Analytical model for active metamaterials with quantum ingredients

We present an analytical model for describing complex dynamics of a hybrid system consisting of resonantly coupled classical resonator and quantum structures. Classical resonators in our model correspond to plasmonic metamaterials of various geometries, as well as other types of nano- and microstructure, the optical responses of which can be described classically. Quantum resonators are represented by atoms or molecules, or their aggregates (for example, quantum dots, carbon nanotubes, dye molecules, polymer or bio-molecules etc), which can be accurately modelled only with the use of the quantum mechanical approach. Our model is based on the set of equations that combines well established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. As a particular example of application of our model, we show that the saturation nonlinearity of carbon nanotubes increases multifold in the resonantly enhanced near field of a metamaterial. In the framework of our model, we discuss the effect of inhomogeneity of the carbon-nanotube layer (bandgap value distribution) on the nonlinearity enhancement. © 2012 IOP Publishing Ltd.

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

Characterizing graph symmetries through quantum Jensen-Shannon divergence

In this paper we investigate the connection between quantum walks and graph symmetries. We begin by designing an experiment that allows us to analyze the behavior of the quantum walks on the graph without causing the wave function collapse. To achieve this, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the quantum Jensen-Shannon divergence between the evolution of two quantum walks with suitably defined initial states is maximum when the graph presents symmetries. Hence, we assign to each pair of nodes of the graph a value of the divergence, and we average over all pairs of nodes to characterize the degree of symmetry possessed by a graph. © 2013 American Physical Society.

Perception of concurrent sentences with harmonic or frequency-shifted voiced excitation:performance of human listeners and of computational models based on autocorrelation

Keyword identification in one of two simultaneous sentences is improved when the sentences differ in F0, particularly when they are almost continuously voiced. Sentences of this kind were recorded, monotonised using PSOLA, and re-synthesised to give a range of harmonic ?F0s (0, 1, 3, and 10 semitones). They were additionally re-synthesised by LPC with the LPC residual frequency shifted by 25% of F0, to give excitation with inharmonic but regularly spaced components. Perceptual identification of frequency-shifted sentences showed a similar large improvement with nominal ?F0 as seen for harmonic sentences, although overall performance was about 10% poorer. We compared performance with that of two autocorrelation-based computational models comprising four stages: (i) peripheral frequency selectivity and half-wave rectification; (ii) within-channel periodicity extraction; (iii) identification of the two major peaks in the summary autocorrelation function (SACF); (iv) a template-based approach to speech recognition using dynamic time warping. One model sampled the correlogram at the target-F0 period and performed spectral matching; the other deselected channels dominated by the interferer and performed matching on the short-lag portion of the residual SACF. Both models reproduced the monotonic increase observed in human performance with increasing ?F0 for the harmonic stimuli, but not for the frequency-shifted stimuli. A revised version of the spectral-matching model, which groups patterns of periodicity that lie on a curve in the frequency-delay plane, showed a closer match to the perceptual data for frequency-shifted sentences. The results extend the range of phenomena originally attributed to harmonic processing to grouping by common spectral pattern.

Green's function for paraxial equation

The theory and experimental applications of optical Airy beams are in active development recently. The Airy beams are characterised by very special properties: they are non-diffractive and propagate along parabolic trajectories. Among the striking applications of the optical Airy beams are optical micro-manipulation implemented as the transport of small particles along the parabolic trajectory, Airy-Bessel linear light bullets, electron acceleration by the Airy beams, plasmonic energy routing. The detailed analysis of the mathematical aspects as well as physical interpretation of the electromagnetic Airy beams was done by considering the wave as a function of spatial coordinates only, related by the parabolic dependence between the transverse and the longitudinal coordinates. Their time dependence is assumed to be harmonic. Only a few papers consider a more general temporal dependence where such a relationship exists between the temporal and the spatial variables. This relationship is derived mostly by applying the Fourier transform to the expressions obtained for the harmonic time dependence or by a Fourier synthesis using the specific modulated spectrum near some central frequency. Spatial-temporal Airy pulses in the form of contour integrals is analysed near the caustic and the numerical solution of the nonlinear paraxial equation in time domain shows soliton shedding from the Airy pulse in Kerr medium. In this paper the explicitly time dependent solutions of the electromagnetic problem in the form of time-spatial pulses are derived in paraxial approximation through the Green's function for the paraxial equation. It is shown that a Gaussian and an Airy pulse can be obtained by applying the Green's function to a proper source current. We emphasize that the processes in time domain are directional, which leads to unexpected conclusions especially for the paraxial approximation.

