Photonic Shankar skyrmion

Abstract

We unveil a new topological quasiparticle of light in 3D space, named the photonic Shankar skyrmion. We show that an elliptically polarized field can be described by an SO(3) order parameter and it can form a texture in 3D space classified by the $π_3(SO(3))$ homotopy group, known as the Shankar skyrmion. We provide ways to construct the photonic Shankar skyrmion in static monochromatic waves and also in propagating wavepackets, the latter give rise to a flying topological quasiparticle. We demonstrate that the transition between the topological configuration and the trivial configuration gives rise to a novel topological singularity, which we call the $L^T$ surface. Such configurations of the electromagnetic field, under light-matter interaction, may lead to new phenomena in condensed matter physics and plasma physics, and are expected to find applications in quantum emulation and optical manipulation.

Figures (4)

• Figure 1: Photonic Shankar skyrmion in monochromatic light. (a) The loop on which the spin densities are oriented along the $(1,-1,0)$ direction (green) and the texture of the triad along the loop. The triad rotates by $4\pi$ along the loop. The inset shows the definition of the triad. (b) Two loops on which the spin densities are oriented along the $(1,-1,0)$ direction (green) and the $(-1,1,0)$ direction (purple). (c) Distribution of the photonic spin density, which forms a hopfion texture. The color corresponds to the orientation of the spin density vector. Its correspondence is shown as the inset on the right side.
• Figure 2: The field profiles of a Shankar skyrmion. (a) Schematic of the RCP envelope $u_r$, which contains a vortex ring of charge 2. (b) Schematic of the LCP envelope $u_l$, which contains a vortex line of charge 2. In (a) and (b) the arrows denote the direction of increasing phase. (c-e) The complex amplitude of $u_r$, $u_l$, and $u_z$ of the field defined in Eq. (\ref{['shankarEfield']}). In each plot, the maximum amplitude is normalized to 1. The white dashed line denotes where $|u_r|=|u_l|$. The inset on the right shows the coloring scheme.
• Figure 3: Photonic spin singularities during topological phase transition. (a) Singular rings in 3D space when $d=1.0$. The inset shows the texture of the triad around the singular line, near $(x,y,z)=(1,0,0)\lambda$. (b) Singular surface in 4D space spanned by $xyz$ and $d$. The value of $d$ is represented by the color.
• Figure 4: Flying topological quasiparticle. The photonic spin density on the $xz$-plane for a photonic Shankar skyrmion moving at velocity $v_g=0.3c$ along the $z$-axis is shown at time $t=(0, 12, 24)\lambda/c$, in (a), (b), and (c) respectively. The spin orientations are represented by various colors using the same scheme as Fig. \ref{['fig_texture']}.