The parabolic equation (PE) has become an important computational tool for approximating underwater acoustic path losses in inhomogeneous environments. The numerical solution of this equation is performed on a grid over the propagation medium which includes the water column, and has also included a homogeneous "false bottom" below the actual ocean bottom. This situation is viewed as one in which the propagation medium can be divided into a horizontally inhomogeneous upper layer and a horizontally homogeneous lower layer. The pressure field in the latter layer is found using standard techniques valid for homogeneous media, and in the former layer is found using an implicit finite difference scheme. These fields and their normal derivatives are matched along the interface between the layers. The result is referred to as a generalized impedance boundary condition (GIBC), which serves to eliminate the need for a false bottom. Predictions obtained using the standard parabolic equation and a completely homogeneous bottom medium indicate improved numerical efficiency, and excellent agreement with other methods. The improved efficiency can be potentially significant for three-dimensional propagation problems.
Realization of the anomalous refraction effects predicted by Huygens' metasurfaces (HMS) have required tedious and timeconsuming trial-and-error numerical full-wave computations. It is shown herein that these requirements can be alleviated for transverse magnetic (TM) propagation by a periodic dielectric-based HMS consisting of an electrically thick array of cascaded Fabry-Pérot etalons. This "Fabry-Pérot HMS" (FP-HMS) is easily designed to mimic the local scattering coefficients of a standard zero-thickness HMS (ZT-HMS) which, according to homogenization theory, should result in the desired anomalous refraction. To probe the characteristics of this practical FP-HMS, a method based on Floquet-Bloch (FB) analysis is derived for predicting the fields scattered from it for arbitrary angles of incidence. This method produces simple closed-form solutions for the FB wave amplitudes and the resulting fields are shown to agree well with full-wave simulations. These predictions and full-wave simulations verify the applicability of homogenization and scattering properties of zero-thickness HMS's to thick structures. They also verify the proposed semi-analytical microscopic design procedure for such structures, offering an effective alternative path to implementation of theoretically envisioned intricate field manipulating devices.
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