Band-edge states of the zero(th)-order gap in quasi-periodic photonic superlattices

The photonic modes of Thue-Morse and Fibonacci lattices with generating layers A and B, of positive and negative indices of refraction, are calculated by the transfer-matrix technique. For Thue-Morse lattices, as well for periodic lattices with AB unit cell, the constructive interference of reflected waves, corresponding to the zero(th)-order gap, takes place when the optical paths in single layers A and B are commensurate. In contrast, for Fibonacci lattices of high order, the same phenomenon occurs when the ratio of those optical paths is close to the golden ratio. In the long wavelength limit, analytical expressions defining the edge frequencies of the zero(th) order gap are obtained for both quasi-periodic lattices. Furthermore, analytical expressions that define the gap edges around the zero(th) order gap are shown to correspond to the = 0 and = 0 conditions.

Band edge states of the < n >=0 gap of Fibonacci photonic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bloch-Kohn and Wannier-Kohn functions in one dimension

Bloch and Wannier functions of the Kohn type for a quite general one-dimensional Hamiltonian with inversion symmetry are studied. Important clarifications on null minigaps and the symmetry of those functions are given, with emphasis on the Kronig-Penney model. The lack of a general selection rule on the miniband index for optical transitions between edge states in semiconductor superlattices is discussed. A direct method for the calculation of Wannier-Kohn functions is presented.

Gel'fand-Levitan equation for deletion of states from Coulomb spectra

The Gel'fand-Levitan formalism is used to study how a selected set of bound states can be eliminated from the spectrum of the Coulomb potential and also how to construct a bound state in the Coulomb continuum. It is demonstrated that a sizeable quantum well can be produced by deleting a large number of levels from the s spectral series and the edge of the Coulomb potential alone can support the von Neumann-Wigner states in the continuum. © 1998 Elsevier Science B.V.

Local structure and hybridization states in Ba0.9Ca0.1Ti1-xZrxO3 ceramic compounds: Correlation with a normal or relaxor ferroelectric character

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)