Mode analysis of fiber Bragg grating random lasers in the presence of mode competition

In the presence of self and cross saturation effects, the laser governing equations are nonlinear. To solve the governing equations of a fiber Bragg grating random laser, on the basis of the transfer matrix method, a simple and fast iterative method is introduced. The method is employed to obtain the frequency, threshold pumping rate and spatial distribution of different laser modes. Numerical calculations show that by increasing the number of fiber Bragg grating, the number of lasing modes increases, while the threshold pumping rate of the first mode decreases. Our theoretical results are in agreement with the experimental observations reported by previous authors.