Stable, intense supercontinuum light generation at 1 kHz by electric field assisted femtosecond laser filamentation in air.

Supercontinuum (SC) light source has advanced ultrafast laser spectroscopy in condensed matter science, biology, physics, and chemistry. Compared to the frequently used photonic crystal fibers and bulk materials, femtosecond laser filamentation in gases is damage-immune for supercontinuum generation. A bottleneck problem is the strong jitters from filament induced self-heating at kHz repetition rate level. We demonstrated stable kHz supercontinuum generation directly in air with multiple mJ level pulse energy. This was achieved by applying an external DC electric field to the air plasma filament. Beam pointing jitters of the 1 kHz air filament induced SC light were reduced by more than 2 fold. The stabilized high repetition rate laser filament offers the opportunity for stable intense SC generation and its applications in air.

Toward 3D imaging of femtosecond laser filament in air by a CCD within a single exposure.

We experimentally demonstrated the 3D propagation of laser filament in air by an Fabry-Pérot (F-P) cavity assisted imaging within a single exposure. The F-P cavity was composed of two parallel mirrors with certain reflectivity and transmission at filament laser, so that the beam was reflected and refracted multiple times between the two mirrors. The cross-sectional intensity patterns at different longitudinal positions along filament within a single exposure of CCD (Charge-coupled Device) were recorded. When keeping the incident angle of the F-P cavity as a constant and reducing its spacing distance, a better longitudinally resolved evolution of cross-sectional filament intensity patterns was obtained. The intensity evolution along laser filament by the F-P cavity assisted imaging method was consistent with the filament fluorescence measurement from the side. As an application, the transition of laser propagation from linear to nonlinear was unveiled by the F-P cavity assisted 3D imaging.

Effects of the interaction of Notch and TLR4 pathways on inflammation and heart function in septic heart.

We investigated the role of the interaction between the Notch and Toll-like receptor 4 (TLR4) pathways in septic myocardial injury. The sepsis model was induced in rats with lipopolysaccharide (LPS). Rats were divided into control, LPS, LPS + TAK242 ((6R)-6-[N-(2-chloro-4-fluorophenyl)sulfamoyl]cyclohex-1-ene-1-carboxylate) and LPS + DAPT (N-[N-(3,5-difluorophenacetyl)-l-alanyl]-s-phenylglycinetbutylester) groups. Heart function was evaluated with a Cardiac Doppler ultrasound. Myocardial morphological changes were detected by hematoxylin-eosin staining (H&E). Apoptosis was assessed by a TUNEL assay. The mRNA and protein levels were detected with real-time PCR, Western blot, and immunohistochemistry analysis. We found that heart function in the LPS + TAK242 group was significantly improved, but not in the LPS + DAPT group. LPS + TAK242 had a lower level of degeneration and necrosis of cardiomyocytes and inflammatory cell infiltration, as well as lower apoptosis and caspase-3 expression than the LPS group. Compared with the LPS group, the inflammatory cell infiltration was reduced in the LPS + DAPT group, while the degeneration and necrosis of cardiomyocytes were not obviously improved. Additionally, the expression levels of tumor necrosis factor-α and Interleukin-6, the protein contents of Notch intracellular domain and Hes1, and the P65 nuclear factor kappa-B (NF-κB) to P-P65 NF-κB ratio in LPS + TAK242 group and LPS + DAPT group were significantly lower than those in LPS group. Conclusively, the interaction between TLR4 and Notch signaling pathways enhances the inflammatory response in the septic heart by activating NF-κB. Blocking the TLR4 pathway with TAK242 can improve heart dysfunction and myocardial damage in sepsis, while blocking the Notch pathway with DAPT cannot effectively prevent heart dysfunction and myocardial damage in sepsis.

Laser ellipticity-dependent supercontinuum generation by femtosecond laser filamentation in air.

We experimentally investigate the laser polarization effect on the supercontinuum (SC) generation through femtosecond laser filamentation in air. By tuning filamenting laser ellipticity from linear polarization to circular polarization, the spectral intensity of the SC after filamentation gradually increases, while the spectral bandwidth of the SC continuously decreases. The laser ellipticity-dependent spectral intensity modulation of the SC is stronger at higher filamenting pulse energy. Laser energy deposits more in linearly polarized laser filaments than in circularly polarized laser filaments. The experimental results are supported by numerical simulations. A physical picture based on the laser ellipticity-dependent clamped intensity inside the filament, together with the Kerr nonlinearity and plasma related self-phase modulations, is proposed to explain the observation.

Couple of the variational iteration method and fractional-order Legendre functions method for fractional differential equations.

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid "noise terms" is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique.