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.
© 1997 Optical Society of America
Ilya Vorobeichik, Nimrod Moiseyev, and Daniel Neuhauser, "Effect of the second-derivative paraxial term in the scalar Maxwell's equation on amplitude losses and reflections in optical fibers," J. Opt. Soc. Am. B 14, 1207-1212 (1997)