A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

Improvement of the PLD process assisted by RF plasma for AlN growth

The pulsed-laser-deposition (PLD) method is particularly well suited for the growth of oxide thin films, but in the case of other compounds, such as nitrides, PLD presents some limitations which are mainly due to the low reactivity of nitrogen in comparison with oxygen. A possible way to overcome this problem is to increase the reactivity of the constituent species, via plasma assisted-pulsed-laser deposition. A plasma is coupled to the ablation chamber, in order to increase the density of reactive atomic species, which can be further incorporated in the growing film. This approach is described in this paper as well as the nature, energy, and concentration of the atomic and molecular species in the plasma as determined by various plasma diagnostics. These results are correlated to the growth of thin films in the particular case of the aluminum nitride compound. The composition and structure of the films are studied as a function of the growth conditions, and the positive effects of the additional discharge are evidenced on the film purity and properties. The fundamental problem with the PLD technique, especially with metallic targets, is the production of unwanted droplets that significantly worsen the properties of the films. To eliminate these droplets, a thin film has been grown with an experimental setup using two targets and crossed laser beams which gave positive results. PACS 81.15.Fg; 52.80.Pi; 77.84.Bw     

Band-edge-induced Bragg diffraction in two-dimensional photonic crystals

Two-dimensional photonic crystals composed of two orthogonal volume diffraction gratings have been photogenerated in photopolymers. When the read beam is set at the Bragg angle, the diffraction efficiency of the transmission grating is strongly enhanced at the band edge of the reflection grating recorded in the material. Such a device provides Bragg operation and enhancement of the diffraction efficiency of the thin diffraction grating together with good wavelength selectivity. Such advantages could be interesting for optical signal processing.     

Song of the dunes as a self-synchronized instrument

Since Marco Polo it has been known that some sand dunes have the peculiar ability to emit a loud sound with a well-defined frequency, sometimes for several minutes. The origin of this sustained sound has remained mysterious, partly because of its rarity in nature. It has been recognized that the sound is not due to the air flow around the dunes but to the motion of an avalanche, and not to an acoustic excitation of the grains but to their relative motion. By comparing singing dunes around the world and two controlled experiments, in the laboratory and the field, we prove that the frequency of the sound is the frequency of the relative motion of the sand grains. Sound is produced because moving grains synchronize their motions. The laboratory experiment shows that the dune is not needed for sound emission. A velocity threshold for sound emission is found in both experiments, and an interpretation is proposed.     

Huge excitonic effects in layered hexagonal boron nitride

The all-electron GW approximation energy band gap of bulk hexagonal boron nitride is shown to be of indirect type. The resulting computed in-plane polarized optical spectrum, obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function, is in excellent agreement with experiment and has a strong anisotropy compared to out-of-plane polarized spectrum. A detailed analysis of the excitonic structures within the band gap shows that the low-lying excitons belong to the Frenkel class and are tightly confined within the layers. The calculated exciton binding energy is much larger than that obtained by Watanabe et al. [Nat. Mater. 3, 404 (2004).] based on a Wannier model assuming h-BN to be a direct-band-gap semiconductor.     

Quasiperiodicity and randomness in tilings of the plane

We define new tilings of the plane with Robinson triangles, by means of generalized inflation rules, and study their Fourier spectrum. Penrose's matching rules are not obeyed; hence the tilings exhibit new local environments, such as three different bond lengths, as well as new patterns at all length scales. Several kinds of such generalized tilings are considered. A large class of deterministic tilings, including chiral tilings, is strictly quasiperiodic, with a tenfold rotationally symmetric Fourier spectrum. Random tilings, either locally (with extensive entropy) or globally random (without extensive entropy), exhibit a mixed (discrete+continuous) diffraction spectrum, implying a partial perfect long-range order.     

Simultaneously suppressing frequency and intensity noise in a Nd:YAG nonplanar ring oscillator by means of the current-lock technique

We show that frequency and intensity noise in a Nd:YAG laser are correlated to a high degree and can be traced to the same underlying cause, namely, power fluctuations of the pump source. Because of this correlation, simultaneous suppression of frequency and intensity noise by 30 dB is achieved by means of a single actuator, the pump power.     

Water vapor: An extraordinary terahertz wave source under optical excitation

In modern terahertz (THz) sensing and imaging spectroscopy, water is considered a nemesis to be avoided due to strong absorption in the THz frequency range. Here we report the first experimental demonstration and theoretical implications of using femtosecond laser pulses to generate intense broadband THz emission from water vapor. When we focused an intense laser pulse in water vapor contained in a gas cell or injected from a gas jet nozzle, an extraordinarily strong THz field from optically excited water vapor is observed. Water vapor has more than 50% greater THz generation efficiency than dry nitrogen. It had previously been assumed that the nonlinear generation of THz waves in this manner primarily involves a free-electron plasma, but we show that the molecular structure plays an essential role in the process. In particular, we found that THz wave generation from H₂O vapor is significantly stronger than that from D₂O vapor. Vibronic activities of water cluster ions, occurring naturally in water vapor, may possibly contribute to the observed isotope effect along with rovibrational contributions from the predominant monomers.