Effect of a Static Electric Field on the Propagation of Electromagnetic Waves in Indium Antimonide

Abstract

The effect of a weak longitudinal static electric field on the propagation of transverse circularly polarized electromagnetic waves traveling along the magnetostatic field in indium antimonide plasma has been studied theoretically. Using the dispersion relationship, the variation of the amplitude constant $\ensuremath{\alpha}$, the phase constant $\ensuremath{\beta}$ of both the left- and right-hand circularly polarized waves with the wave frequency $f$, the static magnetic field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}$, and the static electric field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}}_{0}$ are examined in detail for three cases: case (i), intrinsic indium antimonide at room temperature; case (ii), $n$-type indium antimonide at liquid-nitrogen temperature; and case (iii), $p$-type indium antimonide at liquid-nitrogen temperature. The amplitude constant $\ensuremath{\alpha}$ may be either negative or positive for a positive $\ensuremath{\beta}$ depending upon the particular combination of the system parameters $f$, ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}_{0}$, and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}}_{0}$. When $\ensuremath{\alpha}$ is negative, the wave decays spatially and the decay rate $|\ensuremath{\alpha}|$ tends to decrease while $\ensuremath{\beta}g0$ tends to increase with $|{\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}}_{0}|$ in general. In the presence of carrier drift, i.e., $|{E}_{0}|\ensuremath{\ne}0$, it is possible for the transverse wave to grow spatially ($\ensuremath{\alpha}\ensuremath{\beta}g0$) in indium antimonide for all three cases considered, provided the combination of parameters is proper. For example, in case (i) the product (${\ensuremath{\alpha}}_{l}{\ensuremath{\beta}}_{l}$) for the left-hand wave is positive when ${B}_{0}=13$ kG, $fl0.04$ GHz, ${E}_{0}=80$ V/cm or ${B}_{0}=13$ kG, $f=0.1$ GHz, and ${E}_{0}g120$ V/cm. In case (ii) the product (${\ensuremath{\alpha}}_{l}{\ensuremath{\beta}}_{l}$) for the left-hand wave is positive when ${B}_{0}=10$ kG, $fl0.7$ GHz, ${E}_{0}=36$ V/cm or ${B}_{0}=10$ kG, $f=0.5$ GHz, and ${E}_{0}g30$ V/cm. In case (iii), (${\ensuremath{\alpha}}_{l}{\ensuremath{\beta}}_{l}$) is positive when $2.4l{B}_{0}l54$ kG, $f=0.1$ GHz, ${E}_{0}=120$ V/cm or ${B}_{0}=5$ kG, $fl0.2$ GHz, and ${E}_{0}=120$ V/cm. The influence of the presence of ${E}_{0}$ on the propagation of the helicon wave in case (ii) and the microwave Faraday rotation at $f=35$ GHz in the range $130\ensuremath{\le}{B}_{0}\ensuremath{\le}150$ kG is also considered.