One-Dimensional Photonic Crystal Transfer Matrix Method

The method presented in this text is the one-dimensional photonic crystal transfer matrix method. This approach enables the display of band gap images in MATLAB through systematic computational implementation. We can utilize this method to investigate the characteristics and behaviors of photonic crystals by implementing key algorithms that calculate electromagnetic wave propagation through periodic dielectric structures. By analyzing the transfer matrix, which is computed through iterative multiplication of layer-specific matrices representing different dielectric materials, we can understand the band structure formation and the emergence of photonic band gaps. The MATLAB implementation typically involves creating functions to calculate the transfer matrix for each unit cell, then cascading these matrices to obtain the overall system response. This method proves particularly valuable for studying the optical properties of photonic crystals, as it provides numerical solutions for transmission coefficients across different frequencies. The code implementation allows researchers to parameterize material properties, layer thicknesses, and periodicity to systematically analyze how these factors influence band gap positions and widths. Through proper visualization techniques, the method helps develop deep insights into photonic crystal performance and their potential applications in optical devices and photonic integrated circuits.