Field-controllable Spin-Hall Effect of Light in Optical Crystals: A Conoscopic Mueller Matrix Analysis

Abstract

Electric-field applied perpendicular to the direction of propagation of paraxial beam through an optical crystal dynamically modifies the spin-orbit interaction (SOI), leading to the demonstration of controllable spin-Hall effect of light (SHEL). The electro- and piezo-optic effects of the crystal modifies the radially symmetric spatial variation in the fast-axis orientation of the crystal, resulting in a complex pattern with different topologies due to the symmetry-breaking effect of the applied field. This introduces spatially-varying Pancharatnam-Berry type geometric phase on to the paraxial beam of light, leading to the observation of SHEL in addition to the spin-to-vortex conversion. A wave-vector resolved conoscopic Mueller matrix measurement and analysis provides a first glimpse of the SHEL in the biaxial crystal, identified via the appearance of weak circular birefringence. The emergence of field-controllable fast-axis orientation of the crystal and the resulting SHEL provides a new degree of freedom for affecting and controlling the spin and orbital angular momentum of photons to unravel the rich underlying physics of optical crystals and aid in the development of active photonic spin-Hall devices.

Revealing complex optical phenomena through vectorial metrics

“…Additionally, the fast axis distributions of the two exemplar cases [Fig. 2(b)] demonstrate the transformation of intrinsic topological charges 23 to support the existence of the SHEL from another perspective-that of AM (see Supplementary Material 4 for a detailed analysis). This demonstration newly reveals the AM transfer process in a GRIN lens under the non-meridional plane geometry.…”

“…The SHEL has been gaining large attention in fundamental research, such as geometric phase investigations or angular momentum (AM) transfer processes, [18][19][20][21][22][23] and in applications such as optical edge detection for characterizing boundaries. 19 Traditional methods to validate the SHEL include interferometry 20 or quantum weak measurement; 21,22 however, they are incapable of measuring or tracing the SHEL's presence in the multilayered optical phenomena that result in a complex inhomogeneously polarized beam.…”

“…Hence, MM analysis has become a powerful tool to deal specifically with such complex scenarios. 23 Here we demonstrate the use of M 1 to validate the presence of a circular birefringence (CB) gradient, which serves as an efficient way to trace the SHEL's presence in complex systems. 22 This is illustrated through analysis of the optical properties of a GRIN lens 24 under the condition of oblique illumination.…”

“…As the GRIN lens is also an imaging device, it has the potential to be used as a novel imaging SHEL device, which presents its own applications such as focus manipulation. 27 As the illumination angle of the light beam relative to the lens can be controlled, the SHEL in such a system is field controllable, 23 which would give additional degrees of freedom to harness the SHEL through such a device.…”