Reflection and transmission of electromagnetic waves obliquely incident on a relativistically moving uniaxial plasma slab

Abstract

The reflection and transmission properties of electromagnetic waves obliquely incident on a relativistically moving uniaxial plasma slab are investigated theoretically and the maxima and minima of the power reflection coefficient as a function of the normalized incident wave frequency ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Omega</tex> ) and the slab velocity ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\beta</tex> ) are discussed for slab motion parallel as well as normal to the slab boundaries. One can predict the nature of variation of the reflection coefficient with respect to any parameter from the variation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q'</tex> (the root of the dispersion equation) with that parameter. When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q'</tex> is real and varies rapidly, the oscillations in the reflection coefficient are rapid and when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q'</tex> differs significantly from the free-space value, the amplitude will be large. In the imaginary range of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q'</tex> , the reflection coefficient is nonoscillatory. The discussion of the results is facilitated by introducing a parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> which is a quadratic in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\beta</tex> . For slab motion parallel to the interface, the two slab velocities for a given <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> give rise to same reflection coefficient whilst for normal motion the results are significantly different.