Integrated multi vector vortex beam generator

A novel method to generate and manipulate vector vortex beams in an integrated, ring resonator based geometry is proposed. We show numerically that a ring resonator, with an appropriate grating, addressed by a vertically displaced access waveguide emits a complex optical field. The emitted beam possesses a specific polarization topology, and consequently a transverse intensity profile and orbital angular momentum. We propose a combination of several concentric ring resonators, addressed with different bus guides, to generate arbitrary orbital angular momentum qudit states, which could potentially be used for classical and quantum communications. Finally, we demonstrate numerically that this device works as an orbital angular momentum sorter with an average cross-talk of -10 dB between different orbital angular momentum channels.Comment: 8 pages, 7 figure

Effect of spin on electron motion in a random magnetic field

We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest a new trick replacing the initial Hamiltonian by a Dirac Hamiltonian. This allows us to do easily a perturbation theory and derive a supermatrix sigma model, which takes a form of the conventional sigma model with the unitary symmetry. Using this sigma model we calculate several correlation functions including a spin-spin correlation function. As compared to the model without spin, we get different expressions for the single-particle lifetime and the transport time. The diffusion constant turns out to be 2 times smaller than the one for spinless particles.Comment: 7 pages, revtex, result of the spin correlation function corrected, Appendix adde

Spatial-skin effect for a spectral problem with “slightly heavy” concentrated masses in a thick cascade junction

The asymptotic behavior (as ε→0) of eigenvalues and eigenfunctions of a boundary- value problem for the Laplace operator in a thick cascade junction with concentrated masses is studied. This cascade junction consists of the junction’s body and a great number 5N=(ε−1) of ε−alternating thin rods belonging to two classes. One class consists of rods of finite length and the second one consists of rods of small length of order O(ε). The density of the junction is of order O(ε−α) on the rods from the second class and O(1) outside of them. There exist five qualitatively different cases in the asymptotic behavior of eigenvibrations as ε→0, namely the cases of “light” concentrated masses (α∈(0,1)), “middle” concentrated masses (α=1), “slightly heavy” concentrated masses (α∈(1,2)), “intermediate heavy” concentrated masses (α=2), and “very heavy” concentrated masses (α>2). In the paper we study the influence of the concentrated masses on the asymptotic behavior of the eigen-magnitudes if α∈(1,2)