## 3 Architecture of Hybrid OAM-DM-WDM-OFDM-PON System  
The configuration of the hybrid OAM-DM-WDM-OFDM-PON system with two OAM modes (\(LG_{l=0,p=2}\) and \(LG_{l=0,p=4}\)) over 10-80 km MMF is simulated using Synopsis OptSim as shown in Figure 2a. Here, a classic PON with splitters and one fiber per OLT port is used in the proposed system. It consists of an optical line terminal (OLT), optical fiber link, and optical network unit (ONU). Otherwise, two OAM modes, which have a relatively large effective refractive index difference between each other, are transmitted in MMF, so mode crosstalk would suffer little mode crosstalk. In Figure 2a, OFDM modulation is adopted in the downstream link and the OOK re-modulation technology is used in the upstream link, respectively. In addition, the spatial demultiplexer is used at the receiver, which can de-multiplex spatial signal channel according to wavelength and then separates out all spatial modes associated with each wavelength. There are many ways to generate OAM mode, such as helical phase plate, spatial light modulator, etc. In our work, the LG mode generation method is depicted in Figure 2b. The Laguerre Transverse Mode Generator device is employed, which attaches Laguerre-Gaussian transverse mode profiles to the input Gaussian mode \(x\) and \(y\) polarizations. It's worth noting that the X and Y indexes describe the azimuthal and radial indexes, respectively. The list of mode indexes for each polarization, as well as the spot size and the inverse of the radius of curvature for each mode are also provided. Obviously, the LG mode can be generated successfully with this device. And the transverse electric field intensity of the \(LG_{l=0,p=2}\) and \(LG_{l=0,p=4}\) mode is shown in Figure 3a,b, respectively. A and B represent the optical vortex radius. Due to the optical vortex, the penal shapes are achieved at the mode center and the central ring becomes larger as the radial value \(p\) increases, while the central light intensity gradually decreases, as plotted in Figure 3. Figure 3a,b are the 3D diagram with the transverse mode of \(LG_{l=0,p=2}\) and \(LG_{l=0,p=4}\) signal, respectively. The X(m) and Y(m) denote \(x\) and \(y\) polarization. The colorbar is the normalized optical field intensity distribution corresponding to Figure 3c,d. The employed MMF in the downstream link is a conventional \(Yb^{3+}\) doped multimode fiber with a step-index profile. The radii and refractive index of the fiber core are 3.4 \(\upmu\)m and 1.45, respectively. Yb doping radius is 3.4 \(\upmu\)m as well. Additionally, the standard of the single-mode fiber (SMF) fiber in the upstream link is ITU-T G.652D with dispersion coefficient for 1550 nm about 16.75 ps/nm \(*\)km. OOK re-modulation is used for the upstream link. Therefore, the system structure is simplified and source-free ONU is realized owing to the modulation process without a new optical source. At the OLT side, two random binary sequences with a 10 Gbps data rate are provided by pseudo-random binary sequences (PRBS) generator for each wavelength and then entered into a 4-QAM generator with 2-bits per symbol sequence. Subsequently, the output 4-QAM signal is transmitted to the OFDM modulator for mapping 512 subcarriers, 1024 FFT points, and 64 cyclic prefix points. As shown in Figure 4a, the power of OFDM modulation signals is 30 dBm at both 20 GHz and 40 GHz. After the OFDM modulator, the signal gets into the quadrature modulator (QM) with a 7.5 GHz frequency through the low pass cosine roll-off filter. Both the downstream and the upstream frequencies (193.1 THz and 193.2 THz) are set with an interval of 100 GHz. These frequencies are emitted by utilizing pairs of continuous wave (CW) lasers with a linewidth of 0.01 MHz. Besides, the Gaussian mode is converted to LG mode carrying a special radial index \(p\) in a Laguerre Transverse Mode Generator. The LiNbO3 Mach-Zehnder modulator (MZM) has three input ports comprising LG mode and two electrical signals from QM.