Profiled hologram diffraction gratings based on As2Se3 inorganic photoresist

We devised a method of producing blaze hologram diffraction gratings by transforming symmetric grooves of the original grating into asymmetric ones using an additional oblique irradiation by monochromatic or polychromatic light and a repeated chemical etching of the additionally irradiated grating. Photosensitive As₂Se₃ film layers are used as a photoconductive material for recording gratings. A numerical computer modeling of the formation of asymmetric grooves is conducted. The calculated shape of the groove profile is in good agreement with experimental data. The manifestation of asymmetry of the profile shape of the produced gratings in angular and spectral relations for their diffraction efficiency is considered. It is shown that by varying the parameters of producing the original gratings and the conditions of their additional treatment it is possible to obtain hologram gratings with the required profile shape and blaze angle. To whom correspondence should be addressed. Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 45, Nauka Ave., Kiev, 252028, Ukraine. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 4, pp. 587–590, July–August, 1999.     

Producing and testing binary amplitude gratings using a self-imaging and double-exposure technique

The influence of illuminating beam aberrations and master grating deviations on the performance of the technique of producing arbitrary opening ratio binary gratings using the self-imaging and double-exposure technique is studied analytically and experimentally. It is shown that due to the shear effect encountered in the direction perpendicular to the grating lines and due to the lateral displacement implemented between the two exposures the technique is sensitive to the first derivative of grating in-plane displacements and to the second derivative of the beam and grating out-of-plane errors.     

New glassy liquid crystals for optical data-storage applications

Low-molar-mass liquid crystals consisting of a binary nematic mixture of two-naphthylester which exhibit an anisotropic glassy state at room temperature have recently proven to be a suitable material for erasable optical data-storage applications. Using the holographic-grating technique, it is shown that more than 1000 all-optical write, read and erase cycles can be realized without remarkable loss of reversibility. The recording intensities are of the order of 100 W/cm² and optical erasure can be achieved with about twice that intensity. The times for recording and erasure of the optical gratings range on the millisecond scale and the stored gratings persist several months with a diffraction efficiency of typically 1 %. The spatial resolution has been proven down to 2 µm so far. The obtained results are compared with other reversible recording materials.     

Production of binary amplitude gratings with arbitrary opening ratio and variable period

A simple double exposure technique is proposed for making binary amplitude gratings with preset opening ratio. Commercially available Ronchi type master ruling is imaged onto the photographic plate by a laser projection system. The controlled lateral displacement of the ruling or the photographic plate between two exposures results in the composite grating with the required opening ratio. A zoom-effect spherical beam projection system is suggested for producing binary gratings with continuously variable period.     

Nonlinear diffraction in gratings based on polymer–dispersed TiO 2 nanoparticles

In this letter we report a simple technique to produce volume holographic gratings based on photopolymerizable composites containing TiO₂ nanoparticles. Diffraction gratings with high refractive index modulation amplitude (up to 1.25 × 10⁻²) have been formed due to the periodic distribution of high refractive index nanoparticles in a low refractive index polymer matrix. The diffraction efficiency increases strongly on increasing the nanoparticle concentration. Taking the mixture with 10 wt.% TiO₂ nanoparticles, gratings with high diffraction efficiency, low level of scattering and high transparency in the visible-wavelength range have been obtained. This will ultimately lead to different applications of diffractive optical elements based on nanocomposites. The dependence of the gratings’ diffraction efficiency on the intensity of probe laser pulses at 1064 nm has been explored. It is shown that the nonlinear response of the gratings is attributed mainly to the nonlinear properties of the TiO₂ nanoparticles embedded in the polymer matrix. The mechanism of the grating formation and the reasons for the nonlinear behavior of the diffraction efficiency are discussed.     

A gradient method for design of multiorder varied-depth binary diffraction gratings

A method for the design of perfectly conducting varied-depth binary diffraction gratings is proposed. The design uses the rigorous modal expansion method and is based on the gradient search algorithm for optimization of grating structure from the condition of the generation of a desired array of diffraction orders. The designs of varied-depth binary gratings with equal order intensities are reported with an efficiency of more than 90% and root-mean square errors of 2–7%.     

