Analytic solution for cascaded long-period fiber gratings

The analytic expression for the transmission spectrum of cascaded long-peri od fiber gratings is presented in a closed form. When several identical gra tings are cascaded in-series with a regular distance, the transmission spec trum is revealed to have a series of regularly spaced peaks, suitable for m ulti-channel filters. The analytic solution is obtained by diagonalizing th e transfer matrix of each grating unit that is composed of a single grating acid a grating-free region between adjacent gratings. The spectrum of the device is simply described with the number of cascaded gratings and a singl e parameter that has the information of the phase difference between the mo des. With the derived equation, the spectral behaviors of the proposed devi ce are investigated. The intensity of each peak can be controlled by adjust ing the strength of a single grating. The separation between adjacent grati ngs determines the spacing between the peaks. The finesse of the peaks can be increased by cascading more gratings. The derived analytic results are c ompared with the known results of paired gratings and phase-shifted grating s.