Mathematical studies of optical bistability

Efficient numerical methods are created to examine optical bistability in a multilayer structure with Kerr nonlinearity. It corresponds to computing multiple solutions of the one-dimensional nonlinear Helmholtz equation for an array of frequencies and incident intensities. The input-output characteristics is calculated as a simple initial value problem without the iterations. Bistability intervals of the incident intensity are determined directly without the need for a continuation scheme. The complete transmission spectrum at a fixed incident intensity and a varying frequency is obtained including both stable and unstable solutions. For the multilayer structure, we also research the result of random perturbations in the thickness of the layers. The perturbations are presumed to follow a normal distribution. For the linear case, the analysis is targeted on the resonant transmission. Approximate distributions for the maximum transmission coefficient and the corresponding wavenumber are obtained. For nonlinear multilayer structure, we examine the impact of the random perturbations on the bistability interval. Approximate distributions for the lower and upper ends of the bistability interval are obtained….


1 Propagation in linear multilayer structures
1.1 Transmission spectrum
1.2 Transmission maximum
1.3 Bandgap of 1-D layered structures
2 Computing optical bistability in one-dimensional nonlinear structures
2.1 Background
2.2 Transmission spectrum
2.3 Input intensity calculation
2.4 Bistability interval
2.5 Conclusions
3 Statistical analysis of the maximum transmission for linear structures
3.1 Distribution for the wavenumber of transmission maxima
3.2 Distribution for transmission coeffcient of transmission maxima
3.3 Sensitivity of each layer….

Source: City University of Hong Kong

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