Non-Abelian gauge field optics in the time domain

Abstract

Artificial gauge fields open up burgeoning opportunities for wave engineering in different disciplines. So far,previous works have mostly focused on synthesizing spatial gauge fields, where the pseudo-magnetic fields lie at the heart of these phenomena. In this Letter, we generalize the paradigm of gauge field optics to the time domain by using time-varying media with rotating anisotropy. Dual to its spatial counterpart, the temporal gauge field induces a pseudo-electric field for optical pulses, leading to the spin-dependent longitudinal shift and Zitterbewegung for both trajectory and frequency. In addition, we analyze the temporal non-Abelian interference effect induced by temporally bounded non-Abelian gauge field media, which results in the temporal spin-precession and the temporal analogy of the non-Abelian Aharonov-Bohm effect. Our work not only fills the gap between synthetic gauge fields and time-varying physical systems, but also provides a fundamentally new approach for manipulating light with time-varying media.

Figures (4)

• Figure 1: Motion of the optical pulse in a temporal Abelian gauge field $\mathcal{A}_t=0.01\hat{\sigma}_3\bar{t}$ with $\bm{\mathrm{E}}(\xi,\bar{z}=0)=\mathrm{exp}(-\xi^2/4)\bm{e}_x$. (a) Longitudinal shift of optical pulses. (b) Spin-dependent frequency shift of optical pulses. Here, $T_0=1/\omega_0$. The solid curves and density plots respectively represent the analytical results based on Eqs. (\ref{['4']}-\ref{['6']}) and the numerical calculation of Eq. (\ref{['3']}), while the dots are obtained by full-wave simulations.
• Figure 2: ZB of the optical pulse in the temporal non-Abelian gauge field $\mathcal{A}_t=0.1\cos{0.1\xi}\hat{\sigma}_3+0.1\sin{0.1\xi}\hat{\sigma}_1$ with $\bm{\mathrm{E}}(\xi,\bar{z}=0)=\mathrm{exp}(-\xi^2)\bm{e}_+$. (a) Longitudinal ZB. (b) Frequency ZB. The solid curves and density plots respectively represent the analytical results based on Eqs. (\ref{['4']}-\ref{['6']}) and the numerical calculation of Eq. (\ref{['3']}), while the dots are obtained by full-wave simulations.
• Figure 3: Temporal interference effect of the plane wave in a temporal Abelian gauge field slab $\mathcal{A}_t=0.01\hat{\sigma}_3$. (a) Temporal precession of the pseudo-spin on the Bloch sphere. (b) Evolution of the polarization vector. (c,d) The calculated results of (c) the reflectivity with different $\Delta t$ and (d) the intensity after scattering ($\bar{t}>\Delta t$). Here, the solid and dotted curves represent the analytical and the full-wave simulation results, respectively.
• Figure 4: Non-Abelian interference effect of the plane wave. (a-b) Temporal evolution of the pseudo-spin on the Bloch sphere in gauge fields (a) $\mathcal{A}_{\mathrm{I}}$ (red lines) and $\mathcal{A}_{\mathrm{II}}$ (blue lines), and (b) $\mathcal{A}_c$, with the initial spin $\bm{s}_0=(0,-1/\sqrt{2}, 1/\sqrt{2})$ and $\Delta t=\pi/2|m|$ with $m=0.02$. (c,d) The calculated results of (c) reflectivity and (d) intensity of plane waves after scattering ($\bar{t}>2\Delta t$). Here, the solid and dotted curves represent the analytical and the full-wave simulation results, respectively.