Optical properties of perfect and non-perfect quasi-periodic multilayers: a comparison with periodic and disordered multilayers

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Abstract
A detailed study is presented of the optical transmission through quasi-periodically layered media using a transfer matrix technique. The overall behaviour in multilayers arranged according to the Thue-Morse and Fibonacci sequences is found to be very similar. This is in strong contrast to the marked difference recently found in the electronic wavefunctions for the two corresponding aperiodic crystals in a tight-binding model. Other types of quasi-periodic multilayers are shown to have rather different transmission properties compared to the Thue-Morse and the Fibonacci layering. A thorough comparison with both periodic and disordered multilayers shows clearly that the quasi-periodic multilayers have quite different optical behaviour. When the number of layers is allowed to approach infinity the transmission coefficient is claimed to show a multifractal behaviour. Inspired by the recent interest in the effect of fluctuations in the layer thickness on the physical properties of quasi-periodic superlattices prepared with molecular beam epitaxy, the authors have also studied the sensitivity of the optical transmission to a few per cent variation in the thickness of the layers. The optical transmission is found to be less sensitive to fluctuations in the layer size in the quasi-periodic case than in the periodic case. Compared to randomly layered media on the other hand the transmission coefficient in the quasi-periodic multilayer case is more sensitive to small variations in the length of the layers.