Using linear regression method to provide a mathematical relation to investigate the gap wavelength band in photon structures for use in the design of optoelectronic devices

Photon crystals are on of the most common structures for designing and implementing electronic optical circuits. The photon gap band is of great importance in these structures. The most common mathematical methods for analyzing and calculating photon band diagrams and extracting the forbidden photon band of photon crystals is the flat wave expansion method. This method has many complexities that require special commercial software to perform its calculations. In two-dimensional photonic crystals, two parameters in the photon band are affected, which are the refractive index of the dielectric material and the ratio of the radius of the holes to the constant of the crystal lattice (r / a). In this paper, using mathematics and linear regression, simpler relations for extracting the photon band range of photon crystals are presented. Comparison of the results obtained from the relations with the results obtained with BandSOLVE software for photonic crystals shows that the maximum difference between the two calculation methods for fl and fu is 0.007 and 0.028, respectively, and the average difference is , respectively 0.004 and is 0.01.