Optical Spin Effects Induced by Phase Conjugation at a Space-Time Interface

TL;DR

The paper addresses polarization and spin control at a space-time interface by modeling a deeply subwavelength Lorentz-dispersive layer whose plasma frequency $\omega_p(t)$ is rapidly modulated. An abrupt temporal change excites a resonance polarization $\bm{\mathcal{P}}_m(t)$, yielding a field at the resonance $\omega_0$ that is a coherent superposition of the incident polarization and its phase-conjugate, thereby inducing spin-conversion in the reflected field. The authors derive analytic expressions for the reflected and transmitted fields and demonstrate tunable elliptical polarization, strongly dependent on temporal boundary parameters such as the delay $t_d$ and slab width $\Delta t$, with validation against full-wave simulations. This work shows that phase conjugation and polarization control can be achieved without bi-anisotropy or nonlinearities, suggesting practical implementations in THz to near-infrared regimes using state-of-the-art time-varying metastructures and semiconductors. The findings open avenues for ultrafast spin- and polarization-engineering in space-time photonic systems.

Abstract

Electromagnetic temporal boundaries, emerging when the constitutive parameters of a medium undergo abrupt temporal variations, have garnered significant interest for their role in facilitating unconventional wave phenomena and enabling sophisticated field manipulations. A key manifestation is temporal reflection in an unbounded spatial domain, where a sudden temporal discontinuity induces phase-conjugated backward waves alongside anomalous spin conversion. This study explores distinctive spin-conversion dynamics at a time-dependent spatial interface governed by Lorentz-type dispersion, in which the plasma frequency undergoes rapid modulation over time. The interaction of a circularly polarized wave with a space-time interface excites electromagnetic signals at the system's natural resonance, allowing precise control over polarization states. The scattered field stems from the combined influence of temporal and spatial boundaries, yielding a superposition of the original incident wave's polarization and its phase-conjugated counterpart.

Figures (5)

• Figure 1: Schematic illustration of the proposed mechanism. A time-varying dispersive interface is embedded between two homogeneous and stationary half-spaces with relative permittivities $\varepsilon_L$ and $\varepsilon_R$. The interface is modeled as a thin slab of thickness $L \ll \lambda$, and exhibits Lorentz-type dispersion with a plasma angular frequency $\omega_p$ that varies in time. When a circularly polarized wave packet with positive spin (i.e., RHCP) and angular frequency $\omega_i$ (red arrow) impinges on the interface, the scattering process generates both LHCP and RHCP components at the resonance angular frequency $\omega_0$ (blue arrows).
• Figure 2: Example of electromagnetic scattering, for $\varepsilon_L=\varepsilon_R=1$, $L=0.16 c/\omega_0$, $\gamma=5 \cdot 10^{-3} \omega_0$, $\omega_i=0.3 \omega_0$, $\sigma=20/\omega_0$, $t_d=0$, and $A_1=1$. a) Positive- $(\tilde{I}_+$) and negative-spin ($\tilde{I}_-$) spectra of incident wave. b,c) Corresponding spectra ($\tilde{R}_+$ and $\tilde{R}_-$) of reflected wave in the absence ($A_2 = A_1$) and presence of a temporal boundary ($A_2 = 1.5 A_1$), respectively, as indicated in the insets. All spectra are normalized to the peak value of the incident one.
• Figure 3: Frequency-dependent polarization rotation angle $\varphi_r$ and phase angle $\delta_r$ of reflected wave, corresponding to the spectral components shown in Figure \ref{['fig2']}.
• Figure 4: a,b) Positive- ($\tilde{R}_{+}$) and negative-spin ($\tilde{R}_{-}$) spectra, respectively, of reflected wave as a function of time-delay $t_d$. c) Polarization rotation angle $\varphi_r$ and phase angle $\delta_r$ of reflected (backward) wave at resonance angular frequency $\omega_0$, as a function of $t_d$. Incident field and all parameters are identical to those in Figure \ref{['fig2']}, except for the variation in $t_d$. All spectra are normalized to the peak value of the incident one.
• Figure 5: Scattering of a positive-spin-polarized field from a space-time interface featuring a temporal slab, defined by $A(t)$ as given in Equation (\ref{['AAA']}), with $\varepsilon_L=\varepsilon_R=1$, $L=0.16 c/\omega_0$, $\gamma=5 \cdot 10^{-3} \omega_0$, $\omega_i=0.3 \omega_0$, $\sigma=20/\omega_0$, and $t_d=0$. a) Polarization rotation angle $\varphi_r$ and phase angle $\delta_r$ of reflected wave at the resonance angular frequency $\omega_0$, as a function of the temporal slab width $\Delta t$. b) Linear-polarization spectra of reflected wave in the rotated reference system ($\tilde{R}_{x^\prime}$ and $\tilde{R}_{y^\prime}$; details in the text), for a temporal slab with $\Delta t = 9.34/\omega_0$. c) Circularly polarized spectra of reflected wave for a temporal slab with $\Delta t = 9.70/\omega_0$. All spectra are normalized to the peak value of the incident one.