Numerical analysis for temporal and spectral responses of electromagnetic waves in spatially homogeneous time varying medium

This paper presents simple numerical solutions for electromagnetic plane waves in spatially homogenous time varying medium. The solution is based on converting the resulting second order differential equation into two combined ordinary differential equations which are solved numerically by using the built-in ode113 function in Matlab. By using this method, the time domain responses of the electric and magnetic fields at fixed point in space are obtained. The proposed method is applied on two cases: linearly time varying medium and sinusoidally time varying medium. The corresponding frequency domain response is obtained by using inverse Fourier transformation of the obtained time domain response. The proposed method is compared with FDTD solution. It is found that the proposed method has the same accuracy of FDTD with much less computational time.