Interplay between disorder and local field effects in photonic crystal waveguides

We introduce a theory to describe disorder-induced scattering in photonic crystal waveguides, specifically addressing the influence of local field effects and scattering within high-index-contrast perturbations. Local field effects are shown to increase the predicted disorder-induced scattering loss and result in significant resonance shifts of the waveguide mode. We demonstrate that two types of frequency shifts can be expected, a mean frequency shift and a RMS frequency shift, both acting in concert to blueshift and broaden the nominal band structure. For a representative waveguide, we predict substantial meV frequency shifts and band structure broadening for a telecommunications operating frequency, even for state of the art fabrication. The disorder-induced broadening is found to increase as the propagation frequency approaches the slow light regime (mode edge) due to restructuring of the electric field distribution. These findings have a dramatic impact on high-index-contrast nanoscale waveguides, and, for photonic crystal waveguides, suggest that the nominal slow-light mode edge may not even exist. Furthermore, our results shed new light on why it has hitherto been impossible to observe the very slow light regime for photonic crystal waveguides.Comment: 4 page lette

Solitary confinement and the U.S. prison boom

Solitary confinement is a harsh form custody involving isolation from the general prison population and highly restricted access to visitation and programs. Using detailed prison records covering 30 years of practices in Kansas (1985–2014), we find solitary confinement is a normal event during imprisonment: 38 percent of whites and 46 percent of blacks experienced solitary confinement during their prison term. Long stays in solitary confinement were rare in the late 1980s with no detectable racial disparities, but a sharp increase in capacity after a new prison opening began an era of long-term isolation that most heavily impacted black young adults. A decomposition analysis indicates the increase in the length of stay in solitary confinement almost entirely explains the growth in the proportion of people held in solitary confinement. Our results provide new evidence of increasingly punitive prison conditions and previously unmeasured forms of inequality during the prison boom.Accepted manuscrip

Mechanism of Cloud Cavitation Generation on a 2-D Hydrofoil

When a sheet cavity on a hydrofoil section attains a certain size, it starts violent periodical oscillation shedding a harmful cloud cavity downstream at each oscillation cycle. This phenomenon is due to the occurrence of the re-entrant jet. In this paper, the behavior of the re-entrant jet was observed in detail using a transparent foil section model and a high-speed video camera. Time variation of pressure distribution on the foil was measured simultaneously. It was found that the re-entrant jet can start at any point in sheet cavity elongating stage. Even two re-entrant jets can appear in one cycle. When a re-entrant jet is generated upstream, the jet velocity is lower compared to the case when a re-entrant jet is generated downstream. The jet velocity is almost constant at the value determined by the location of the generation. As a result, the cavity oscillation cycle becomes constant when it is normalized by the sheet cavity surface velocity and the maximum sheet cavity length. The jet velocity is calculated from the pressure gradient at the sheet cavity T.E., using a simple theoretical model. The calculated jet velocity agrees with the measurement, showing that the jet velocity increases as its generation point shifts downstream. It is possible that pressure gradient at the sheet cavity T.E. is the driving force of re-entrant jet

Coherent states, Path integral, and Semiclassical approximation

Using the generalized coherent states we argue that the path integral formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$ being given by a linear combination of generators. In our case,WKB approximation is achieved by taking a large ``spin'' limit: $J,K\rightarrow \infty$. The result is obtained directly by knowing that the each coefficient vanishes under the $J^{-1}$($K^{-1}$) expansion and is examined by another method to be legitimated. We also point out that the discretized form of path integral is indispensable, in other words, the continuum path integral expression leads us to a wrong result. Therefore a great care must be taken when some geometrical action would be adopted, even if it is so beautiful, as the starting ingredient of path integral.Comment: latex 33 pages and 2 figures(uuencoded postscript file), KYUSHU-HET-19 We have corrected the proof of the WKB-exactness in the section