Influence of random media on orbital angular momentum quantum states of optical vortex beams

Photonic orbital angular momentum (OAM) carrying orthogonal modes exhibits fascinating nature for information encoding. Here we focus on the propagation of OAM states in random media to investigate the turbulence-induced OAM degradation. We utilize the quadratic approximation of the phase structure function to derive a global continuous expression of OAM probability at the single-photon level. The expression provides a general insight into the energy transition between signal and crosstalk modes in random media. Especially for each crosstalk mode, our expression is accurate in predicting the second-order energy transition. The effectiveness of our model is validated via experimental data and simulations in various random media. We also reveal the universality of entangled optical vortex beams and obtain an expression of concurrence. It is demonstrated that utilizing high-order optical vortex beams can effectively improve the antijamming ability and enhance the propagation distance of entanglement. Our results provide a universal framework for OAM propagation through different random media.

Figure 1

Illustration of using the purely phase perturbation model to simulate the propagation of OAM state through random media.

Figure 2

Signal ($\mathrm{\Delta }l=0$) detection probability calculated by different expressions as a function of $D/{\rho }_0$.

Figure 3

(a) Crosstalk probabilities calculated by different expressions of the $\mathrm{\Delta }l=1$ mode as a function of $D/{\rho }_0$. (b) Crosstalk probability of different $\mathrm{\Delta }l$ as a function of $D/{\rho }_0$, where results of Eqs. (4) and (10) are displayed as discrete data points and lines, respectively.

Figure 4

OAM spectra after (a) atmospheric turbulence (real world, $l_0=1$, the green-colored region denotes the fluctuations of ${\rho }_0$), (b) oceanic turbulence (lab, $l_0=-3$), (c) atmospheric turbulence (“Theory” part is calculated according to Ref. [3], and “Simulation” part is obtained by extended Huygens-Fresnel principle, $l_0=1$) and (d) maritime atmospheric turbulence (dashed blue line) and biological tissue (dot-dashed red line) (numerical simulation, $l_0=1$, colored regions denote the results of multiple simulations). The theory curves are calculated by Eq. (10).

Figure 5

(a) Concurrence $C$ and (b) relative crosstalk amplitude $\tilde{b}$ as a function of $\zeta \left(l_0\right)/{\rho }_0$ for different OAM modes. The discrete data points are calculated by Eq. (15), and the solid line is calculated by Eq. (17).