Multifractal properties of one dimension quasi-period photonic crystal

Using transfer matrix method and multi-fractal theory, we studied the transmission properties of one-dimensional generalized Fibonacci structures GF(m,n), in which m, n different intervals are integer according to a substitution rule. By using a transfer-matrix method, the optical transmission through GF(m,n) is obtained. Multi-fractal analysis is employed to characterize the transmission spectra. It is demonstrated that the transmission coefficient has a rich structure, which depends on the wavelength of light and the number of different integer m, n.