Abstract

When one replaces the Helmholtz equation by the related parabolic equation, the resulting gain is the relative numerical ease of solving the parabolic equation using a marching type algorithm. However, one is left with the problem of providing the initial data—or the starting field for the PE model. Although it is well known that the normal mode starter is the corrected initial data, it is not widely used because of the expense involved in the compuation. In this approach, however, the idea that one need not compute the normal modes individually to obtain the correct starting field is exploited. If one considers the function represented by a weighted sum of the normal modes, then it is found that the correct starting field can be obtained by computing the −14 power of the matrix generated from the FFT of the index of refraction. This result is derived and some examples of the starting fields are presented and compared to starters computed or approximated in other ways. Further, the effects on PE model outputs using the various starters are demonstrated.

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