The rotation of the plane of polarization of light upon transmission through a magnetized medium is known as Faraday rotation (FR). In non-magnetic semiconductors FR can be produced by optically orienting the spin of electrons. The main objectives of this thesis is (i) to demonstrate large FR due to optically oriented electrons using an n-doped bulk GaAs microcavity, and (ii) to show that the FR can also be used to measure the nuclear spin dynamics without disturbing it. By using optical orientation of electron gas in n-doped bulk GaAs confined in a microcavity (MC), FR up to 19$^\circ$ in the absence of magnetic field is obtained. This strong rotation is achieved because the light makes multiple round trips inside the MC. Fast optical switching of FR in sub-microsecond time scale is demonstrated by sampling the FR in a one shot experiment under pulsed excitation. A concept of FR cross-section as a proportionality coefficient between FR angle, electron spin density and optical path is introduced. This FR cross-section which defines the efficiency of spin polarized electrons in producing FR is estimated quantitatively and compared with the experimental results. Non-destructive measurement of nuclear magnetization in n-GaAs via cavity enhanced FR of an off-resonant light beam is also demonstrated. In contrast with the existing optical methods, this detection scheme does not require the presence of non-equilibrium electrons. Applying this detection scheme to the metallic n-GaAs sample, nuclear FR is found to vary non-monotonously after pump beam is switched off. It consists of two components: one with short decay time ($\sim$10 s) and another with longer decay time and opposite sign ($\sim$200 s). These two contributions to nuclear FR are attributed to two groups of nuclei: (i) nuclear spins situated within the localization radius of donor-bound electrons, which are characterized by fast dynamics, and (ii) all other nuclear spins in the sample characterized by much slower relaxation rate. The results suggest that, even in degenerate semiconductors nuclear spin relaxation is limited by the presence of localized electron states and spin diffusion, rather than by Korringa mechanism. Nuclear FR in the insulating sample, in contrast with the metallic sample, is found to vary monotonously, but again consists of two components. The fast component is even faster than that of the metallic sample ($\sim$1 s), and the slow component decays in the same time scale as that of the metallic sample. Main microscopic mechanisms responsible for nuclear FR is found to be conduction band spin splitting induced by Overhauser field. It dominates nuclear FR in both metallic (conduction band states partly occupied) and insulating (Fermi level below the bottom of the conduction band) samples. FR resulting from the spin unbalanced occupation of donor bound electron states is only observed in metallic sample.
