Scattering of light by an electron in the presence of a magnetic field and a strong microwave field

Classical electrodynamics is used to analyze the scattering of light by an electron embedded simultaneously in a uniform magnetic field and a microwave field. The presence of the magnetic field is shown to increase the intensities of the different components of the scattered light. Coherent quantum states of the electron in the same field configuration are then constructed and used in describing the scattering process; in this, semiclassical methods are employed. A comparison is made of the classical and semiclassical calculations, and consideration is given to various limiting cases to illustrate the connection with earlier studies. The calculations are seen as having practical value in that they indicate how a microwave field close to resonance with the cyclotron frequency may add to the observation of the Bernstein modes (Bernstein, 1958) and thus represent an additional diagnostic tool.