Spin Hall Effect of Light in Semiconductors

The lateral spatial separation between the circular polarization components of a linearly polarized light beam impinging at off-normal incidence on an air-semiconductor interface is investigated experimentally and theoretically. This fundamental optical phenomenon is referred to as the Spin Hall effect of light (SHEL).\nAn optical pump-probe technique is demonstrated to resolve in situ the nanometer size SHEL displacement of a beam transmitted inside an absorptive material. Three different types of optical interactions in silicon and GaAs demonstrate the technique’s general applicability. First, resonant ∼150 fs pump and probe pulses at λ = 820 nm resolve the SHEL displacement via free-carrier absorption in a 10 μm thick silicon sample. The measured SHEL displacements for a p-polarized probe beam are obtained between −10 to 150 nm as a function of the angle of incidence on the sample. Different angles of incidence are achieved by keeping a fixed angular separation between the pump and the probe beams while rotating the sample about the axis perpendicular to the plane of incidence. In another experiment, an optically thin (500 nm thick) GaAs sample allows one to use Pauli-blocking as an optical interaction to investigate the polarization and angular dependence of the SHEL in the probe beam. For such a polarization-dependent imaging technique, the SHEL displacement in the pump beam also contributes to the measured signal and is evaluated experimentally. A probe beam at normal incidence is used to measure a SHEL displacement of ∼180 nm in a transmitted p-polarized pump beam impinging on the sample with an angle of incidence of 55 degrees. Finally, two-photon absorption is used to resolve the SHEL in a (001) oriented 500 μm thick GaAs wafer using an optical source generating sub-bandgap radiation (λ = 1550 nm) with a pulse duration of 120 fs. Linearly p- and s- co-polarized pump and probe beams are also used to investigate the polarization dependence of the SHEL. All the experimental results obtained using these different optical interactions agree with the theory within the experimental error. \nFinally, analytical expressions of the shifts experienced by the circular components of a beam impinging at an interface between two optical media are also derived for an incident beam with an arbitrary spatial distribution.

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