Shift-Operator Finite difference Time Domain: An efficient unified approach for simulating wave propagation in different dispersive media

Shift-Operator Finite difference Time Domain (SO-FDTD) method is presented as a new efficient technique for simulating electromagnetic wave interaction with different types of dispersive media like ferrite material, chiral media and left-hand metamaterials. The main idea of this method is to formulate the problem in frequency domain and to present the dispersive relations between the fields inside the medium as polynomials of jω. These polynomials are converted to time domain by replacing jω by the time derivative operator. Then this time derivative operator is converted to the corresponding time shift operator which is used directly to obtain the corresponding update equations of electric and magnetic field components. The resulting update equations do not require time convolution or additional vector components. The present analysis does not require also any transformation. Significant improvement is obtained in memory requirements by using this method while the computational time is nearly the same compared with other similar techniques like Z-transformation FDTD.