Application of rational Chebyshev polynomials to optical problems

Abstract

We present the use of the rational Chebyshev polynomials for discretising the transverse dimension(s) of beam propagation problems within the field of nonlinear optics. How a beam propagates in an optical medium, whether linear or nonlinear, is a common problem and important in both theoretical studies and optical design. The infinite domain and convergence properties of these polynomials allows one to handle the boundary conditions with greater correctness than methods that impose periodic boundary conditions such as Fourier methods. The beam is propagated forward by exponential integration for fast and accurate numerical simulations. The techniques employed to solve the beam propagation problems are easily applied to problems in other fields with mathematically similar models. References

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