7

Numerical Beam Propagation Methods

7.1      Introduction

Analytical or semi-analytical solutions of the beam coupling equations, such as the ABDP expressions [1] given in terms of Jacobian elliptic functions or the Boyd and Kleinman solutions [2] in terms of double integrals, provide insight, allow quick analysis and can serve as checks for the accuracy of the full numerical solutions of the equations. However, in many cases of interest, simplifying assumptions cannot be made and analytic solutions cannot be found. In these cases numerical beam propagation methods need to be used to find the solutions.

Much work has been done to find efficient methods of numerically solving the problem of electromagnetic field propagation through air, ...

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