Conservative finite-difference scheme for the problem of THz pulse interaction with multilevel layer covered by disordered structure based on the density matrix formalism and 1D Maxwell’s equation

On the basis of the Crank-Nicolson method, we develop a conservative finite-difference scheme for investigation of the THz pulse interaction with a multilevel medium, covered by a disordered layered structure, in the framework of the Maxwell-Bloch equations, describing the substance evolution and the electromagnetic field evolution. For this set of the partial differential equations, the conservation laws are derived and proved. We generalize the Bloch invariant with respect to the multilevel medium. The approximation order of the developed finite-difference scheme is investigated and its conservatism property is also proved. To solve the difference equations, which are nonlinear with respect to the electric field strength, we propose an iteration method and its convergence is proved. To increase the computer simulation efficiency, we use the well-known solution of Maxwell’s equations in 1D case as artificial boundary condition. It is approximated using Cabaret scheme with the second order of an accuracy. On the basis of developed finite-difference scheme, we investigate the broadband THz pulse interaction with a medium covered by a disordered structure. This problem is of interest for the substance detection and identification. We show that the disordered structure dramatically induces an appearance of the substance false absorption frequencies. We demonstrate also that the spectrum for the transmitted and reflected pulses becomes broader due to the cascade mechanism of the high energy levels excitation of molecules. It leads to the substance emission at the frequencies, which are far from the frequency range for the incident pulse spectrum. Time-dependent spectral intensities at these frequencies are weakly disturbed by the disordered cover and, hence, they can be used for the substance identification.