Analysis for reflection peaks of multiple-phase-shift based sampled fiber Bragg gratings and application in high channel-count filter design

摘要

An analytical expression for calculating the reflection-peak wavelengths (RPWs) of a uniform sampled fiber Bragg grating (SFBG) with the multiple-phase-shift (MPS) technique is derived through Fourier transform of the index modulation. The new expression can accurately depict the RPWs incorporating various parameters such as the duty cycle and the DC index change. The effectiveness of the derived expression is further confirmed by comparing the RPWs estimated from the expression with the simulated reflective spectra using the piecewise uniform method. And the reflective spectrum has been well optimized by introducing the Gaussian apodization function to suppress the sidelobes without any wavelength shift on the RPWs. Then, a high-channel-count comb filter based on MPS is proposed by cascading two or more SFBGs with different Bragg periods but with the same RPWs. Noticeably, the RPWs of the new structured SFBG can also be accurately calculated through the expression. Furthermore, the number of spectral channels can be controlled by choosing gratings with specified difference Bragg periods.