Spin polarization separation of reflected light at Brewster angle

Abstract: A novel spin polarization separation of reflected light is observed, when a linearly polarized Gaussian beam impinges on an air-glass interface at Brewster angle. In the far-field zone, spins of photons are oppositely polarized in two regions along the direction perpendicular to incident plane. Spatial scale of this polarization is related to optical properties of dielectric and can be controlled by experimental configuration. We believe that this study benefits the manipulation of spins of photons and the development of methods for investigating optical properties of materials.

• The paper demonstrates that absorption-induced phase shifts in BK7 glass generate a millimeter-scale separation of left- and right-circular polarization components.
• The experimental setup uses Gaussian beam reflection at the Brewster angle with polarization tomography to map detailed ellipticity and orientation profiles.
• The findings validate a complex refractive index model that bridges theoretical predictions with applications in photonic spin manipulation and material metrology.

Spin Polarization Separation of Reflected Light at Brewster Angle

Introduction

The study investigates a novel phenomenon in the reflection of a Gaussian beam at the Brewster angle on an air-glass interface: spatial spin polarization separation. Unlike the canonical spin Hall effect of light (SHEL) and the in-plane spin separation of light (IPSSL), the observed effect manifests as two strongly spin-polarized regions in the reflected beam, separated by over a millimeter—orders of magnitude greater than the beam waist. The experimental and theoretical analysis provides insight into boundary-induced spin phenomena and the role of material absorption in reflected field profiles.

Background and Motivation

SHEL has been widely studied as a spin-dependent transverse displacement for reflected or transmitted beams, typically manifesting as subtle, sub-wavelength spatial shifts perpendicular to the incident plane. These effects, along with IPSSL, require sensitive measurement techniques due to the small separation and significant overlap of opposite spin components. However, at the Brewster angle, theoretical treatments for SHEL break down because the standard displacement picture becomes ill-defined and the reflected field is considerably distorted—exhibiting higher-order mode formation rather than beam translation. Previous studies have noted the emergence of mixed TEM10–TEM01 modes, with associated radial or non-uniform polarization fields, but have not resolved the spin structure at the scale investigated here.

Experimental Methodology

The experimental setup utilizes a highly focused horizontally polarized Gaussian beam (632.8 nm, He-Ne) incident on a BK7 glass prism at precisely the Brewster angle. Critical to the analysis is the use of a rotating quarter-wave plate (QWP) and a secondary linear polarizer (P2) to perform polarization state tomography via Stokes parameter estimation. The far-field polarization profile is probed after collimation, enabling reconstruction of both ellipticity and orientation across the beam profile.

A secondary experiment, omitting the focusing and collimating optics, quantifies the amplitude and phase of the reflected $p$-polarized component. This establishes the presence of nonzero reflectivity and a finite $\pm 90^\circ$ phase shift—consistent with material absorption, modeled via a nonzero imaginary part of the refractive index.

Results

Observation of Spin Polarization Separation

Analysis of the reflected beam reveals two high-ellipticity regions, symmetrically placed along the axis orthogonal to the incidence plane ($y$-axis), with nearly pure left- and right-circular polarization at displacement maxima ($|\chi|\approx 45^\circ$). The measured spatial separation between polarization peaks is approximately 1.1 mm, vastly exceeding the characteristic displacements associated with SHEL. The polarization orientation field displays a bifurcation structure, indicative of two sources (odd points) rather than a single radial pattern as predicted by simple mode-interference models.

Theoretical Modeling

To accurately describe the observed phenomenon, the reflection problem is treated with a complex refractive index for the dielectric. The field is decomposed into polarized Hermite-Gaussian modes: a horizontally polarized TEM10, a weaker vertically polarized TEM01, and a fundamental mode component (TEM00) with a $90^\circ$ phase delay. This nontrivial superposition, resulting from absorption-induced phase retardation for the $p$ component, yields spatially varying spin structures with symmetry breaking along the $y$-axis.

Explicit calculation confirms that for an ideal dielectric ($k = 0$), spin amplitudes are symmetric and no net separation occurs. For real glass ($k > 0$), symmetry is broken and spatial spin polarization emerges, with the scale of separation proportional to $k$ and the collimation focal length ($f_2$). The theory quantitatively matches experimental polarization maps, validating the model.

Quantification of Material Effects

Direct measurement of the $p$-polarized reflection coefficient yields approximately $1.4 \times 10^{-3}$ amplitude reflectivity at Brewster angle and confirms the required $\pm 90^\circ$ phase shift. This experimental observation justifies the use of complex refractive index values in the extended Fresnel equations, from which an effective imaginary part of $(7.7\pm0.4)\times 10^{-3}$ is extracted for BK7 glass in the experiment.

Implications and Future Directions

This work demonstrates a macroscopic and controllable spin-separation effect in reflected fields, distinct in origin and scale from spin-orbit interaction-induced beam shifts such as SHEL. Unlike displacement-based effects, the observed spin polarization involves spatial amplitude redistribution driven by material absorption and is scalable by optical configuration. This provides a direct avenue for:

• Photonic Spin Manipulation: The ability to generate spatially separated spin-polarized beams may benefit spin-encoded information processing or quantum photonic device engineering.
• Surface and Material Metrology: The dependence of polarization separation on the imaginary part of the refractive index allows for sensitive, non-contact measurements of dielectric loss tangents—potentially at interfaces or in thin-film systems.
• Extension to Other Materials and Geometries: The generality of the effect for any interface with significant complex index suggests possible exploration in metals, 2D materials, and engineered metamaterials.

Further theoretical development to rigorously connect absorption-induced symmetry breaking and non-Hermitian photonics could refine predictive control of these polarization structures.

Conclusion

The paper rigorously establishes the existence of a novel, large-scale spin polarization separation effect in the reflection of focused beams at Brewster angle from absorbing dielectrics. The effect is underpinned by the interplay of optical absorption, complex-index boundary conditions, and vectorial field decomposition, and stands apart from previously catalogued spin Hall or in-plane separations. This experimental and theoretical advance enhances the understanding of spin-momentum photonics at interfaces, marking new directions for optical control and material diagnostics.