Termination of Periodic Waveguides by PMLs in Time-Harmonic Integral Equation-Like Techniques

In this letter, a new way for the termination of periodic waveguides in integral equation like simulation techniques is introduced. Exploiting the complex coordinate interpretation of a perfectly matched layer (PML), we can terminate a periodic waveguide by adding a couple of periods in the complex plane. If the waveguide enters the complex plane in a smooth way, the reflections caused by the periodicity disturbance are very low and at the same time one achieves a significant absorption. This idea is applied to a two-dimensional electromagnetic crystal waveguide structure. The validity of our approach is demonstrated by comparison with a rigorous method based on the exact calculation of the excitation coefficients of the eigenmodes in the waveguide and by comparison of a more complex example (a two-channel multi-plexer-demultiplexer) from literature.