An energy window study of light transmission-disorder relationship in 1D photonic structures

While the light transmission of photonic crystals is characterized by the photonic band gap, the one of disordered photonic structures is typified by a multiplicity of transmission depths. The total transmission over a range of wavelengths is related to the width of such range, but also to the type of disorder. Less homogeneous disordered structures transmit more light than the ordered counterpart regardless of the wavelengths range width. More homogeneous disordered structures transmit more light than the ordered counterpart only above a certain value of the width. We studied this behaviour with a statistical analysis over 5000 permutations of structures for each wavelength width and for each homogeneity degree (Shannon-Wiener index).Comment: 8 pages, 4 figure

Complexity spectrum of some discrete dynamical systems

We first study birational mappings generated by the composition of the matrix inversion and of a permutation of the entries of $3 \times 3$ matrices. We introduce a semi-numerical analysis which enables to compute the Arnold complexities for all the $9!$ possible birational transformations. These complexities correspond to a spectrum of eighteen algebraic values. We then drastically generalize these results, replacing permutations of the entries by homogeneous polynomial transformations of the entries possibly depending on many parameters. Again it is shown that the associated birational, or even rational, transformations yield algebraic values for their complexities.Comment: 1 LaTex fil