In this thesis, a new even-odd cycled high-order splitting finite difference time domain scheme for Maxwell's equations in two dimensions is developed. The scheme uses fourth order spatial difference operators and even-odd time step technique to make it more accurate in both space and time. The scheme is energy-conserved, unconditionally stable and very efficient in computation. We analyze in detail the stability, dispersion and phase error for the scheme. We also prove its energy conservation, convergence of high order accuracy and convergence of divergence free approximation. Numerical experiments confirm the theoretical analysis results. Further, the developed scheme is applied to computations of the grounded coplanar waveguides, the elevated CPW and the complex transitions between CPW and rectangular waveguides.