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


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Georgieva, A; Kriecherbauer, T; Venakides, S

Published Date

  • January 1, 2001

Published In

Volume / Issue

  • 61 / 5

Start / End Page

  • 1802 - 1815

International Standard Serial Number (ISSN)

  • 0036-1399

Digital Object Identifier (DOI)

  • 10.1137/S0036139999365341

Citation Source

  • Scopus