Abstract
Compared with coupled-mode theory (CMT), which is widely used for studies involving optical fiber Bragg gratings (FBGs), the proposed investigation scheme is visualized, diagrammatic, and simple. This method combines the finite element method (FEM) and eigenmode expansion method (EEM). The function of the FEM is to calculate all guided modes that match the boundary conditions of optical fiber waveguides. Moreover, the FEM is used for implementing power propagation for HE11 in optical fiber devices. How the periodic characteristic of FBG causes this novel scheme to be substantially superior to CMT is explained in detail. Regarding current numerical calculation techniques, the scheme proposed in this paper is the only method capable of the 3D design and analysis of large periodic components. Additionally, unlike CMT, in which deviations exist between the designed wavelength λD and the maximal reflection wavelength λmax, the proposed method performs rapid scans of the periods of optical FBG. Therefore, once the operating wavelength is set for the component design, the maximal reflection wavelength of the final products can be accurately limited to that of the original design, such as λ = 1550 nm. Furthermore, a comparison between the period scan plot and the optical spectra plot for FBG indicated an inverse relationship between the periods and wavelengths. Consequently, this property can be used to predict the final FBG spectra before implementing time-consuming calculations. By employing this novel investigation scheme involving a rigorous design procedure, the graphical and simple calculation method reduces the studying time and professional expertise required for researching and applying optical FBG.
Highlights
In recent decades, optical fiber Bragg gratings (FGBs) have been developed into essential devices with numerous applications for optical fiber telecommunication and small sensor systems
fiber Bragg gratings (FBGs) can function as mirrors [16], incorporating a copropagating HE11, which is coupled to a counterpropagating mode of an identical type, and a loss filter [17], in which the leakage wave away from the optical fiber can be effectively suppressed
The findings indicate that eigenmode expansion method (EEM) and coupled-mode theory (CMT) can be used to expand modes
Summary
Optical fiber Bragg gratings (FGBs) have been developed into essential devices with numerous applications for optical fiber telecommunication and small sensor systems. The geometric configuration of a communication optical fiber consists of three layers: the core, cladding, and surrounding. The corresponding effective refractive index n eff of each guided mode is determined by solving the dispersion relation equations [13,18,19,20]. From a purely mathematical perspective, guided modes are solutions to differential equations that satisfy certain boundary conditions. Defining the Mathematical Model of FBG and Explaining the Coupled-Mode Equation. For FBG production, a single-mode communication optical fiber containing photosensitive materials in the core layer was used. The phase mask obtaining specific period was irradiated using ultraviolet light to create constructive and destructive interference on the single-mode optical fiber, thereby changing the refractive index of the core layer. All optical fiber guided modes are mutually orthogonal before FBG appears
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