Reflection of radio waves from a layer with a varying dielectric permittivity

Plane-Wave Reflection from a Special Inhomogeneous Plasma Slab

“…To model the former, we use a symmetric, single-extremum, frequency-dependent profile that has a form (Pogorelov, 1990) (3) with = z/d, b = f p /f, where f is the frequency of incident wave and f p is the penetration frequency. As is seen, « 0 (z) is positive at each point of the slab when f p /f < 1, whereas it can be either positive or negative at f p /f > 1.…”

“…As a result, one obtains the first-order differential equation of the Riccati type (see, for example, Kunitsyn, Smorodinov, & Usachev, 1989;Pogorelov, 1990;Cui, Liang, & Wiesbeck, 1997;Titchener & Willis, 1991;Bailey, 1954). Exact and approximate analytical solutions for R can be obtained only for several profiles.…”

“…Because of this, we solve the Riccati equation numerically. In our study, this equation is used in the form obtained in Pogorelov (1990), that is,…”

“…In this case one deals with the plasma wavetrain. In Pogorelov (1990), the sinusoidal modulation has been applied to the frequency-dependent part of the single-minimum permittivity profile. In particular, it has been shown that new extrema can appear in this case.…”

“…In this paper, we use a more complicated modulating term that contains the band-limited fractal function (Kim & Jaggard, 1988;Jaggard & Sun, 1989, 1990, in order to model the multiscale inhomogeneities of the profile with arbitrary maximum value. The main goal of our study is to analyze the effect of parameters of the fractal modulating function on the frequency-selective properties of the slab in the vicinity of the frequency limiting the pass band of the regular profile.…”