Resonance absolute quantum reflection at selected energies

The possibility of the resonance reflection (100 % at maximum) is revealed. The corresponding exactly solvable models with the controllable numbers of resonances, their positions and widths are presented.Comment: 5 pages, 2 figure

Recovering the M-channel Sturm-Liouville operator from M+1 spectra

For a system of M coupled Schroedinger equations, the relationship is found between the vector-valued norming constants and M+1 spectra corresponding to the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The double set of norming vectors and associated spectrum of one of the M+1 boundary value problems uniquely specifies the matrix of potentials in the multichannel Schroedinger equation.Comment: 8 pages, no figure

Elimination of cracks in self-assembled photonic band gap crystals

Thin colloidal crystals (or synthetic opals) composed of Stober silica spheres typically develop cracks when they are utilized to obtain photonic band gap crystals (or inverted opals). We find that by sintering the silica spheres prior to assembly of the opal these cracks can be avoided. We report the effects of temperature and duration of the heat treatment on 850 nm silica spheres using electron microscopy, thermogravimetry, and light scattering. We also find a large dependence of the refractive index of the silica on the temperature of the heat treatment. This may allow tuning of the refractive index of silica spheres.Comment: REvTex: 4 pages, 3 figure