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We demonstrate theoretically that in gyrotropic semiconductors andsemiconductor nanosystems the Brownian motion of electrons results in temporalfluctuations of the polarization plane of light passing through or reflectedfrom the structure, i.e., in stochastic Faraday or Kerr rotation effects. Thetheory of the effects is developed for a number of prominent gyrotropic systemssuch as bulk tellurium, ensembles of chiral carbon nanotubes, and GaAs-basedquantum wells of different crystallographic orientations. We show that thepower spectrum of these fluctuations in thermal equilibrium is proportional tothe ac conductivity of the system. We evaluate contributions resulting from thefluctuations of the electric current, as well as of spin, valley polarization,and the spin current to the noise of the Faraday/Kerr rotation. Hence,all-optical measurements of the Faraday and Kerr rotation noise provide anaccess to the transport properties of the semiconductor systems.

Stochastic Faraday rotation induced by the electric current fluctuations in nanosystems