Heuristic scalar paraxial beam propagation method taking into account continuous reflections

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Abstract
A scalar paraxial beam propagation method is developed, on a heuristic basis, that takes into account continuous reflections. The corresponding algorithm has a time–space-marching character that mimics the actual evolution of the wave as it propagates, even though the basic treatment is really time independent in a strict sense. The verification of the algorithm is illustrated by two examples of one-dimensional and two-dimensional configurations in inhomogeneous media. The algorithm is also applied to counterpropagating beams in a Kerr medium, and the empirical stability criteria for this case are discussed.