Effects of a Magnetic Field on Optical Mixing Due to Nonparabolicity inn-InSb

We have studied the effects of a magnetic field on the third-order optical mixing ${\omega }_3=2\mathrm{}{\omega }_1-{\omega }_2$ in $n$-InSb, where ${\omega }_1$ and ${\omega }_2$ are produced by a C${\mathrm{O}}_2$ laser. The mixing occurs because of the nonparabolic conduction band in InSb. The results at high carrier concentrations can be described by a semiclassical theory which includes the effects of Faraday rotation and Voigt phase shift, coherence effects, and a field-dependent scattering time, except that the enhancement predicted at ${\omega }_1, {\omega }_2, {\omega }_3\approx {\omega }_c$, the cyclotron frequency, is largely canceled by the decreased scattering time, by cyclotron absorption of the input and output beams, and by loss of coherence at resonance. For lower carrier concentrations, we observe marked enhancement corresponding to interband resonances at the virtual intermediate frequency $2{\omega }_1$, which is not reduced by any absorption at $2{\omega }_1$. These enhancements are predicted by a quantum-mechanical treatment of the third-order mixing.