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

Abstract

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.

Substance Detection and Identification Using Frequency Doubling of the THz Broadband Pulse

“…A more explicit description of the pulse shape transform can be provided depending on the choice of the model of the medium. In particular, in [45], we developed the finite-difference scheme for the computer simulation of the THz pulse's interaction Figure 1. Scheme of verification of the substance absorption frequencies observed under the action of the incident broadband THz pulse.…”

“…A more explicit description of the pulse shape transform can be provided depending on the choice of the model of the medium. In particular, in [45], we developed the finite-difference scheme for the computer simulation of the THz pulse's interaction with a medium whose response is described in the framework of density matrix formalism, and demonstrated some examples of the reflection and transmission of the THz pulse through a layer of the medium.…”

“…We also used matrix density formalism to obtain a description of the broadband THz pulse interaction with the multi-level medium [45,51]. The THz pulse propagation is governed by Maxwell's equations.…”

“…Its efficiency depends on the THz pulse's maximal intensity. However, there is another physical mechanism of the frequency up-conversion of the broadband THz pulse that was described in [45,51]. Because the THz pulse interacts with a medium by exploring vibration energy levels of molecules (gaseous medium) or phonons (solid), the difference between the energy levels is many times less than that for electronic levels.…”