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从麦克斯韦方程组出发,通过将光纤波导扰动和光栅折射率调制扰动效应转换成等效的耦合系数,推导出光纤布拉格光栅耦合器的统一特征方程。采用打靶法并结合朗格-库塔(Runge-Kutta)数值积分对两种光纤布拉格光栅耦合器型上下话路滤波器的传输特性进行了详细的分析。结果表明,对于光栅破坏耦合器,利用光栅引入的强色散效应,滤波器的波长选择能力得到极大的提高,低于1 nm的带宽能够满足波分复用(WDM)系统的需求,并且当光栅调制的等效耦合远远超过两光纤消逝场间的耦合效率时,不仅有效地抑制了反射信号,使满足布拉格匹配条件的信号透射输出,还消除了旁瓣纹波;而对于光栅辅助耦合器,其非干涉本质使得器件性能更加稳定,并可通过调整光栅长度进一步改善滤波响应。
Starting from the Maxwell equations, the unified characteristic equation of fiber Bragg grating (FBG) coupler is deduced by converting the disturbance of fiber waveguide and grating refractive index modulation into equivalent coupling coefficient. The propagation characteristics of the two kinds of fiber Bragg grating coupler-type up-and-down path filters are analyzed in detail by the shooting method and the Runge-Kutta numerical integration. The results show that for the grating-destructive coupler, the wavelength selectivity of the filter can be greatly improved by the strong dispersion effect introduced by the grating. The bandwidth below 1 nm can meet the requirements of a wavelength division multiplexing (WDM) system. When The equivalent coupling of the grating modulation far exceeds the coupling efficiency between two optical fiber evanescent fields, which not only effectively suppresses the reflection signal but also transmits the signal satisfying the Bragg matching condition and eliminates the side lobe ripple. For the grating auxiliary coupling The non-interference nature of the device makes the device performance more stable, and the filter response can be further improved by adjusting the length of the grating.