Nonlinear Model of Record and Readout of Holographic Transmission Diffraction Gratings in Absorbent Photopolymers. Part I. Theoretical Analysis

In the present study, record and readout of holographic transmission diffraction gratings in photopolymer media are investigated with allowance for an arbitrary degree of nonlinearity of photopolymerization, contrast of interference patterns, and absorption and arbitrary relative contributions of polymerization and diffusion recording mechanisms. A theoretical model of (N + 1) 3-D harmonics of the refractive index grating, based on a solution of the coupled kinetic photopolymerization equations, allows the time dynamics of harmonic amplitudes, 3-D refractive index profile, diffraction efficiency, and angular selectivity of the recorded gratings to be investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 56–63, May, 2005.     

Apodization‐Assisted Subdiffraction Near‐Field Localization in 2D Phase Diffraction Grating

Conventional phase diffraction gratings can be used to localize the incoming optical radiation in the near‐field region. A new design of the binary phase diffraction grating is proposed with embedded pupil opaque mask inside each stripe. By means of numerical simulations, it is shown that with this masked phase grating the spatial resolution of the near‐field localization can be substantially improved and brought even beyond the solid immersion limit (λ/2n). Moreover, due to anomalous apodization effect, the subdiffraction field localization is accompanied by intensity enhancement as compared to the non‐masked design. The pupil mask rearranges the optical fluxes within the stripes and promotes the Fano resonances excitation in the periodic step lattice. This can be important for advancing the phase grating‐based super‐resolution technologies, including subdiffraction imaging, interferometry, and surface fabrication.     

Dynamics of light-induced diffraction gratings in silicon excited by picosecond pulses

On the basis of a numerical solution of the system of continuity equations we analyze the formation and decay of light-induced diffraction gratings in silicon under excitation by picosecond pulses. The concentration of nonequilibrium carriers generated at excitation-pulse intensities I₀ 10¹⁰ W/cm² reaches values of 10¹⁹–10²⁰ cm^–3. Estimates of the relaxation time of diffraction gratings from widely used formulas are shown to be too low because of the nonlinearity of the evolution of nonequilibrium carriers. The internal electric fields are calculated. The dynamics of diffraction gratings that are nonuniform over the depth of the sample have been studied experimentally as a function of the intensity of the excitation pulses. The experimental data accord with the results of numerical calculations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 53–58, March, 1990.     

Explicit form and convergence of 1-differential formal deformations of the poisson Lie algebra

Introducing the notion of an admissible graded Lie subalgebra A of the Nijenhui-Richardson algebra A(V) of the vector space V, it is shown that each cohomology class of a subcomplex C _A of the Chevalley-Eilenberg complex (C ⁰ M), extends in a cononical way as a graded cohomology class of weight — 1 of A. Applying this when V is the space N of smooth functions of a smooth manifold M, shows that the de Rham cohomology of M is induced by the graded cohomology of weight — 1 of the Schouten graded Lie algebra of M. This allows us to construct explicitly all 1-differential, nc formal deformations of the Poisson bracket of a symplectic manifold. The construction also applies for an arbitrary Poisson manifold but leads to only part of these deformations when the structure degenerates, as shown by an example.     

Finite Euler hierarchies and integrable universal equations

Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field theories,classical topological field theories — whose classical solutions span topological classes of manifolds — and reparametrisation invariant theories — generalising ordinary string and membrane theories. On the other hand,finite Euler hierarchies are constructed for all three classes of theories. These hierarchies terminate withuniversal equations of motion, probably defining new integrable systems as they admit an infinity of Lagrangians. Speculations as to the possible relevance of these theories to quantum gravity are also suggested.Presented at the Colloquium on the Quantum Groups, Prague, 18–20 June 1992.The author would like to thank A. Morozov and especially D. B. Fairlie for a very enjoyable and stimulating collaboration, and the organisers of the Colloquium for their efficient organisation of a most pleasant and informative meeting. This work is supported through a Senior Research Assitant position funded by the S.E.R.C.     

