Atmospheric Turbulence and Orbital Angular Momentum of Single Photons for Optical Communication

The effects of propagation through random aberrations on coherence for single-photon communication systems based on orbital angular momentum states are quantified. A rotational coherence function is derived which leads to scattering equations for azimuthal modes of different orbital angular momentum states. The effect on a single-photon communication system is quantified using the channel capacity. The work shows that the decoherence effect of atmospheric turbulence on such systems is important even for weak turbulence.

Figure 1

Example intensity (gray scale) and phase map ($\pi /4$-spaced contours) of a pure ${\mathrm{LG}}_1^0$ beam (left) and the same beam with aberrations caused by propagation through Kolmogorov turbulence (right).

Figure 2

OAM scattering coefficients $\Theta (r,\Delta l)$ between modes $l_0$ and $l_0\pm \Delta l$ for an annulus of radius $r$ in a beam for aberrations with Fried parameter $r_0$. The $\Delta l=0$ plot corresponds to the unscattered light.

Figure 3

Probabilities of obtaining different OAM measurements $P(l=l_0\pm \Delta l)$ for a ${\mathrm{LG}}_1^0$ beam plotted against the ratio of the Gaussian beam width parameter $b$ to the Fried parameter $r_0$. The probability of obtaining the original eigenvalue ($\Delta l=0$), i.e., the correct signal, decreases rapidly as the Fried parameter becomes comparable to the beam width parameter. There is a corresponding increase in the probabilities of obtaining OAM measurements different from the initial eigenvalue ($\Delta l\ne 0$), with those corresponding to adjacent azimuthal modes increasing most rapidly.

Figure 4

Probabilities of obtaining the original eigenvalue $P(l=l_0)$ for several different LG beam modes plotted against the ratio of the rms beam radius $r_{p,l}$ to the Fried parameter.

Figure 5

Plots of the channel capacity for a communication link employing OAM states of single photons for different numbers of OAM states $l=-L,\dots ,L$ using LG beams ${\mathrm{LG}}_l^p$. The dashed line shows the capacity for a polarization-based channel (two-state) for comparison.