Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n _1ef and n _2ef, can be applied. Analytical dependences of n _1ef and n _2ef on the modulation amplitudes of the refractive index n ₁ and n ₂ at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.     

Anisotropic Bragg diffraction of finite-sized volume holographic grating in photorefractive crystals

Anisotropic diffraction of uniform plane wave by finite-sized volume holographic grating in photorefractive crystals is considered. It is found that the anisotropic diffraction can take place when some special conditions are satisfied. The diffracted image is obtained in experiment for the anisotropic Bragg diffraction in Fe:LiNbO₃ crystals. A coupled wave analysis is presented to study the properties of anisotropic diffraction. An analytical integral solution for the amplitudes of the diffracted beams is submitted. A trade off between high diffraction efficiency and the deterioration of reconstruction fidelity is analyzed. Numerical evaluations also show that the finite-sized anisotropic volume grating exhibits strong angular and wavelength selectivity. All the results are useful for the optimizing design of VHOE based on finite-sized volume grating structures.     

Effect of recording conditions on the anisotropic diffraction of volume holographic gratings

The anisotropic Bragg diffraction of the volume holographic gratings in photorefractive crystals are investigated based on the model of anisotropic coupled-wave theory. The effect of the initial intensity ratio and the recording angles of the two recording waves on the anisotropic Bragg diffraction properties is discussed. It is shown that both the ratio of the initial intensity and the incident angles of the recording waves are selective action for the anisotropic Bragg diffraction efficiency of the volume holographic gratings, while these two recording conditions are not selective action for the isotropic Bragg diffraction. Furthermore, the Bragg phase matching condition of anisotropic diffraction is analyzed when the recording angles change.     

Multiple Nonlinear Stimulated Echoes

Three-pulse sequences in the presence of magnetic field gradients at high magnetic fields produce multiple nonlinear stimulated echoes (NOSE) at timesnτ₁after the third pulse, wherenis an integer and τ₁the interval between the first two pulses. These phenomena are due to the demagnetizing field produced by the spatial modulation of the nuclear magnetization arising in the sample after the first two pulses. The theory is presented and compared with experiments. The dependence of the NOSE amplitudes on the flip angles and on the pulse intervals is described. Implications for multidimensional NMR experiments based on sequences of three or more pulses in the presence of field gradients are discussed.     

Two and four photon absorption and nonlinear refraction in undoped,chromium doped and copper doped ZnS quantum dots

The ZnS quantum dots (QDs) with Cr and Cu doping were synthesized by chemical co-precipitation method. The nanostructures of the prepared undoped and doped ZnS QDs were characterized by UV–vis spectroscopy, Transmission electron microscopy (TEM) and X-ray diffraction (XRD). The sizes of QDs were found to be within 3–5 nm range. The nonlinear parameters viz. Two photon absorption coefficient (β₂), nonlinear refractive index (n₂), third order nonlinear susceptibility (χ³) at wavelength 532 nm and Four photon absorption coefficient (β₄) at wavelength 1064 nm have been calculated by Z-scan technique using nanosecond Nd:YAG laser in undoped, Cr doped and Cu doped ZnS QDs. Higher values of nonlinear parameters for doped ZnS infer that they are potential material for the development of photonics devices and sensor protection applications.     

Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1:n

A study has been made of the influence of the phase-difference of two ultrasonic beams, a fundamental and its nth harmonic, on the intensities or amplitudes of diffracted lightwaves. After showing the similarity between superposed and adjacent ultrasound in the Raman-Nath region ρ ? 1, simplified expressions for the intensities have been set up to draw conclusions concerning the symmetry of the diffracted pattern, the amplitude modulation, and the numerical calculation of the factor α_n, from the intensities in which α_n represents the ratio of the ultrasonic pressures. All results are illustrated in the case of a fundamental and its second or third harmonic.     

