Title

Solitary Waves Due To Chi((2))/Chi((2)) Cascading

Authors

Authors

C. R. Menyuk; R. Schiek;L. Torner

Comments

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Abbreviated Journal Title

J. Opt. Soc. Am. B-Opt. Phys.

Keywords

BIREFRINGENT OPTICAL FIBERS; DISPERSION WAVELENGTH; PULSE-PROPAGATION; SOLITONS; AMPLITUDES; STABILITY; KTP; Optics

Abstract

Solitary waves in materials with a cascaded chi((2)):chi((2)) nonlinearity are investigated, and the implications of the robustness hypothesis for these solitary waves are discussed. Both temporal and spatial solitary waves are studied. First, the basic equations that describe the chi((2)):chi((2)) nonlinearity in the presence of dispersion or diffraction are derived in the plane-wave approximation, and we show that these equations reduce to the nonlinear Schrodinger equation in the limit of large phase mismatch and can be considered a Hamiltonian deformation of the nonlinear Schrodinger equation. We then proceed to a comprehensive description of all the solitary-wave solutions of the basic equations that can be expressed as a simple sum of a constant term, a term proportional to a power of the hyperbolic secant, and a term proportional to a power of the hyperbolic secant multiplied by the hyperbolic tangent. This formulation includes all the previously known solitary-wave solutions and some exotic new ones as well. Our solutions are derived in the presence of an arbitrary group-velocity difference between the two harmonics, but a transformation that relates our solutions to zero-velocity solutions is derived. We find that all the solitary-wave solutions are zero-parameter and one-parameter families, as opposed to nonlinear-Schrodinger-equation solitons, which are a two-parameter Finally, we discuss the prediction of the robustness hypothesis that there should be a two-parameter family of solutions with solitonlike behavior, and we discuss the experimental requirements for observation of solitonlike behavior.

Journal Title

Journal of the Optical Society of America B-Optical Physics

Volume

11

Issue/Number

12

Publication Date

1-1-1994

Document Type

Article

Language

English

First Page

2434

Last Page

2443

WOS Identifier

WOS:A1994PX51000015

ISSN

0740-3224

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