We introduce a new identity that relates the exponential of the sum of two noncommuting operators to the exponentials of the individual operators. This formula generates rapid fourth-order split-step fast-Fourier-transform, split-operator finite-difference, split-operator finite-element, and real-space propagation algorithms. To illustrate the procedure, we model the focusing of a light beam by a spherical integrated-optic microlens.
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Hermansson et al. (1991) studied this question.
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