Z-scan measurements of optical nonlinearity in acid blue 29 dye

The third order nonlinear optical properties of acid blue 29 solutions have been studied using Z-scan technique. Experiments are performed using a CW He–Ne laser at 632.8 nm wavelength and 3 mW power. The linear absorption coefficient α₀, nonlinear absorption coefficient β, nonlinear refractive index n₂, Re χ³, and Im χ³ are measured at three different concentrations. Our results show that higher concentration gives better nonlinear optical properties. Also, it was found that there is an increasing trend in the value of the nonlinear refractive index n₂ as the concentration increases.     

SUPER AND COMBINATORIAL HARMONIC RESPONSE OF FLEXIBLE ELASTIC CABLES WITH SMALL SAG

The paper deals with the analysis of cables in stayed bridges and TV-towers, where the excitation is caused by harmonically varying in-plane motions of the upper support point with the amplitude U. Such cables are characterized by a sag-to-chord-length ratio below &0uml;02, which means that the lowest circular eigenfrequencies for in-plane and out-of-plane eigenvibrations, ω₁and ω₂, are closely separated. The dynamic analysis is performed by a two-degree-of-freedom modal decomposition in the lowest in-plane and out-of-plane eigenmodes. Modal parameters are evaluated based on the eigenmodes for the parabolic approximation to the equilibrium suspension. Superharmonic components of the ordern , supported by the parametric terms of the excitation and the non-linear coupling terms, are registered in the response for circular frequency ω?ω₁/n. At moderate U, the cable response takes place entirely in the static equilibrium plane. At larger amplitudes the in-plane response becomes unstable and a coupled whirling superharmonic component occurs. In the paper a first order perturbation solution to the superharmonic response is performed based on the averaging method. For ω?(m/n)ω₁, m<n, the geometrical non-linear restoring forces gives rise to a substantial combinatorial harmonic component with the circular frequency (n/m)ω. Both entirely in-plane and coupled in-plane and out-of-plane responses occur. Based on an initial frequency analysis of the response, an analytical model for these vibrations is formulated with emphasis on superharmonics of the order n=3 and combinatorial harmonics of the order (n, m)=(3,2). All analytical solutions have been verified by direct numerical integration of the modal equations of motion.     

Wavelength modulation absorption spectrometry from optically saturated collision-broadened transitions

A theoretical investigation of the influence of optical saturation on wavelength modulation absorption spectrometry (WMAS) signals from collision-broadened transitions is presented. Expressions are derived for the nth Fourier coefficient of the analytical detector signal, and thereby also for the nth harmonic signal from a WMAS instrumentation (i.e. the nf-WMAS signal), from a wavelength modulated collision-broadened transition exposed to optical saturation. The flux- (or irradiance-) and modulation-amplitude dependences of the nf-WMAS signal on resonance are scrutinized in detail. It is shown that the nth Fourier coefficient of the wavelength modulated analytical detector signal from an optically saturated collision-broadened transition can be written as a product of a flux-dependent (φ) bleaching function, given by (1+φ/φ_sat)^-1 and identical to that appearing for ordinary, unmodulated absorption spectrometry (AS), and a flux-, detuning-, and modulation-amplitude-dependent wavelength modulated peak-normalized saturation-broadened Lorentzian lineshape function, specific for the WMAS technique. It is found that the nf-WMAS signal on resonance decreases faster than an ordinary AS signal as a function of laser flux when smaller-than-optimum modulation amplitudes are used, but slower when larger-than-optimum modulation amplitudes are used. When optimum (or close-to-optimum) modulation amplitudes are being used, on the other hand, the flux dependence of the WMAS signal resembles to a large degree that of ordinary AS. The conditions for when WMAS from collision-broadened transitions has the same flux dependence as ordinary AS are identified.     

