Mode coupling at an imperfect Fresnel surface in a fluorine-trench dual-mode fiber

Mode coupling, often overlooked at an imperfect Fresnel surface, is now examined in a fluorine-trench dual-mode fiber to avoid energy losses and signal degradation. For invisible defects on the reflecting surface, the orthogonal forward LP₀₁ (LP₁₁) mode with group velocity v_g^LP₀₁ (v_g^LP₁₁) partially converts to the backward LP₁₁ (LP₀₁) mode with v_g^LP₁₁ (v_g^LP₀₁) through a transfer matrix, respectively. Consequently, this interaction generates a unique hybrid backward mode, which results in an average round-trip time delay and the mean of the velocities, (v_g^LP₀₁ + v_g^LP₁₁)/2. Upon harvesting and analyzing the backward reflections using a high-resolution coherent optical frequency domain reflectometry, a Fresnel reflection peak corresponding to the hybrid mode is observed with a high signal-to-noise ratio precisely between the LP₀₁ and LP₁₁ peaks. Additionally, the frequency difference between the hybrid and LP₀₁ (or LP₁₁) modes is calculated to be 20.625 Hz exactly half of the 41.250 Hz difference between the LP₀₁ and LP₁₁ modes. Further testing on five additional fiber segments ranging from 8.812 m to 10.812 m corroborates this theory, as their v_g^hybrid values align closely with (v_g^LP₀₁ + v_g^LP₁₁)/2. Our analytical insights detail the dynamic mode coupling at an imperfect Fresnel surface, promising a flexible method for dynamic mode observation and regulation for mode division multiplexing optical fiber communications, particularly in enhancing the detection and mitigation of defects at fiber lasing end faces.