Bijective Proofs of Gould's and Rothe's Identities

We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.Comment: 4 page

Terahertz Wave Guiding by Femtosecond Laser Filament in Air

Femtosecond laser filament generates strong terahertz (THz) pulse in air. In this paper, THz pulse waveform generated by femtosecond laser filament has been experimentally investigated as a function of the length of the filament. Superluminal propagation of THz pulse has been uncovered, indicating that the filament creates a THz waveguide in air. Numerical simulation has confirmed that the waveguide is formed because of the radially non-uniform refractive index distribution inside the filament. The underlying physical mechanisms and the control techniques of this type THz pulse generation method might be revisited based on our findings. It might also potentially open a new approach for long-distance propagation of THz wave in air.Comment: 5 pages, 6 figure

Impulsive rotational Raman scattering of N2 by a remote "air laser" in femtosecond laser filament

We report on experimental realization of impulsive rotational Raman scattering from neutral nitrogen molecules in a femtosecond laser filament using an intense self-induced white-light seeding "air laser" generated during the filamentation of an 800 nm Ti: Sapphire laser in nitrogen gas. The impulsive rotational Raman fingerprint signals are observed with a maximum conversion efficiency of ~0.8%. Our observation provides a promising way of remote identification and location of chemical species in atmosphere by rotational Raman scattering of molecules.Comment: 4 pages, 4 figure

High-brightness switchable multi-wavelength remote laser in air

Remote laser in air based on amplified spontaneous emission (ASE) has produced rather well-collimated coherent beams in both backward and forward propagation directions, opening up possibilities for new remote sensing approaches. The remote ASE-based lasers were shown to enable operation either at ~391 and 337 nm using molecular nitrogen or at ~845 nm using molecular oxygen as gain medium, depending on the employed pump lasers. To date, a multi-wavelength laser in air that allows for dynamically switching the operating wavelength has not yet been achieved, although this type of laser is certainly of high importance for detecting multiple hazard gases. In this Letter, we demonstrate, for the first time to our knowledge, a harmonic-seeded switchable multi-wavelength laser in air driven by intense mid-infrared femtosecond laser pulses. Furthermore, population inversion in the multi-wavelength remote laser occurs at an ultrafast time-scale (i.e., less than ~200 fs) owing to direct formation of excited molecular nitrogen ions by strong-field ionization of inner-valence electrons, which is fundamentally different from the previously reported pumping mechanisms based either on electron recombination of ionized molecular nitrogen or on resonant two-photon excitation of atomic oxygen fragments resulting from resonant two-photon dissociation of molecular oxygen. The bright multi-wavelength laser in air opens the perspective for remote detection of multiple pollutants based on nonlinear spectroscopy.Comment: 18 pages, 5 figure