D-scan measurement of nonlinear refractive index in fibers heavily doped with GeO2

Concentration dependence of nonlinear refractive index n2 in fibers heavily doped with GeO2 is studied by using the D-scan method. Good agreement with an empirical dependence established earlier with lower GeO2 concentrations by the cw dual-frequency beat signal technique is shown for GeO2 concentrations up to approximately 100 mol.%. The highest values of the nonlinear coefficient gamma at 1.25 microm of 47.9, 57.7, and 70.9 W(-1) km(-1) were obtained in fibers doped with 67, 75, and 97 mol.% GeO2, respectively.     

Growth of Fe on Ge(1 1 1) at room temperature studied by X-ray photoelectron diffraction

The growth of ultrathin Fe films of various coverages on Ge(1 1 1) at room temperature using molecular beam epitaxy (MBE) was studied via X-ray photoelectron diffraction (XPD or XPED) together with low energy electron diffraction (LEED) and X-ray photoelectron spectroscopy (XPS). All experimentally observed XPD patterns suggested local order structures of the Fe layers for all thicknesses studied. The short-range order of the resulting structures was found to be enhanced for thinner layers whereas the long-range order was gradually lost with increasing Fe thicknesses. At a very low coverage of 0.8 Å Fe and Ge tend to react to the partly ordered structure in which Fe atoms were located in local environments similar to those for higher Fe coverages. Comparison of theoretical and experimental XPD patterns, along with XPS results, showed that intermixing between Fe and Ge occurred during the pseudomorphic growth with a stacking fault near the interface for all Fe coverages under study. Nevertheless, small percentage of domains without the stacking fault was also found to coexist with those with the stacking fault by performing a quantitative analysis of a reliability factor R of the Fe2p pattern for 5.4 Å. The orientation changes of the Ge2p and Ge3d XPD patterns with Fe thickness were unambiguously explained in terms of their different dependencies on the overlayer thickness due to the different inelastic mean free path lengths used in the simulations. Also, Fe got increasingly enriched in the grown layers with increased Fe coverage. The resulting structures and intermixing are discussed in detail.     

Hierarchical ferromagnetic vector spin model possessing the Lee-Yang property. Thermodynamic limit at the critical point and above

The hierarchical ferromagneticN-dimensional vector spin model as a sequence of probability measures onR ^N is considered. The starting element of this sequence is chosen to belong to the Lee-Yang class of measures that is defined in the paper and includes most known examples (⁴ measures, Gaussian measures, and so on). For this model, we probe two thermodynamic limit theorems. One of them is just the classical central limit theorem for weakly dependent random vectors. It describes the convergence of classically normed sums of spins when temperature is sufficiently high. The other theorem describes the convergence of more than normally normed sums that holds for some fixed temperature. It corresponds to the strong dependence of spins, which appears at the critical point of the model.     

Spatial optical solitons supported by mutual focusing

We study composite spatial optical solitons supported by two-wave mutual focusing induced by cross-phase modulation in Kerr-like nonlinear media. We find the families of both single- and two-hump solitons and discuss their properties and stability. We also reveal remarkable similarities between recently predicted holographic solitons in photorefractive media and parametric solitons in quadratic nonlinear crystals.     

Universal scaling in transient creep

We present experimental evidence that pressure solution creep does not establish a steady-state interface microstructure as previously thought. Conversely, pressure solution controlled strain and the characteristic length scale of interface microstructures grow as the cubic root of time. Transient creep with the same scaling is known in metallurgy (Andrade creep). The apparent universal scaling of pressure solution transient creep is explained using an analogy with spinodal dewetting.     

Master Equation in Phase Space for a Uniaxial Spin System

A master equation, for the time evolution of the quasi-probability density function of spin orientations in the phase space representation of the polar and azimuthal angles is derived for a uniaxial spin system subject to a magnetic field parallel to the axis of symmetry. This equation is obtained from the reduced density matrix evolution equation (assuming that the spin-bath coupling is weak and that the correlation time of the bath is so short that the stochastic process resulting from it is Markovian) by expressing it in terms of the inverse Wigner-Stratonovich transformation and evaluating the various commutators via the properties of polarization operators and spherical harmonics. The properties of this phase space master equation, resembling the Fokker-Planck equation, are investigated, leading to a finite series (in terms of the spherical harmonics) for its stationary solution, which is the equilibrium quasi-probability density function of spin “orientations” corresponding to the canonical density matrix and which may be expressed in closed form for a given spin number. Moreover, in the large spin limit, the master equation transforms to the classical Fokker-Planck equation describing the magnetization dynamics of a uniaxial paramagnet.     

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

We study a spatial birth-and-death process on the phase space of locally finite configurations \({\varGamma }^+ \times {\varGamma }^-\) over \({\mathbb {R}}^d\). Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator \(L^+(\gamma ^-) + \frac{1}{\varepsilon }L^-\), \(\varepsilon > 0\). Here \(L^-\) describes the environment process on \({\varGamma }^-\) and \(L^+(\gamma ^-)\) describes the system process on \({\varGamma }^+\), where \(\gamma ^-\) indicates that the corresponding birth-and-death rates depend on another locally finite configuration \(\gamma ^- \in {\varGamma }^-\). We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states \(\mu _t^{\varepsilon }\) on \({\varGamma }^+ \times {\varGamma }^-\). Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let \(\mu _{\mathrm {inv}}\) be the invariant measure for the environment process on \({\varGamma }^-\). In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of \(\mu _t^{\varepsilon }\) onto \({\varGamma }^+\) converges weakly to an evolution of states on \({\varGamma }^+\) associated with the averaged Markov birth-and-death operator \({\overline{L}} = \int _{{\varGamma }^-}L^+(\gamma ^-)d \mu _{\mathrm {inv}}(\gamma ^-)\).     

Carbon-nanotube-based saturable absorbers for near infrared solid state lasers

We demonstrate the passive mode-locking of a diode-pumped Nd⁺³:YAG (central wavelength: 1.32 μm; pulse duration: 50 ps; output energy: up to 70 μJ) laser using a polymer film containing single-wall carbon nanotubes. The mode-locking regime is stable at a pump repetition rate of up to 1 kHz. We also investigate the temporal evolution of the light-induced absorption change of the polymer film containing carbon nanotubes in the spectral range of 1.3–1.5 μm by femtosecond time-resolved pump-probe measurements. The measurements reveal that light-induced transmission exhibits fast and slow components that last 280 fs and more than 10 ps, respectively. The third-order susceptibility of the polymer film containing single wall carbon nanotubes is as high as 10⁻¹¹ esu.     

How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...