Reflection spectra of fiber Bragg gratings with random fluctuations

Fiber Bragg gratings (FBGs) with random fluctuations are investigated theoretically by using the coupled-mode theory. The fluctuation of the period causes interference inside the grating, which makes some light with wavelength inside the reflection bandwidth transmit through the grating and thus split the reflection spectrum. Simulation results show that low-frequency disturbed random fluctuation easily forms interference because the coupling wavelength in different position of the grating is different, while small high-frequency disturbed random fluctuation has almost no influence on the reflection spectrum and large high-frequency disturbed random fluctuation makes the grating incontinuous, which results in the interference. At the same time, a numerical method based on the fourth-order Runge–Kutta formula is developed to solve the coupled equations directly. By using this method, a grating with complex index modulation does not need to be treated as a superposition of a set of uniform grating with sinusoidal index modulation through the Fourier transform.