Characteristic Brewster angles for anisotropic interfaces

The effect of nanoscopically stratified anisotropic transmission layer between two isotropic dielectric medium on the characteristic Brewster angles is carried out. The analysis is based on the second-order approximate formulas for the quasi-Brewster, polarization (second Brewster), and principal (third Brewster) angles obtained in the framework of a long-wavelength approximation. The accuracy of these analytical expressions is estimated by using exact numerical methods for the solution of the anisotropic reflection problem. It is shown that the characteristics Brewster angles for real physical interfaces may differ considerably from the classical Brewster angle ϕ_B = arctg(n_b/n_a), for certain material parameters even then, if the thickness of a transition layer is very significantly smaller than the wavelength of optical radiation.     

Light-induced variation in the refractive index in a polyimide-fullerene system

Light-induced variation in the refractive index of the polyimide-C₇₀ system is studied. This process makes a contribution to the nonlinear transmission of this system in the study of the optical limitation of laser radiation and determines the prospects of using this system as a nonlinear holographic medium for reversible data storage. The nonlinear optical coefficients n ₂ and χ⁽³⁾ of fullerene-sensitized polyimides are determined for the first time by the methods of dynamic holography.     

Synthesis, characterization and studies on the nonlinear optical parameters of hydrazones

Three hydrazones, 2-(4-methylphenoxy)-N′-[(1E)-(4-nitrophenyl)methylene]acetohydrazide (compound-1), 2-(4-methylphenoxy)-N′-[(1E)-(4-methylphenyl)methylene]acetohydrazide ((compound-2) and N′-{(1E)-[4-(dimethylamino)phenyl]methylene}-2-(4-ethylphenoxy) acetohydrazide(compound-3) were synthesized and their third order nonlinear optical properties were investigated using a single beam z-scan technique with nanosecond laser pulses at 532 nm. Open aperture data obtained from the three compounds indicates two photon absorption at this wavelength. The nonlinear refractive index n₂, the nonlinear absorption coefficient β, the magnitude of the effective third order susceptibility χ⁽³⁾, the second order hyperpolarizability γ_h and the coupling factor ρ have been estimated. The values obtained are comparable with the values obtained for 4-methoxy chalcone derivatives and dibenzylidene acetone derivatives. Among the compounds studied, compounds-1 and 3 exhibited the better optical power limiting behaviour at 532 nm. Our studies suggest that compounds-1, 2 and 3 are potential candidates for optical device applications such as optical limiters and optical switches.     

On Ohm’s law in the thin current sheets of the Earth’s magnetosphere

The analytical and numerical dependences of the total transverse current on an electric field, the normal component of a magnetic field and the ion and electron temperatures are obtained using analytical approximation of numerical results provided by a self-consistent model of the magnetospheric thin sheet. The dependence of current on the parameters ?, T _i , b _n is shown to be nonlinear. The relative contributions of different plasma components into the total current are estimated.     

Control of reflectivity and stop bands in a Bragg stack with a four-layer period

We provide a general expression for the band dispersion in a Bragg stack with a four-layer period, and show how the expression is considerably simplified in the case of a perturbed two-layer Bragg stack, where every second layer has refractive index n₁ and n₂, respectively. We present a range of analytical expressions to describe key features of the band dispersion, including the dependence of the band gap and of the evanescent decay length on variations in layer thickness for TE and TM polarized light incident perpendicular and at an angle to the Bragg stack.     

On the evaluation of bragg intensities in the low-temperature phase of C60

The temperature dependence of Bragg intensities in C₆₀ is discussed for the simple cubic Pa3 phase occurring below 260 K. It is shown that, generally, the intensities of Bragg reflections may be surprisingly strongly affected even by seemingly minor variations of certain parameters. Among these the most important are the respective molecular orientational angles of the so-called pentagon and hexagon orientations, the fractions of molecules adopting these orientations and the lattice parameter. Correct determination of the Debye-Waller factor is found to be unusually difficult because of this behaviour. Numerical calculations are used to provide explicit examples and lead to the conclusion that the evaluation of Bragg intensities in this system requires considerable care.     

