Analysis of retroreflector-introduced spectrum distortion in birefringent crystal-based interleaver filters

Spectrum distortion in a birefringent crystal-based interleaver filter introduced by the right-angle total internal reflection retroreflector is studied. The phase shift between two perpendicularly polarized components of the polarized light incident onto the retroreflector is calculated. The sensitivity of the phase shift to the incident angle for different materials from which the retroreflector is made is also considered. This study indicates that the phase shift is less sensitive to the incident angle for retroreflectors having a higher index of refraction, suggesting a fixed-phase compensator that can be used to cancel out the phase shift introduced by the retroreflector to recover the interleaver filter's spectrum. The fold-back 50 GHz channel spacing birefringent crystal interleaver filter is fabricated to demonstrate that the spectrum distortion due to the phase shift introduced by retroreflector can be eliminated by a phase compensator.     

A microscopic pedestrian-simulation model and its application to intersecting flows

We develop a microscopic pedestrian-simulation model in which pedestrian positions are updated at discrete time steps. At each time step, each pedestrian probabilistically selects a direction of movement from a predetermined set according to a logit-type function that considers the dynamics of other pedestrians around, and then selects a step size that satisfies a certain distribution. We perform a number of field experiments on real intersecting pedestrian flows with four different angles. We then validate and calibrate the model using sample data on the deviation angles, step velocities, and velocity–density relations obtained from the experiments.     

Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Pd Uptake and H2S Sensing by an Amphoteric Metal–Organic Framework with a Soft Core and Rigid Side Arms

Molecular components of opposite character are often incorporated within a single system, with a rigid core and flexible side arms being a common design choice. Herein, molecule L has been designed and prepared featuring the reverse design, with rigid side arms (arylalkynyl) serving to calibrate the mobility of the flexible polyether links in the core. Crystallization of this molecule with Pb^II ions led to a dynamic metal–organic framework (MOF) system that not only exhibits dramatic, reversible single‐crystal‐to‐single‐crystal transformations, but combines distinct donor and acceptor characteristics, allowing for substantial uptake of PdCl₂ and colorimetric sensing of H₂S in water.