Abstract
High-frequency fields radiated by sources in transversely inhomogeneous waveguides or ducts are conventionally analyzed by ray or normal-mode techniques. When the duct width is very large, the excessive number of relevant rays or modes introduces computational difficulties. An alternative approach is provided by a hybrid representation that involves ray fields and modal fields in well-defined combinations: With respect to the angular domain centered at the source point, the modes fill those angular intervals left vacant by rays, and vice versa, the mode angles being defined as the angles of the upgoing and downgoing modal ray congruences as seen from the source. The hybrid mix is dependent on the position of the observer, and an additional remainder field assures the smooth transition from one hybrid combination to another. The analytical formulation, involving partial Poisson summation of the formal ray series, is applied to various ducting environments that cause wave trapping by refraction, reflection from boundaries, or both. For the special case of monotonically varying refractive index in a parallel-plane waveguide, the results from the asymptotic method are verified by rigorous Green’s function methods. Special examples, supported by numerical comparisons with exact reference solutions, are presented to demonstrate the validity and utility of the hybrid scheme.
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