## 4 Results and Discussion  
Figure 7 illustrates the impact of varying receiver aperture diameter and beam divergence on the received power per mode in the MDM-FSO link. Figure 7a examines the effect of changes in receiver aperture diameter on the received power per mode. A significant increase in received power is observed as the receiver aperture size increases. The power ratio penalties across the three mode channels can be attributed to two primary factors: multipath dispersion and optical path loss. Consequently, careful optimization of the receiver aperture size is essential, as improper selection may adversely affect the power distribution among the transmission modes. Figure 6: (**a**) MDM power spectra after 13 km transmission; (**b**) variation of mode power with wavelength. Figure 7: (**a**) Variation of receiver aperture diameter on the received power per mode. (**b**) Effect of variation beam divergence on individual received mode power. Figure 7b shows the effect of beam divergence variation on the received power per mode for the three MDM-FSO channels. The analysis reveals that the power penalty increases with the number of modes. For instance, at a reference beam divergence of 2 mrad, the LP01 mode exhibits a received power of \(-13.78\) dBm, while the LP11 and LP02 modes show received powers of \(-14.31\) dBm and \(-16.8\) dBm, respectively. This demonstrates that as beam divergence increases, the power received by higher-order modes is more significantly impacted, which must be taken into account when designing the MDM-FSO system. Figure 8a examines the impact of varying transmitter loss on the received power per mode. As transmitter loss increases, the energy received per mode decreases, indicating the need for careful optimization to select an appropriate value for transmitter loss to prevent performance degradation. In this study, the desirable value for transmitter loss is found to be approximately 0.6 dB for all three modes, at which point the transmission power received by the modes is maximized. Figure 8b presents the signal-to-noise ratio (SNR) and maximum received power for the proposed MDB-MDM-FSO link model. The system performance was evaluated under clear weather conditions, demonstrating the potential of the link to deliver high-quality signal reception in ideal environmental conditions. As shown in Figure 8b, the SNR for the LP01 mode is calculated to be 37.13 dB, 36.11 dB, and 34.13 dB for transmission distances of 2 km, 4 km, and 12 km, respectively. For the LP11 mode, the SNR values are 35.11 dB, 33.12 dB, and 27.56 dB, while for the LP02 mode, the calculated SNR values are 27.11 dB, 24.11 dB, and 17.13 dB at the same distances. This significant difference may be due to factors like mode crosstalk or fiber loss, indicating that the LP01 mode better preserves signal integrity. Mode crosstalk is one possible explanation. In MMFs, higher-order modes like LP02 tend to interact more with other modes, leading to increased interference and reduced signal fidelity. Additionally, the LP01 mode generally has a lower effective refractive index, which provides a more uniform light distribution. In contrast, the complex field distribution of the LP02 mode can result in greater coupling into the cladding, causing losses from scattering and absorption as distance increases. Other factors, such as the operating wavelength and fiber design, also influence modal behavior. For instance, in high-bandwidth fibers, the choice of mode can significantly impact the SNR. In essence, while mode crosstalk and fiber loss help explain the difference in SNR between the LP01 and LP02 modes, further investigation is needed to quantify their effects. Understanding these dynamics is crucial for optimizing performance in FMF applications as network demands rise. Figure 8c illustrates the total received power for each mode. For the LP01 mode, the received power is \(-13.24\) dBm, \(-13.57\) dBm, and \(-14.24\) dBm at 2 km, 4 km, and 12 km, respectively.