Gouy phase-assisted Zeno effect for protecting light structure in random media

TL;DR

The paper tackles preserving information encoded in orbital angular momentum (OAM) of structured light as it travels through turbulent media. It introduces Gouy phase-assisted optical Zeno protection, using frequent Gouy-phase kicks—implemented via simple imaging systems like 2f or 4f setups—to induce a Zeno-like slowdown of mode cross-talk without destroying power in the initial OAM mode. The authors compare projective measurements and unitary kicks, showing that repeated Gouy-phase-induced kicks markedly suppress intermodal scattering and thereby maintain high OAM purity, with a regime distinction governed by the coherence length $r_0$ and kick spacing $\Delta z_k$. They provide a scalable framework including Laguerre-Gaussian mode descriptions, turbulence modeling via Kolmogorov statistics, and a dimensional analysis that maps experimental parameters to preserve disturbance characteristics. The work outlines practical routes for experimental verification and potential extensions to quantum regimes and other forms of structured light, underscoring the broad relevance of the Gouy-phase-assisted Zeno mechanism for robust information transmission in complex media.

Abstract

Identifying physical mechanisms that protect the information carried by various forms of structured light is one of the cornerstones of today's classical and quantum communications. Here we show that the purity of orbital angular momentum (OAM) modes can be protected against degradation in random media by leveraging two fundamental features of their own Schrödinger Hamiltonian dynamics, namely, Zeno effect -- frequent observations slow down the evolution -- , and Gouy phase -- the back-action of the observation. Repeated, OAM-dependent Gouy phase kicks imparted along the disturbing path by simple imaging systems trigger the optical Zeno effect that protects the input OAM mode against mode cross-talk that would broaden the OAM spectrum. Given the universality of the mechanism, the Gouy phase-assisted Zeno effect would protect propagation modes other than those of OAM, and the diverse forms of structured light built with them.

Figures (5)

• Figure 1: Zeno-protection of light propagating through environment. An image gets distorted when propagates through random medium (top), but preserves its spatial features when it frequently acquires intermodal Gouy phase shifts (bottom) via a $4f-$ system.
• Figure 2: Projective measurement-based Zeno effect in a turbulent medium. (a) In the absence of intermediate measurements, propagation of OAM-carrying light through a turbulent medium of $z_{\rm max}=18m$ results in an exponential decay of the mean survival probability. The inset shows the input $(\ell,p)=(1,0)$ mode and representative output intensity patterns. (b) Averaged over multiple trials OAM spectrum at $z=4.5m$ showing its characteristic broadening. The inset shows the helical phases of the respective subspaces $\Delta\ell$ is the difference between the azimuthal index of the output and input ($\ell=+1$) modes. (c) $N$ projective measurements (equally spaced along the propagation pass) suppress the mode cross-talk resulting in a slower decay of the survival probability. (d) The survival probability at $z=4.5m$ increases and its fluctuation due to the medium randomness decreases with more frequent measurements (larger $N$). Data: $w_0=3mm$, $C_n^2=3e-12m\tothe{-2/3}$, $l_0=w_0/20$, $L_0=500\cdot w_0$.
• Figure 3: ZE with unitary transformations. Decay of the mean SP for increasing number of (a) $\hat{U}_k$ with $\Phi=\pi$ and (b) $\hat{U}_k^{4f}$ (inset). (c) Averaged OAM spectra at the final plane for $N=2^{10}$$\hat{U}_k^{2f}$ (left) and $\hat{U}_k^{2f}$ (right) unitary kicks. The inset shows the phase difference $\Delta$ (rad) induced between initial $LG_{\ell_0,p_0}$ and adjacent modes: $\Delta=0$ (green), $\pm\pi/2$ (yellow) and $\pi$ (red). (d) SP at the final plane for increasing number of Gouy-phase kicks. Simulation data is the same as in Fig. \ref{['f1']}.
• Figure 4: ZE regimes in turbulent media and Zeno distances. (a) Free decay ($N=0$) of the SP for different beam widths $w_0=1.5mm$-green and $w_0=4.5mm$-blue. (b) Slowing down of the SP decay for increasing number of $\pi-\hat{U}_k$ for different initial widths $w_0$. (c) SP at the final plane for decreasing distance between kicks $\Delta z_k=z_{\rm max}/N$ (increasing kick frequency) and different initial widths $w_0$. (d) Weak and strong Zeno domains for different widths, the transition of which happens when $\Delta z_k$ is of the order of $r_0$. Simulation data is the same as in Fig. \ref{['f1']} with 400 random realizations.
• Figure 5: Decay of the survival power for increasing number of imaging systems $\hat{U}_k^{2f}$. The lower curve shows evolution without $\hat{U}_k^{2f}$, and the distance between consecutive $\hat{U}_k^{2f}$ is shown in the inset. Data $C_n^2=1.5e-16m^{-2/3}$, $z_{\rm max}=250m$, $w_0=4.5cm$, $\ell=1$, $p=0$. Results averaged over $400$ random realizations.