Isogyres – Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference

Abstract

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

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

“…4(a,b and c) . The rotationally symmetric conoscopic pattern consisting of entangled isochromate rings and isogyre cross pattern confirm the uniaxial phase of the KDP crystal at 34 (Fig. 4(a) ), while the broken symmetry of the pattern under the applied electric field shows the weak and strong biaxial phases of the crystal (Fig.…”

“…To exemplify this, we consider the plane wave component in the paraxial beam, which makes an angle θ with the z -axis. The final state, after propagation through the crystal, can be expressed in the right- (R), and left- (L), CP basis as 34 where δ is the phase retardation experienced by the linear polarization component of the plane wave due to linear birefringence of the crystal. The second term in eqn.…”

“…1(b) , the topological structures identified as node (green circle) and lemon (red circles) play a significant role in the SOC, and the linear gradient portion (blue lines) contribute to the SHEL, respectively via azimuthally and linearly varying PB phase for a range of plane-waves ( Δk ) in the paraxial beam around the central plane wave. The SOC is typically characterized by extracting the associated helical phase structure either using the Fourier fringe analysis 34 or wavevector resolved Stokes polarimetry 18 respectively representing the scalar and vector optics treatment.…”

Generation and decomposition of scalar and vector modes carrying orbital angular momentum: a review

“…This led to the realization that VVBs can also be identified by the presence or absence of TAM carried by the beam, and geometric phase has been shown to play a critical role in this beam attribute. In addition to TMFs, [150][151][152][153]162 VVBs have also been generated using a variety of methods, including interferometry, [145][146][147]175 LC Q-plates, 125,176 optical crystals, [177][178][179] stressed optical element, 154,180 and, more recently, using structured metasurfaces [181][182][183] and in plasmonicfields. 184 Generation of the family of VVBs using LCoS devices 74,[185][186][187] and their recent off-shoot the DMDs 132,188 were notably missed in the above discussion as they belong to active and flexible generation methods.…”

Spin-Hall effect in the scattering of structured light from plasmonic nanowire

“…Hall or orbital-Hall) and also known as optical Magnus effect [6]. This effect is observed in beam reflection or refraction [7,8], propagation through medium [9][10][11] or metamaterial [12] and scattering [13][14][15]. Spin-orbit effects cover a wide class of electromagnetic phenomena such as focusing, reflection, scattering, light propagation and light-matter interactions.…”