Higher order modes are detrimental for distributed feedback (DFB) fiber lasers. The thresholds of these modes are calculated as functions of gain, loss, and various types of grating defects, like harmonic, linear, quadratic,and random chirp, and discrete phase errors. The higher order modes are particularly enhanced by high gain, quadratic chirp, and discrete phase errors close to the center of the grating.
Sigurd Weidemann Løvseth and Erlend Rønnekleiv, "Fundamental and Higher Order Mode Thresholds of DFB Fiber Lasers," J. Lightwave Technol. 20, 494- (2002)