Pushing indium phosphide quantum dot emission deeper into the near infrared

Cadmium-free near infrared (NIR) emitting quantum dots (QDs) have significant potential for multiplexed tissue-depth imaging applications in the first optical tissue window (i.e., 650 – 900 nm). Indium phosphide (InP) chemistry provides one of the more promising cadmium-free options for biomedical imaging, but the full tunability of this material has not yet been achieved. Specifically, InP QD emission has been tuned from 480 – 730 nm in previous literature reports, but examples of samples emitting from 730 nm to the InP bulk bandgap limit of 925 nm are lacking. We hypothesize that by generating inverted structures comprising ZnSe/InP/ZnS in a core/shell/shell heterostructure, optical emission from the InP shell can be tuned by changing the InP shell thickness, including pushing deeper into the NIR than current InP QDs. Colloidal synthesis methods including hot injection precipitation of the ZnSe core and a modified successive ion layer adsorption and reaction (SILAR) method for stepwise shell deposition were used to promote growth of core/shell/shell materials with varying thicknesses of the InP shell. By controlling the number of injections of indium and phosphorous precursor material, the emission peak was tuned from 515 nm to 845 nm (2.41 – 1.47 eV) with consistent full width half maximum (FWHM) values of the emission peak ~0.32 eV. To confer water solubility, the nanoparticles were encapsulated in PEGylated phospholipid micelles, and multiplexing of NIR-emitting InP QDs was demonstrated using an IVIS imaging system. These materials show potential for multiplexed imaging of targeted QD contrast agents in the first optical tissue window

On the Casselman-Jacquet functor

We study the Casselman-Jacquet functor $J$, viewed as a functor from the (derived) category of $(\mathfrak{g},K)$-modules to the (derived) category of $(\mathfrak{g},N^-)$-modules, $N^-$ is the negative maximal unipotent. We give a functorial definition of $J$ as a certain right adjoint functor, and identify it as a composition of two averaging functors $\text{Av}^{N^-}_!\circ \text{Av}^N_*$. We show that it is also isomorphic to the composition $\text{Av}^{N^-}_*\circ \text{Av}^N_!$. Our key tool is the pseudo-identity functor that acts on the (derived) category of (twisted) $D$-modules on an algebraic stack.Comment: Very minor modifications, compared to previous version (to appear in Proceedings of Symposia in Pure Mathematics volume, titled "Representations of Reductive Groups"

A random wave model for the Aharonov-Bohm effect

We study an ensemble of random waves subject to the Aharonov-Bohm effect. The introduction of a point with a magnetic flux of arbitrary strength into a random wave ensemble gives a family of wavefunctions whose distribution of vortices (complex zeros) are responsible for the topological phase associated with the Aharonov-Bohm effect. Analytical expressions are found for the vortex number and topological charge densities as functions of distance from the flux point. Comparison is made with the distribution of vortices in the isotropic random wave model. The results indicate that as the flux approaches half-integer values, a vortex with the same sign as the fractional part of the flux is attracted to the flux point, merging with it at half-integer flux. Other features of the Aharonov-Bohm vortex distribution are also explored.Comment: 16 pages, 5 figure