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Legumes, in particular beans, differ significantly from cereals in protein content, amino acids, micro- and macroelements, so it can be argued that the addition of beans to the composite mixture will improve the nutrient composition and use the final products (pasta or bakery products) as specialized with increased protein content. The purpose of the work is to study the effect of red bean flour on the rheological properties of dough from a composite mixture based on durum wheat grits, as well as to confirm the possibility of using this product for the production of pasta with high protein content. The influence of beans has been determined by establishing a correlation between the qualitative characteristics of the components of the composite mixture and the rheological properties of the dough based on them. The objects of research are grains of durum wheat variety Krasnokutka-13, whole-ground flour from red food beans and composite mixtures based on them in a percentage ratio: 90 : 10, 80 : 20, 70 : 30, 60 : 40, 50 : 50, 40 : 60, 30 : 70, 20 : 80, and 10 : 90, as well as pasta from composite mixtures. The expediency of using bean flour for the production of pasta has been confirmed. The data obtained are applicable for the preparation and conduct of clinical trials of universal mixtures with high protein content based on bean flour in patients with diabetes mellitus, obesity, and metabolic syndrome.

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral equations for the scattering amplitudes are solved nonperturbatively by a rigorous computer simulation approach. The results of these calculations are used to calculate the full angular distribution of the mean differential reflection coefficient. For isotropic surfaces, the results of the present calculations for in-plane scattering are compared with those of earlier studies of this problem. The reflectivities of Dirichlet and Neumann surfaces are calculated as functions of the polar angle of incidence, and the reflectivities for the two kinds of surfaces of similar roughness parameters are found to be different. For an increasing level of surface anisotropy, we study how the angular intensity distributions of the scattered waves are affected by this level. We find that even small to moderate levels of surface anisotropy can significantly alter the symmetry, shape, and amplitude of the scattered intensity distributions when Gaussian beams are incident on the anisotropic surfaces from different azimuthal angles of incidence.

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral equations for the scattering amplitudes are solved nonperturbatively by a rigorous computer simulation approach. The results of these calculations are used to calculate the full angular distribution of the mean differential reflection coefficient. For isotropic surfaces, the results of the present calculations for in-plane scattering are compared with those of earlier studies of this problem. The reflectivities of Dirichlet and Neumann surfaces are calculated as functions of the polar angle of incidence, and the reflectivities for the two kinds of surfaces of similar roughness parameters are found to be different. For an increasing level of surface anisotropy, we study how the angular intensity distributions of the scattered waves are affected by this level. We find that even small to moderate levels of surface anisotropy can significantly alter the symmetry, shape, and amplitude of the scattered intensity distributions when Gaussian beams are incident on the anisotropic surfaces from different azimuthal angles of incidence.

We measure and calculate the optical response of a structure consisting of a square array of subwavelength silicon posts on a silicon substrate at telecommunication wavelengths. By the use of the reduced Rayleigh equations and the Fourier modal method (rigorous coupled wave analysis) we calculate the reflectivity of this structure illuminated from vacuum by normally incident light. The calculated reflectivities together with experimentally determined ones, are used to test the accuracy of effective medium theories of the optical properties of structured silicon surfaces, and to estimate the effective refractive index of such surfaces produced by a homogeneous layer model.

The effects of induced optical polarization by Dirac electrons in graphene on the hybridization of radiative and evanescent fields are found. Such effects result in a localized polarization field which significantly modifies an incident surface-plasmon-polariton (SPP) field. This yields a high sensitivity to local dielectric environments and provides an investigative tool for molecules or proteins selectively bound with carbons. A scattering matrix is utilized with varied frequencies in the vicinity of the surface-plasmon (SP) resonance for the increase, decrease, and even a full suppression of the polarization field, which enables accurate effective-medium theories to be constructed for Maxwell-equation finite-difference time-domain methods. Moreover, double peaks in the absorption spectra for hybrid SP and graphene-plasmon modes are significant only with a large conductor plasma frequency, but are overshadowed by a round SPP peak at a small plasma frequency as the graphene is placed close to the conductor surface. These resonant absorptions facilitate polariton-only excitations, leading to polariton condensation for a threshold-free laser.

