Mixed Perturbative Expansion: the Validity of a Model for the Cascading

DOI

10.2991/jnmp.2002.9.2.1How to use a DOI?

Abstract

A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized pulses, fundamental and second harmonic, propagating together in a bulk uniaxial crystal with non-vanishing second order susceptibility (2) , and interacting through the nonlinear effect known as "cascading" in nonlinear optics. The perturbative method mixes a multi-scale expansion with a power series expansion of the susceptibility, and must be carefully adapted to the physical situation. It allows the determination of the physical conditions under which the model is valid: the order of magnitude of the walk-off, phase-mismatch, and anisotropy must have determined values.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Hervé Leblond
PY  - 2002
DA  - 2002/05/01
TI  - Mixed Perturbative Expansion: the Validity of a Model for the Cascading
JO  - Journal of Nonlinear Mathematical Physics
SP  - 126
EP  - 143
VL  - 9
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.2.1
DO  - 10.2991/jnmp.2002.9.2.1
ID  - Leblond2002
ER  -