The vibrational spectra of rectangular plates

The wire drive pulse-echo system has been extensively used to excite and measure modes of vibration of thin rectangular plates. The frequency spectra of different modes have been investigated as a function of the material elastic moduli and the plate geometry. Most of the work was carried out on isotropic materials. For square plates a wide selection of materials were used. These were made isotropic in their in-plane dimensions where the displacements are taking place. The range of rnaterials enabled the dependence on Poisson's ratio to be investigated. A method of determining the value of Poisson's ratio resulted from this investigation. Certain modes are controlled principally by the shear modulus. Of these the fundamental has two nodal lines across the plate surface. One of them, which has nodes at the corners, (the Lame mode) is uniquely a pure shear mode where the diagonal is a full wave length. One controlled by the Young's modulus has been found. The precise harmonic relationship of the Lame mode series in square and rectangular plates was established. Use of the Rayleigh-Lamb equation has extended the theoretical support. The low order modes were followed over a wide range of sides ratios. Two fundamental types of modes have been recognised; These are the longitudinal modes where the frequency is controlled by the length of the plate only and the 2~f product has an asymptotic value approaching the rod velocity. The other type is the in-plane flexural modes (in effect a flexurally vibrating bar where the -2/w is the geometrical parameter). Where possible the experimental work was related to theory. Other modes controlled by the width dimension of the plate were followed. Anisotropic materials having rolled sheet elastic symmetry were investigated in terms of the appropriate theory. The work has been extended to examine materials from welds in steel plates.

3D reconstruction of complex dielectric function of the glass during the femtosecond micro-fabrication

We measure complex amplitude of scattered wave in the far field, and justify theoretically and numerically solution of the inverse scattering problem. This allows single-shot reconstructing of dielectric function distribution during direct femtosecond laser micro-fabrication.

Resonant two-wave mixing in photorefractive materials with the aid of dc and ac fields

A recently predicted resonant effect for the enhancement of two-wave mixing in photorefractive materials is investigated. The resonance occurs when the frequency of the applied ac field agrees with the eigenfrequency of the excited space-charge wave. Experimentally a clear resonance is found, as predicted by the theory, for high dc electric fields, but the resonance is smeared out for lower fields. A modified theory, taking into account the second temporal harmonic of the space-charge wave, shows good agreement with the experimental results.

Observations of Spatial Subharmonics arising during Two-Wave Mixing in BSO

During two-wave mixing experiments in BSO, output beams have been observed which result from diffraction of the pump beams from subharmonics of the grating vector recorded within the crystal. The subharmonic beams are characterised as a function of pump beam detuning and electric field, and our observations are contrasted with those reported earlier.

Contrast summation across eyes and space is revealed along the entire dipper function by a "Swiss cheese" stimulus.

Previous contrast discrimination experiments have shown that luminance contrast is summed across ocular (T. S. Meese, M. A. Georgeson, & D. H. Baker, 2006) and spatial (T. S. Meese & R. J. Summers, 2007) dimensions at threshold and above. However, is this process sufficiently general to operate across the conjunction of eyes and space? Here we used a "Swiss cheese" stimulus where the blurred "holes" in sine-wave carriers were of equal area to the blurred target ("cheese") regions. The locations of the target regions in the monocular image pairs were interdigitated across eyes such that their binocular sum was a uniform grating. When pedestal contrasts were above threshold, the monocular neural images contained strong evidence that the high-contrast regions in the two eyes did not overlap. Nevertheless, sensitivity to dual contrast increments (i.e., to contrast increments in different locations in the two eyes) was a factor of ∼1.7 greater than to single increments (i.e., increments in a single eye), comparable with conventional binocular summation. This provides evidence for a contiguous area summation process that operates at all contrasts and is influenced little, if at all, by eye of origin. A three-stage model of contrast gain control fitted the results and possessed the properties of ocularity invariance and area invariance owing to its cascade of normalization stages. The implications for a population code for pattern size are discussed.