The transmission of polarized light through a two-dimensional randomly rough interface between two dielectric media has been much less studied, by any approach, than the reflection of light from such an interface. We have derived a reduced Rayleigh equation for the transmission amplitudes when p- or s-polarized light is incident on this type of interface, and have obtained rigorous, purely numerical, nonperturbative solutions of it. The solutions are used to calculate the transmissivity and transmittance of the interface, the mean differential transmission coefficient, and the full angular distribution of the intensity of the transmitted light. These results are obtained for both the case where the medium of incidence is the optically less dense medium and in the case where it is the optically more dense medium. Optical analogs of Yoneda peaks observed in the scattering of x rays from metallic and nonmetallic surfaces are present in the results obtained in the former case. For p-polarized incident light we observe Brewster scattering angles, angles at which the diffuse transmitted intensity is zero in a single-scattering approximation, which depend on the angle of incidence in contrast to the Brewster angle for flat-surface reflection.

A periodically corrugated interface between vacuum and a high-index dielectric medium supports a p-polarized leaky surface electromagnetic wave whose sagittal plane is perpendicular to the generators of the interface. This wave is bound to the surface in the vacuum region, but radiates into the high-index dielectric medium. We study the excitation of this wave by p-polarized light incident from a prism on whose planar base the highindex dielectric medium in the form of a film is bonded. The unilluminated surface of the film is periodically corrugated, and is in contact with vacuum. Peaks and dips in the dependence of several low-order diffraction efficiencies on the angle of incidence (Wood anomalies) are the signatures of the excitation of the surface wave.

The scattering of polarized light from a dielectric film sandwiched between two different semi-infinite dielectric media is studied experimentally and theoretically. The illuminated interface is planar, while the back interface is a two-dimensional randomly rough interface. We consider here only the case in which the medium of incidence is optically more dense than the substrate, in which case effects due to the presence of a critical angle for total internal reflection occur. A reduced Rayleigh equation for the scattering amplitudes is solved by a rigorous, purely numerical, nonperturbative approach. The solutions are used to calculate the reflectivity of the structure and the mean differential reflection coefficient. Optical analogues of Yoneda peaks are present in the results obtained. The computational results are compared with experimental data for the in-plane mean differential reflection coefficient, and good agreement between theory and experiment is found.

The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the case where p- or s-polarized light is incident on this interface, with no assumptions being made regarding the dielectric functions of the media. Rigorous, purely numerical, nonperturbative solutions of this equation are obtained. They are used to calculate the reflectivity and reflectance of the interface, the mean differential reflection coefficient, and the full angular distribution of the intensity of the scattered light. These results are obtained for both the case where the medium of incidence is the optically less dense medium and in the case where it is the optically more dense medium. Optical analogs of the Yoneda peaks observed in the scattering of x rays from metal surfaces are present in the results obtained in the latter case. Brewster scattering angles for diffuse scattering are investigated, reminiscent of the Brewster angle for flat-interface reflection, but strongly dependent on the angle of incidence. When the contribution from the transmitted field is added to that from the scattered field it is found that the results of these calculations satisfy unitarity with an error smaller than 10-4.

An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a two-dimensional randomly rough dielectric surface when the latter is illuminated by s-polarized light. This result forms the basis for an approach to inverting experimental light-scattering data to obtain the normalized-surface-height autocorrelation function of the surface. Several parametrized forms of this correlation function, and the minimization of a cost function with respect to the parameters defining these representations, are used in the inversion scheme. This approach also yields the rms height of the surface roughness, and the dielectric constant of the dielectric substrate if it is not known in advance. The input data used in validating this inversion consist of computer simulation results for surfaces defined by exponential and Gaussian surface-height correlation functions, without and with the addition of multiplicative noise, for a single or multiple angles of incidence. The reconstructions obtained by this approach are quite accurate for weakly rough surfaces, and the proposed inversion scheme is computationally efficient.

A planar surface on which a scalar wave satisfies the Neumann boundary conditions does not support a surface wave. However, a structured Neumann surface can support such a wave. By means of a Rayleigh equation for a scalar field in the region above the two-dimensional rough surface of a semi-infinite medium on which the Neumann boundary condition is satisfied, we derive the dispersion relation for surface waves on both doubly periodic and randomly rough surfaces. Dispersion curves for these waves on doubly periodic surfaces with three forms of the surface profile function are presented together with dispersion curves for surface waves on a two-dimensional randomly rough surface.

