We present a multilayer modal method to investigate electromagnetic scattering from a lossy inhomogeneous aperture in a perfectly conducting thick screen. We consider inhomogeneous apertures that consist of two homogeneous zones filled with different isotropic materials that are characterized by complex refraction indices. The shape of the boundary between adjacent homogeneous zones is rather arbitrary, which makes it possible to model a great number of interesting geometries, such as slanted slabs or wedges. We illustrate the behavior of eigenvalues (solutions of the transcendental equation that has to be solved whenever a modal method is applied) as the imaginary part of the complex refraction index is varied. The method is used to study the electromagnetic response of a thick aperture with a sloping internal border. Calculation of power losses at the aperture walls and curves of scattered intensity versus observation angle are shown for different polarizations of the incident beam.
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