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.

Quantification of stability in an agility drill using linear and nonlinear measures of variability

This study implemented linear and nonlinear methods of measuring variability to determine differences in stability of two groups of skilled (n = 10) and unskilled (n = 10) participants performing 3m forward/backward shuttle agility drill. We also determined whether stability measures differed between the forward and backward segments of the drill. Finally, we sought to investigate whether local dynamic stability, measured using largest finite-time Lyapunov exponents, changed from distal to proximal lower extremity segments. Three-dimensional coordinates of five lower extremity markers data were recorded. Results revealed that the Lyapunov exponents were lower (P < 0.05) for skilled participants at all joint markers indicative of higher levels of local dynamic stability. Additionally, stability of motion did not differ between forward and backward segments of the drill (P > 0.05), signifying that almost the same control strategy was used in forward and backward directions by all participants, regardless of skill level. Furthermore, local dynamic stability increased from distal to proximal joints (P < 0.05) indicating that stability of proximal segments are prioritized by the neuromuscular control system. Finally, skilled participants displayed greater foot placement standard deviation values (P < 0.05), indicative of adaptation to task constraints. The results of this study provide new methods for sport scientists, coaches to characterize stability in agility drill performance.

An Empirical Comparison of Linear and Nonlinear Volatility Models for Nordic Stock Returns

This paper examines how volatility in financial markets can preferable be modeled. The examination investigates how good the models for the volatility, both linear and nonlinear, are in absorbing skewness and kurtosis. The examination is done on the Nordic stock markets, including Finland, Sweden, Norway and Denmark. Different linear and nonlinear models are applied, and the results indicates that a linear model can almost always be used for modeling the series under investigation, even though nonlinear models performs slightly better in some cases. These results indicate that the markets under study are exposed to asymmetric patterns only to a certain degree. Negative shocks generally have a more prominent effect on the markets, but these effects are not really strong. However, in terms of absorbing skewness and kurtosis, nonlinear models outperform linear ones.

Effect of screening of intermicellar interactions on the linear and nonlinear rheology of a viscoelastic gel

We report our studies of the linear and nonlinear rheology of aqueous solutions of the surfactant cetyl trimethylammonium tosylate (CTAT) with varying amounts of sodium chloride (NaCl). The CTAT concentration is fixed at 42 mM, and the salt concentration is varied between 0 and 120 mM. On increasing the salt (NaCl) concentration, we see three distinct regimes in the zero-shear viscosity and the high-frequency plateau modulus data. In regime 1, the zero-shear viscosity shows a weak increase with salt concentration due to enhanced micellar growth. The decrease in the zero-shear viscosities with salt concentration in regimes II and III can be explained in terms of intermicellar branching. The most intriguing feature of our data, however, is the anomalous behavior of the high-frequency plateau modulus in regime II (0.12 less than or equal to [NaCl]/[CTAT] less than or equal to 1.42). In this regime, the plateau modulus increases with an increase in NaCl concentration. This is highly interesting, since the correlation length of concentration fluctuations and hence the plateau modulus G(0) are not expected to change appreciably in the semidilute regime. We propose to explain the changes in regime II in terms of a possible unbinding of the organic counterions (tosylate) from the CTA(+) surfaces on the addition of NaCl. In the nonlinear flow curves of the samples with high salt content, significant deviations from the predictions of the Giesekus model for entangled micelles are observed.

Linear and nonlinear optical properties of expanded porphyrins: a DMRG study

We study absorption spectra and two photon absorption coefficient of expanded porphyrins (EPs) by the density matrix renormalization group (DMRG) technique. We employ the Pariser-Parr-Pople (PPP) Hamiltonian which includes long-range electron-electron interactions. We find that, in the 4n+2 EPs, there are two prominent low-lying one-photon excitations, while in 4n EPs, there is only one such excitation. We also find that 4n+2 EPs have large two-photon absorption cross sections compared to 4n EPs. The charge density rearrangement in the one-photon excited state is mostly at the pyrrole nitrogen site and at the meso carbon sites. In the two-photon states, the charge density rearrangement occurs mostly at the aza-ring sites. In the one-photon state, the C-C bond length in aza rings shows a tendency to become uniform. In the two-photon state, the bond distortions are on C-N bonds of the pyrrole ring and the adjoining C-C bonds which connect the pyrrole ring to the aza or meso carbon sites.

Linear and nonlinear optical studies on 3,6-bis (2 pyridyl) pyridazine

3,6-Bis (2 pyridyl) pyridazine has been synthesized and characterized by NMR, XRD and elemental analyses. The vibrational studies were carried out by using FTIR and Raman spectroscopy and the modes of vibrations were analysed and compared with the theoretically calculated values. The nonlinear optical property of the title compound was examined by Kurtz-Perry method and Hyper Raleigh scattering with the fundamental wavelength of 1064nm. This compound possesses less SHG efficiency but large first hyperpolarizability. (C) 2013 Elsevier GmbH. All rights reserved.

