Satellite-to-ground optical downlink model using mode mismatching multi-mode photonic lanterns

Photonics lanterns (PLs) provide an effective mode diversity solution to mitigate atmospheric turbulence interference in free-space optical communications (FSOC). This paper presents mode-mismatching multimode photonic lanterns (MM-PLs) for diversity receiver in satellite-to-ground downlink scenarios. Our study evaluates the coupling characteristics of the mode-selective PLs (MSPLs) and non-mode-selective PLs (NSPLs) for the influence of strong-to-weak turbulence and confirms that MSPLs outperform NSPLs under weak turbulence conditions. The research further explores the impact of fiber position error (FPE) on the spatial light-to-fiber coupling, including the optimal focal length deviation and lateral offset of receiving fiber devices. We have calculated and compared the coupling power and signal-to-noise ratio (SNR) of few-mode PLs (FM-PLs) and MM-PLs for various turbulence intensities. The results indicate that the optimal focal length tolerance, which corresponds to a decrease of approximately 1 dB in the average coupling power, is 2-3 m and 5-6 m for FM-PLs and MM-PLs, respectively. Furthermore, regardless of whether it is strong or weak turbulence, MM-PL exhibits a lateral offset tolerance exceeding 12 µm for a 0.5 dB drop in the mean coupled power, whereas the lateral offset tolerance of FM-PL is only 3 µm under weak turbulence. Additionally, the decrease in the average SNR of MM-PLs is gentle, only 0.67-1.16 dB at a 12 µm offset under weak turbulence, whereas there is a significant reduction of 6.50-8.49 dB in the average SNR of FM-PLs. These findings demonstrate the superiority of MM-PLs over FM-PLs in turbulence resistance and fiber position tolerance in the satellite-ground downlink.