We describe a surface structure consisting of a metal-air interface where the metallic part consists of two metallic segments with a periodic modulation of the interface between them. Such a structure possesses a different transmissivity for a surface plasmon polariton incident on it from one side of it than it has for a surface plasmon polariton incident on it from the opposite side. This asymmetric transmission of a surface plasmon polariton is based on the suppression of the zero-order Bragg beam which, for a certain value of the modulation depth, is not transmitted through the structure, while the diffraction efficiencies of the +1 and -1 Bragg beams can be modified by varying the period of the grating and/or the angle of incidence. For a certain range of the incidence angle one can observe asymmetry in transmittance for the -1 mode, while the +1 mode is completely suppressed. By varying the material and geometrical parameters of the diffractive structure one can control the contrast transmission that characterizes the degree of the asymmetry. This property of the structure is demonstrated by the results of computer simulation calculations.

The reduced Rayleigh equation for the scattering of a surface plasmon polariton incident non-normally on a one-dimensional ridge or groove on an otherwise planar metal surface is solved by a purely numerical approach. The solution is used to calculate the transmission, reflection, and out-of-plane scattering coefficients of the surface plasmon polariton. The angular dependence of the out-of-plane scattering is found to have a conical nature.

The article provides a way to increase the productivity of a screw press variety – the expander. The use of an expander makes it possible to produce compound feed in the form of non-solid whole meals, which has a beneficial effect on the process of digestibility by animals. To correct the existing drawback of the expander – the reverse extrusion of the working mass through the gap between the screw and the body, the authors proposed a combined profile of the screw spiral groove: the left lateral (pushing) surface of the groove has the shape of a semicircle, and the right lateral surface has a semicircular shape in the lower part, and in the middle and upper – the shape of a sloping straight line. Theoretical studies have shown that this profile contributes to the appearance of a difference in lateral pressure forces from the side of boundary particles on the bulk of the material, in contrast to screws with a standard spiral groove made in the form of a triangle, trapezium, or semicircle. In turn, the uneven distribution of lateral pressure will prevent backward extrusion of the processed material through the gap between the auger and the body, thereby increasing the performance of the expander. Theoretical dependencies have been obtained that allow, on the basis of the basic geometric parameters of the screw, to describe geometrically the configuration of the screw of the proposed design for its subsequent manufacture.

The resonant scattering of surface plasmou-polariton waves (SPP) by embedded semiconductor quantum dots above the dielectric/metal interlace is explored in the strong-coupling regime. In contrast to non-resonant scattering by a localized dielectric surface defect, a strong resonant peak in the spectrum of the scattered field is predicted that is accompanied by two side valleys. The |>eak height depends nonlincarly on the amplitude of SPP waves, reflecting the feedback dynamics from a photon-dressed electron-hole plasma inside the quantum dots. This unique behavior in the scattered field peak strength is correlated with the occurrence of a resonant dip in the absorption spectrum of SPP waves due to the interband photon-dressing effect. Our result on the scattering of SPP waves may be experimentally observable and applied to spatially selective illumination and imaging of individual molecules.

We present rigorous, nonperturbative, purely numerical solutions of the Rayleigh equations for the scattering of p- and s-polarized light from a two-dimensional randomly rough perfectly conducting surface. The solutions are used to calculate the reflectivity of the surface, the mean differential reflection coefficients, and the full angular distribution of the intensity of the scattered field. These results are compared with previously published rigorous numerical solutions of the Stratton-Chu equations, and very good agreement is found.

We study properties of a p-polarized surface plasmon polariton propagating circumferentially around a portion of a cylindrical interface between a vacuum and a metal, a situation investigated earlier by Berry (J. Phys. A: Math. Gen. 8 (1975) 1952). When the metal is convex toward the vacuum this mode is radiative and consequently is attenuated as it propagates on the cylindrical surface. An approximate analytic solution of the dispersion relation for this wave is obtained by an approach different from the one used by Berry, and plots of the real and imaginary parts of its wave number are presented. When the metal is concave to the vacuum, the resulting dispersion relation possesses a multiplicity of solutions that have the nature of waveguide modes that owe their existence to the curvature of the interface. © 2013 Elsevier B.V.

