Rational Chebyshev Spectral Transform for the dynamics of high-power laser diodes

Abstract: This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of high-power laser diodes, either broad area lasers, index guided lasers or monolithic master oscillator power amplifier devices. This spectral method can be used in combination with the delay algebraic equation approach developed in \cite{JB-OE-12}, which allows to substantially reduce the computation time. The theory is presented in such a way that it encompasses the case of the Fourier spectral transform presented in \cite{PJB-JSTQE-13} as a particular case. It is also extended to the consideration of index guiding with an arbitrary profile. Because their domain of definition is infinite, the convergence properties of the Chebyshev Rational functions allow handling the boundary conditions with higher accuracy than with the previously studied Fourier method. As practical examples, we solve the beam propagation problem with and without index guiding: we obtain excellent results and an improvement of the integration time between one and two orders of magnitude as compared with a fully distributed two dimensional model.