Geometry Driven Spin Polarization Effects in Waveguiding Plasmonic Crystal

TL;DR

This work addresses how geometry can control spin–orbit interactions in waveguiding plasmonic crystals (WPCs) by modulating polarization with incidence geometry. It combines finite-element simulations in COMSOL with Jones–Mueller formalisms to extract Mueller-matrix parameters and their decomposition into linear diattenuation and retardance, under varying $ heta_i$ and azimuth $oldsymbol{\u03b1_i}$. A two-subsystem model $M_{net}=M_{waveguide} M_{grating}$ explains the emergence of a geometry-driven circular anisotropy, evidenced by nonzero off-block-diagonal elements $M_{14}$ and $M_{41}$ that satisfy $M_{14} eq M_{41}$ when $oldsymbol{\u03b1_i} eq 0$, linking to SOI phenomena. These results reveal a mechanism for spin-polarization control in inversion-symmetric metasurfaces, with potential applications in spin-dependent nanophotonic devices.

Abstract

We investigated the modulation in the polarization-dependent optical behaviour of the waveguiding plasmonic crystal by varying the illumination and detection geometry. We employed the finite element method-based COMSOL simulation and Jones-Mueller formalisms to probe the variations in optical parameters by systematically varying the angle of incidence and azimuthal angle of the incident plane wave source, thereby quantifying the variations in the polarization anisotropy parameters. The enhancement of optical properties at various resonances and the tunability of the hybridized modes are discussed. Importantly, our study reveals that despite the system being perfectly inversion-symmetric and achiral, it exhibits circular polarization anisotropy effects for non-zero finite azimuthal angles, manifested in the off-block-diagonal elements of the constructed Mueller matrices. The origin of this intriguing circular anisotropy effect is unravelled using the sequential linear birefringence and linear diattenuation effects arising from geometrical polarization transformation. Its implications in the spin-orbit interaction of light in the plasmonic crystal system are discussed.

Figures (9)

• Figure 1: Schematic representation of the simulation geometry for scattering of light from waveguiding plasmonic crystal. (a) Schematic of the simulation geometry. The incident wave vector $\vec{k}_{0}$, shown in red, is defined by the incidence angle $\theta_{i}$ and azimuthal angle $\phi$. PSG and PSA denote the polarization state generator and analyzer, respectively. The gold grating (period $d_{x} = 450\,\text{nm}$) is placed on top of an indium tin oxide (ITO) waveguide layer of height $h = 140\,\text{nm}$, supported by a quartz substrate. (b) Computed extinction spectra for s (senkrecht) and p (plane) polarized light in the wavelength range $400\text{–}900\,\text{nm}$. From top to bottom, the incidence angle $\theta$ is varied from $0^{\circ}$ to $20^{\circ}$ in increments of $2^{\circ}$, while the azimuthal angle is fixed at $\phi = 0^{\circ}$. The spectra are shifted vertically to facilitate comparison.
• Figure 2: Spectral polarization characteristics of the WPC system encoded in $4\times 4$ Mueller matrix for varying angle of incidence ($\theta_{i}$). The extinction spectra for s and p polarizations with incidence angles (a) $\theta_{i}=0^{\circ}$, $\phi_{i}=0^{\circ}$, (b) $\theta_{i}=30^{\circ}$, $\phi_{i}=0^{\circ}$. The computed Mueller matrix at the wavelengths of interest marked in (a), (b) is shown in (c): The black diamond and saffron star markers correspond to the peak wavelengths in (a) (652nm, 686nm, 754nm), (b) (526nm, 694nm) respectively, while those circled in green indicate the non-peak wavelengths in (a) (680nm, 714nm) and (b) (512nm, 606nm).
• Figure 3: Spectral polarization characteristics of the WPC system encoded in $4\times 4$ Mueller matrix for varying azimuthal angle ($\phi_{i}$). (a) The computed extinction spectra for s and p polarizations. From top to bottom, $\phi_{i}$ is increased from $0^{\circ}$ to $90^{\circ}$, in steps of $10^{\circ}$, while $\theta_{i}=30^\circ$ remains constant. The extinction spectra for s and p polarizations with incidence angles (b) $\theta_{i}=30^{\circ}$, $\phi_{i}=0^\circ$, (c) $\theta_{i}=30^\circ$, $\phi_{i}=30^\circ$. The computed Mueller matrix at the wavelengths of interest marked in (b), (c) is shown in (d): The saffron star and blue diamond markers correspond to the peak wavelengths (b) (526nm, 694nm), (c) (540nm, 712nm, 858nm) respectively, those circled in green indicate the non-peak wavelengths in (b) (512nm, 606nm) and (c) (530nm, 630nm).
• Figure 4: Schematic illustration of the geometric origin of circular polarization (spin) dependent response from the achiral WPC system. (a), (b) show the preferred direction of propagation of plasmon excitations and waveguide modes, respectively. The optic axis does not vary with $\phi_{i}$ in (a) for the plasmonic system but does so in (b) for the waveguide. (c), (d) show the circular polarizance and circular diattenuation spectra respectively for various incident $\phi$, with $\theta_{i}$=$30^\circ$ constant.
• Figure S1: Schematic of a unit cell of the waveguiding plasmonic crystal with individual regions labeled is shown to the left. To its right is the averaging method shown in detail, for obtaining the output electric field.