Magneto‐Optical Effects on the Generation of the Third Harmonic in Semiconductors

Abstract

The generation of higher harmonics and the optical mixing effect by free carr i e r s in semiconductors are a subject of interest for a number of authors. It has been proposed that the observed higher harmonics and optical mixing arise from the momentum dependence of the conduction electron mass /1, 2/ due to the non-parabolicity of the conduction band, and from the momentum dependence of the relaxation time /3, 4/. In an earlier theoretical investigation the nonlinear effect depends critically on the dependence of the carrier momentum relaxation mechanism, thus for r = 0 (where r describes the type of the scatteriw mechanism) the current density J(3) vanishes, describing the nonlinear magneto-optical effects in semiconductors. 9In our note we are going to present some of the final results of the theory It is well established that in a strong ac electric field (laser beam) the high frequency charge carrier transport in semiconductors is influenced by the momentum -cm and energy zE relaxation time /5/.To obtain the magneto-conductivity of the third harmonic one can use the method described in /6/. At low enough magnetic field, for the non-oscillatory part of different transport properties, the behaviour of the electron system can be described by the Boltzmann equation. Due to the nonlinearities in the Boltzmann equation higher harmonics in the current density a r e observed Hence we consider the cases where the momentum relaxation time is independent of energy r = 0, f m --Tmo, where the energy band is parabolic with spherical surfaces and where the electron gas is strongly degenerate. The tensor 6 ' ' ) will be calculated for the transverse polarization of the incident r a d i a t i o z k l d ' ) , For this case the magneto-conductivity of the third 1) ul. Hoia 69, 00-681 Warsaw, Poland.