Hysteretic three-photon excitation of a cyclotron resonance in semiconductors

Abstract

In the earlier work1 the three-photon resonance at cyclotron frequency Ω c , in semiconductors pumped by two lasers with their frequency difference close to Ω c , has been predicted and observed. Here we consider the feasibility of hysteretic excitation of such a resonance in narrow-gap semiconductors which is based on the nonparabolicity of the narrow-gap semiconductor conduction band. The expected effect is analogous to three-photon hysteretic resonance of free cyclotron electrons in vacuum.2 However, this quasi-relativistic nonlinearity caused by nonparabolicity in semiconductors is much larger than that caused by free relativistic electrons, since the nonlinearity in semiconductors is scaled to the gap energy Eg, which is much smaller than rest energy of free electron m0c2. We consider an example where two different lines 10.6 and 9.4 µm of a CO2 laser used as driving radiations, with the cyclotron three-photon excitation expected at λc ≃ 83.03 µm. Assuming the momentum relaxation time to be of the order of 10−11 s, we estimate the critical intensity required to obtain a hysteretic frequency difference cyclotron excitation to be 3.4 × 104 W/cm2 for InSb; 2.2 × 105 W/cm2 for HgTe; 2.2 × 106 W/cm2 for GaAs.