Radiation 'damping' in atomic photonic crystals

The force exerted on a material by an incident beam of light is dependent upon the material's velocity in the laboratory frame of reference. This velocity dependence is known to be diffcult to measure, as it is proportional to the incident optical power multiplied by the ratio of the material velocity to the speed of light. Here we show that this typically tiny effect is greatly amplified in multilayer systems composed of resonantly absorbing atoms (e.g. optically trapped 87Rb), which may exhibit ultra-narrow photonic band gaps. The amplification of the effect is shown to be three orders of magnitude greater than previous estimates for conventional photonic-band-gap materials, and significant for material velocities of a few ms/s.Comment: 5 pages, 3 figure

Assessing skewness in financial markets

It is common knowledge that investors like large gains and dislike large losses. This translates into a preference for right-skewed return distributions, with right tails heavier than left tails. Skewness is thus interesting not only as a way to describe the shape of a distribution, but also for risk measurement. We review the statistical literature on skewness and provide a comprehensive framework for its assessment. We present a new measure of skewness, based on a relative comparison between above average and below average returns. We show that this measure represents a valid complement to the state of the art

Assessing skewness in financial markets

It is a matter of common observation that investors value substantial gains but are averse to heavy losses. Obvious as it may sound, this translates into an interesting preference for right-skewed return distributions, whose right tails are heavier than their left tails. Skewness is thus not only a way to describe the shape of a distribution, but also a tool for risk measurement. We review the statistical literature on skewness and provide a comprehensive framework for its assessment. Then, we present a new measure of skewness, based on the decomposition of variance in its upward and downward components. We argue that this measure fills a gap in the literature and show in a simulation study that it strikes a good balance between robustness and sensitivity

Recovery of Interdependent Networks

Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy of nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery $\gamma$, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction $1-p$ of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane $\gamma-p$ of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot avoid the system collapse

Role of anisotropy in the F\"orster energy transfer from a semiconductor quantum well to an organic crystalline overlayer

We consider the non-radiative resonant energy transfer from a two-dimensional Wannier exciton (donor) to a Frenkel exciton of a molecular crystal overlayer (acceptor). We characterize the effect of the optical anisotropy of the organic subsystem on this process. Using realistic values of material parameters, we show that it is possible to change the transfer rate within typically a factor of two depending on the orientation of the crystalline overlayer. The resonant matching of donor and acceptor energies is also partly tunable via the organic crystal orientation.Comment: 6 pages, 8 figure

Spatial Kramers–Kronig relations and the reflection of waves

When a planar dielectric medium has a permittivity profile that is an analytic function in the upper or lower half of the complex position plane x = x′ + ix″ then the real and imaginary parts of its permittivity are related by the spatial Kramers–Kronig relations. We find that such a medium will not reflect radiation incident from one side, whatever the angle of incidence. Using the spatial Kramers–Kronig relations, one can derive a real part of a permittivity profile from some given imaginary part (or vice versa) such that the reflection is guaranteed to be zero. This result is valid for both scalar and vector wave theories and may have relevance for designing materials that efficiently absorb radiation or for the creation of a new type of anti-reflection surface

Polaritonic stop-band transparency via exciton-biexciton coupling in CuCl

Radiation is almost completely reflected within the exciton-polariton stop band of a semiconductor, as in the typical case of CuCl. We predict, however, that a coherently driven exciton-biexciton transition allows for the propagation of a probe light beam within the stop band. The phenomenon is reminiscent of electromagnetically induced transparency effects occurring in three-level atomic systems, except that it here involves delocalized electronic excitations in a crystalline structure via a frequency and wave-vector selective polaritonic mechanism. A well-developed transparency, favored by the narrow linewidth of the biexciton, is established within the stop band where a probe pulse may propagate with significant delays. The transparency window can be controlled via the pump beam detuning and intensity