# Generation of Orbital Angular Momentum Modes Using Fiber Systems
## 4 Advances in Fiber OAM Generation Systems
### Fiber Grating-Based OAM Generation Systems
The OAM modes obtained by [34; 35; 37; 43] are all generated by a combination of two or four degenerated modes in the same mode group and the associated eigenmodes must maintain a stable phase and polarization. In addition, in ideal cylindrical waveguides such as fiber, the propagation constants of the \(TE_{01}\) and \(TM_{01}\) mode are different. For example, the effective index separation between the \(TE_{01}\) and \(TM_{01}\) mode is measured to be 6.6 \(\times\) 10\({}^{-4}\) in the fiber [36]. The purity of CP-OAM generated by combination of \(TM_{01}\pm iTE_{01}\) or \(HE_{21}^{even}\pm iTE_{01}\) cannot be maintained when the length of optical fiber is changed. However, the OAM modes generated by a single CV mode don't have this problem. However, the generated OAM modes obtained by the studies mentioned above are dependent on the polarization state of the input light, namely, these all-fiber generators exhibited a sensitivity requiring specialized polarization states for the input light without adjusting the PC. [PERSON] et al. have proposed a polarization-independent OAM generator based on a chiral fiber grating (CFG) fabricated by twisting a fused few-mode fiber during hydrogen-oxygen flame heating [44]. They experimentally fabricate a left-handed CFG (LCFG) and a right-handed CFG (RCFG) to convert the fundamental mode to the OAM mode, and experimentally investigate the polarization characteristics, helical phase of the coupled mode in CFG for varying polarization state of input light. Their results showed that the coupled OAM mode had the same polarization state with the input fundamental mode. And the chirality of the generated OAM mode was polarization-independent and determined solely by the helicity of the CFG, as shown in Figure 9. The OAM mode generated by the RCFG can only be \(OAM_{+1}\) mode, while OAM mode generated by the LCFG can only be \(OAM_{-1}\) mode. Compared to other mode converters, LPFGs have many advantages, such as low loss, small size, easy fabrication, and high coupling efficiency up to 99%, and so on. However, LPFGs also have many disadvantages compared with the mode selective coupler and the photonic lantern, for example, the narrow bandwidth and one LPFG can only convert the fundamental mode (the zeroth order mode) to a phase-matching higher order mode. Thus, there have been many attempts to increase the bandwidth of an LPFG, such as chirped LPFG [69], length-apodized LPFG [70], the cascading of several LPFGs [43], operating an LPFG at its turning point along its phase-matching curve [71], shortening the length of the LPFG, namely decreasing the number of grooves [72], and so on. However, chirping can significantly decrease the mode conversion efficiency and the bandwidth increase is still limited. For LPFG operating at its turning point, such a turning point may not exist for a given set of guided modes. For shortening the length of LPFG, it will decrease the coupling efficiency. For the cascading of several LPFGs, for example, the bandwidth of cascading two LPFGs that one LPFG convert fundamental mode to the first order mode and the other LPFG convert the first order mode to the second order mode is wider than the bandwidth of LPFG that directly converts fundamental mode to the second order mode [43], However, this method needs the fabrication of several LPFGs, which brings about extra loss.