Electromagnetic scattering by a circular cavity of arbitrary shape placed in a perfect electric conductor

An efficient modal expansion technique for scattering by a circular cavity with an arbitrary arc in a perfect electric conductor is developed. In contrast to the existing methods proposed for a shallow or semi-circular cavity, the proposed method can be utilised for a circular cavity of arbitrary shape while is computationally efficient. The authors first introduce an auxiliary circular border that divides half-space above the cavity into two separate subregions. Then, the tangential fields in the two subregions, which satisfy the Helmholtz equation, are expanded in terms of an infinite series of radial wave functions. The fields are matched at the auxiliary border to construct three independent equations in two different coordinate systems. By employing the addition theorem, all equations are transferred into the same coordinate system. Finally, the equations are converted into a system of linear equations and then solved through regular matrix techniques for the expansion coefficients. The solution is verified by the Method of Moments used in FEKO electromagnetic simulation software. This method is employed to study the effects of cavity shape and incident wave polarisation on the scattering signature.