The propagation of a surface plasmon polariton on a planar metal surface perturbed by N equally spaced rectangular grooves, each with the same width but with varying depths, is investigated by the finite-difference time-domain method. For a linear dependence of the depth of the nth groove on n, the transmissivity of the surface plasmon polariton and of the power radiated into the vacuum above the surface, as functions of its frequency, consist of N equally spaced dips and peaks, respectively. These are the signatures of the surface plasmon polariton analog of a Wannier-Stark ladder.

The propagation of a surface plasmon polariton on a planar metal surface perturbed by N equally spaced rectangular grooves, each with the same width but with varying depths, is investigated by the finite-difference time-domain method. For a linear dependence of the depth of the nth groove on n, the transmissivity of the surface plasmon polariton and of the power radiated into the vacuum above the surface, as functions of its frequency, consist of N equally spaced dips and peaks, respectively. These are the signatures of the surface plasmon polariton analog of a Wannier-Stark ladder. © 2014 Optical Society of America.

Both dynamic and static approaches are proposed and investigated for controlling the optical phase of a p-polarized light wave guided through a surface-patterned metallic structure with subwavelength features. For dynamic control, the important role of photo-excited electrons in a slit-embedded atomic system with field-induced transparency (FIT) is discovered within a narrow frequency window for modulating the intensity of focused transmitted light in the near-field region. This is facilitated by electromagnetic coupling to surface plasmons between the two FIT-atom embedded slits. The near-field distribution can be adjusted by employing a symmetric (or asymmetric) slit configuration and by a small (or large) slit separation. In addition, the cross-transmission of a light beam is also predicted as a result of this strong coupling between optical transitions in embedded FIT atoms and surface plasmons. For static control, the role of surface curvature is found for focused transmitted light passing through a Gaussian-shaped metallic microlens embedded with a linear array of slits. A negative light-refraction pattern, which is associated with higher-order diffraction modes, was also found for large angles of incidence in the near-field region. This anomalous negative refraction can be suppressed when higher-order waveguide modes of light leak through a very thin film. In addition, this negative refraction can also be suppressed with a reinforced reflection at the left foothill of a Gaussian-shaped slit array of the forward-propagating surface-plasmon wave at large angles of incidence. A prediction is given of near-field focusing of light with its sharpness dynamically controlled by the frequency of the light in a very narrow window. Moreover, a different scheme based on Green's second integral identity is proposed for overcoming a difficulty in calculating the near-field distribution very close to a metallic surface by means of a finite-difference-time-domain method. © 2013 AIP Publishing LLC.

We calculate all the elements of the Mueller matrix for light scattering from a two-dimensional randomly rough lossy metal surface. The calculations are carried out for arbitrary angles of incidence by the use of nonperturbative numerical solutions of the reduced Rayleigh equations. We foresee that the ability to model polarization effects in light scattering from surfaces will enable better interpretation of experimental data and allow for the design of surfaces which possess useful polarization effects. © 2012 American Physical Society.

A nonperturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of p- and s-polarized light from a dielectric film with a two-dimensional randomly rough surface deposited on a planar metallic substrate, has been carried out. It is found that satellite peaks are present in the angular dependence of the elements of the mean differential reflection coefficient in addition to an enhanced backscattering peak. This result resolves a conflict between the results of earlier approximate theoretical studies of scattering from this system.

Numerical results for the distributions of light transmitted through metallic planar lenses composed of symmetric nanogroove arrays on the surfaces of a gold film are presented and explained. Both the near- and far-field distributions of the intensity of light transmitted are calculated by using a Green's function formalism. Results for an optimal transverse focus based on a quadratic variation of groove width are obtained. Meanwhile, a significant dependence of the focal length on the wavelength of light incident from the air side through the gold film into a dielectric substrate is found for this detector configuration. © 2011 Elsevier B.V. All rights reserved.

A misprint in our manuscript is reported and corrected.

An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the Müller equations and an impedance boundary condition for a two-dimensional rough surface yields a pair of coupled two-dimensional integral equations for the sources on the surface in terms of which the scattered field is expressed through the Franz formulas. By this approach, we calculate the full angular intensity distribution of the scattered field that is due to a finite incident beam of p-polarized light. We specifically check the energy conservation (unitarity) of our simulations. Only after a detailed numerical treatment of both diagonal and close-to-diagonal matrix elements is the unitarity condition found to be well satisfied for the nonabsorbing case (U>0.995), a result that testifies to the accuracy of our approach.