The Green-function transform and wave propagation

Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogenous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given

Temporal reshaping of two-dimensional pulses.

An analytic study of complete cylindrical focusing of pulses in two dimensions is presented, and compared with the analogous three-dimensional case of focusing over a complete sphere. Such behavior is relevant for understanding the limiting performance of ultrafast, planar photonic and plasmonic devices. A particular spectral distribution is assumed that contains finite energy. Separate ingoing and outgoing pulsed waves are considered, along with the combination that would be generated in free space by an ingoing wave. It is shown that for the two dimensional case, in order to produce a temporally symmetrical pulse at the focus, an asymmetric pulse must be launched. A symmetrical outgoing pulse is generated from a source with asymmetric time behavior, or an anti-symmetric input pulse. These results are very different from the corresponding three-dimensional case, and imply fundamental limitations on the performance of ultrafast, tightly focused, two-dimensional devices

Mode-matching metasurfaces: coherent reconstruction and multiplexing of surface waves

Metasurfaces are promising two-dimensional metamaterials that are engineered to provide unique properties or functionalities absent in naturally occurring homogeneous surfaces. Here, we report a type of metasurface for tailored reconstruction of surface plasmon waves from light. The design is generic in a way that one can selectively generate different surface plasmon waves through simple variation of the wavelength or the polarization state of incident light. The ultra-thin metasurface demonstrated in this paper provides a versatile interface between the conventional free-space optics and a two-dimensional platform such as surface plasmonics.Comment: 7 figures, supplementary information at the end of the documen

On the relation between the mass of Compact Massive Objects and their host galaxies

Supermassive black holes and/or very dense stellar clusters are found in the central regions of galaxies. Nuclear star clusters are present mainly in faint galaxies while upermassive black holes are common in galaxies with masses $\geq 10^{10}$ M$_\odot$. In the intermediate galactic mass range both types of central massive objects (CMOs) are found. Here we present our collection of a huge set of nuclear star cluster and massive black hole data that enlarges significantly already existing data bases useful to investigate for correlations of their absolute magnitudes, velocity dispersions and masses with structural parameters of their host galaxies. In particular, we directed our attention to some differences between the correlations of nuclear star clusters and massive black holes as subsets of CMOs with hosting galaxies. In this context, the mass-velocity dispersion relation plays a relevant role because it seems the one that shows a clearer difference between the supermassive black holes and nuclear star clusters. The $M_{MBH}-{\sigma}$ has a slope of $5.19\pm 0.28$ while $M_{NSC}-{\sigma}$ has the much smaller slope of $1.84\pm 0.64$. The slopes of the CMO mass- host galaxy B magnitude of the two types of CMOs are indistinguishable within the errors while that of the NSC mass-host galaxy mass relation is significantly smaller than for supermassive black holes. Another important result is the clear depauperation of the NSC population in bright galaxy hosts, which reflects also in a clear flattening of the NSC mass vs host galaxy mass at high host masses.Comment: 12 pages, 22 figures, 2 tables, accepted for publication in MNRA

High glucose on the expression of N-cadherin and fibronectin in retinal pigment epithelium cells

AIM: To observe the expression of N-cadherin and fibronectin in retinal pigment epithelium(RPE)cells <i>in vitro </i>under high glucose conditions, furthermore, to explore the effects of high glucose on epithelial-mesenchymal transition(EMT)in RPE cells.<p>METHODS: Human RPE(hRPE)cells were cultured <i>in vitro</i>. Containing a final concentration of 60mmol/L glucose was used for high glucose treatment. The cells were divided into normal glucose group(5.5mmol/L, NG)and high glucose group(24, 48 and 72h)respectively. The expression of N-cadherin and fibronectin in hRPE cells were evaluated by immunofluorescence and real-time PCR.<p>RESULTS:RPE cells became disorganized and swollen over time under high glucose conditions, especially in 72h subgroup. Immunohistochemical analysis revealed that the expression of N-cadherin in RPE cells under high glucose conditions was decreased compared with that in the control group, while the expression of fibronectin was increased. Real-time PCR results showed that the expression of N-cadherin mRNA in high glucose group was decreased at 24h compared with that in the control group, and declined markedly at 72h(<i>F</i>=12.252, <i>P</i>=0.000). There were no significant differences between the control group and the high glucose group at 24h, while the differences between the control group and the high glucose group(48 and 72h)were significant respectively(<i>P</i><0.05). Meanwhile, the expression of fibronectin mRNA in RPE cells was increased in high glucose group at 24h, and reached the peak at 72h(<i>F</i>=50.543, <i>P</i>=0.000). There were no significant differences between the control group and the high glucose group at 24h. Compared with the control group, the expression of fibronectin mRNA in hRPE cells was increased significantly in high glucose group(48 and 72h)respectively(<i>P</i>=0.000, <i>P</i>=0.000).<p>CONCLUSION: The expression of epithelium marker N-cadherin is down-regulated under high glucose conditions in hRPE cells <i>in vitro</i>. Meanwhile, the expression of mesenchymal maker fibronectin is induced and appeared to EMT changes. Results of this study will enrich our growing understanding in proliferative diabetic retinopathy and hopefully lead to novel insights for the pathogenesis and therapeutic treatments