High-frequency radiation pressure and Hall effect in semiconductors

The paper discusses high-frequency Hall effect as the counterpart of that portion of the radiation pressure which arises within a material medium when an electromagnetic wave is propagated through it. Radiation pressure due to reflection of the wave at the surface of the medium, when surrounded by free space, can have no counterpart Hall effect. In a previous paper the author showed that, in general, there are two components of Hall effect, one of which is dependent upon the conduction current in the material medium and the other upon the corresponding displacement current. The first of these Hall effects is associated with the progressive dissipation of energy as heat in the material medium as the wave moves forward, while the second corresponds to the transfer of stored energy to the material medium from the space occupied by it, or vice versa. For simplicity, the problem is first considered in relation to a plane wave propagating through a finite thickness of homogeneous medium which extends without boundary in the transverse plane. Attention is concentrated on what happens within the material medium itself, and bearing in mind that the Hall effect and `internal¿ radiation pressure are produced by the same mechanism, expressions are derived for both these quantities. Extending the discussion to the more practical arrangement in which most of the power consumed by a load is transmitted around the sides of a Hall plate, the analysis leads to a simple method of computing the total Hall e.m.f. generated in the plate from a knowledge of the power dissipated in the semiconductor by the oppositely directed travelling waves in it. The effect due to transfer of stored energy is relatively very small and in most cases may be neglected. Any discontinuities within the Hall plate setting up internal reflections can significantly increase the total radiation pressure, but, in general, this tends to reduce the Hall effect.