Interaction of Waves of Current and Polarization

The system considered here is a polarizable semiconductor through which a current is flowing in response to an externally applied electric field. Phenomenological equations relating the charge density, polarization, electric and magnetic fields, and atomic displacements in such a system are described. It is shown that a traveling wave of small amplitude oscillations of these quantities satisfies the equations when the frequency ω and propagation vector q satisfy a certain dispersion relation which is derived. For some choices of system parameters the dispersion relation admits solutions in which ω is real and q is complex with real and imaginary parts of opposite sign, suggesting the possibility that the system might support amplifying waves. Examples are given in which the parameters are as nearly as possible those appropriate to a crystal of indium antimonide. Some of the parameters which must be assigned depend on the drift velocity of the electrons, and it is difficult to determine appropriate values or ranges of values for them in the interesting region of large drift velocities.