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.

Continuous-wave ultraviolet light induced fiber Bragg gratings in few- and single-mode microstructured polymer optical fibers

Reported are observations and measurements of the inscription of fibre Bragg gratings in two different types of microstructured polymer optical fibre: few-moded and endlessly single mode. Contrary to FBG inscription in silica microstructured fibre, where high energy laser pulses are a prerequisite, we have successfully used a low power CW laser source operating at 325nm to produce 1-cm long gratings with a reflection peak at 1570 nm. Peak reflectivities of more than 10% have been observed.

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.

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.

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.

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.

Continuous wave ultraviolet light-induced fiber Bragg gratings in few- And single-mode microstructured polymer optical fibers

We report observations and measurements of the inscription of fiber Bragg gratings (FBGs) in two different types of microstructured polymer optical fiber: few-mode and an endlessly single mode. Contrary to the FBG inscription in silica microstructured fiber, where high-energy laser pulses are a prerequisite, we have successfully used a low-power cw laser source operating at 325 nm to produce 1 cm long gratings with a reflection peak at 1570 nm. Peak reflectivities of more than 10% have been observed. © 2005 Optical Society of America.

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).

Applications of ultralong Raman fibre lasers in photonics

This thesis presents a numerical and experimental investigation on applications of ultralong Raman fibre lasers in optical communications, supercontinuum generation and soliton transmission. The research work is divided in four main sections. The first involves the numerical investigation of URFL intra-cavity power and the relative intensity noise transfer evolution along the transmission span. The performance of the URFL is compared with amplification systems of similar complexity. In the case of intracavity power evolution, URFL is compared with a first order Raman amplification system. For the RIN transfer investigation, URFL is compared with a bi-directional dual wavelength pumping system. The RIN transfer function is investigated for several cavity design parameters such as span length, pump distribution and FBG reflectivity. The following section deals with experimental results of URFL cavities. The enhancement of the available spectral bandwidth in the C-band and its spectral flatness are investigated for single and multi-FBGs cavity system. Further work regarding extended URFL cavity in combination with Rayleigh scattering as random distributed feedback produced a laser cavity with dual wavelength outputs independent to each other. The last two sections relate to URFL application in supercontinuum (SC) generation and soliton transmission. URFL becomes an enhancement structure for SC generation. This thesis shows successful experimental results of SC generation using conventional single mode optical fibre and pumped with a continuous wave source. The last section is dedicated to soliton transmission and the study of soliton propagation dynamics. The experimental results of exact soliton transmission over multiple soliton periods using conventional single mode fibre are shown in this thesis. The effect of the input signal, pump distribution, span length and FBGs reflectivity on the soliton propagation dynamics is investigated experimentally and numerically.

Characterization of 45º-tilted fiber grating and its polarization function in fiber ring laser

We have proposed and demonstrated a fiber ring laser with single-polarization output using an intracavity 45°-tilted fiber grating (45°-TFG). The properties of the 45°-TFG have been investigated both theoretically and experimentally. The fiber ring laser incorporating the 45°-TFG has been systematically characterized, showing a significant improvement in the polarization extinction ratio (PER) and achieving a PER of >30 dB. The slope efficiencies of the ring laser with and without the 45°-TFG have been measured. This laser shows a very stable polarized output with a PER variation of less than 2 dB for 5 hours at laboratory conditions. In addition, we also demonstrated the tunability of the laser.

Surface acoustic wave devices with low loss and high frequency operation

This thesis describes an industrial research project carried out in collaboration with STC Components, Harlow, Essex. Technical and market trends in the use of surface acoustic wave (SAW) devices are reviewed. As a result, three areas not previously addressed by STC were identified: lower insertion loss designs, higher operating frequencies and improved temperature dependent stability. A review of the temperature performance of alternative lower insertion loss designs,shows that greater use could be made of the on-site quartz growing plant. Data is presented for quartz cuts in the ST-AT range. This data is used to modify the temperature performance of a SAW filter. Several recently identified quartz orientations have been tested. These are SST, LST and X33. Problems associated with each cut are described and devices demonstrated. LST quartz, although sensitive to accuracy of cut, is shown to have an improved temperature coefficient over the normal ST orientation. Results show that its use is restricted due to insertion loss variations with temperature. Effects associated with split-finger transducers on LST-quartz are described. Two low-loss options are studied, coupled resonator filters for very narrow bandwidth applications and single phase unidirectional transducers (SPUDT) for fractional bandwidths up to about 1%. Both designs can be implemented with one quarter wavelength transducer geometries at operating frequencies up to 1GHz. The SPUDT design utilised an existing impulse response model to provide analysis of ladder or rung transducers. A coupled resonator filter at 400MHz is demonstrated with a matched insertion loss of less than 3.5dB and bandwidth of 0.05%. A SPUDT device is designed as a re-timing filter for timing extraction in a long haul PCM transmission system. Filters operating at 565MHz are demonstrated with insertion losses of less than 6dB. This basic SPUDT design is extended to a maximally distributed version and demonstrated at 450MHz with 9.8dB insertion loss.

The perceptual organization of sine-wave speech under competitive conditions

Speech comprises dynamic and heterogeneous acoustic elements, yet it is heard as a single perceptual stream even when accompanied by other sounds. The relative contributions of grouping “primitives” and of speech-specific grouping factors to the perceptual coherence of speech are unclear, and the acoustical correlates of the latter remain unspecified. The parametric manipulations possible with simplified speech signals, such as sine-wave analogues, make them attractive stimuli to explore these issues. Given that the factors governing perceptual organization are generally revealed only where competition operates, the second-formant competitor (F2C) paradigm was used, in which the listener must resist competition to optimize recognition [Remez et al., Psychol. Rev. 101, 129-156 (1994)]. Three-formant (F1+F2+F3) sine-wave analogues were derived from natural sentences and presented dichotically (one ear = F1+F2C+F3; opposite ear = F2). Different versions of F2C were derived from F2 using separate manipulations of its amplitude and frequency contours. F2Cs with time-varying frequency contours were highly effective competitors, regardless of their amplitude characteristics. In contrast, F2Cs with constant frequency contours were completely ineffective. Competitor efficacy was not due to energetic masking of F3 by F2C. These findings indicate that modulation of the frequency, but not the amplitude, contour is critical for across-formant grouping.