6,929 research outputs found
On the variational distance of two trees
A widely studied model for generating sequences is to ``evolve'' them on a
tree according to a symmetric Markov process. We prove that model trees tend to
be maximally ``far apart'' in terms of variational distance.Comment: Published at http://dx.doi.org/10.1214/105051606000000196 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Hyperbolic Metamaterial Resonator-Antenna Scheme for Large, Broadband Emission Enhancement and Single Photon Collection
We model the broadband enhancement of single-photon emission from color
centres in silicon carbide nanocrystals coupled to a planar hyperbolic
metamaterial, HMM resonator. The design is based on positioning the single
photon emitters within the HMM resonator, made of a dielectric index-matched
with silicon-carbide material. The broadband response results from the
successive resonance peaks of the lossy Fabry Perot structure modes arising
within the high-index HMM cavity. To capture this broadband enhancement in the
single photon emitters spontaneous emission, we placed a simple gold based
cylindrical antenna on top of the HMM resonator. We analyzed the performance of
this HMM coupled antenna structure in terms of the Purcell enhancement, quantum
efficiency, collection efficiency and overall collected photon rate. For
perpendicular dipole orientation relative to the interface, the HMM coupled
antenna resonator leads to a significantly large spontaneous emission
enhancement with Purcell factor of the order of 250 along with a very high
average total collected photon rate, CPR of about 30 over a broad emission
spectrum, 700 nm to 1000 nm. The peak CPR increases to about 80 at 900 nm,
corresponding to the emission of silicon-carbide quantum emitters. This is a
state of the art improvement considering the previous computational designs
have reported a maximum average CPR of 25 across the nitrogen-vacancy centre
emission spectrum, 600 nm to 800 nm with the highest value being about 40 at
650 nm
On Describing Multivariate Skewness: A Directional Approach
Most multivariate measures of skewness in the literature measure the overall skewness of a distribution. While these measures are perfectly adequate for testing the hypothesis of distributional symmetry, their relevance for describing skewed distributions is less obvious. In this article, we consider the problem of characterising the skewness of multivariate distributions. We define directional skewness as the skewness along a direction and analyse parametric classes of skewed distributions using measures based on directional skewness. The analysis brings further insight into the classes, allowing for a more informed selection of particular classes for particular applications. In the context of Bayesian linear regression under skewed error we use the concept of directional skewness twice. First in the elicitation of a prior on the parameters of the error distribution, and then in the analysis of the skewness of the posterior distribution of the regression residuals.Bayesian methods, Multivariate distribution, Multivariate regression, Prior elicitation, Skewness.
Canonical quantization of macroscopic electrodynamics in a linear, inhomogeneous magneto-electric medium
We present a canonical quantization of macroscopic electrodynamics. The
results apply to inhomogeneous media with a broad class of linear
magneto-electric responses which are consistent with the Kramers-Kronig and
Onsager relations. Through its ability to accommodate strong dispersion and
loss, our theory provides a rigorous foundation for the study of quantum
optical processes in structures incorporating metamaterials, provided these may
be modeled as magneto-electric media. Previous canonical treatments of
dielectric and magneto-dielectric media have expressed the electromagnetic
field operators in either a Green function or mode expansion representation.
Here we present our results in the mode expansion picture with a view to
applications in guided wave and cavity quantum optics.Comment: Submitted to Physical Review A 24/07/201
Slow light with flat or offset band edges in multi-mode fiber with two gratings
We consider mode coupling in multimode optical fibers using either two Bragg
gratings or a Bragg grating and a long-period grating. We show that the
magnitude of the band edge curvature can be controlled leading to a flat,
quartic band-edge or to two band edges at distinct, nonequivalent -values,
allowing precise control of slow light propagation.Comment: 6 pages, 3 figure
Invisibility and supervisibility: Radiation dynamics in a discrete electromagnetic cloak
We study the radiation dynamics of an electric dipole source placed near or inside a discrete invisibility cloak. We show that the main features of radiation dynamics can be understood in terms of the interaction of the source with a nonideal cloak in which local-field effects associated with the discrete geometry play a crucial role. As a result, radiation dynamics in a discrete cloak can differ drastically from what a source would experience in an ideal, continuous cloak. This can lead, for instance, to an enhancement of the emission by the cloak, thus making the source more visible to an outside observer than it would be without the cloak. The two main physical mechanisms for enhanced, or inhibited, radiation dynamics are the coupling of the source to leaky modes inside the cloak, and the coupling of the source with the lattice of the discrete cloak, via the local field. We also explore the robustness of the effect to material dispersion and losses
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