Transmission of electromagnetic waves through a nonlinear over-dense plasma slab
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RESEARCH
Transmission of electromagnetic waves through a nonlinear over‑dense plasma slab M. Tohfeh1 · L. Rajaei2 · S. Miraboutalebi1 · L. F. Matin1 Received: 15 June 2020 / Accepted: 13 August 2020 © Islamic Azad University 2020
Abstract A study on the transmission of the electromagnetic waves from a structure consisting of an over-dense plasma layer with nonlinear effects is undertaken. The applied nonlinearity is presented due to the series expansion of the polarization in the medium. The nonlinear plasma layer is supposed to be placed between two linear dielectric layers. The transparency conditions are investigated for the p-polarized obliquely incident waves. It is shown that the formation of the surface waves can eventuate to the transmission of the incident waves. This fact has already be seen in the case of the linear over-dense plasma, but, here, it is examined in the presence of the nonlinear effects. To determine the propitious conditions for the surface wave excitation, the exact solutions of the electromagnetic field equations are used in all regions. The transmission, the reflection, and the dissipation rates of the electromagnetic waves from the entire structure are obtained, and the effects of the main parameters on them are discussed. Keywords Surface wave · Nonlinear effect · Over-dense plasma · Transition amplitude · Reflection amplitude
Introduction
* S. Miraboutalebi s_mirabotalebi@iau‑tnb.ac.ir
excitation [10–12]. However, one of the most important initials to trigger this mechanism is to producing the evanescent waves which can simply be provided by placing dielectrics or under-dense plasma layers adjacent to the over-dense plasma [13, 14]. Also, equipping the dielectric with diffraction grating facilitates the production of the evanescent waves. Also, by applying an appropriate density profile for the plasma density, one can produce the required evanescent waves without using the dielectric layers [15]. It is well known that the susceptibility of the dielectric can generally be a function of the electric field. Hence, the nonlinear plasma property considered here comes from the expansion of the polarization in power series of the electric field E [16, 17]. The corresponding electric susceptibility 𝜒 then can be written as:
M. Tohfeh [email protected]
𝜒 = 𝜒l + 𝜒nl(1) E + 𝜒nl(2) E2 + ⋯ ,
There is a great deal of interest in the studying of the lefthanded materials [1–3] today, due to their many applications in science and technology [4–9]. The high-density plasma also behaves as the left-handed material in response to the incident electromagnetic wave in frequency 𝜔 smaller than the plasma frequency 𝜔p , where the plasma permittivity 𝜔2
is defined as 𝜀p = 1 − 𝜔p2 . The anomalous transmission of the electromagnetic waves through left-handed materials takes place due to the mechanism of the surface waves
L. Rajaei l‑[email protected] L. F. Matin [email protected] 1
Department of Physics, North Tehran Branch, Islamic Azad University, Tehran, Iran
Department of Physics,
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