Generalized analytic formula for spin Hall effect of light: shift enhancement and interface independence

Area of Science:

• Optics and Photonics
• Quantum Optics
• Condensed Matter Physics

Background:

• The spin Hall effect of light (SHEL) describes the spin-dependent splitting of light at optical interfaces.
• Existing models for SHEL are well-established for linearly polarized light but often rely on numerical methods for elliptical or circular polarization.
• A need exists for analytical solutions to better understand and control SHEL under diverse polarization states.

Purpose of the Study:

• To derive an explicit analytic formula for the spin Hall shift under arbitrarily polarized light.
• To demonstrate methods for enhancing the spin Hall shift using polarization control.
• To investigate the relationship between SHEL and Fresnel coefficients under circular polarization.

Main Methods:

• Development of a novel analytical framework to describe the spin Hall effect of light.
• Derivation of an explicit mathematical formula for the spin Hall shift.
• Analysis of the derived formula to explore polarization-dependent SHEL phenomena.

Main Results:

• An explicit analytic formula for the spin Hall shift is successfully derived for arbitrarily polarized incident light.
• The study demonstrates that the spin Hall shift can be enhanced at any incident angle by manipulating the light's polarization.
• For circularly polarized light, the spin Hall shift is shown to be independent of the interface's Fresnel coefficients.

Conclusions:

• The derived analytic formula provides an intuitive understanding of SHEL under general polarization states.
• The findings enable unprecedented modulation and enhancement of the spin Hall effect of light through polarization control.
• This work paves the way for advanced optical devices and applications leveraging spin-dependent light behavior.