Non-linear structure of the light-intensity-output versus pump-input characteristics in self-pulsing lasers

This paper is intended to show that laser-intensity-output versus excitation characteristics of bad-cavity configured lasers deviate from the linearly expected evolution when these are driven beyond the instability threshold. These deviations result in collapsed curves with marked and discernible intensity-reduction at the onset of instability. Such behaviors are shown to be rooted in the fundamental and intrinsic aspects of both the single mode homogeneously-broadened laser and the inhomogeneously-broadened system. In addition, we clarify, for the first example, the physical origin of a hysteresis effect which is known to occur when the pump-input power is scanned from levels above to levels below the instability threshold. As for the inhomogeneous case, a lateral hole-burning effect, which takes place in the spectral profile at high excitations, is shown to shift the output-intensity towards higher levels, with respect to the steady-state values. Simple theoretical elements are put forward to identify the physical origin of these features.     

Dynamical response of modulated Nd-doped kilometric fibre lasers

The response to pump-power modulation of Nd-doped fibre lasers with lengths in the kilometre range is reported. The timescales involved are close to those of subcritical regimes so that the transient relaxation oscillations are strongly damped. Furthermore, no competing effects (antiphase dynamics) occur between the two polarization eigenstates of the laser. Simple rate equations are shown to predict these behaviours. The experimental side of this study furnishes a definite demonstration of the importance of timescales in the dynamical properties of nonlinear and nonautonomous physical systems.     

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.     

Band Theory in the Context of the Hamilton-Jacobi Formulation

In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence postulate of quantum mechanics. Then, without appealing to the wave function properties, we reproduce the well-known dispersion relations which predict the band structure for the energy spectrum in the Krönig-Penney model.     

Search for effects beyond the born approximation in polarization transfer observables in e(over→)p elastic scattering

Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, G(E)/G(M), obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic H(e[over →],e(')p[over →]) reaction for three different beam energies at a Q(2)=2.5 GeV(2), spanning a wide range of the kinematic parameter ε. The ratio R, which equals μ(p)G(E)/G(M) in the Born approximation, is found to be independent of ε at the 1.5% level. The ε dependence of the longitudinal polarization transfer component P(?) shows an enhancement of (2.3±0.6)% relative to the Born approximation at large ε.     

Measurements of the proton elastic-form-factor ratio mu pG p E/G p M at low momentum transfer

High-precision measurements of the proton elastic form-factor ratio, mu pG p E/G p M, have been made at four-momentum transfer, Q2, values between 0.2 and 0.5 GeV2. The new data, while consistent with previous results, clearly show a ratio less than unity and significant differences from the central values of several recent phenomenological fits. By combining the new form-factor ratio data with an existing cross-section measurement, one finds that in this Q2 range the deviation from unity is primarily due to G p E being smaller than expected.     

Microwave Michaelis–Becker synthesis of diethyl phosphonates,tetraethyl diphosphonates,and their total or partial dealkylation

Diethyl phosphonates and tetraethyl alkyldiphosphonates were efficiently and rapidly prepared via the Michaelis–Becker reaction, under microwave irradiation. These compounds were then hydrolyzed to phosphonic and diphosphonic acids or selectively monodealkylated to give monoesters of phosphonic acids and symmetrical diethyl esters of diphosphonic acids. These reactions were also achieved rapidly in satisfactory yields with microwave methodology. This methodology was applied with success to the functionalization of a polymer resin. © 2009 Wiley Periodicals, Inc. Heteroatom Chem 20:369–377, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20561     

Weak versus strong harmonic-expansion analyses of self-pulsing lasers: I—the Laser Lorenz model

We apply a simple harmonic expansion method to the single-mode laser equations to analyze their dynamic properties. First, we extend the well-known small signal analysis to predict the transient pulsations of the relaxation oscillations. Such transients are characteristic of the laser signal relaxing towards its long-term solution, at any level of excitation, both beyond and below the instability threshold. Secondly, we extend the method to a strong harmonic expansion to analyze the properties of the long-term solutions. These properties are derived for typical examples, extending well beyond the boundary region of the instability domain, for which the laser field amplitude undergoes regular pulsations around zero-mean values.