Abstract
A standing wave of a periodic dielectric waveguide is a special guided mode with zero Bloch wavenumber. For two-dimension linear and symmetry periodic waveguides, standing waves are protected by symmetry and only exist at a discrete set of frequencies. While for a periodic array of circular cylinders with Kerr nonlinearity, standing waves exist continuously on frequency and there are infinite number of them for each frequency. In this paper, we consider standing waves on a periodic array of circular cylinders made of saturable nonlinear media. We show numerically that the standing waves in Kerr and saturable nonlinear media are mainly different in two ways: (1) their existence about frequency, and (2) the number of them for fixed frequency. A new iterative scheme based on Newton’s method is developed to solve the nonlinear problems. Approximate analytical expressions of the amplitude-frequency relations of standing waves in saturable nonlinear media are obtained by a perturbation analysis when amplitudes are small or large.
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This paper is partially supported by the National Natural Science Foundation of China (11201508).
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Yuan, L. Standing waves on a periodic array of circular cylinders with saturable nonlinear media. Opt Quant Electron 48, 182 (2016). https://doi.org/10.1007/s11082-016-0445-x
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DOI: https://doi.org/10.1007/s11082-016-0445-x