Physiological and pathological human ocular perfusion characteristics

There were three principle aims to this thesis. Firstly, the acquisition protocols of clinical blood flow apparatus were investigated in order to optimise them for both cross-sectional and longitudinal application. Secondly, the effects of physiological factors including age and systematic circulation on ocular blood flow were investigated. Finally, the ocular perfusion characteristics of patients diagnosed with ocular diseases considered to be of a vascular origin were investigated. The principle findings of this work are:- 1) Optimisation of clinical investigationsPhotodiode sensitivity of the scanning laser Doppler flowmeter should be kept within a range of 70-150 DC when acquiring images of the retina and optic nerve head in order to optimise the reproducibility of capillary blood flow measures. Account of the physiological spatial variation in retinal blood flow measures can be made using standard analysis protocols of the scanning laser Doppler flowmeter combined with a local search strategy. Measurements of pulsatile ocular blood flow using the ocular blood flow analyser are reproducible, however this reproducibility can be improved when consecutive intraocular pressure pulses are used to calculate pulsatile ocular blood flow. Spectral analysis of the intraocular pressure pulse-wave is viable and identifies the first four harmonic components of the waveform. 2) Physiological variation in ocular perfusionAge results in a significant reduction in perfusion of the retinal microcirculation, which is not evident in larger vessel beds such as the choroid. Despite known asymmetry in the systemic vasculature, no evidence of interocular asymmetry in ocular perfusion is apparent. 3) Pathological variation in ocular perfusionIn primary open angle glaucoma, perfusion is reduced in the retinal microcirculation of patients classified as having early to moderate visual field defects. However, ocular pulsatility defects are masked when patients and subjects are matched for systemic variables (pulse rate and mean arterial pressure); differentiation is facilitated by the application of waveform analysis to the continuos intraocular pressure curve even in the early stages of disease. Diabetic patients with adequate glycaemic control, exhibit maintenance of macular blood flow, macular topography and visual function following phacoemulsification.

Retinal and systemic vascular function in health and disease: the effect of smoking and coronary artery disease

The purpose of the following studies was to explore the effect of systemic vascular and endothelial dysfunction upon the ocular circulation and functionality of the retina. There are 6 principal sections to the present work. Retinal vessel activity in smokers and non-smokers: the principal findings of this work were: chronic smoking affects retinal vessel motion at baseline and during stimulation with flickering light; chronic smoking leads to a vaso-constrictory shift in retinal arteriolar reactivity to flicker; retinal arteriolar elasticity is decreased in chronic smokers. The effect of acute smoking on retinal vessel dynamics in smokers and non-smokers: the principal finding of this work was that retinal reactivity in chronic smokers is blunted when exposed to clicker light provocation immediately after smoking one cigarette. Ocular blood flow in coronary artery disease: The principal findings of this work were: retrobulbar and retinal blood flow is preserved in CAD patients, despite a change pulse wave transmission; arterial retinal response to flickering light provocation is significantly delayed in CAD patients; retinal venular diameters are significantly dilated in CAD patients. Autonomic nervous system function and peripheral circulation in CAD: The principal findings in this work were: CAD patients demonstrate a sympathetic overdrive during a 24 period; a delay in peripheral vascular reactivity (nail-fold capillaries) as observed in patients suffering from CAD could be caused by either arteriosclerotic changes of the vascular walls or due to systemic haemodynamic changes. Visual function in CAD: The principal findings in this work were: overall visual function in CAD patients is preserved, despite a decrease in contrast sensitivity; applying a filtering technique selecting those with greater coefficient of variance which in turn represents a decrease in reliability, some patients appear to have an impaired visual function as assessed using FDT visual field evaluation. Multiple functional, structural and biochemical vascular endothelial dysfunctions in patients suffering from CAD: relationships and possible implications: The principal findings of this work were: BMI significantly correlated with vWF (a marker of endothelial function) in CAD patients. Retinal vascular reactivity showed a significant correlation with peripheral reactivity parameters in controls which lacked in the CAD group and could reflect a loss in vascular endothelial integrity; visual field parameters as assessed by frequency doubling technology were strongly related with systemic vascular elasticity (ambulatory arterial stiffness index) in controls but not CAD patients.

Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.

Microscopic optical buffering in a harmonic potential

In the early days of quantum mechanics, Schrödinger noticed that oscillations of a wave packet in a one-dimensional harmonic potential well are periodic and, in contrast to those in anharmonic potential wells, do not experience distortion over time. This original idea did not find applications up to now since an exact one-dimensional harmonic resonator does not exist in nature and has not been created artificially. However, an optical pulse propagating in a bottle microresonator (a dielectric cylinder with a nanoscale-high bump of the effective radius) can exactly imitate a quantum wave packet in the harmonic potential. Here, we propose a tuneable microresonator that can trap an optical pulse completely, hold it as long as the material losses permit, and release it without distortion. This result suggests the solution of the long standing problem of creating a microscopic optical buffer, the key element of the future optical signal processing devices.