The theoretical model of etched fiber Bragg grating (FBG) backward cladding-mode resonances for ambient refractive index sensing is presented. The dependent behaviors of the mode resonances have been analyzed in the etching process and the ambient refractive index changed. The analysis is based on the classical coupling-mode theory while considering interactions among multiple modes and developed on a three-layer step-index fiber geometry. Experimental data match the theoretical model wonderfully. This model not only describes the relationship between the FBG backward cladding-mode resonances and the ambient index but also is valuable for the design of a flexible highly sensitive ambient index sensor.
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