Exact Time-Domain Solution for Step-like H-Wave Radiation near a Dielectric Interface

An exact analytical solution is developed for the problem of transient electromagnetic field radiated from a circular source placed near the interface between free space and an ideal dielectric. The evolutionary approach is used to represent the incident wave by means of the Riemann function, while the reflected and transmitted components are derived through the separation of variables method. Boundary conditions for the tangential field components are rigorously applied to determine the sought-for coefficients, which are functions of the spectral parameter and depend on the properties of the media. The Fourier-Bessel transform is employed to eliminate the explicit time dependence. As a result, the problem is reduced to solving systems of linear algebraic equations for the spectral coefficients. Closed-form expressions for these coefficients are obtained, enabling exact presentation of the electromagnetic field throughout space and time.