1:2 resonance mediated second harmonic generation in a 1-D nonlinear discrete periodic medium

Document Type

Article

Publication Date

1-1-2001

Abstract

We derive traveling wave solutions in a nonlinear diatomic particle chain near the 1:2 resonance (κ*, ω*), where ω* = D(κ*), 2ω* = D(2κ*) and ω = D(κ) is the linear dispersion relation. To leading order, the waves have form ±εsin(κn - ωt) + δsin(2κn - 2ωt), where the near-resonant acoustic frequency ω and the amplitude ε of the first harmonic are given to first order in terms of the wavenumber difference κ - κ* and the amplitude δ of the second harmonic. These traveling wave solutions are unique within a certain set of symmetries. We find that there is a continuous line in parameter space that transfers energy from the first to the second harmonic, even in cases where initially almost all energy is in the first harmonic, connecting these waves to pure optical waves that have no first harmonic content.

Identifier

0035186525 (Scopus)

Publication Title

SIAM Journal on Applied Mathematics

External Full Text Location

https://doi.org/10.1137/S0036139999365341

ISSN

00361399

First Page

1802

Last Page

1815

Issue

5

Volume

61

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