Abstract
The field of the fundamental waveguide mode, when it propagates at extremely high intensities or when the core or cladding material has a large nonlinear coefficient, may be quite significantly distorted from that of the corresponding linear mode. We derive a variational formulation of the scalar wave equation for waveguides with arbitrary nonlinearity in the core and show that this formulation can be used to find simple, but accurate, analytical approximations for these nonlinear fields. In particular, we find Gaussian and equivalent-step-index approximations for a variety of planar waveguide and optical-fiber structures and show how they can be used to calculate quantities such as the effective area and group-velocity dispersion.
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