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Trapezoidal waveguides: first-order propagation equivalence with rectangular waveguides

“…The reduction in the maximum error for these modes is by a factor of approximately 2 for the (2, 1) mode and approximately 6 for the mode (3,1). Interestingly enough, for the dominant mode (1, 1) the maximum error has essentially the same value in both graphs.…”

“…As a first test of the validity and accuracy of the propagation equivalence between trapezoidal waveguides and their rectangular counterparts we have considered the dispersion data β/k versus k for various propagation modes (p, q) of these structures. Since from the theoretical standpoint the dominant mode for trapezoidal waveguides is the (1, 1) mode [1], and since from the experimental viewpoint it appears that the (1, 1) mode is the lowest mode supported by such structures [5], we have restricted our numerical analysis only to propagation modes with p, q 1. Explicitly, we have chosen for our investigation the modes with p = 1, 2, 3 and q = 1, and we have compared the dispersion curves β T /k versus k of the structures T 1 and T 2 with the dispersion curves β ERD /k versus k of the corresponding equivalent rectangular structures.…”

“…As was mentioned in section 1, it is possible to construct for any given trapezoidal waveguide, an equivalent rectangular waveguide that has to the first order of perturbation the same propagation constant as the original trapezoidal waveguide. The method underlying this construction was first developed in [3], and was briefly investigated numerically for the case of rib-waveguide structures 1 . In this section, we apply this method to the study of strip-loaded waveguide structures, and we show that in this latter case it yields a very simple geometrical criterion that allows one to construct the equivalent rectangular waveguide without recourse to any numerical calculations.…”

“…This would indeed be a valid argument if one were to limit oneself only to the study of electromagnetic waveguides. Indeed, more exact theoretical treatments of trapezoidal waveguides exist in the literature [1,[4][5][6]-although not exceedingly manywhich can provide more accurate numerical results than the perturbative method presented here.…”

“…Trapezoidal cross-sections of semiconductor waveguides-besides specialized applications, e.g. [1]-can be considered with reasonable accuracy to be the most common deviation from the rectangular shape that occurs during the fabrication process of such devices. Indeed, and unless special precautions that are very costly and time consuming are taken (e.g.…”