The scalar Maxwell's equation, including the often-neglected second-derivative paraxial term, is solved. This term is shown to increase the loss of the amplitude of the light beam inside a single-mode optical fiber. The reflected (backward-traveling) wave that is due to the second-derivative term is obtained from the calculation of the scattering matrix as formulated in quantum-mechanical dynamical problems.
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Vorobeichik et al. (1997) studied this question.
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