Optical-Mechanical Analogy Approach for the Purposes of Detection of IR-MW Radiation

A.V. Bogatskaya, N.V. Klenov, M.V. Tereshonok and A.M. Popov D. V. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia, annabogatskaya@gmail.com P. N. Lebedev Physical Institute, RAS, Moscow Russia Moscow Technical University of Communication and Informatics, 111024, Moscow, Russia Department of Physics, Moscow State University, 119991, Moscow, Russia 5 Moscow Technological University (MIREA), 119454, Moscow, Russia

Here we propose a generalized physical approach providing possible technical realizations of a number of urgent problems related to the interaction of electromagnetic radiation with plasma and conducting media. Proposed approach is based on the use of wellknown optical-mechanical analogy which exploit mathematical identity of the stationary Schroedinger equation in quantum mechanics for the particle motion in potential field and Helmholtz equation in wave theory.
Let us consider spatially inhomogeneous nonmagnetic medium characterized by the susceptibility ) (r   , or permittivity In the case of monochromatic field ,  is the radiation frequency) Maxwell equations for electric and magnetic field strength can be written as: From (1) one can obtain the following equation for electric field strength E For the case when permittivity depends only on one spatial coordinate ) (z   = and wave field propagates alone this direction the equation (2) transforms to the well-known Helmholtz equation for the spatial distribution of electric field strength E : 0 )) ( 4 1 ( (3) Here electric field propagates in the direction perpendicular to z-axis.
Equation (3) is mathematically equivalent to the stationary Schrödinger equation in quantum mechanics for the particle wave function ) (z  in the potential field ) (z V : is the wave vector of the particle with energy  . Direct comparison of eq. (3) and (4) leads to the conclusion that potential function in quantum mechanics is similar to the susceptibility in electromagnetic theory . Thus the eigenvalue problem for the Hamiltonian in quantum theory turns out to be mathematically identical to the problem of calculating the stationary distribution of the electric field strength in a wave. The medium with 0   can be associated with an attrac- . In particular, the transport of the electron flux in heterostructures is mathematically identical to the problem propagation of electromagnetic waves through inhomogeneous media.
If the potential curve ) (z V has the piecewisecontinuous structure (Fig. 1), both the  -function and its derivative dx d should be continuous functions in the potential breaking points. Similar boundary conditions appear to exist in electromagnetic theory: the tangential components of H E   , should also be continuous functions at the interface regions. Using Maxwell equations one can rewrite the boundary conditions as the continuity of tangential components of E  and its derivative. For the normal incidence when only tangential components of H E   , have the nonzero values these boundary conditions are equivalent to boundary conditions for the wave function in quantum mechanics. The above conclusion known as an optical-mechanical analogy in quantum theory gives rise to a lot of practical applications and transfer the quantum theory problem solutions to optics and vice versa.
We perform an analysis of the possibility of penetration of electromagnetic waves through opaque media using the analogy of tunneling of a quantumparticle flux through a potential barrier with a height greater than its kinetic energy. As an example, we consider plasma sheath surrounding the hypersonic vehicle as a potential barrier and analyze the overcoming of radiocommunication blackout problem [1].
Really, for the collisionless plasma the permittivity reads    The role of collisions in plasma as well as cases of normal and oblique incidence of radiofrequency waves on the vehicle surface are studied in [1].
One more promising application of the suggested approach implies a method for increasing the efficiency of bolometric photodetectors. The results of calculations show that by choosing thickness and dielectric constant of the substrate-resonator under a thin layer of metal (superconductor) one could bring the fraction of absorbed radiation in the detector to a value close to unity at a certain frequency of the infrared range [2]. This work was supported by the Russian Science Foundation (project no. 18-72-00125).