Electro-optic light modulation with holographic gratings stored in a Cu-diffused LiNbO3 plate

Investigations have been made on the electro-optic modulation of a laser beam using Bragg reflection from holographic gratings stored in a Cu-diffused LiNbO₃ plate. A new device configuration is proposed which makes it possible to use the holographic recording characteristics of LiNbO₃ more effectively than previous other devices. A modulation of about 50% with a 45° deflection angle was obtained at an applied voltage of 500 V.     

Phase effects at second harmonic generation in the layer media

An analysis is made of quasi-phase-matched interaction at second harmonic generation in a regular domain structure with accounts for losses and change of phases of all the interacting waves. The constant-intensity approximation of basic radiation is applied for this purpose, not to regular domain structure as a whole, but to each separately taken domain. It allows to carry out more strict analysis of quasi-synchronous interaction during the frequency conversion to the polydomain consisting of n layers, forming “grating” periods of modulation of the nonlinear susceptibility. With this, the values of complex amplitudes of basic radiation and second harmonic wave at the outlet of each domain are entrance values of the corresponding complex amplitudes to the following domain. The analytical expression is given for the case of n domains and the factors limiting the efficiency of the process of frequency conversion are analyzed. In the constant-intensity approximation, in contrast to the constant field approximation, the coherent length of domain depends on pump intensity. With increasing pump intensity the optimum length decreases. In a regular domain structure at frequency conversion from a layer to a layer, intensity of the basic radiation changes. Also the optimum length of domains at which conversion efficiency is maximal therefore changes. Thus, it is possible to obtain the high values of conversion frequency at the outlet of a regular domain structure by choice of optimum parameters of a task (length of domains, phase mismatch, pump intensity), as well as using the layers-domains of high quality.     

Investigation of continuous-time quantum walk via spectral distribution associated with adjacency matrix

Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph C_n, complete graph K_n, graph G_n, finite path and some other finite and infinite graphs, where all are connected with orthogonal polynomials such as Hermite, Laguerre, Tchebichef, and other orthogonal polynomials. It is shown that using the spectral distribution, one can obtain the infinite time asymptotic behavior of amplitudes simply by using the method of stationary phase approximation (WKB approximation), where as an example, the method is applied to star, two-dimensional comb lattices, infinite Hermite and Laguerre graphs. Also by using the Gauss quadrature formula one can approximate the infinite graphs with finite ones and vice versa, in order to derive large time asymptotic behavior by WKB method. Likewise, using this method, some new graphs are introduced, where their amplitudes are proportional to the product of amplitudes of some elementary graphs, even though the graphs themselves are not the same as the Cartesian product of their elementary graphs. Finally, by calculating the mean end to end distance of some infinite graphs at large enough times, it is shown that continuous-time quantum walk at different infinite graphs belong to different universality classes which are also different from those of the corresponding classical ones.     

Study on measuring refractive index modulation of volume phase holographic gratings

In this paper, we present an approach to measure the refractive index modulation of volume phase holographic gratings (VPHG) by use of its angular selectivity, with the advantage of avoiding the diffraction efficiency errors induced by noise. Based on Kogelnik's coupled wave theory for volume holographic gratings, the wave vectors matching relationship for reflective VPHG at different readout wavelengths is deduced and the diffraction efficiency as a function of readout angle is also obtained. Then an all-fiber experimental system is designed to measure corresponding diffraction efficiency with different readout angles for VPHG recorded in dichromate gelatin. By seeking the Bragg angle where diffraction efficiency is maximum and the blank angle where diffraction efficiency drops to the minimum value, the refractive index modulation can be calculated. The experiment results proves the feasibility of the method.     

Self-consistent expansion of a multicomponent plasma into a vacuum

The problem of the one-dimensional collisionless expansion of a multicomponent plasma into a vacuum is considered. In the hydrodynamic approximation, an approximate analytical solution for an arbitrary set of ion species with masses M₁,..., M_n and charge numbers Z₁e, Z₂e,..., Z_ne is found by using the technique of self-similar variables employed by Gurevich, Pariiskaya, and Pitaevskii for the case of single-species ions. A numerical iterative algorithm is developed in which the analytical solution is used as a first approximation.