Design Method of High Signal-to-Noise Ratio Reflective Volume Bragg Grating Filter
Objective Wavelength division multiplexing (WDM) in optical fiber communications is widely recognized as the most effective method for increasing communication capacity due to its low cost and ease of implementation. Wavelength division multiplexing and demultiplexer devices (WDMDs) are essential components for implementing WDM technology and have remained at the forefront of optical multiplexing research. Volume Bragg gratings (VBGs) recorded in photo-thermo-refractive glass (PTRG) exhibit extremely narrow spectral bandwidths. These gratings are capable of filter different wavelengths of light by adjusting the incident angle,offering high efficiency,high transmission rates,low insertion loss,and excellent environmental stability. Therefore,they hold great potential for dense wavelength division multiplexing (DWDM) applications. However,the sidelobes caused by sudden changes in coupling strength at both ends of the grating will lead to interchannel interference,preventing the reduction of channel spacing and thereby affecting application performance. In periodic waveguide structures,a method to suppress sidelobes by varying the distribution of coupling strengths is known as apodization. Current research on apodization techniques for VBGs predominantly focuses on using a single function,such as sinc or Gaussian functions,to achieve sidelobe suppression. As far as we know,there has been no systematic comparison of the effects of different apodization functions. Therefore,this study systematically compares and analyzes the results of different types of apodization functions.Methods We build the apodization theoretical model of reflective volume Bragg grating (RVBG) based on F-matrix theory. The diffraction efficiency of different apodized volume Bragg gratings is normalized by defining effective refractive index modulation. The apodization effects of cosine,Gaussian,and secant functions are systematically compared and analyzed. An RVBG filter for the C-band is designed based on the established model,providing a theoretical design basis for the development of high signal-to-noise ratio RVBG filters.Results and Discussions The performance of three refractive index modulation distribution functions,namely cosine,Gaussian,and hyperbolic secant,is examined in RVBGs with a center wavelength of 1550 nm and a thickness of 5 mm. The simulations are conducted to evaluate the efficacy of sidelobe suppression in both the spectral and angular domains. The cosine function exhibits exceptional utilization efficiency in PRRG,with the best diffraction efficiency without additional peaks at the edges of the spectrum for samples of the same thickness and exposure. Gaussian and hyperbolic secant functions demonstrate deeper out-of-band suppression capabilities through parameter adjustments unattainable by the cosine function. However,the hyperbolic secant function exhibits subpar sidelobe suppression,leading to decreased efficiency in utilizing the same glass substrate. The diffraction efficiency of the main lobe in RVBGs is determined by the effective refractive index modulation (ERIM). When the ERIM remains constant,increasing thickness (or refractive index modulation) affects the bandwidth without changing the diffraction efficiency magnitude or spectral shape. Conversely,keeping the thickness constant but changing the maximum refractive index modulation affects both the diffraction efficiency and the spectral features. By adjusting the refractive index modulation and thickness according to requirements,controlling the magnitude of ERIM,and ensuring that the center of the apodization function deviates minimally from the center of the sample,RVBGs with the required performance can be designed and prepared. In addition,Gaussian and hyperbolic secant apodized gratings generate additional peaks at the first zero point,which change periodically with the increase of ERIM. When ERIM is appropriate,these additional peaks disappear.Conclusions Based on F-matrix theory,a theoretical model to analyze the apodized RVBG of various function types is established. By defining the ERIM,normalization of the refractive index modulation for the apodization function is achieved,facilitating easier comparison of results from various apodization functions. We further analyze the apodization influences of cosine,Gaussian,and hyperbolic secant functions. Simulation results demonstrate that apodized gratings significantly suppress sidelobes. With constant diffraction efficiency,all three functions reduce the first and second sidelobes to below 1.1％ and 0.3％,respectively. The study concludes that the main lobe diffraction efficiency and the shape of the diffraction efficiency spectrum are determined by the ERIM. When the ERIM is fixed,the diffraction efficiency remains consistent,while the spectral bandwidth expands as the grating thickness increases. With a constant thickness,both the diffraction efficiency and bandwidth increase with the maximum refractive index modulation. The capability to reduce the intensity of the first-order sidelobes decreases gradually from cosine to Gaussian to hyperbolic secant functions. An RVBG filter is designed to have a high signal-to-noise ratio based on theoretical research. Utilizing a Gaussian function (m=3) as the apodization function,it achieves an efficiency exceeding 90％ and a spectral bandwidth of less than 0.8 nm. This design allows for the continuous wavelength selection for C-band filters by adjusting the angle,resulting in a sideband suppression of around 50 dB.
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