Power loss at an abrupt but small step discontinuity in an asymmetrical single-mode waveguide is analyzed. An integral expression is given for the power loss suffered by the transverse-electric and transverse-magnetic modes as a function of wavelength, film index, cover index, substrate index, and input and output waveguide widths so that any slab-waveguide discontinuity can be analyzed. Normalized power-loss plots are presented for two specific, commonly used waveguides with different degrees of asymmetry. It is shown that the magnitude of the power loss at a discontinuity depends more on the mismatch in the modal effective width than on the geometrical mismatch in waveguide width. In particular, close to cutoff, guides exhibit severe power loss even for small step size, whereas waveguides that are sufficiently far away from cutoff can tolerate a relatively large step discontinuity with surprisingly low power loss.
© 1984 Optical Society of America
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