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Quantitative analysis for the cladding mode coupling in a linearly chirped fiber Bragg grating (FBG) with broad bandwidth is theoretically and experimentally demonstrated for the first time. It is found that due to the cladding mode effect, there exists a strong slope in the reflection spectrum, which could be larger than 5 dB within the 10-nm bandwidth of FBG. Based on this phenomenon, a novel temperature sensor working in the range of 17°C-181°C is first demonstrated by using a power-interrogation technique. Unlike most of the previous FBG-based sensors, here the proposed FBG is simultaneously utilized as both the sensing and the interrogating element.