基于耦合模理论的波导光栅特性研究

Research on Characterization of Waveguide Gratings Based on Coupled-wave Theory

为了深入研究波导光栅中电磁波的传输特性,本文以布拉格光栅为例,从光场的波动方程出发得到了光栅的耦合模方程,进而通过求解耦合模方程得到表征光栅特性的2×2矩阵。针对均匀布拉格光栅和取样光栅,采用MATLAB数值模拟方法研究了各个参数对其反射谱和透射谱的影响。结果表明,光栅长度、有效折射率以及耦合强度会影响均匀布拉格光栅反射谱和透射谱的峰值、位置和宽高,光栅段长度、空白段长度以及周期数目会导致取样光栅反射谱的反射峰间隔增减和各级峰值的变化。相关仿真分析可以为光纤光栅传感、分布式布拉格反馈(DBR)激光器、光栅滤波器等设计应用提供理论支撑。

Bragg gratings are used in various applications including optical communication systems and sensors.The influencing parameters of the reflectivity of Bragg gratings hold significant importance in the research of optical sensors.Both domestically and internationally,there exist various external parameters including vibration sensing characteris temperature sensing characteristics and lateral force characteristics of fiber gratings.However,the comprehensive exploration on how these external parameters impact the fiber grating is insufficient.Thus,it is crucial to delve into the internal characteristics of waveguide gratings.This paper investigates the transmission characteristics of electromagnetic waves in waveguide gratings by changing internal parameters.The Bragg grating is taken as an example in this paper to derive the coupling mode equation of the grating from the wave equation of the light field,and then the 2×2 matrix characterizing the grating characteristics is reproduced by solving the coupling mode equation and applied to a matrix derivation that can characterize the characteristics of the sampling grating.The formula of the equations is deduced,and a simplified formulation linking the reflection coefficient to the grating length,effective refractive index,and coupling intensity is obtained.For uniform Bragg grating and sampling grating,the influence of parameters on their reflectance spectrum and transmission spectrum was studied by MATLAB numerical simulation method.As the influential factors,the grating length,effective refractive index,coupling intensity,grating segment length,blank segment length and grating period are included.The numerical simulation spectrum and experimental results are also given.The results demonstrate that,for the uniform Bragg grating,as the length of the grating segment increases,both the reflectance peaks in the reflection spectrum and transmission spectrum exhibit an upward;a decrease in effective refractive index leads to a blue shift in the position of both reflection and transmission spectra;an increase in coupling intensity results in higher reflectance peak heights and wider spectral widths.For the sampling grating,the increase in the length of the grating segment leads to an increase in the coupling intensity of the sampling grating,resulting in a wider interval between the reflection peaks;the length of the blank segment increased,while the reflection peaks at all levels remained unchanged and there is a decrease in the spacing between the reflection peaks;the increase in the number of grating periods leads to a longer transmission distance of the light field within the grating,resulting in an increased number of backward transmissions and enhanced intensity of reflection peaks at all levels in the reflection spectrum.The simulation analysis presented in our work offers theoretical support for the preparation and design of target gratings in various applications,such as FBG sensing,distributed Bragg feedback(DBR)lasers and grating filters.