Applications of Time Domain Simulation to Coupler Design for Periodic   Structures
  We present numerical procedures for analyzing the properties of periodic structures and associated couplers based upon time domain simulation. Simple post processing procedures are given for determining Brillouin diagrams and complex field distributions of the traveling wave solutions, and the reflection coefficient of the traveling waves by the input and output. The availability of the reflection coefficient information facilitates a systematic and efficient procedure for matching the input and output. The method has been extensively applied to coupler design for a wide variety of structures and to a study directed towards elimination of the surface field enhancement commonly experienced in coupler cells. 
N. M. Kroll, C.-K. Ng and D. C. Vier