title: Nonlinear standing waves on a periodic array of circular cylinders.
abstract: A periodic array of parallel and infinitely long dielectric circular cylinders surrounded by air can be regarded as a simple two-dimensional periodic waveguide. For linear cylinders, guided modes exist continuously below the lightline in various frequency intervals, but standing waves, which are special guided modes with a zero Bloch wavenumber, could exist above the lightline at a discrete set of frequencies. In this paper, we consider a periodic array of nonlinear circular cylinders with a Kerr nonlinearity, and show numerically that nonlinear standing waves exist continuously with the frequency and their amplitudes depend on the frequency. The amplitude-frequency relations are further investigated in a perturbation analysis.
authors.forename: Lijun
authors.initials: L
authors.lastname: Yuan
authors.forename: Ya Yan
authors.initials: YY
authors.lastname: Lu