A transmission filter composed of a Sagnac loop and a fiber Bragg grating is studied in detail. It is found that the transmission spectrum of this filter is the splitting of the reflection spectrum of the fiber Bragg gratings. The filter can behave as a multiple-passband filter when the fiber Bragg grating is strong and as a single-band filter when the fiber Bragg grating is weak. Very narrow transmission filters can be Obtained in this way.
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