Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T20:23:47.899Z Has data issue: false hasContentIssue false
  • English
  • Français

A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP

Published online by Cambridge University Press:  15 March 2004

Christophe Besse ,
Brigitte Bidégaray-Fesquet ,
Antoine Bourgeade ,
Pierre Degond  and
Olivier Saut
Christophe Besse
Affiliation:
MIP, UMR 5640 (CNRS-UPS-INSA), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France, [email protected]., [email protected]., [email protected].
Brigitte Bidégaray-Fesquet
Affiliation:
LMC, UMR 5523 (CNRS-UJF-INPG), B.P. 53, 38041 Grenoble Cedex 9, France, [email protected].
Antoine Bourgeade
Affiliation:
CEA/CESTA, B.P. 2, 33114 Le Barp, France, [email protected].
Pierre Degond
Affiliation:
MIP, UMR 5640 (CNRS-UPS-INSA), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France, [email protected]., [email protected]., [email protected].
Olivier Saut
Affiliation:
MIP, UMR 5640 (CNRS-UPS-INSA), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France, [email protected]., [email protected]., [email protected]. CEA/CESTA, B.P. 2, 33114 Le Barp, France, [email protected].
Get access

Abstract

This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell's equations for the wave field coupled with a version of Bloch's equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material.

Keywords

Nonlinear opticsoptical susceptibilityharmonic generationquantum description of light and matternonlinear optical crystals.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 2 , March 2004 , pp. 321 - 344
Copyright
© EDP Sciences, SMAI, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

P.W. Atkins and R.S. Friedman, Molecular Quantum Mechanics. Oxford University Press (1996).
Bakker, H.J., Planken, P.C.M., Kuipers, L. and Lagendijk, A., Phase modulation in second-order nonlinear-optical processes. Phys. Rev. A 42 (1990) 4085–4101. CrossRef
Bakker, H.J., Planken, P.C.M. and Muller, H.G., Numerical calculation of optical frequency-conversion processes: a new approach. J. Opt. Soc. Am. B 6 (1989) 1665–1672. CrossRef
Bidégaray, B., Bourgeade, A. and Reignier, D., Introducing physical relaxation terms in Bloch equations. J. Comput. Phys. 170 (2001) 603–613. CrossRef
Bidégaray, B., Time discretizations for Maxwell-Bloch equations. Numer. Methods Partial Differential Equations 19 (2003) 284–300. CrossRef
D.M. Bishop, Group theory and chemistry. Dover Press (1973).
Bourgeade, A. and Freysz, E., Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations. J. Opt. Soc. Am. B 17 (2000) 226–234. CrossRef
R.W. Boyd, Nonlinear Optics. Academic Press (1992).
Choy, M.M. and Byer, R.L., Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals. Phys. Rev. B 14 (1976) 1693–1706. CrossRef
Ditmire, T., Rubenchik, A.M., Eimerl, D. and Perry, M.D., Effects of cubic nonlinearity on frequency doubling of high-power laser pulses. J. Opt. Soc. Am. B 13 (1996) 649–655. CrossRef
Eckardt, R., Masuda, H., Fan, Y.X. and Byer, R.L., Absolute and relative nonlinear optical coefficients of KDP, KDP*, BaB2O4, LiIO3>, MgO:LiNbO3 and KTP measured by phase-matched second-harmonic generation. IEEE J. of Quantum Electr. 26 (1990) 922–933. CrossRef
Eimerl, D., Electro-optic, linear and nonlinear optical properties of KDP and its isomorphs. Ferroelectrics 72 (1987) 95–139. CrossRef
Jerphagnon, J. and Kurtz, S.K., Optical nonlinear susceptibilities: accurate relative values for quartz, ammonium dihydrogen phosphate, and potassium dihydrogen phosphate. Phys. Rev. B 1 (1970) 1739–1744. CrossRef
Kothari, N.C. and Carlotti, X., Transient second-harmonic generation: influence of effective group-velocity dispersion. J. Opt. Soc. Am. B 5 (1988) 756–764. CrossRef
Kurtz, S.K., Jerphagnon, J. and Choy, M.M., Nonlinear dielectric susceptibilities. Landolt-Boernstein new series 3 (1979) 671–743.
Levine, B.F., Bond-charge calculation of nonlinear optical susceptibilities for various crystal structures. Phys. Rev. B 7 (1973) 2600–2626. CrossRef
Maleck Rassoul, R., Ivanov, A., Freysz, E., Ducasse, A. and Hache, F., Second-harmonic generation under phase-velocity and group-velocity mismatch: influence of cascading self-phase and cross-phase modulation. Opt. Lett. 22 (1997) 268–270. CrossRef
Miller, R.C., Optical harmonic generation in piezoelectric crystals. Appl. Phys. Lett. 5 (1964) 17–19. CrossRef
O. Saut, Étude numérique des nonlinéarités d'un cristal par résolution des équations de Maxwell-Bloch, Ph.D. Thesis, INSA Toulouse (2003).
O. Saut, Computational modeling of ultrashort powerful laser pulses in an anisotropic crystal. J. Comput. Phys. (2004) (to appear).
L.I. Schiff, Quantum Mechanics. Mc Graw-Hill International Editions (1995).
J.P. Serre, Représentations linéaires des groupes finis. Hermann (1998).
Shoji, I., Kondo, T., Kitamoto, A., Shirane, M. and Ito, R., Absolute scale of second-order nonlinear-optical coefficients. J. Opt. Soc. Am. B 14 (1997) 2268–2294. CrossRef
Van Der Ziel, J.P. and Bloembergen, N., Temperature dependence of optical harmonic generation in KH2PO4 ferroelectrics. Phys. Rev. 135 (1964) 1662–1669. CrossRef
Zernicke, F., Refractive indices of ADP and KDP between 2000 Å and 1.5 µm. J. Opt. Soc. Am. 54 (1964) 1215–1220. CrossRef
Ziolkowski, R.W., Arnold, J.M. and Gogny, D.M., Ultrafast pulse interactions with two-level atoms. Phys. Rev. A 52 (1995) 3082–3094. CrossRef