Discrete-Time Analysis of Inner-Band Dispersion of Fiber Bragg Grating

采用多层介质的离散传输线模型表征光纤光栅响应特性，并利用数字信号处理方法对光纤光栅的相位特性进行了分析，研究了用于密集波分复用窄带滤波的变迹光纤光栅的带内色散特性，表明对称变迹光纤光栅的幅度响应与相位响应之间满足希尔伯特变换关系，幅度响应越接近理想的矩形，带内色散越大。并采用耦合模理论数值计算了对称变迹的光纤光栅的反射相位响应和带内群时延情况，验证了分析结果。A discrete-time transmission model is proposed to characterize the response of fiber gratings, and the digital-processing methods are used to analyze the phase response of fiber gratings. The inner-band dispersion characteristics of apodized fiber gratings used for DWDM filtering is studied. It is shown that the amplitude and phase responses of symmetrical apodized fiber grating are related by means of the Hilbert transform, the closer to ideal rectangle the amplitude response is, the greater the inner-band dispersion is. The coupled mode theory is used to calculate the reflection phase response and inner-band dispersion of apodized fiber gratings, the above analysis is verified