Why can a tilted grating sense changes in the surrounding liquid?
Tilted Fiber Grating (TFG or TFBG) can sense external liquid variations. Its core physical mechanism stems from cladding mode coupling induced by broken spatial symmetry.
1. Why ordinary Fiber Gratings (FBG) cannot sense liquids?
In a standard ordinary Fiber Grating, the grating fringes are perpendicular to the fiber axis (i.e., tilt angle \theta = 0^\circ ).
Under this configuration, the forward-propagating core fundamental mode ( LP_{01} mode) can only couple to the reflected core fundamental mode propagating backward. Since the electromagnetic field energy of the core fundamental mode is highly concentrated within the fiber core (typically only about 9\ \mu\text{m} in diameter), which is surrounded by a thick glass cladding (typically 125\ \mu\text{m} in diameter). Variations in the refractive index of the external liquid and environment cannot affect the optical field inside the core at all, making ordinary FBGs completely insensitive to external liquid refractive indices.
2. “Broken Symmetry” and Cladding Mode Coupling in Tilted Gratings
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