Optimal modes for spatially multiplexed free-space communication in atmospheric turbulence

Abstract

In near-field free-space optical (FSO) communication, spatial-mode multiplexing (SMM) increases transmission capacity by transmitting independent information streams in orthogonal modes. Propagation through atmospheric turbulence causes phase and amplitude distortions that can degrade SMM performance. In this paper, we show there exist optimal modes for transmission through turbulence with minimum degradation, under a realistic assumption that a transmitter knows the turbulence statistics but not the instantaneous state of the atmosphere. These modes are determined by performing a Karhunen-Loève expansion of the optical electric field in the receiver aperture. We show that these modes are Laguerre-Gauss (LG) modes whose beam waist is chosen depending on the field coherence length in the receiver plane. These adaptive-waist LG modes, when ordered by decreasing eigenvalue, can approximate a received signal field by a finite number of modes with lowest mean-square error among all orthonormal mode sets. Hence, they represent optimal transmit and receive bases for SMM FSO. Using numerical simulation, we study SMM FSO transmission at various turbulence strengths and signal-to-noise ratios. We compare the performance using the adaptive-waist LG modes to that using fixed-waist LG modes (which assume no knowledge of turbulence statistics) and instantaneous eigenmodes (which assume knowledge of the instantaneous state of the turbulence). We also study the performance using the orbital angular momentum subsets of the adaptive-waist LG mode and fixed-waist LG mode sets.