Topics in linear and nonlinear dispersive waves

The various singularities and instabilities which arise in the modulation theory of dispersive wavetrains are studied. Primary interest is in the theory of nonlinear waves, but a study of associated questions in linear theory provides background information and is of independent interest.

The full modulation theory is developed in general terms. In the first approximation for slow modulations, the modulation equations are solved. In both the linear and nonlinear theories, singularities and regions of multivalued modulations are predicted. Higher order effects are considered to evaluate this first order theory. An improved approximation is presented which gives the true behavior in the singular regions. For the linear case, the end result can be interpreted as the overlap of elementary wavetrains. In the nonlinear case, it is found that a sufficiently strong nonlinearity prevents this overlap. Transition zones with a predictable structure replace the singular regions.

For linear problems, exact solutions are found by Fourier integrals and other superposition techniques. These show the true behavior when breaking modulations are predicted.

A numerical study is made for the anharmonic lattice to assess the nonlinear theory. This confirms the theoretical predictions of nonlinear group velocities, group splitting, and wavetrain instability, as well as higher order effects in the singular regions.

Determining the role of linear and nonlinear interactions in records of climate change: possible solar influences in annual to century-scale records

Time series analysis methods have traditionally helped in identifying the role of various forcing mechanisms in influencing climate change. A challenge to understanding decadal and century-scale climate change has been that the linkages between climate changes and potential forcing mechanisms such as solar variability are often uncertain. However, most studies have focused on the role of climate forcing and climate response within a strictly linear framework. Nonlinear time series analysis procedures provide the opportunity to analyze the role of climate forcing and climate responses between different time scales of climate change. An example is provided by the possible nonlinear response of paleo-ENSO-scale climate changes as identified from coral records to forcing by the solar cycle at longer time scales.

Global linear and nonlinear stability of viscous confined plane wakes with co-flow

The global stability of confined uniform density wakes is studied numerically, using two-dimensional linear global modes and nonlinear direct numerical simulations. The wake inflow velocity is varied between different amounts of co-flow (base bleed). In accordance with previous studies, we find that the frequencies of both the most unstable linear and the saturated nonlinear global mode increase with confinement. For wake Reynolds number Re = 100 we find the confinement to be stabilising, decreasing the growth rate of the linear and the saturation amplitude of the nonlinear modes. The dampening effect is connected to the streamwise development of the base flow, and decreases for more parallel flows at higher Re. The linear analysis reveals that the critical wake velocities are almost identical for unconfined and confined wakes at Re ≈ 400. Further, the results are compared with literature data for an inviscid parallel wake. The confined wake is found to be more stable than its inviscid counterpart, whereas the unconfined wake is more unstable than the inviscid wake. The main reason for both is the base flow development. A detailed comparison of the linear and nonlinear results reveals that the most unstable linear global mode gives in all cases an excellent prediction of the initial nonlinear behaviour and therefore the stability boundary. However, the nonlinear saturated state is different, mainly for higher Re. For Re = 100, the saturated frequency differs less than 5% from the linear frequency, and trends regarding confinement observed in the linear analysis are confirmed.

Linear and nonlinear model large-eddy simulations of a plane jet

The nonlinear Kosovic, and mixed Leray and α subgrid scale models are contrasted with linear Smagorinsky and Yoshizawa Large Eddy Simulations for a Re = 4000 plane jet simulation. Comparisons are made with Direct Numerical Simulation data and measurements. Global properties of the jet such as the spreading and centreline velocity decay rates are investigated. The mean-flow and turbulence parameters in the self-similar region are also studied. All models generally give encouraging agreement with the Direct Numerical Simulation data and reliable measurements. Solution differences for the models are relatively minor, none giving clear improvements for all data comparisons.

Linear and nonlinear intersubband optical properties in a step quantum well with an applied electric field

Within the framework of the effective-mass envelope-function theory, the field-dependent intersubband optical properties of a Al0.4Ga0.6As/Al0.2Ga0.8As/GaAs step quantum well are investigated theoretically based on the periodic boundary condition. A very large Stark shift occurs when the lowest subband electron remains confined to the small well while the higher subband electron confined to the big well. The optical nonlinearity in a step well due to resonant intersubband transition (ISBT) is analyzed using a density-matrix approach. The second-harmonic generation coefficient chi(2 omega)((2)) and nonlinear optical rectification chi(0)((2)) have also been investigated theoretically. The results show that the ISBT in a step well can generate very large second order optical nonlinearities, chi(0)((2)) and chi(2 omega)((2)) can be tuned by the electric field over a wide range.