Application of group theory in transfer matrix technique for band structure calculation in 1D photonic crystal

In this paper, transfer matrix technique for computing the band structure and transmittance of one dimensional photonic crystal is analyzed using group theoretical approach and a novel algorithm is developed for the purpose to reduce the time for computation. The advantage of this algorithm is that it bypasses the implicit N times matrix multiplication that is performed by a digital computer when calculating the band structure of periodic dielectric structures consisting of N cells when N is moderately large. The formulation indicates that the simplified algorithm can significantly ease the numerical burden and reduce the requirement on computer memory space.