Efficient generation of Second-order beam Based on angular modulated Long-period fiber grating

• A simple refractive index (RI) mudulation model is proposed to illustrate the RI modulation of CO 2 laser exposure. • This model illustrated the reason why traditional fabrication method using CO 2 laser is difficult to generate second-order mode. • Theoretical analysis shows that changing the RI modulation area from semicircle to sector with certain angle can significantly enhance the mode coupling between LP 01 and LP 21 modes. The theoretical analysis has been verified by experiments. • Finally, a second-order mode converter with low insertion loss of 0.27 dB and a high conversion efficiency of over 99.48% (corresponding spectrum dip is ∼ 22.83 dB) is achieved. Higher-order mode generation using long-period fiber grating (LPFG) has a lot of advantages such as simple structure and compatibility with optical fiber system. However, due to the large effective refractive index difference and very small cross-coupling coefficient between fundamental core mode and higher-order core modes in a few-mode fiber, it is difficult to achieve a high coupling efficiency and low insertion loss at the same time. In this paper, we demonstrated a simple model to illustrate the relationship between refractive index (RI) modulation and coupling coefficient in a CO 2 laser LPFG fabrication system. Theoretical analysis shows that changing the RI modulation area from semicircle to sector with certain angle can significantly enhance the mode coupling between LP 01 and LP 21 modes. We also proposed an easy way who can achieve an angular modulation to fabricate LPFG which could generate second-order modes with a high efficiency as well as a low insertion loss. Experimental results are in good agreement with theoretical analysis. Finally, we get a LPFG mode converter who has a conversion efficiency of over 99% and an insertion loss of only 0.27 dB. Furthermore, the CO 2 laser has almost no damage on the fiber structure. This fabrication method and analyzation model has a great guiding significance to regular the coupling coefficient and realize higher-order mode excitation in the future.