Application of Fractional Fourier Transform to finite difference time domain method

With the improvement in the computer speed and memory, Numerical Methods are frequently used in the solution of electromagnetic problems. Numerical Methods can be classified as the frequency domain and the time domain based methods. While the time domain methods are suitable for modeling of the transient response and wideband problems, the frequency domain methods are suitable for modeling of the steady state response and narrow band problems. A numerical method that has the advantages of both time and frequency domain approaches can be developed. Applying Fractional Fourier Transform in space and/or time can reduce the computational complexity for some cases. The Fractional Fourier Transform is a generalization of the continuous Fourier Transform. In last decades, there are several studies and applications concerning this transform. Generally, it is used in signal processing and noise filtering. In this study, Fractional Fourier Transform is applied to the Maxwell´s Equations for the first time in literature. Finite difference equations are obtained by the application of finite difference approximation to the differential equations.