In this paper we study the propagation of light through an asymmetric array of dielectric multilayers built by joining two porous silicon substructures in a Fibonacci sequence. Each Fibonacci substructure follows the well-known recursive rule but in the second substructure dielectric layers A and B are exchanged. Even without mirror symmetry, this array gives rise to multiple transparent states, which follow the scaling properties and self-similar spectra of a single Fibonacci multilayer. We apply the transfer matrix formalism to calculate the transmittance. By setting the transfer matrix of the array equal to ± I, the identity matrix, frequencies of perfect light transmission are reproduced in our theoretical calculations. Although the light absorption of porous silicon in the optical range limits our experimental study to low Fibonacci generations, the positions of the transparent states are well predicted by the above-mentioned condition. We conclude that mirror symmetry in arrays of Fibonacci multilayers is sufficient but not necessary to generate multiple transparent states, opening broader applications of quasiperiodic systems as filters and microcavities of multiple frequencies.

We calculate the optical constants of porous silicon ͑por-Si͒ from the electronic band structure obtained by means of an sp 3 s* tight-binding Hamiltonian and a supercell model, in which the pores are columns dug in crystalline Si. The position of the absorption edge of the material is defined by two competing effects: ͑i͒ transitions assisted by the scattering of carriers on the lattice of pores, which effectively decrease the ''indirectness'' of por-Si and result in a redshift of the absorption edge, and ͑ii͒ quantum confinement, which increases the band gap. The interplay between these effects is illustrated by calculating the imaginary part of the dielectric function for 8-, 32-, and 128-atom supercells with different porosities. We also show how the supercell model can be extended to take into account weak disorder, which produces nonvertical optical transitions in k space and smoothens the absorption spectra. Our results, obtained without any adjustable parameters, are compared with experimental data. ͓S0163-1829͑99͒05023-7͔

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Two of the most important properties of a porous silicon multilayer for photonic applications are flat interfaces and a relative large refractive index contrast between layers in the optical wavelength range. In this work, we studied the effect of the current density and HF electrolyte concentration on the refractive index of porous silicon. With the purpose of increasing the refractive index contrast in a multilayer, the refractive index of porous silicon produced at low current was studied in detail. The current density applied to produce the low porosity layers was limited in order to keep the electrolyte flow through the multilayer structure and to avoid deformation of layer interfaces. We found that an electrolyte composed of hydrofluoric acid, ethanol and glycerin in a ratio of 3:7:1 gives a refractive index contrast around 1.3/2.8 at 600 nm. Several multilayer structures with this refractive index contrast were fabricated, such as dielectric Bragg mirrors and microcavities. Reflectance spectra of the structures show the photonic quality of porous silicon multilayers produced under these electrochemical conditions. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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