Linear and nonlinear propagation of localised plasmon in metallic nanostructures

A major challenge in modern photonics and nano-optics is the diffraction limit of light which does not allow field localisation into regions with dimensions smaller than half the wavelength. Localisation of light into nanoscale regions (beyond its diffraction limit) has applications ranging from the design of optical sensors and measurement techniques with resolutions as high as a few nanometres, to the effective delivery of optical energy into targeted nanoscale regions such as quantum dots, nano-electronic and nano-optical devices. This field has become a major research direction over the last decade. The use of strongly localised surface plasmons in metallic nanostructures is one of the most promising approaches to overcome this problem. Therefore, the aim of this thesis is to investigate the linear and non-linear propagation of surface plasmons in metallic nanostructures. This thesis will focus on two main areas of plasmonic research –– plasmon nanofocusing and plasmon nanoguiding. Plasmon nanofocusing – The main aim of plasmon nanofocusing research is to focus plasmon energy into nanoscale regions using metallic nanostructures and at the same time achieve strong local field enhancement. Various structures for nanofocusing purposes have been proposed and analysed such as sharp metal wedges, tapered metal films on dielectric substrates, tapered metal rods, and dielectric V-grooves in metals. However, a number of important practical issues related to nanofocusing in these structures still remain unclear. Therefore, one of the main aims of this thesis is to address two of the most important of issues which are the coupling efficiency and heating effects of surface plasmons in metallic nanostructures. The method of analysis developed throughout this thesis is a general treatment that can be applied to a diversity of nanofocusing structures, with results shown here for the specific case of sharp metal wedges. Based on the geometrical optics approximation, it is demonstrated that the coupling efficiency from plasmons generated with a metal grating into the nanofocused symmetric or quasi-symmetric modes may vary between ~50% to ~100% depending on the structural parameters. Optimal conditions for nanofocusing with the view to minimise coupling and dissipative losses are also determined and discussed. It is shown that the temperature near the tip of a metal wedge heated by nanosecond plasmonic pulses can increase by several hundred degrees Celsius. This temperature increase is expected to lead to nonlinear effects, self-influence of the focused plasmon, and ultimately self-destruction of the metal tip. This thesis also investigates a different type of nanofocusing structure which consists of a tapered high-index dielectric layer resting on a metal surface. It is shown that the nanofocusing mechanism that occurs in this structure is somewhat different from other structures that have been considered thus far. For example, the surface plasmon experiences significant backreflection and mode transformation at a cut-off thickness. In addition, the reflected plasmon shows negative refraction properties that have not been observed in other nanofocusing structures considered to date. Plasmon nanoguiding – Guiding surface plasmons using metallic nanostructures is important for the development of highly integrated optical components and circuits which are expected to have a superior performance compared to their electronicbased counterparts. A number of different plasmonic waveguides have been considered over the last decade including the recently considered gap and trench plasmon waveguides. The gap and trench plasmon waveguides have proven to be difficult to fabricate. Therefore, this thesis will propose and analyse four different modified gap and trench plasmon waveguides that are expected to be easier to fabricate, and at the same time acquire improved propagation characteristics of the guided mode. In particular, it is demonstrated that the guided modes are significantly screened by the extended metal at the bottom of the structure. This is important for the design of highly integrated optics as it provides the opportunity to place two waveguides close together without significant cross-talk. This thesis also investigates the use of plasmonic nanowires to construct a Fabry-Pérot resonator/interferometer. It is shown that the resonance effect can be achieved with the appropriate resonator length and gap width. Typical quality factors of the Fabry- Pérot cavity are determined and explained in terms of radiative and dissipative losses. The possibility of using a nanowire resonator for the design of plasmonic filters with close to ~100% transmission is also demonstrated. It is expected that the results obtained in this thesis will play a vital role in the development of high resolution near field microscopy and spectroscopy, new measurement techniques and devices for single molecule detection, highly integrated optical devices, and nanobiotechnology devices for diagnostics of living cells.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Nonlinear H_infinity control of UAVs for collision avoidance in gusty environments

This paper proposes a nonlinear H_infinity controller for stabilization of velocities, attitudes and angular rates of a fixed-wing unmanned aerial vehicle (UAV) in a windy environment. The suggested controller aims to achieve a steady-state flight condition in the presence of wind gusts such that the host UAV can be maneuvered to avoid collision with other UAVs during cruise flight with safety guarantees. This paper begins with building a proper model capturing flight aerodynamics of UAVs. Then a nonlinear controller is developed with gust attenuation and rapid response properties. Simulations are conducted for the Shadow UAV to verify performance of the proposed con- troller. Comparative studies with the proportional-integral-derivative (PID) controllers demonstrate that the proposed controller exhibits great performance improvement in a gusty environment, making it suitable for integration into the design of flight control systems for cruise flight of UAVs.

