Abstract
A rigorous Surface Impedance (SI) formulation for planar waveguides is presented. This modal technique splits the modal analysis of the waveguide in two steps. First, we obtain the modes characteristic equations as a function of the SI and, second, we need to obtain the surface impedance values using either analytical or numerical methods. We validate the technique by comparison with well-known analytical cases: the parallel-plate waveguide with losses and the dielectric slab waveguide. Then, we analyze an optical hollow-core waveguide defined by two high-contrast subwavelength gratings validating our results by comparison with reported values. Finally, we show the potential of our formulation with the analysis of a THz hollow-core waveguide defined by two surface-relief subwavelength gratings, including material losses in our formulation.
Highlights
W AVEGUIDES with special microstructured boundaries are being proposed to improve guidance of electromagnetic waves, in the frequency ranges where materials’ absorption is a critical drawback
In hollow-core waveguides with microstructured boundaries and large transverse dimension, the needed run-time may be considerable on the one hand, and on the other hand, their driven modal solvers provide the first propagating modes of the waveguide, which requires a huge amount of memory, and they are not well suited for analyzing the lowloss propagating mode in the air region of such waveguides
This has not been done in previous works that have analyzed similar waveguides in the optical regime, whose techniques use some basic ray-optics approximations based on the computation of the power reflection coefficient on the gratings constituting the waveguide walls, being limited to lossless dielectric materials
Summary
W AVEGUIDES with special microstructured boundaries are being proposed to improve guidance of electromagnetic waves, in the frequency ranges where materials’ absorption is a critical drawback. The use of a vectorial modal method in combination with a novel developed surface impedance formulation, allows to rigorously obtain the complex propagation factor of the fundamental mode propagating in this kind of waveguides (including the reflection losses and the dielectric losses of the grating materials) This has not been done in previous works that have analyzed similar waveguides in the optical regime (e.g., in [5], [6]), whose techniques use some basic ray-optics approximations based on the computation of the power reflection coefficient on the gratings constituting the waveguide walls, being limited to lossless dielectric materials (this fundamental limitation is discussed for example in [19]). It is worthwhile to point out that we will consider here only planar waveguides, our approach could be extended to cylindrical waveguides following the fundamentals developed in [14]
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