# Generation of Orbital Angular Momentum Modes Using Fiber Systems
## 4 Advances in Fiber OAM Generation Systems  
### Fiber Grating-Based OAM Generation Systems  
Optical fiber gratings, a diffraction grating formed by the axially periodic refractive index modulation of fiber core using a certain method, have been developed into a mature technology and have been widely used in optical communications and fiber sensing in recent decades [55]. It is well-known that optical fiber gratings can be classified into two types, that is, fiber Bragg grating (FBG) [56] and long-period fiber grating (LPFG) [57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68], according to the grating period. The grating period of FBG is usually hundreds of nanometers or a few micrometers and the grating period of LPFG is usually hundreds of micrometers. In the FBG or LPFG, the fundamental mode in fiber core is coupled to the backward- or forward-propagating cladding mode or core mode at distinct wavelengths respectively. LPFG, written into a few-mode fiber, is the most commonly used an OAM conversion device. The working principle of the LPFG is the coupled mode theory. When the grating period satisfies the phase-matching condition \(\lambda_{m}=(n_{\mathit{eff1}}-n_{\mathit{eff2}})\lambda\), where \(\lambda_{m}\) is the resonant wavelength, \(n_{\mathit{eff1}}\) and \(n_{\mathit{eff2}}\) are the effective refractive index (ERI) of fundamental mode and higher-order core mode, respectively, the fundamental mode in the fiber core will be coupled to higher-order core mode, thereby leading to the transmission spectrum of the fundamental mode with one or a few notches, as shown in Figure 7c. Figure 6: (**a**) Interference patterns with different TCs, wave vectors and tilted degrees. The interference patterns of OAM beams (\(OAM_{-1},OAM_{-2},OAM_{-3}\)) with (**b**) the tilted plane light wave; (**c**) itself with a translation when the initial phase interference \(\phi_{s}-\phi_{f}=0\) or \(\pi\). There have been several methods used to fabricate an LPFG, including ultraviolet laser [57], femtosecond laser irradiation [58], CO\({}_{2}\) laser irradiation [59; 60; 61; 27; 32; 43; 27], cleaving-splicing method [62], arc discharge [63], acousto-optic interaction [64], mechanical micro-bending [31; 33; 34; 35; 65], and so on. The CO\({}_{2}\) laser irradiation and mechanical micro-bending are the two frequently-used methods to fabricate the LPFG to generate the OAM modes. The working principle of the mechanically induced LPFG is shown in Figure 7a. The few-mode fiber is placed between two plates with periodically grooves or between a plate with periodically grooves and a flat plate. When the period satisfies the phase-matching condition and putting pressure on the one of the two plates, the fundamental mode will be coupled to the higher-order core mode. The advantages of this method are that one can adjust the resonant wavelength or the order of coupled higher order mode, by adjusting the grating period. In addition, the length of the fiber under pressure, which controls the linewidths of the notch, can easily be changed. In addition, the depth of the notches can be tuned by adjusting the pressure. Finally, when the pressure is removed, the transmission spectrum of the fiber returns to its initial spectrum. The disadvantage of this method is some fiber cannot be used to fabricate an LPFG. Compared with the methods mentioned above, a high-frequency CO\({}_{2}\) pulse is an attractive tool used to fabricate an LPFG owing to its convenience, economy and high efficiency. As shown in Figure 7b, the CO\({}_{2}\) laser irradiation method uses a high-frequency CO\({}_{2}\) laser to continuously notch grooves on one side of the few-mode fiber to form a series of periodic structures. Because of the advantages of a CO\({}_{2}\) laser writing technique, the LPFGs can be successfully written into various types of special fiber, such as multi-core fiber [66] and photonic crystal fiber [67; 61], and different types of LPFG, such as a sampled or a chirped grating, can be inscribed in the fiber [68].