## 3 Results and Analysis  
The proposed design is investigated in the OptiSystem simulation software. The system's performance is evaluated for four downlink wavelengths (1596, 1596.8, 1597.6, and 1598.4 in nm) and four uplink wavelengths (1524, 1524.8, 1525.6, and 1526.4 in nm) at the LP[0,1] mode. Clear air and weak turbulence under the Gamma\(-\)Gamma model are considered. The atmospheric turbulence and different weather conditions can lead to several detrimental effects, like beam wander, optical loss, angular fluctuation, and received-signal fluctuations, which result in a deteriorated system performance and an increase in BER. Additionally, atmospheric turbulence arises owing to wind pressure and temperature gradients causing random air density fluctuations, temporal phases, and spatial distortions in LP modal systems. In optical networks, the BER is a dominant performance metric, which quantifies the bit error probability owing to interference and noise over a fiber-PSO channel. The \(BER\) performance of the system is expressed as follows [18]:  
\[BER=\frac{1}{2}erfc\sqrt{\frac{Signal\ to\ Noise\ Ratio}{8}} \tag{1}\]  
where \(erfc\) means complementary error function. In the GIMMF link, losses are generated owing to four-wave mixing effects in the fiber, which is quite less compared to other systems where the bidirectional fiber is used instead of separate fibers. However, the GIMMF link enhances the system's capacity. Four-wave mixing (FWM) is a nonlinear optical effect that occurs in multi-wavelength systems. Due to the interaction of multiple optical signals in an optical fiber, new frequency signals are generated. The FWM effect degrades the system's performance by introducing crosstalk and unwanted interference. Mathematically, generated FWM wavelengths are expressed as follows [19]:  
\[\lambda_{FWM}=\lambda_{1}\pm\lambda_{2}\pm\lambda_{3}\pm\lambda_{4} \tag{2}\]  
and the number of generated FWM wavelengths \(M\) are described as follows [19]:  
\[M=\frac{N^{2}}{2(N-1)} \tag{3}\]  
As shown in Figure 3a,b, multiple wavelengths are generated in addition to the main four lobes for both the downlink and uplink transmissions. Here, the launch power of 10 dB decreases to \(-10\) and \(-5\) dBm after transmission in the DN and UP directions, respectively, over a 5 km fiber and a 100 m FSO link. The maximum number of generated modes due to FWM in the DN and UP directions is three at a \(-100\) dB noise floor. It is also depicted that the DN transmission is more susceptible to the FWM effect comparedto the UP transmission, as L-band (1565-1625 nm) wavelengths are more affected by fiber nonlinearity compared to C-band (1530-1565 nm) wavelengths. Figure 4a,b depict the BER performance of all downlink and uplink wavelengths operating at the LP[0,1] mode at a 10 Gbps per channel data rate. As shown in Figure 4a, the BERs of all downlink wavelengths are below the \(1\times 10^{-9}\) BER limit when the distance is not more than 5.5 km at 1596 nm, 5.45 km at 1596.8 nm, 5.4 km at 1597.6 nm, and 5.47 km at 1598.4 nm. Also, for the uplink wavelengths, viz., 1524, 1524.8, 1525.6, and 1526.4 nm, the reliable GIMMF distance is 5.5 km, as shown in Figure 4b. The results demonstrate the successful transmission of the four downlink and four uplink signals, showing the considerable potential to enhance the communication capacity of PONs. For the 1524 nm wavelength, deviation in the BER performance is obtained owing to the  
Figure 3: Obtained spectra at 10 dBm input power for (**a**) downlink and (**b**) uplink transmission over a 5 km range. impact of atmospheric effects (air and weak turbulence), modal dispersion, inter-symbol interference (ISI), geometric loss, and fiber nonlinearities over the large coverage. With the increase in fiber distance, the signal quality deteriorates owing to the impact of MMF fiber nonlinearity, spatial connectors, and thin lens losses. The sharp increase in BER at 1597.6 nm beyond 5.4 km is due to the presence of fiber nonlinearities, dispersion, and atmospheric absorption in the free space.