The general relativistic hydrogen atom

The general relativistic Dirac equation is formulated in an arbitrary curved space-time using differential forms. These equations are applied to spherically symmetric systems with arbitrary charge and mass. For the case of a black hole (with event horizon) it is shown that the Dirac Hamiltonian is self-adjoint, has essential spectrum the whole real line and no bound states. Although rigorous results are obtained only for a spherically symmetric system, it is argued that, in the presence of any event horizon there will be no bound states. The case of a naked singularity is investigated with the results that the Dirac Hamiltonian is not self-adjoint. The self-adjoint extensions preserving angular momentum are studied and their spectrum is found to consist of an essential spectrum corresponding to that of a free electron plus eigenvalues in the gap (–mc ², +mc ²). It is shown that, for certain boundary conditions, neutrino bound states exist.Supported in part by the National Science Foundation     

Nonlinear laser-induced regime of surface-electromagnetic-wave generation and submicron periodic relief during liquid-phase photochemical etching of n-III–V semiconductors

This paper is devoted to an experimental study of the physical processes underlying the phenomenon of laser-induced generation of periodic relief on the surface of n-III–V semiconductors during liquid-phase photochemical or photoelectrochemical etching accompanying the resonance interaction of surface electromagnetic waves (SEWs). The increments of the exponentially increasing amplitudes of the dominant Fourier harmonics of the relief have been measured at the initial (linear) stage of the time evolution of the surface profile. It is proven by comparing the theoretical and experimental results that the mechanism for forming periodic structures that we have proposed is adequate. Ways of monochromatizing the generated relief and controlling the line shape of the surface grating are studied. It is experimentally detected for the first time that the nonlinear stage of the time evolution of the relief is characterized, in accordance with the predictions of the theory developed by the authors, by amplitude and phase oscillations of the first and second Fourier harmonics of the surface profile. It is shown to be possible to generate relief that suppresses specular reflection from the surface. A new nonmasked laser method is developed for forming high-quality submicron relief diffraction gratings, combining a holographic method and a method involving laser-induced relief generation during resonance excitation of SEWs. Diffraction gratings with a period of d=0.24–0.54 μm and a depth of h=0.1–0.2 μm over an area of 0.5×31 cm have been created on an n-InP surface. Zh. éksp. Teor. Fiz. 111, 174–198 (January 1997)     

Optimizing and characterizing grating efficiency for a soft X‐ray emission spectrometer

The efficiency of soft X‐ray diffraction gratings is studied using measurements and calculations based on the differential method with the S‐matrix propagation algorithm. New open‐source software is introduced for efficiency modelling that accounts for arbitrary groove profiles, such as those based on atomic force microscopy (AFM) measurements; the software also exploits multi‐core processors and high‐performance computing resources for faster calculations. Insights from these calculations, including a new principle of optimal incidence angle, are used to design a soft X‐ray emission spectrometer with high efficiency and high resolution for the REIXS beamline at the Canadian Light Source: a theoretical grating efficiency above 10% and resolving power E/ΔE > 2500 over the energy range from 100 eV to 1000 eV are achieved. The design also exploits an efficiency peak in the third diffraction order to provide a high‐resolution mode offering E/ΔE > 14000 at 280 eV, and E/ΔE > 10000 at 710 eV, with theoretical grating efficiencies from 2% to 5%. The manufactured gratings are characterized using AFM measurements of the grooves and diffractometer measurements of the efficiency as a function of wavelength. The measured and theoretical efficiency spectra are compared, and the discrepancies are explained by accounting for real‐world effects: groove geometry errors, oxidation and surface roughness. A curve‐fitting process is used to invert the calculations to predict grating parameters that match the calculated and measured efficiency spectra; the predicted blaze angles are found to agree closely with the AFM estimates, and a method of characterizing grating parameters that are difficult or impossible to measure directly is suggested.     

Nonlinear model of sequential recording of superimposed holographic gratings in photopolymer composites with allowance for the self-diffraction from spatial harmonics

The problems of sequential recording of superimposed holographic diffraction structures of transmission and reflection types in photopolymer composites have been investigated taking into account an arbitrary degree of photopolymerization nonlinearity and the interference pattern contrast at an arbitrary ratio of the photopolymerization and diffusion mechanisms of recording and self-diffraction processes. A theoretical model for N superimposed phase diffraction structures has been constructed by solving interrelated kinetic equations of photopolymerization for H + 1 spatial harmonics of each diffraction structure. This approach makes it possible to investigate the temporal dynamics of the harmonic amplitudes, spatial profile, diffraction efficiency, and angular selectivity of recorded gratings. The model proposed takes into account the diffraction of recording beams from the first harmonic of the ith grating during formation of the (i + 1)th grating.     

