The losses for TE and TM waves in infrared biconcave metallic waveguides are calculated. The guiding region is approximated first as a portion of a sphere, and then of an oblate spheroid; Maxwell's equations are then set up in corresponding coordinate systems. They are solved to find the leading-order term of all 6 field components. These are used to express the boundary conditions at the finite-conductivity wall, and to calculate the fields propagating into the metal. From these, the propagation losses in the guide are calculated. It is found in particular that the TE losses depend only weakly on the curling curvature. Thus it should be possible to make MIR waveguides exhibiting losses of a few percent per turn, for most anticipated shape choices.
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