A rigorous theoretical model of guided waves excitation in a plane dielectric layer under electromagnetic diffraction by a conducting strip

• Scattered fields are considered as integrals over propagation parameter.
• Their poles correspond to waveguide modes of a transparent layer.
• Scattered field is presented by fields of two types.
• Usual diffraction field, decaying at moving away from an obstacle.
• Waveguide field in a dielectric layer with finite amplitudes at infinity.

An exact solution of two-dimensional problem of plane electromagnetic wave scattering by a perfectly conducting strip in the presence of a parallel plane dielectric layer is presented. The given solution is constructed using the mode-matching technique in the form of diffraction integrals over propagation parameter, i.e. in the form of superposition of a large number of homogeneous and inhomogeneous plane waves with continuous spectrum of spatial frequencies. These integrals have poles, which are caused by the presence of a transparent dielectric layer and correspond to its waveguide modes. Because of this, diffraction integrals need the procedure of regularization with explicit extraction of pole terms and smoothing of integrands, whereupon the residual diffraction integrals are computed using simple numerical methods. They describe usual scattered field of a bounded obstacle, which is determined by regularized diffraction integrals and decreases in all directions from an obstacle. Besides, the total diffraction field contains a discrete finite sum of waveguide fields of guided modes of a plane dielectric layer, which correspond to the extracted pole terms of initial diffraction integrals. These fields correspond to pairs of guided waves, which move apart from the region of their excitation near a strip, propagating parallel to the boundaries of a layer and conserving finite amplitude at infinity.