Tensor products in generalized measure theory

Kläy, Randall, and Foulis established that the signed weight space of the tensor product of two quasimanuals each having a positive, finite-dimensional state space is isomorphic to the algebraic tensor product of the signed-weight spaces of the factors. We obtain a generalization of this result for arbitrary quasimanuals. A compactness condition due to Cook—here calleddiscreteness—is discussed and shown to be preserved under the formation of tensor products. It is shown that the predual of the signed weight space of a tensor product of discrete manuals is the projective (ordered) tensor product of the preduals of the signed weight spaces of the factors.     

Measurement of small phase shifts of radio signals using acoustooptic reduction

Results are presented of model-based experimental investigations of an interference correlator intended for the measurement of small phase shifts of radar signals received from two antennas. The correlator is based on a Mach-Zender interferometer system. Introduction of a radio signal for the data reduction was simulated by phase diffraction gratings placed in the interferometer arms and displaced relative to one another. The operation of the system was investigated in a regime with measurements in the region of the extrema of the correlation function and in a regime with measurements near zeros (extrema of the derivative) of the correlation function. The investigations were carried out for signals formed in first, second, and third order of diffraction. It is shown that the sensitivity of the system for measurements in the region of a correlation-function zero is higher by an order of magnitude than in the extrem~ m region. It is shown that for radio signals in the 100-MHz band, with allowance for the experimental measurement error, the accuracy of determining the time delays reaches 10^–11 sec. The accuracy with which geometric displacements of diffraction gratings are determined reaches 5·10^-5 mm.Lebedev Physics Institute. Severo-Osetinsk State University.     

Axiomatic renormalization of the stress tensor of a conformally invariant field in conformally flat spacetimes

Using only the general properties which the renormalized stress-energy tensor T_μν should satisfy—and not relying on any assumptions associated with specific renormalization techniques—we derive the expression for T_μν for conformally invariant fields in conformally flat spacetimes of two and four dimensions. In two dimensions, these arguments rederive the Davies-Fulling-Unruh expression for the stress tensor of a scalar field; in four dimensions the results agree with those of Brown and Cassidy, except that we exclude the local curvature term depending on fourth-order derivatives of the metric. The dynamics of a k = 0 Robertson-Walker universe filled with radiation of the conformally invariant field is investigated and it is found that the equations cease to admit a solution when the Planck density is reached.     

Gravitation in the Fractal D = 2 Inertial Universe: New Phenomenology in Spiral Discs and a Theoretical Basis for MOND

A particular interpretation of Mach's Principle led us to ask if it was possible to have a globally inertial universe that was irreducibly associated with a non-trivial global matter distribution, Roscoe [1]. This question received a positive answer, subject to the condition that the global matter distribution is necessarily fractal, D = 2. The present paper shows how gravitational processes can arise in this universe. We begin by showing how classical Newtonian gravitation arises from point-source perturbations of this D = 2 inertial background. We then use the insights gained from this initial analysis to arrive at a general theory for arbitrary material distributions. We illustrate the process by using it to model an idealized spiral galaxy. One particular subclass of solutions, (the logarithmic spiral) has already been extensively tested (Roscoe [2, 3]), and shown to resolve large samples of optical rotation curve data to a very high statistical precision. These analyses also led to the discovery of a major new phenomenology in spiral discs—that of discrete dynamical classes, [3]. In this paper, we analyse the theory more comprehensively, showing how this phenomenology has a possible explanation in terms of an algebraic consistency condition which must necessarily be satisfied.Of equal significance, we apply the theory with complete success to the detailed modelling of eight Low Surface Brightness spirals (LSBs) which, hitherto, have been successfully modelled only by the MOND algorithm (Milgrom [5–7]. We are able to conclude that the essence of the MOND algorithm must be contained within the presented theory.     

The momentum constraints of general relativity and spatial conformal isometries

Transverse-tracefree (TT-) tensors on (R ³,g _ab), withg _ab an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall-off at infinity, TT tensors allow a multipole-type expansion. Wheng _ab has no conformal Killing vectors (CKV's) it is proven that any finite but otherwise arbitrary set of moments can be realized by a suitable TT tensor. When CKV's exist there are obstructions — certain (combinations of) moments have to vanish — which we study.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P9376-PHY.Partially supported by Forbairt Grant SC/94/225.