Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations
JOSA B, Vol. 17, Issue 2, pp. 226-234 (2000)
http://dx.doi.org/10.1364/JOSAB.17.000226
Acrobat PDF (215 KB)
Abstract
A numerical study of second-harmonic generation based on direct solutions of full-wave vector Maxwell equations, conducted by use of a finite-difference time-domain scheme, is reported. Although nonlinear problems have already been solved by finite-difference time-domain schemes, this is the first finite-difference time-domain computation of second-harmonic generation in a nonlinear crystal with a complete description of the electric field. Only spatially plane waves are considered, but the three components of the electric field are taken into account. The advantages and the drawbacks of this new approach are shown: On the one hand, all the spectral components of the waves are computed, but, on the other, the phase mismatch, which is imposed rather than computed, requires the use of a fine temporal mesh. The numerical results obtained for second-harmonic generation of femtosecond pulses in a thin KDP crystal are compared with those obtained by solution of the nonlinear Schrödinger equations. They illustrate the advantages of this method.
© 2000 Optical Society of America
OCIS Codes
(000.4430) General : Numerical approximation and analysis
(190.0190) Nonlinear optics : Nonlinear optics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.2250) Ultrafast optics : Femtosecond phenomena
Citation
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)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-17-2-226
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References
- Y. Combes, “Méthodes numériques pour la résolution des systèmes quasi-linéaires en électromagnétisme,” Ph.D. dissertation (Université Bordeaux 1, Talence, France, 1996).
- Ph. Donnat, “Quelques contributions mathématiques en optique nonlinéaire,” Ph.D. dissertation (Ecole Polytechnique, Palaiseau, France, 1994).
- 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).
- P. M. Goorjian and A. Taflove, “Direct time integration of Maxwell’s equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons,” Opt. Lett. 17, 180–182 (1992).
- R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antennas Propag. 45, 364–374 (1997).
- C. V. Hile and W. L. Kath, “Numerical solutions of Maxwell’s equations for nonlinear-optical pulse propagation,” J. Opt. Soc. Am. B 13, 1135–1145 (1996).
- 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).
- H. J. Bakker, P. C. M. Planken, and H. G. Muller, “Numerical calculation of optical frequency-conversion processes: a new approach,” J. Opt. Soc. Am. B 6, 1665–1672 (1989).
- R. Maleck Rassoul, A. Ivanov, E. Freysz, A. Ducasse, and F. Hache, “Second-harmonic generation under phase-velocity and group-velocity mismatch: influence of cascading self-phase and cross-phase modulations,” Opt. Lett. 22, 268–270 (1997).
- N. C. Kothari and X. Carlotti, “Transient second-harmonic generation: influence of effective group-velocity dispersion,” J. Opt. Soc. Am. B 5, 756–764 (1988).
- N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).
- V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Heidelberg, 1997).
- R. Luebbers, F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider, “A frequency-dependent finite-difference time-domain formulation for dispersive materials,” IEEE Trans. Electromagn. Compat. 32, 222–227 (1990).
- 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).
- P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
- F. Zernike, Jr., “Refractive indices of ammonium dihydrogen phosphate and potassium dihydrogen phosphate between 2000 Å and 1.5 μm,” J. Opt. Soc. Am. 54, 1215–1220 (1964).
- G. I. Stegeman, D. J. Hagan, and L. Torner, “χ^{(2)} cascading phenomena and their applications to all-optical signal processing, mode locking pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
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