Self-similar optical transmittance for a deterministic aperiodic multilayer structure

We study theoretically the spectral transmission properties of a multilayer structure in which the refractive index of the layers follows a self-similar arithmetical sequence named 'The 1s-counting sequence', which is related to the Pascal's triangle. The transmittance spectrum is intermediate between that of a periodic structure and that of a random structure, and shows clearly properties of scaling and self-similarity for all incident angles and TE and TM polarizations.