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

*(English)*Zbl 1032.78015In this paper tools of nonlinear diffractive optics for studying the propagation of diffractive laser beams are generalized in order to model large-spectrum lasers and lasers with ultrashort pulses. The generalization relies on the algebra of oscillations with a continuous oscillatory spectrum. The authors perform the analysis of general nonlinear hyperbolic systems, both in the dispersive and in the nondispersive cases. The developed methods allow to simplify the nonlinearities considerably and to determine the qualitative differences between the dispersive and nondispersive cases. The results are applied to a detailed study of the two physical examples, mentioned above, which are out of the range of usual methods.

Reviewer: Gunther Schmidt (Berlin)

##### MSC:

78A60 | Lasers, masers, optical bistability, nonlinear optics |

35L40 | First-order hyperbolic systems |

35Q55 | NLS equations (nonlinear Schrödinger equations) |

35Q60 | PDEs in connection with optics and electromagnetic theory |

35S99 | Pseudodifferential operators and other generalizations of partial differential operators |