推导并验证了非啁啾取样光纤布拉格光栅(SFBG)反射谱中反射峰值波长的表达式。基于种子光栅中心波长对应的折射率调制深度和取样光纤布拉格光栅折射率调制函数的傅里叶级数展开式,提炼出取样光纤布拉格光栅的折射率调制深度和各阶光栅周期,从而导出其反射峰值波长的表达式。由于考虑了占空比、取样周期等取样光纤布拉格光栅的结构参量,因而表达式能够描述反射峰的分布。仿真实验中,不同占空比或取样周期下计算出的反射峰值波长、信道间隔符合数值反射谱。该表达式既适用于均匀取样光纤布拉格光栅,也适用于交流切趾和交直流切趾取样光纤布拉格光栅。

Analytic expression for the reflection peak wavelengths (RPWs) of sampled fiber Bragg grating (SFBG) without chirp is derived and confirmed. Firstly, the refractive-index modulation depth, corresponding to center wavelength, of seeding grating and Fourier series of sampled fiber Bragg grating's refractive-index modulation are obtained. Then the refractive-index modulation depth and local grating periods of sampled fiber Bragg grating are derived. Aided with them, the expression for reflection peak wavelengths of sampled fiber Bragg grating is achieved. Since the duty cycle and the sampling period are involved, the expression guarantees the accuracy of calculated reflection peak wavelengths. In the simulations, with different duty cycle or sampling period, there are agreements between the calculated reflection peak wavelengths (or channel spacing) and numerical reflection spectra. Moreover, this expression is not only available for uniform sampled fiber Bragg grating, but also for AC-apodized and AC-DC-apodized sampled fiber Bragg grating.