A general framework for diffractive optics and its applications to lasers with large spectrums and short pulses

SIAM Journal on Mathematical Analysis

Volumn 34, Issue 3, 2003, Pages 636-674

  Barrailh, Karen ^a,b   Lannes, David ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b CEA CESTA   (France)

Author keywords

Continuous oscillatory spectrum; Diffractive optics; Large spectrum; Maxwell equations; Nonlinear hyperbolic systems; Nonlinear Schr dinger equation; Short pulse

Indexed keywords

EID: 0038134927     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141001398976     Document Type: Article

References (17)

1. D. ALTERMAN, Diffractive Nonlinear Geometric Optics for Short Pulses, Ph.D. thesis, University of Michigan, Ann Arbor, MI, 1999.
2. D. ALTERMAN AND J. RAUCH, Diffractive short pulse asymptotics for nonlinear wave equations, Phys. Lett. A, 264 (2000), pp. 390-395.
3. D. ALTERMAN AND J. RAUCH, Diffractive nonlinear geometric optics for short pulses, to appear.
4. D. ALTERMAN AND J. RAUCH, Nonlinear geometric optics for short pulses, J. Differential Equations, 178 (2002), pp. 437-465.
5. R. BENEDETTI AND J.-J. RISLER, Real algebraic and semi-algebraic sets, Actualités Math., Hermann, Paris, 1990.
6. J. BOCHNAK, M. COSTE, AND M.-F. ROY, Géométrie algébrique réelle, Ergeh. Math. Grenzgeb. (3) 12, Springer-Verlag, Berlin, 1987.
7. P. DONNAT, Quelques contributions en optique non linéaire, Ph.D. thesis, École Polytechnique, Palaiseau, France, 1994.
8. P. DONNAT, J.-L. JOLY, G. METIVIER, AND J. RAUCH, Diffractive nonlinear optics, in Sémin. Équ. Dériv. Partielles Exp. XVII, École Polytechnique, Palaiseau, France, 1996.
9. J.-L. JOLY, Sur la propagation des oscillations par un système hyperbolique semi-linéaire en dimension 1 d'espace, C, R. Acad. Sci. Paris Sér. I Math., 296 (1983), pp. 669-672.
10. J.-L. JOLY, G. MÉTIVIER, AND J. RAUCH, Diffractive nonlinear geometric optics with rectification, Indiana Univ. Math. J., 47 (1998), pp. 1167-1241.
11. D. LANNES, Dispersive effects for nonlinear geometrical optics with rectification, Asymptot. Anal., 18 (1998), pp. 111-146.
12. D. LANNES, Nonlinear geometrical optics for oscillatory wave trains with continuous oscillatory spectrum, Adv. Differential Equations, 6 (2001), pp. 731-768.
13. O. MORICE, Obtention de l'équation de schrödinger modifiée, personal communication, 1999.
14. A. NEWELL AND J. MOLONEY, Nonlinear Optics, Addison-Wesley, Reading, MA, 1992.
15. J. RAUCH, Nonlinear pulse propagation, in Journées "Équations aux Dérivées Partielles" (Plestin-les-grèves, 2001), Exp. XI, École Polytechnique, Palaiseau, France, 2001.
16. A. YOSHIKAWA, Solutions containing a large parameter of a quasi-linear hyperbolic system of equations and their nonlinear geometric optics approximation, Trans. Amer. Math. Soc., 340 (1993), pp. 103-126.
17. A. YOSHIKAWA, Asymptotic expansions of the solutions to a class of quasilinear hyperbolic initial value problems, J. Math. Soc. Japan, 47 (1995), pp. 227-252.