Calculation of band structures in a fractal photonic crystal waveguide

Abstract

Many applications implemented today are based on the study of specific geometric tools, such as aunique geometry known as fractals. This work presents an integral method developed to calculate the band structures of a photonic crystal waveguide, which consists of two plane-parallel conducting plates and an array of inclusions incorporating perfect electric conductor Koch snowflake fractal structures. The numerical technique employed is known as the Integral Equation Method, which utilizes Green's second identity to solve the two-dimensional Helmholtz equation. Our findings indicate that varying the inclusion size over several iterations of the Koch fractal structure allows us to effectively control the band structure of the system. The results reveal the emergence of multipleband gaps that significantly modify the fractal photonic band structure. Additionally, discrete modes can be obtained within a specific frequency range, allowing the fractal photonic crystal waveguide to function as a unimodal filter. These optical properties are of considerable interest from a technological perspective.