Nonlinear pedagogy underpins intrinsic motivation in sports coaching

A key challenge for sports coaches is to provide performers with learning environments that result in sustainable motivation. In this paper, we will demonstrate that programmes based around the principles of Nonlinear Pedagogy can support the three basic psychological needs that underpin self-determined motivation. Coaches can therefore ensure that practice sessions provide for intrinsic motivation with its associated motivational and emotional benefits.

Kaolinite particle sizes in the <2 µM range using laser scattering

The Clay Minerals Society Source Clay kaolinites, Georgia KGa-1 and KGa-2, have been subjected to particle size determinations by 1) conventional sedimentation methods, 2) electron microscopy and image analysis, and 3) laser scattering using improved algorithms for the interaction of light with small particles. Particle shape, size distribution, and crystallinity vary considerably for each kaolinite. Replicate analyses of separated size fractions showed that in the <2 µm range, the sedimentation/centrifugation method of Tanner and Jackson (1947) is reproducible for different kaolinite types and that the calculated size ranges are in reasonable agreement with the size bins estimated from laser scattering. Particle sizes determined by laser scattering must be calculated using Mie theory when the dominant particle size is less than ∼5 µm. Based on this study of two well-known and structurally different kaolinites, laser scattering, with improved data reduction algorithms that include Mie theory, should be considered an internally consistent and rapid technique for clay particle sizing.

Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.

Fiber Bragg grating strain modulation based on nonlinear string transverse force amplifier

The only effective method of Fiber Bragg Grating (FBG) strain modulation has been by changing the distance between its two fixed ends. We demonstrate an alternative being more sensitive to force based on the nonlinear amplification relationship between a transverse force applied to a stretched string and its induced axial force. It may improve the sensitivity and size of an FBG force sensor, reduce the number of FBGs needed for multi-axial force monitoring, and control the resonant frequency of an FBG accelerometer.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Sensitivity of peak positions to flight-path parameters in a deep-inelastic scattering neutron TOF spectrometer

The effects of small changes in flight-path parameters (primary and secondary flight paths, detector angles), and of displacement of the sample along the beam axis away from its ideal position, are examined for an inelastic time-of-flight (TOF) neutron spectrometer, emphasising the deep-inelastic regime. The aim was to develop a rational basis for deciding what measured shifts in the positions of spectral peaks could be regarded as reliable in the light of the uncertainties in the calibrated flight-path parameters. Uncertainty in the length of the primary or secondary flight path has the least effect on the positions of the peaks of H, D and He, which are dominated by the accuracy of the calibration of the detector angles. This aspect of the calibration of a TOF spectrometer therefore demands close attention to achieve reliable outcomes where the position of the peaks is of significant scientific interest and is discussed in detail. The corresponding sensitivities of the position of peak of the Compton profile, J(y), to flight-path parameters and sample position are also examined, focusing on the comparability across experiments of results for H, D and He. We show that positioning the sample to within a few mm of the ideal position is required to ensure good comparability between experiments if data from detectors at high forward angles are to be reliably interpreted.

Measurement of anisotropies of the kinetic energy and anharmonicity in pyrolytic graphite by neutron Compton scattering

Neutron Compton scattering (NCS) measurements of the anisotropy of the momentum distribution and the mean Laplacian of the interatomic potential ∇2V have been performed using electron volt neutrons, with wave vector transfers between 24 Å−1 and 98 Å−1. The measured momentum distribution of the atoms displays significantly more anisotropy than a calculation using a model density of states. We have observed anisotropies in ∇2V for the first time. The results suggest that the atomic potential is harmonic within the graphite planes, but anharmonic for vibrations perpendicular to the planes.

Neutron Compton scattering from selectively deuterated acetanilide

With the aim of developing the application of neutron Compton scattering (NCS) to molecular systems of biophysical interest, we are using the Compton spectrometer EVS at ISIS to characterize the momentum distribution of protons in peptide groups. In this contribution we present NCS measurements of the recoil peak (Compton profile) due to the amide proton in otherwise fully deuterated acetanilide (ACN), a widely studied model system for H-bonding and energy transfer in biomolecules. We obtain values for the average width of the potential well of the amide proton and its mean kinetic energy. Deviations from the Gaussian form of the Compton profile, analyzed on the basis of an expansion due to Sears, provide data relating to the Laplacian of the proton potential. (C) 1998 Elsevier Science B.V. All rights reserved.