Theoretical and experimental investigation of the mode-spacing of fiber Bragg grating Fabry-Perot cavity

The mode-spacing of the fiber Bragg grating Fabry-Perot (FBG F-P) cavity is calculated by using the effective cavity length which contains the effective length of the FBG. The expression of the effective length, defined by using the phase-time delay, is obtained and simplified as a function of the peak reflectivity at the Bragg wavelength, the band edges, and the first zero-reffectivity wavelength. The effective length is discussed from the energy penetration depth point of view. Three FBG F-P cavities are fabricated in order to validate the effective length approach. The experimental data fits well with the theoretical predictions. The limitation of this method is also pointed out and the improved approach is proposed.