光纤布拉格光栅及其构成的法布里-珀罗腔的相位谱特性研究

Investigation on Phase Spectra of Fiber Bragg Gratings and the Constructed Fabry-Perot Cavity

光纤光栅的相位谱对光纤光栅法布里-珀罗(F-P)腔的光谱特性有重要影响。对光纤布拉格光栅(FBG)光谱,特别是FBG相位谱进行了深入分析,推导了低反射率FBG的线性相位谱的一般表达式,提出了高反射率FBG的三段线性相位近似方法,得到了简洁直观的相位谱数学表达式。然后采用和普通F-P腔对比的方式,以等效腔长的概念分析了FBG构成的F-P(FBG-FP)腔相位谱特性,并讨论了拟合法、周期法和傅里叶变换法这3种常用的FBG-FP腔长估计算法。设计了FBG-FP腔光谱测量方案,得到了高精度的光谱曲线,对比分析了前述3种腔长估计方法的计算结果,验证了理论分析的正确性。

Phase spectrum of fiber Bragg grating （FBG） has a major effect on spectral characteristics of the constructed Fabry-Pérot （F-P） cavity. By the analysis of spectral characteristics of an FBG, especially its phase spectrum, the linear phase spectrum of a weak grating is derived. Furthermore, the three-segment linear approximation is proposed for strong gratings with a concise expression. Then, based on the deduced analytic expressions of phase spectra, spectral characteristics of FBG based Fabry-Pérot （FBG-FP） cavities are investigated by the conception of effective cavity in comparison with general F-P cavities. The fitting method, periodic method and Fourier transform method for FBG-FP cavity length estimation are discussed. A scheme of spectral measurement of FBG-FP cavities is designed, which obtains spectral curves with a high accuracy. The above three methods for cavity length estimation are compared mutually with tested spectra, and theoretical analyses are validated.