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.

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.

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.

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.

Determination of excitation profile and dielectric function spatial nonuniformity in porous silicon by using WKB approach

We develop an analytical model based on the WKB approach to evaluate the experimental results of the femtosecond pump-probe measurements of the transmittance and reflectance obtained on thin membranes of porous silicon. The model allows us to retrieve a pump-induced nonuniform complex dielectric function change along the membrane depth. We show that the model fitting to the experimental data requires a minimal number of fitting parameters while still complying with the restriction imposed by the Kramers-Kronig relation. The developed model has a broad range of applications for experimental data analysis and practical implementation in the design of devices involving a spatially nonuniform dielectric function, such as in biosensing, wave-guiding, solar energy harvesting, photonics and electro-optical devices.

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.

Nonlinear Wave Equation with Vanishing Potential

We study the Cauchy problem for utt − ∆u + V (x)u^5 = 0 in 3–dimensional case. The function V (x) is positive and regular, in particular we are interested in the case V (x) = 0 in some points. We look for the global classical solution of this equation under a suitable hypothesis on the initial energy.

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12

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.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Performance study of the Galway Bay wave energy test site floating power system

The Galway Bay wave energy test site promises to be a vital resource for wave energy researchers and developers. As part of the development of this site, a floating power system is being developed to provide power and data acquisition capabilities, including its function as a local grid connection, allowing for the connection of up to three wave energy converter devices. This work shows results from scaled physical model testing and numerical modelling of the floating power system and an oscillating water column connected with an umbilical. Results from this study will be used to influence further scaled testing as well as the full scale design and build of the floating power system in Galway Bay.

Estimation of the Crustal Bulk Properties Beneath Mainland Portugal from P-Wave Teleseismic Receiver Functions

In this work, we present results from teleseismic P-wave receiver functions (PRFs) obtained in Portugal, Western Iberia. A dense seismic station deployment conducted between 2010 and 2012, in the scope of the WILAS project and covering the entire country, allowed the most spatially extensive probing on the bulk crustal seismic properties of Portugal up to date. The application of the H-kappa stacking algorithm to the PRFs enabled us to estimate the crustal thickness (H) and the average crustal ratio of the P- and S-waves velocities V (p)/V (s) (kappa) for the region. Observations of Moho conversions indicate that this interface is relatively smooth with the crustal thickness ranging between 24 and 34 km, with an average of 30 km. The highest V (p)/V (s) values are found on the Mesozoic-Cenozoic crust beneath the western and southern coastal domain of Portugal, whereas the lowest values correspond to Palaeozoic crust underlying the remaining part of the subject area. An average V (p)/V (s) is found to be 1.72, ranging 1.63-1.86 across the study area, indicating a predominantly felsic composition. Overall, we systematically observe a decrease of V (p)/V (s) with increasing crustal thickness. Taken as a whole, our results indicate a clear distinction between the geological zones of the Variscan Iberian Massif in Portugal, the overall shape of the anomalies conditioned by the shape of the Ibero-Armorican Arc, and associated Late Paleozoic suture zones, and the Meso-Cenozoic basin associated with Atlantic rifting stages. Thickened crust (30-34 km) across the studied region may be inherited from continental collision during the Paleozoic Variscan orogeny. An anomalous crustal thinning to around 28 km is observed beneath the central part of the Central Iberian Zone and the eastern part of South Portuguese Zone.