Determining the luminosity function of Swift long gamma-ray bursts with pseudo-redshifts

The determination of luminosity function (LF) of gamma-ray bursts (GRBs) is of an important role for the cosmological applications of the GRBs, which is however hindered seriously by some selection effects due to redshift measurements. In order to avoid these selection effects, we suggest to calculate pseudo-redshifts for Swift GRBs according to the empirical L-E_p relationship. Here, such a $L-E_p$ relationship is determined by reconciling the distributions of pseudo- and real redshifts of redshift-known GRBs. The values of E_p taken from Butler's GRB catalog are estimated with Bayesian statistics rather than observed. Using the GRB sample with pseudo-redshifts of a relatively large number, we fit the redshift-resolved luminosity distributions of the GRBs with a broken-power-law LF. The fitting results suggest that the LF could evolve with redshift by a redshift-dependent break luminosity, e.g., L_b=1.2\times10^{51}(1+z)^2\rm erg s^{-1}. The low- and high-luminosity indices are constrained to 0.8 and 2.0, respectively. It is found that the proportional coefficient between GRB event rate and star formation rate should correspondingly decrease with increasing redshifts.Comment: 5 pages, 5 figures, accepted for publication in ApJ

The 3+1 holographic superconductor with Weyl corrections

In this paper we study $3+1$ holographic superconductors with Weyl corrections. We find that the critical temperature of a superconductor with Weyl corrections increases as we amplify the Weyl coupling parameter $\gamma$, indicating the condensation will be harder when the parameter $\gamma$ decreases. We also calculate the conductivity and the ratio of gap frequency over critical temperature $\omega_{g}/T_{c}$ numerically for various coupling parameters. We find that the ratio $\omega_g/T_c$ becomes larger when the Weyl coupling parameter $\gamma$ decreases. We also notice that when $\gamma< 0$ there is an extra spike that appears inside the gap.Comment: 16 pages, 7 figures and 1 table, typos corrected and reference added, appendix A added, version to be published in PL

Far-Field Tunable Nano-focusing Based on Metallic Slits Surrounded with Nonlinear-Variant Widths and Linear-Variant Depths of Circular Dielectric Grating

In this work, we design a new tunable nanofocusing lens by the linear-variant depths and nonlinear-variant widths of circular grating for far field practical applications. The constructively interference of cylindrical surface plasmon launched by the subwavelength metallic structure can form a subdiffraction-limited focus, and the focal length of the this structures can be adjusted if the each groove depth and width of circular grating are arranged in traced profile. According to the numerical calculation, the range of focusing points shift is much more than other plasmonic lens, and the relative phase of emitting light scattered by surface plasmon coupling circular grating can be modulated by the nonlinear-variant width and linear-variant depth. The simulation result indicates that the different relative phase of emitting light lead to variant focal length. We firstly show a unique phenomenon for the linear-variant depths and nonlinear-variant widths of circular grating that the positive change and negative change of the depths and widths of grooves can result in different of variation trend between relative phases and focal lengths. These results paved the road for utilizing the plasmonic lens in high-density optical storage, nanolithography, superresolution optical microscopic imaging, optical trapping, and sensing.Comment: 14pages,9figure

Broadband enhanced transmission through the stacked metallic multi-layers perforated with coaxial annular apertures

This paper theoretically and experimentally presents a first report on broadband enhanced transmission through stacked metallic multi-layers perforated with coaxial annular apertures (CAAs). Different from previous studies on extraordinary transmission that occurs at a single frequency, the enhanced transmission of our system with two or three metallic layers can span a wide frequency range with a bandwidth about 60% of the central frequency. The phenomena arise from the excitation and hybridization of guided resonance modes in CAAs among different layers. Measured transmission spectra are in good agreement with calculations semi-analytically resolved by modal expansion method.Comment: 9 pages,4 figure