A new mathematical algorithm for representing the phase delay on uniform fiber Bragg grating (FBG) reflection by a three-straight-line approximation has been developed to facilitate the mathematical treatment of the FBG response. The validity of the approximation is numerically demonstrated. By means of the developed algorithm, the mode equation in a distributed feedback reflector (DBR) linear cavity has been analytically solved, to the best of the author’s knowledge, and thereby the single-mode operation of the cavity could be theoretically analyzed by tractable mathematics. It is found that the mode selectivity is dependent on the ratio of cavity spacing to FBG length, rather than the spacing itself. The developed algorithm numerically has revealed the mode selectivities that remain unknown in single-frequency DBR fiber laser studies to date.
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