Modal Diversity for Robust Free-Space Optical Communications

Free-space communication links are severely affected by atmospheric turbulence, which causes degradation in the transmitted signal. One of the most common solutions to overcome this is to exploit diversity. In this approach, information is sent in parallel over different paths using two or more transmitters that are spatially separated, with each beam therefore experiencing different atmospheric turbulence, lowering the probability of a receive error. In this work we propose and experimentally demonstrate a alternative method of diversity based on spatial modes of light, which we call modal diversity. We remove the need for a physical separation of the transmitters by exploiting the fact that spatial modes of light experience different perturbations, even when traveling along the same path. For this proof-of-principle, we select identical radius modes from the Hermite-Gaussian and Laguerre-Gaussian basis sets and demonstrate an improvement in bit error rate by up to 54% without increasing the total transmit power or receive aperture radius.

Figure 1

Illustrative comparison of spatial multiplexing that is used for increased bandwidth (top left), conventional spatial diversity that is used for increased robustness (top right), and our modal diversity scheme that does not require path separation (bottom). In conventional diversity the transmitted beams, irrespective of mode, take different paths separated by some distance greater than $r_0$. In modal diversity, different modes are used with half the original transmit power ($g_i$) but with each traveling the same path: the separation is in mode space not physical space.

Figure 2

Experimental demonstration of the orthogonality of ${\mathrm{HG}}_2^2$ and ${\mathrm{LG}}_2^1$ modes with no turbulence ($\mathrm{SR}=1.0$ or $D/R_0<0.01$) and slight turbulence ($\mathrm{SR}=0.95$ or $D/r_0=0.05$) with measurement points shown as +. On the left, only an ${\mathrm{HG}}_2^2$ is transmitted and it is clear that there is no ${\mathrm{LG}}_2^1$ component after modal decomposition. Similarly, on the right there is an ${\mathrm{LG}}_2^1$ component but no ${\mathrm{HG}}_2^2$ component in the decomposed beam.

Figure 3

Experimental setup showing two transmitters and a single receiver for transmit diversity with example turbulence as an inset (a). The holograms along the bottom are for (b) generating an ${\mathrm{LG}}_{\ell =2}^{p=1}$ beam, (c) generating an ${\mathrm{HG}}_{n=2}^{m=2}$ beam, and (d) superposition for decomposition of the generated LG and HG beams to a single detector. The flat gray areas on the holograms is due to complex amplitude modulation.

Figure 4

Bit error rate of modes with order $N=4$ and 8, where $D=1.4$ and 1.98 mm, respectively, with varying turbulence strength showing a clear improvement for the diversity cases. Larger modes are expected to experience lower turbulence in comparison to smaller modes.

Figure 5

Bit error rate of modes with order $N=4$ and 8, with varying turbulence strength in terms of the Strehl ratio for $D=1.4\mathrm{mm}$. The diversity case is typically better than the nondiversity cases with significant gains in weaker turbulence.