Photonic localization in one-dimensional k-component Fibonacci structures

We studied the photonic localization of one-dimensional k-component Fibonacci structures (KCFS's), in which k different intervals are ordered according to a substitution rule. By using a transfer-matrix method, the optical transmission through KCFS's is obtained. It is demonstrated that the transmission coefficient has a rich structure, which depends on the wavelength of light and the number of different incommensurate intervals k. For the KCFS's with an identical ic, by increasing the layer number of the sequences. more and more transmission dips develop and some of them approach zero transmission, which may finally make a one-dimensional photonic band gay. For a series of finite KCFS's, by increasing the number of different incommensurate intervals k, the total transmission over the spectral region of interest decreases gradually and the width of photonic band gap becomes larger. This property may be useful in the design of the high-performance optical and electronic devices, As for the infinite KCFS's, the transmission coefficient is singularly continuous and multifractal analysis is employed to characterize the transmission spectra. A dimensional spectrum of singularities associated with the transmission spectrum f(alpha) demonstrates that the light propagation in the KCFS's presents scaling properties and hence shows a genuine multifractality.