Coincidence isometries of a shifted square lattice

Coincidence isometries of a shifted square lattice

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by identifying the square lattice with the ring of Gaussian integers. To illustrate them, we calculate the set of coincidence isometries, as well as generating func...

Indices of coincidence isometries of the hypercubic lattice Z n.

The problem of computing the index of a coincidence isometry of the hypercubic lattice Z{n} is considered. The normal form of a rational orthogonal matrix is analyzed in detail and explicit formulas for the indices of certain coincidence isometries of Z{n} are obtained. These formulas generalize the known results for n < or = 4.

On Isometries of Square Sets

A Note on Coincidence Isometries of Modules in Euclidean Space

It is shown that the coincidence isometries of certain modules in Euclidean n-space can be decomposed into a product of at most n coincidence reflections defined by their non-zero elements. This generalizes previous results obtained for lattices to situations that are relevant in quasicrystallography.

Optical sensing of square lattice photonic crystal point-shifted nanocavity for protein adsorption detection

We propose a point-shifted D0 nanocavity formed by locally modulating four central air holes in square lattice photonic crystal for optical sensing application. Three defect modes in this nanocavity, including monopole, whispering-gallery, and dipole modes, are identified in experiments. We also apply a chemical treatment on InGaAsP surface to form a 1-octadecanethiol linking monolayer, which e...