Abstract
Variational techniques are exploited to develop systematic approximations to the electromagnetic fields in beam-carrying irregular waveguides and open resonators containing dielectric and magnetic materials. For an axisymmetric system the simplest, so-called single mode approximation, requires only the numerical solution of a second order ordinary differential equation. Comparison of the results with numerical solutions of the governing partial differential equation indicates that the approximation is good. Higher order approximate descriptions are derived, and the so-called double mode approximation is shown to be very good indeed. The general theory is presented for the case of linear waveguides of arbitrary cross section joined by a section of arbitrary shape.
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