## 4 Experimental Results
### MMF-Based Optical Beam-Shaping  
Altering the spatial intensity distribution of a Gaussian beam offers an intuitive approach to addressing inhomogeneities. In this context, a segment of MMF is introduced between the SMF pigtailed laser source and the emitting collimator. By intentionally perturbing the transmission matrix of the MMF, the optical beam can be adaptively focused on any desired position within the coverage area. To assess the bit error rate (BER) performance across the coverage area, an experimental setup, as depicted in Figure 8, is implemented utilizing the MMF-based optical transmitter. Figure 6: Experimental setup for measuring ROP distribution of a divergent Gaussian beam. C1: Emitting collimator; C2: Receiving collimator; OPM: Optical power meter. Figure 7: Theoretical and experimental ROP distribution of Gaussian beams. Initially, a Mach-Zehnder modulator (MZM, Fujitsu, FTM7937 EZ) modulates the 10 Gbps baseband signal generated by a bit-error tester (BERT, 10 Gbps multi-channel BER tester, Luceo) onto the 1550 nm optical beam emitted by the laser source (Santec, MLS-2100). The modulated optical signal is then amplified through an Erbium-Doped Fiber Amplifier (EDFA, Amonics, AEDFA-BO-13) to 10 dBm. Next, the signal is directed into a 5 m long multi-mode patch cable (OM1 62.5/125 um graded-index, Thorlabs, GIF625) with a radial offset distance of around 30 um. The MMF is carefully wound around three three-paddle polarization controllers (nine control units in total, Thorlabs, FPC560). The optimized ROP is obtained by sequentially adjusting the rotation angle of each paddle in iterations. Then, the modulated optical signal is emitted into free space via the emitting collimator (Thorlabs, F810 FC-1550) and the divergent lens (Thorlabs, AL2520M-C). After 2.5 m free-space transmission, the optical beam covers an area of 0.61 m\({}^{2}\), and a receiving collimator (Thorlabs, C40 FC-C) is applied to capture the incoming light and then project it into another multi-mode patch cable (OM4 50/125 um graded-index, Thorlabs, GIF50E). The light coupled by the OM4 multi-mode patch cable is directly input into an MMF-PIN device (Thorlabs, DXM12 DF), enabling optical-to-electrical (O/E) conversion. The received electrical signal is then compared to the transmitted electrical signal using the BERT, allowing for the counting of error bits. The optimization process for MMFs is iterative, requiring the measured ROP at each iteration to be transmitted back to the transmitter side until the desired target ROP is achieved. The optimized ROPs from 0 to 10\({}^{\circ}\) (1\({}^{\circ}\) interval) at a transmission distance of 2.5 m are sequentially measured. Figure 9a shows the great homogenizing ability of MMF-based optical transmitters, and the optimized ROP variance within the coverage area is less than 2 dB. In contrast, SMF-based transmitters exhibit a significant ROP variance of 10 dB, owing to the Gaussian-shaped intensity distribution. Furthermore, at a 0 degree receiving angle, a notable ROP gain of 5.9 dB is observed, with the gain further increasing as the receiving angle expands. At a receiving angle of 10\({}^{\circ}\), the ROP gain reaches 12.9 dB. This enhanced ROP substantially reduces the sensitivity requirements of direct detection receivers. Using a simple PIN-TIA photodiode as the O/E device without any optical pre-amplification, the BER performance of a 10 Gbps LOS OWC system through 2.5 m free-space transmission (Receiving angle = 8\({}^{\circ}\)) and an optical back-to-back link without free-space transmission are compared in Figure 9b. Remarkably, the MMF-based beam-shaping approach has a negligible ROP penalty (<0.2 dB), and the penalty may mainly caused by optical distortion at the edge of receiving lenses. We can conclude that the proposed scheme enables a 10 Gbps error-free transmission over an angular coverage of 10\({}^{\circ}\)\(\times\) 10\({}^{\circ}\) at 2.5 m.  
Figure 8: The MMF-based optical transmitter in OWC.