Spectral properties of soft quantum waveguides

Periodic Optical Waveguides: Exact Floquet Theory and Spectral Properties

We consider the steady propagation of a light beam in a planar waveguide whose width and depth are periodically modulated in the propagation direction. Using methods of soliton theory, a class of periodic potentials is presented for which the complete set of Floquet solutions of the linear Schrödinger equation can be found exactly at a particular optical frequency. For potentials in this class,...

Propagation properties of light in AlGaN/GaN quantum-well waveguides

Spectral Properties of Finite Quantum Hall Systems ∗

In this note we review spectral properties of magnetic random Schrödinger operators Hω = H0 + Vω + Ul + Ur defined on L 2(R × [ −L2 , L2 ] , dxdy) with periodic boundary conditions along y. Ul and Ur are two confining potentials for x ≤ −L2 and x ≥ L2 respectively and vanish for −L2 ≤ x ≤ L2 . We describe the spectrum in two energy intervals and we classify it according to the quantum mechanica...

Quantum waveguides with corners

The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we consider V-shaped guides. Their spectral properties depend essentially on a sole parameter, the opening of the V. The free energy band is a semi-infinite interval bounded from below. As soon as the V is not flat, ther...

Numerical Simulation of Quantum Waveguides

Abstract. This chapter is a review of the research of the authors from the last decade and focuses on the mathematical analysis of the Schrödinger model for nano–scale semiconductor devices. We discuss transparent boundary conditions (TBCs) for the time–dependent Schrödinger equation on a two dimensional domain. First we derive the two dimensional discrete TBCs in conjunction with a conservativ...