Reflection and transmission of a light on a dielectric boundary in a time domain

The description and understanding of the propagating of THz pulses in optical systems has recently attracted considerable research efforts. Common methods to generate sub-picosecond, single-cycle electromagnetic pulses evoke great interest and there is an excitation of a biased semiconductor or an electro-optic crystal with a femtosecond light pulse among them. It needs a detailed investigation of the propagation properties of ultrashort pulse beams scattered by interfaces with time-varying properties. In this paper we obtain integral operators that describe in time domain in the 3-D case an interaction of complex electromagnetic signals with the flat interface between dielectric media when the medium in one of the two halfspaces changes its permittivity and acquires a conductivity