High-order harmonic generation yielding tunable extreme-ultraviolet radiation of high spectral purity

Production of extreme-ultraviolet radiation by high-order harmonic generation is demonstrated to yield unprecedented spectral purity of λ/Δλ=2.5×105 at wavelengths covering the entire range 40–100 nm. Tunability and sub-cm-1 bandwidth of the harmonics are demonstrated in recordings of the He (1s4p) and Ar (3p53d′) resonance lines at 52.2 and 86.6 nm. Frequency shift of the harmonics due to chirp-induced phenomena are investigated and found to be small, resulting in a frequency accuracy of about 5×10-7 in the domain of extreme-ultraviolet radiation

Generation of the second-harmonic Bessel beams via nonlinear Bragg diffraction

We generate conical second-harmonic radiation by transverse excitation of a two-dimensional annular periodically-poled nonlinear photonic structure with a fundamental Gaussian beam. We show that these conical waves are the far-field images of the Bessel beams generated in a crystal by parametric frequency conversion assisted by nonlinear Bragg diffraction.Comment: 4 pages, 5 figures. submitte

A search for transits of GJ 581\lowercase{e} and characterization of the host star variability using MOST space telescope photometry

The GJ 581 system has been amply studied since its discovery in 2005: the number of known planets in the system has increased and their orbital parameters are among the most precisely determined for radial velocity detected exoplanets. We have acquired MOST space-based photometry during 2007 and 2009, with the aims of measuring the stellar variability and searching for transits of GJ 581e, respectively. We quantify our sensitivity to shallow transit signals using Monte Carlo simulations, and perform a transit search within the 3$\sigma$ transit windows corresponding to both the circular and Keplerian orbit ephemerides. Our analysis rules out transits for a planet with an orbital period of 3.15 days (GJ 581 e) having a radius larger than 1.62 $R_{\oplus}$ (or a density lower than 2.39 g cm$^{-3}$ for an orbital inclination of 90$^{\circ}$) to 2$\sigma$ confidence. Thus, if the planet transits, we can exclude hydrogen, helium and water theoretical model compositions. The MOST photometry also allows us to rule out transits of GJ 581b within the Keplerian orbit-derived transit window for impact parameter values smaller than $\sim$0.4 and confirm previous results which exclude transits for this planet within the circular orbit-derived transit window, for all plausible interior compositions. We find that the stellar brightness of GJ 581 is stable to within 1%, a characteristic which is favourable to the development of life in the habitable zone of the system. In the 2009 photometry, we detect a stellar signal with a period of 5.586 $\pm$ 0.051 days, which is close to the orbital period of GJ 581b ($P=$5.37 days). However, further monitoring of the system is necessary to verify the nature of this variation.Comment: 11 pages, 2 tables, 10 figures; accepted for publication in Ap

Testing Identifiable Kernel P Systems Using an X-machine Approach

This paper presents a testing approach for kernel P systems (kP systems), based on the X-machine testing framework and the concept of cover automaton. The testing methodology ensures that the implementation conforms the speci cations, under certain conditions, such as the identi ably concept in the context of kernel P systems

Some results for the class of analytic functions involving Salagean differential operator

Let denote the class of function , analytic and univalent in the open unit disk , which are defined involving the Salagean differential operator , such that , . In this paper, some properties such as a representation theorem and coefficient estimates for the class are obtained

Non-detection of previously reported transits of HD 97658b with MOST photometry

The radial velocity-discovered exoplanet HD 97658b was recently announced to transit, with a derived planetary radius of 2.93 \pm 0.28 R_{Earth}. As a transiting super-Earth orbiting a bright star, this planet would make an attractive candidate for additional observations, including studies of its atmospheric properties. We present and analyze follow-up photometric observations of the HD 97658 system acquired with the MOST space telescope. Our results show no transit with the depth and ephemeris reported in the announcement paper. For the same ephemeris, we rule out transits for a planet with radius larger than 2.09 R_{Earth}, corresponding to the reported 3\sigma lower limit. We also report new radial velocity measurements which continue to support the existence of an exoplanet with a period of 9.5 days, and obtain improved orbital parameters.Comment: 16 pages, 4 figures; 1 Table; accepted for publication in ApJL, includes changes made in response to the referee repor

On transversally elliptic operators and the quantization of manifolds with ff-structure

An $f$-structure on a manifold $M$ is an endomorphism field \phi\in\Gamma(M,\End(TM)) such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure E_{1,0}\subset T_\C M given by the $+i$-eigenbundle of $\phi$. Using a compatible metric $g$ and connection $\nabla$ on $M$, we construct an odd first-order differential operator $D$, acting on sections of $\S=\Lambda E_{0,1}^*$, whose principal symbol is of the type considered in arXiv:0810.0338. In the special case of a CR-integrable almost $\S$-structure, we show that when $\nabla$ is the generalized Tanaka-Webster connection of Lotta and Pastore, the operator $D$ is given by D = \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann operator. We then describe two "quantizations" of manifolds with $f$-structure that reduce to familiar methods in symplectic geometry in the case that $\phi$ is a compatible almost complex structure, and to the contact quantization defined in \cite{F4} when $\phi$ comes from a contact metric structure. The first is an index-theoretic approach involving the operator $D$; for certain group actions $D$ will be transversally elliptic, and using the results in arXiv:0810.0338, we can give a Riemann-Roch type formula for its index. The second approach uses an analogue of the polarized sections of a prequantum line bundle, with a CR structure playing the role of a complex polarization.Comment: 31 page

Nonlinear Aharonov-Bohm scattering by optical vortices

We study linear and nonlinear wave scattering by an optical vortex in a self-defocusing nonlinear Kerr medium. In the linear case, we find a splitting of a plane-wave front at the vortex proportional to its circulation, similar to what occurs in the scattered wave of electrons for the Aharonov-Bohm effect. For larger wave amplitudes, we study analytically and numerically the scattering of a dark-soliton stripe (a nonlinear analog of a small-amplitude wavepacket) by a vortex and observe a significant asymmetry of the scattered wave. Subsequently, a wavefront splitting of the scattered wave develops into transverse modulational instability, ``unzipping'' the stripe into trains of vortices with opposite charges.Comment: 4 pages, 4 figure