# A Review of Tunable Orbital Angular Momentum Modes in Fiber: Principle and Generation
## 4 Methods for Generation of Tunable OAM
### The Fiber-Based Generation of Tunable OAM  
For the fiber-based devices, the methods for tunable OAM mode generation can be classified into three types according to the adjusting schemes. Figure 9 simply shows schematic diagram usually used to generate the tunable OAM mode based on the fiber. The components marked by green arrows are the adjusted ones in the experiment. For the first type, the tunable OAM modes can be generated by the superposition of two orthogonal LP or HE (EH) modes with tunable relative phase difference between LP (HE) modes passing through a polarizer with a fixed direction. The flow chart of the mode generation is shown in Figure 10, and the yellow parts are the variations that need to be adjusted. The tunable OAM on the orbital PS can be generated by using the first four formulas, and the tunable OAM on the higher-order PS can be generated by the last one. Firstly, the LP\({}_{01}\) mode can be converted to LP\({}_{lm}\) mode by many kinds of mode converters, for example, photonic lanterns [57], mode selective couplers [58] and gratings [59]. The LP\({}_{lm}\) mode can be thought of as the combining result of LP\({}_{lma}\) and LP\({}_{lmb}\) without relative phase. The HE and EH modes can be directly generated by gratings with appropriate period [60]. When the converted two LP or HE (EH) modes pass through a length L of few-mode fiber (FMF), the relative phase between the two modes at the output of the FMF can always be written as \(\Delta\delta=\frac{2\pi\mathrm{L}\mathrm{Am}\mathrm{e}\mathrm{f}}{\lambda}\). The \(\Delta\)neff represents the RI difference between two modes and \(\lambda\) represents the operating wavelength. Thus, in order to achieve flexible control of the relative phase between the two modes in the fiber, changing the operating wavelength \(\lambda\)[61; 62] and the refractive index difference \(\Delta\)neff are two commonly used methods. So far, ways of controlling \(\Delta\)neff mainly depend on adjusting the pressure loaded on the fiber and rotating the paddles of few-mode polarization controller [63; 64; 65]. In addition, the LP\({}_{11}\) and LP\({}_{11}\)b can be generated by respectively injecting two LP\({}_{01}\) modes with slight horizontal and vertical displacement from the fiber axis and the relative phase can be controlled by using a piezo-driven delay stage [26; 27; 66]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Adjustable Variation** & **Reference** & **Device** & **The Type of Tunable OAM** \\ \hline Phase distribution & [17; 42; 43; 44; 45] & SLM & Orbital PS \\  & [46; 47] & SLM + QWP & Three PSs \\  & [51] & DMs & Orbital PS \\  & [52] & Q-plate & Hybrid-order PS \\ \hline Interference & [48; 49] & SLM & Higher- or Hybrid-order PS \\ \hline Input polarization & [50] & SLM + QWP & Higher-order PS \\  & [52; 53; 54; 55] & Q plate + SPP & Higher- or Hybrid-order PS \\  & [56] & Metasurface & Higher-order PS \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The free-space generation methods. Figure 9: A typical experimental setup based on fiber to generate tunable OAM modes. PC: polarization controller, MC: mode converter. The second type, the tunable OAM modes can be achieved by filtering the mixing modes which are produced by the combination of different vector modes or two spatially orthogonal LP modes owning orthogonal polarization directions with a \(\pm\pi\)/2 phase shift. The phase shift can be obtained in the same ways as mentioned above. Then, the continually tunable OAM can be achieved by adjusting direction of the polarizer at the output of the FMF [62, 63, 66, 67]. The specific process is shown in Figure 11 and the \"p\" is the angle between the direction of the polarizer and the positive direction of the x-axis.