Long-Period Fiber Grating Transmission Matrix MATLAB Code Segment

Long-Period Fiber Gratings (LPFGs) are optical fiber devices that modulate light intensity through periodic refractive index modifications along the fiber core. These gratings operate by coupling light from the fundamental core mode to co-propagating cladding modes, creating wavelength-dependent attenuation bands. LPFGs find extensive applications in telecommunications (as gain flattening filters), sensing systems (for temperature, strain, and refractive index measurements), and optical signal processing. The transmission matrix method provides an effective computational approach for modeling LPFG performance. This MATLAB implementation constructs a transfer matrix that characterizes light propagation through the grating structure. The code typically involves: - Discretizing the grating into multiple short segments - Calculating the phase matching conditions and coupling coefficients for each segment - Implementing matrix multiplication to cascade individual segment effects - Solving eigenvalue problems to determine resonance conditions Key algorithmic components include: 1. Grating parameter initialization (period, length, index modulation depth) 2. Mode coupling coefficient calculations using overlap integrals 3. Transfer matrix formulation for bidirectional propagation 4. Spectral response computation across wavelength ranges This MATLAB code segment enables researchers to predict critical LPFG characteristics including resonance wavelengths, bandwidth, and transmission spectra. The implementation allows for parameter optimization by varying grating geometry, refractive index profiles, and environmental conditions, facilitating the design of application-specific LPFG devices. The matrix-based approach efficiently handles complex grating structures and provides numerical stability compared to analytical solutions. Engineers can extend the code to model chirped gratings, apodized profiles, or multiple grating cascades by modifying the matrix elements and multiplication sequences.