach-Zehnder switching due to cascaded nonlinearities," Appl. Phys. Lett. 68, 2055-2057 (1996).
3. G. Y. Wang, J. Zhao, Q. Chen, and M. Cronin-Golomb, "Widely tunable efficient intracavity quasiphase-matched midinfrared generation," Appl. Phys. Lett. 70, 2218-2220 (1997).
4. 3," Opt. Lett. 23, 171-173 (1998).
5. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918 (1962).
6. B. Hermansson, D. Yevick, and L. Thylen, "A propagating beam method analysis of nonlinear effects in optical waveguides," Opt. Quantum Electron. 16, 525-534 (1984).
7. K. Hayata and M. Koshiba, "Numerical study of guided-wave sum-frequency generation through second-order nonlinear parametric processes," J. Opt. Soc. Am. B 8, 449-458 (1991).
8. P. S. Weitzman and U. Osterberg, "A modified beam propagation method to model second harmonic generation in optical fibers," IEEE J. Quantum Electron. 29, 1437-1443 (1993).
9. H. M. Masoudi and J. M. Arnold, "Modeling second-order nonlinear effects in optical waveguides using a parallel-processing beam propagation method," IEEE J. Quantum Electron. 31, 2107-2113 (1995).
10. H. F. Chou, C. F. Lin, and S. Mou, "Comparisons of finite difference beam propagation methods for modeling second-order nonlinear effects," J. Lightwave Technol. 17, 1481-1486 (1999).
11. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 2000).
12. A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
13. B. D'Urso, O. Painter, J. O'Brien, T. Tombrello, A. Yariv, and A. Scherer, "Modal reflectivity in finite-depth two-dimensional photonic-crystal microcavities," J. Opt. Soc. Am. B 15, 1155-1159 (1998).
14. M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
15. R. W. Ziolkowski and M. Tanaka, "FDTD analysis of PBG waveguides, power splitters and switches," Opt. Quantum Electron. 31, 843-855 (1999).
16. S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, "FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators," J. Lightwave Technol. 15, 2154-2165 (1997).
17. 2 microring resonator optical channel dropping filiters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
18. R. X. Bian, R. C. Dunn, and X. S. Xie, "Single molecule emission characteristics in near-field microscopy," Phys. Lett. A 75, 4772-4775 (1995).
19. G. Liu, J. F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barness, and T. N. Tiouririne, "Mode selectivity study of vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 73, 726-728 (1998).
20. T. W. Lee, S. C. Hagness, D. L. Zhou, and L. J. Mawst, "Modal characteristics of ARROW-type vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 13, 770-772 (2001).
21. D. W. Prather and S. Y. Shi, "Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements," J. Opt. Soc. Am. A 16, 1131-1142 (1999).
22. P. M. Goorjian, A. Taflove, R. M. Joseph, and S. C. Hagness, "Computational modeling of femtosecond optical solitons from Maxwell's equations," IEEE J. Quantum Electron. 28, 2416-2422 (1992).
23. R. W. Ziolkowski and J. B. Judkins, "Full-wave vector Maxwell equation modeling of the self-focusing of ultrashort optical pulses in a nonlinear Kerr medium exhibiting a finite response time," J. Opt. Soc. Am. B 10, 186-198 (1993).
24. D. M. Sullivan, "Nonlinear FDTD formulation using Z transforms," IEEE Trans. Microwave Theory Tech. 43, 676-682 (1995).
25. A. Bourgeade and E. Freysz, "Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations," J. Opt. Soc. Am. B 17, 226-234 (2000).
26. R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997).
27. Q. H. Liu, "The PSTD algorithm: a time-domain method requiring only two cells per wavelength," Microwave Opt. Technol. Lett. 15, 158-165 (1997).
28. B. Fornberg, A Practical Guide to Pseudospectral Methods (Cambridge U. Press, Cambridge, UK, 1996).
29. Q. H. Liu, "Large-scale simulations of electromagnetic and acoustic measurements using the pseudo-spectral time-domain (PSTD) algorithm," IEEE Trans. Geosci. Remote Sens. 37, 917-926 (1999).
30. T. W. Lee and S. C. Hagness, "A compact wave source condition for the pseudospectral time-domain method," IEEE Wireless Propag. Lett. (to be published).
31. J. Fang, "Time-domain finite-difference computations for Maxwell's equations," Ph.D. dissertation (Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, Calif., 1989).
32. R. W. Ziolkowski, "The incorporation of microscopic material models into the PDTD approach for ultrashort opti-calpulse simulation," IEEE Trans. Antennas Propag. 45, 375-391 (1997).
33. Q. H. Liu and N. Nguyen, "An accurate algorithm for non-uniform fast Fourier transform (NUFFT)," IEEE Micro-wave Gruid. Wave Lett. 8, 18-20 (1998).
34. W. K. Leung, Y. Chen, and R. Mittra, "Transformed-space non-uniform pseudo-spectral time-domain (NU-PSTD) algorithm without use of non-uniform FFT," in IEEE AP-S International Symposium (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), pp. 498-501.
35. S. T. Yang and S. P. Velsko, "Frequency-agile kilohertz repetition-rate optical parametric oscillator based on periodically poled lithium niobate," Opt. Lett. 24, 133-135 (1999).
36. R. M. Joseph, S. C. Hagness, and A. Taflove, "Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses," Opt. Lett. 16, 1412-1414 (1991).