Emergence of transverse optical spin in a subwavelength grating ring resonator

TL;DR

The paper introduces a planar subwavelength-grating ring resonator that supports two quasi-degenerate modes. By bending the SWG waveguide, these modes hybridize to form ring resonances with a predominantly rotating electric field, yielding a non-zero transverse optical spin and a measurable average degree of circular polarization $\langle C \rangle$ even in a symmetric geometry. The authors develop a coupled-mode theory framework and validate the concepts experimentally in the microwave regime, demonstrating DoCP values ranging from $\langle C \rangle \approx -0.71$ to $+0.60$ for different ring modes and showing robust polarization features under bus-waveguide coupling. The results enable on-chip optical spintronic and valleytronic interfaces with potential applications in spin-dependent light–matter interactions and integrated non-reciprocal photonics, and the approach is scalable across spectral ranges.

Abstract

The local polarization of the electromagnetic field plays a crucial role in the interaction of light with spin- and valley-polarized quantum sources. Unlike free-space electromagnetic waves, whose polarization degeneracy enables flexible polarization manipulation, planar integrated optical structures lack such degree of freedom owing to intrinsic structural anisotropy. Here, we propose a planar optical ring resonator based on a subwavelength grating waveguide that supports two quasi-degenerate modes. We demonstrate that coupling of these modes in the ring resonator leads to the formation of the resonances with a predominant direction of electric-field rotation in the vicinity of the resonator, resulting in the non-zero transverse optical spin. The average degree of circular polarization in the proposed structures reaches values of up to 70%. The theoretical predictions are corroborated by experimental validation in the microwave spectral range. Our findings suggest a viable route toward realization of on-chip optical spintronic and valleytronic interfaces.

Figures (10)

• Figure 1: (a) Two quasi-degenerate modes of a SWG waveguide exhibit antisymmetric distributions of the z-component of the electric contribution to the optical spin density, $s_z^{(E)}$. The unit-cell average $\langle s_z^{(E)} \rangle$ vanishes for both modes. (b) Bending of the waveguide breaks the mirror symmetry and induces hybridization of the two modes, resulting in a finite unit-cell-averaged spin density, $\langle s_z^{(E)} \rangle \ne 0$. (c) Hybridized counter-clockwise propagating resonant modes in a ring resonator exhibit a quasi-uniform sign of $s_z^{(E)}$, yielding non-zero $\langle s_z^{(E)} \rangle$ with opposite signs for the two resonances, indicated by arrows in the centres of the rings.
• Figure 2: (a) Dispersion of the straight SWG waveguide (solid lines) and resonance frequencies of the ring resonator formed from this waveguide. Purple (orange) circles denote resonances with negative (positive) unit cell averaged $s_z^{(E)}$; the circle size encodes the magnitude of $s_z^{(E)}$ integrated over the unit cell. Structural parameters are given in the text. Insets show the waveguide unit cell and the corresponding unit sector of the ring. (b--e) Distributions of (b,c) the electric field and (d,e) the $z$-component of the electric contribution to the optical spin density, normalized to the maximum value of $|s_z^{(E)}|$ across both modes, for the two straight-waveguide modes near the degeneracy frequency ($\approx 202~\mathrm{THz}$). The fields are plotted in the $y=0$ plane, indicated by the red dashed contour in the inset of (a). (f--i) Same as (b--e), but for the two ring resonances with $m=26$.
• Figure 3: (a) Transmission spectra of the ring resonator excited by a bus waveguide, as shown in the inset. Structural parameters are given in the text. The labels (P/N)$_m$ denote the "P"/"N" mode type with azimuthal number $m$. (b,c) Spatial distribution of the normalized optical spin density $\tilde{s}_z^{(E)}$ in a plane located $30~\mathrm{nm}$ above the ring surface, evaluated at the frequencies marked as P$_{24}$ and N$_{26}$ in panel (a).
• Figure 4: (a) Schematic of the experimental setup. (b) Spatial distributions of the electric-field amplitude (top panels) and the $z$-component of the optical spin density (bottom panels) for the $N_{14}$ and $P_{12}$ eigenmodes of the ring resonator. (c) Measured and (d) calculated $|S_{11}|^2$ parameter for the full structure (ring resonator coupled to the bus waveguide; red solid lines) and for the bus waveguide alone (gray dashed lines), excited by a WR137 waveguide. The data are normalized to the maximum value obtained for the structure with the ring. (e) Measured and (f) calculated absolute square of the difference between $S_{11}$ parameters with and without ring for several values of the gap between the ring and the bus waveguide. The curves are normalized to the maximum value corresponding to the smallest gap.
• Figure 5: (a,b) Measured amplitudes (top) and phases (bottom) of the (a) $E_x$ and (b) $E_y$ components at a height of $\approx 2~\mathrm{mm}$ above the ring, at $6.515~\mathrm{GHz}$.(c) Simulated (solid lines) and measured (markers) spectra of $|E_x|$, $|E_y|$, and $E_t=\sqrt{|E_x|^2+|E_y|^2}$, normalized to the maximum of $E_t$. (d,e) Angular power spectrum $|c_m|^2$ as a function of azimuthal number $m$ obtained from the (d) measured and (e) calculated $E_r(\phi)$ and $E_{\phi}({\phi})$ distributions.