An HCMT model of optical microring-resonators

Analytical modes of the bus and cavity cores are combined into a 2-D hybrid analytical / numerical coupled mode theory (HCMT) model of integrated optical ring-resonators. The variational technique generates 1-D FEM-discretized solutions for the amplitude functions in their natural Cartesian and polar coordinates

Collective excitations in circular atomic configurations, and single-photon traps

Correlated excitations in a plane circular configuration of identical atoms with parallel dipole moments are investigated. The collective energy eigenstates, their level shifts and decay rates are computed utilizing a decomposition of the atomic state space into carrier spaces for the irreducible representations of the symmetry group \ZZ_N of the circle. It is shown that the index $p$ of these representations can be used as a quantum number analogously to the orbital angular momentum quantum number $l$ in hydrogen-like systems. Just as the hydrogen s-states are the only electronic wave functions which can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the atoms in the circle can occupy the central atom only for vanishing \ZZ_N quantum number $p$. If a central atom is present, the $p=0$ state splits into two and shows level-crossing at certain radii; in the regions between these radii, damped Rabi oscillations between two "extreme" $p=0$ configurations occur. The physical mechanisms behind super- and subradiance at a given radius and the divergence of the level shifts at small interatomic distances are discussed. It is shown that, beyond a certain critical number of atoms in the circle, the lifetime of the maximally subradiant state increases exponentially with the number of atoms in the configuration, making the system a natural candidate for a {\it single-photon trap}.Comment: Shortened version, accepted for publication in Phys. Rev.

Pathways to Accountability II

This report summarises the results of the 2009-2010 review process on the One World Trust Global Accountability Framework and the piloting of the draft framework during 2011, and presents the full One World Trust Pathways to Accountability II indicator framework. Our work in this field work is motivated by a concern about the persisting weakness and insufficient effectiveness of global organisations from all sectors in responding to the challenge of delivering global public goods to citizens and communities, the very people whom they claim to serve and benefit, and who are most often dependent on them

A variational formulation of guided wave scattering problems

A functional of the six electromagnetic components is proposed as a variational basis for 3-D frequency domain problems in integrated optics. Stationarity implies that the Maxwell equations in the interior of the domain of interest and transparent influx conditions for incoming waveguides on its boundary port planes are satisfied

Hybrid analytical/numerical coupled-mode modeling of guided-wave devices

A general version of coupled-mode-theory for frequency domain scattering problems in integrated optics is proposed. As a prerequisite a physically reasonable field template is required, that typically combines modes of the optical channels in the structure with coefficient functions of in principle arbitrary coordinates. Upon 1-D discretizations of these amplitude functions into finite elements, a Galerkin procedure reduces the problem to a system of linear equations in the element coefficients, where given input amplitudes are included. Smooth approximate solutions are obtained by solving the system in a least squares sense. The versatility of the approach is illustrated by means of a series of 2-D examples, including a perpendicular crossing of waveguides, and a grating-assisted rectangular resonator. As an appendix, we show that alternatively a similar procedure can be derived by variational means, i.e. by restricting a suitable functional representation of the full 2-D/3-D vectorial scattering problem (with transparent influx boundary conditions for inhomogeneous exterior) to the respective field templates.\u