Transmission properties of one dimensional fractal structures

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure and the single golden-section fractal structure. By using the transfer matrix method the transmission spectra of these structures are simulated. The calculation results shows that the transmission spectrum of the symmetric dual cantor-like fractal structure is self-similar and the peak numbers in the transmission spectra of the SDGSFS also follow the principals of special fractal structures. It is also shown that in the symmetric dual golden-section fractal structure the localization of modes which appears within the stop band increases and getting closer to the middle of the gap by increasing the number of string.