Layer Peeling Algorithm Combined with Fourier Transform Method

The integration of layer peeling algorithm with Fourier transform provides an efficient and precise approach for analyzing fiber Bragg grating (FBG) characteristics. This method employs hierarchical stripping of optical fiber structural parameters while leveraging Fourier transform's spectral analysis capabilities to investigate FBG reflection spectra, transmission spectra, and group delay properties.

The core concept of the layer peeling algorithm involves processing FBG parameters (such as refractive index modulation, periodicity, etc.) in layered fashion, calculating grating reflection and transmission characteristics layer by layer. The primary advantage lies in effectively reducing computational complexity while maintaining high accuracy. Each layer's analysis results serve as input for the subsequent layer, progressively building a comprehensive grating response model. In MATLAB implementation, this can be structured using recursive functions or iterative loops with properly initialized parameter matrices.

Fourier transform facilitates conversion from temporal or spatial domain signals to frequency domain, enabling efficient analysis of FBG spectral characteristics. Through fast Fourier transform (FFT) algorithms, key FBG reflection spectrum features can be efficiently extracted, including Bragg wavelength, bandwidth, and side-lobe suppression ratio. The implementation typically involves applying fft() function to time-domain data with proper windowing and zero-padding for spectral resolution enhancement. Additionally, this method supports dispersion characteristic analysis, providing theoretical foundations for optical communication system design.

In MATLAB environment, this methodology can leverage numerical computation toolboxes for optimized computational efficiency. Through matrix operations and vectorization techniques, significant algorithm speed improvements can be achieved, making it suitable for large-scale grating structure simulations. Key implementation aspects include preallocating arrays for efficiency, using built-in FFT functions, and optimizing matrix manipulations for layered calculations. This approach finds extensive applications in fiber optic sensing, wavelength division multiplexing systems, and fiber laser design.