Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra

Principal parameters of the nonlinear-optical crystals are analyzed, which govern the spectral sensitivity of the terahertz wave detectors based on the frequency conversion from terahertz to optical range. A method is developed and experimentally demonstrated for characterizing these parameters. The method is founded on the spontaneous parametric down-conversion spectra observation without external terahertz wave radiation.     

Study of thermal transformations of aluminum phosphate binder and composites on its basis with various fillers

Results are reported obtained in a study of the physicochemical processes occurring under heating in the temperature range 150–1100°C of an aluminum phosphate binder and composites on its basis with various fillers (SiO₂, Al₂O₃, BN, and TiO₂ nanoparticles) with the use of an X-ray diffraction analysis.     

On the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer

The problem of parabolic spline interpolation, according to Subbotin, of functions with large gradients in the boundary layer is considered. In the case of a uniform grid it is proved and in the case of the Shishkin mesh it is experimentally shown that with a parabolic spline interpolation of functions with large gradients in the exponential boundary layer, the error can unrestrictedly increase when the small parameter tends to zero and the number of grid nodes is fixed. An approximation process using parabolic splines with defect 1 is proposed; the error estimates are found to be uniform in the small parameter.     

On the threshold stress in superplasticity

The problem of threshold stress, as applied to superplasticity, is considered in terms of rheological and dynamic approaches. The necessity of introducing threshold stress in rheological relationships is shown. In a dynamic case, the threshold stress is a consequence of model constructions and is an evolution parameter.     

Conditional ε-uniform boundedness of Galerkin projectors and convergence of an adaptive mesh method as applied to singularly perturbed boundary value problems

The Galerkin finite element method is applied to nonself-adjoint singularly perturbed boundary value problems on Shishkin meshes. The Galerkin projection method is used to obtain conditionally ε-uniform a priori error estimates and to prove the convergence of a sequence of meshes in the case of an unknown boundary layer edge.     

Convergence of a Bakhvalov grid adaptation method for singularly perturbed boundary value problems

In this paper, a Galerkin finite element method for non-self-adjoint boundary value problems on Bakhvalov grids is considered. Using the Galerkin projectionmethod, the convergence of a sequence of computational grids with an unknown boundary of the boundary layer is proved. Some numerical examples are presented.     

Stochastic Equations of Sobolev Type with Relatively $$p $$ -Radial Operators in Spaces of Differential Forms

Differential Equations - We consider the Showalter–Sidorov problem for the stochastic version of the linear Ginzburg–Landau equation in Hilbert spaces of smooth differential forms...     

Visible and infrared dispersion of the refractive indices in periodically poled and single domain Nd:Mg:LiNbO3 crystals

3 crystals are measured in the transparency region (with the accuracy ±0.0002) and for the upper phonon polariton branch (with the accuracy ±0.003–±0.05), from 0.44 μm up to 10.5 μm. The method of spontaneous parametric light scattering is used for measurement of the ordinary refractive index dispersion in the mid-infrared region and for determination of the domain grating period d=5.6±0.2 μm in the periodically-poled crystal. Received: 29 January 1997/Revised version: 10 July 1997     

Characterization of periodically poled LiTaO3 crystals by means of spontaneous parametric down-conversion

We describe the observation of quasi-phase-matched spontaneous parametric down-conversion in eee-geometry in periodically poled LiTaO₃ crystals. For scattered light, the two-dimensional angular-frequency intensity distribution was studied. Several detuning curves were recorded, corresponding to high orders m=-2, -3, -4, -5 of quasi-phase matching. The measured periods of domain gratings agree with the data obtained by atomic-force microscopy for the etched crystal surfaces. The presence of both odd and even orders indicates that the lengths of positive and negative domains are unequal. To determine the mean duty cycle for regular domain gratings we propose comparing of the intensities of spontaneous parametric down-conversion in different orders of quasi-phase-matching. PACS 42.65.Lm; 42.70.Mp; 81.70.Fy; 78.67.Pt; 42.65.Yj