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.

Nonlinear ion-acoustic surface waves on a dusty plasma

A nonlinear theory for ion-acoustic surface waves propagating at the interface between a dusty plasma and a dielectric is presented. The nonlinear effects are associated with density modulations caused by surface-wave induced anomalous ionization. The negative charge of the massive dust grains is assumed to be constant. It is shown that the effect of the ionization nonlinearity arising from the ion-acoustic surface waves can result in the formation of surface envelope solitons. The wave phase shifts and the widths of the solitons are estimated for typical gas discharge plasmas.

Nonlinear interactions of azimuthal surface waves in magnetoactive plasma filled waveguides

This paper deals with the theoretical studies of nonlinear interactions of azimuthal surface waves (ASW) in cylindrical metal waveguides fully filled by a uniform magnetoactive plasma. These surface-type wave perturbations propagate in azimuthal direction across an external magnetic field, which is directed along the waveguide axis. The ASW is a relatively new kind of surface waves and so far the nonlinear effects associated with their propagation are outside the scope of scientific issues. They are characterized by a discrete set of mode numbers values which define the ASW eigenfrequencies. This fact leads to several peculiarities of ASW compared with ordinary surface-type waves.

Nonlinear analysis of a thin pre-twisted and delaminated anisotropic strip

The present work is aimed at the development of an efficient mathematical model to assess the degradation in the stiffness properties of an anisotropic strip due to delamination. In particular, the motive is to capture those nonlinear effects in a strip that arise due to the geometry of the structure, in the presence of delamination. The variational asymptotic method (VAM) is used as a mathematical tool to simplify the original 3D problem to a 1D problem. Further simplification is achieved by modeling the delaminated structure by a sublaminate approach. By VAM, a 2D nonlinear sectional analysis is carried out to determine compact expression for the stiffness terms. The stiffness terms, both linear and nonlinear, are derived as functions of delamination length and location in closed form. In general, the results from the analysis include fully coupled nonlinear 1D stiffness coefficients, 3D strain field, 3D stress field, and in-plane and warping fields. In this work, the utility of the model is demonstrated for a static case, and its capability to capture the trapeze effect in the presence of delamination is investigated and compared with results available in the literature.

Nonlinear mode coupling and internal resonances in MoS2 nanoelectromechanical system

Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances. (C) 2015 AIP Publishing LLC.

Magnetic field and pressure effects in a saturated gas laser amplifier

Theoretical and experimental studies of a gas laser amplifier are presented, assuming the amplifier is operating with a saturating optical frequency signal. The analysis is primarily concerned with the effects of the gas pressure and the presence of an axial magnetic field on the characteristics of the amplifying medium. Semiclassical radiation theory is used, along with a density matrix description of the atomic medium which relates the motion of single atoms to the macroscopic observables. A two-level description of the atom, using phenomenological source rates and decay rates, forms the basis of our analysis of the gas laser medium. Pressure effects are taken into account to a large extent through suitable choices of decay rate parameters.

Two methods for calculating the induced polarization of the atomic medium are used. The first method utilizes a perturbation expansion which is valid for signal intensities which barely reach saturation strength, and it is quite general in applicability. The second method is valid for arbitrarily strong signals, but it yields tractable solutions only for zero magnetic field or for axial magnetic fields large enough such that the Zeeman splitting is much larger than the power broadened homogeneous linewidth of the laser transition. The effects of pressure broadening of the homogeneous spectral linewidth are included in both the weak-signal and strong-signal theories; however the effects of Zeeman sublevel-mixing collisions are taken into account only in the weak-signal theory.

The behavior of a He-Ne gas laser amplifier in the presence of an axial magnetic field has been studied experimentally by measuring gain and Faraday rotation of linearly polarized resonant laser signals for various values of input signal intensity, and by measuring nonlinearity - induced anisotropy for elliptically polarized resonant laser signals of various input intensities. Two high-gain transitions in the 3.39-μ region were used for study: a J = 1 to J = 2 (3s₂ → 3p₄) transition and a J = 1 to J = 1 (3s₂ → 3p₂) transition. The input signals were tuned to the centers of their respective resonant gain lines.

The experimental results agree quite well with corresponding theoretical expressions which have been developed to include the nonlinear effects of saturation strength signals. The experimental results clearly show saturation of Faraday rotation, and for the J = 1 t o J = 1 transition a Faraday rotation reversal and a traveling wave gain dip are seen for small values of axial magnetic field. The nonlinearity induced anisotropy shows a marked dependence on the gas pressure in the amplifier tube for the J = 1 to J = 2 transition; this dependence agrees with the predictions of the general perturbational or weak signal theory when allowances are made for the effects of Zeeman sublevel-mixing collisions. The results provide a method for measuring the upper (neon 3s₂) level quadrupole moment decay rate, the dipole moment decay rates for the 3s₂ → 3p₄ and 3s₂ → 3p₂ transitions, and the effects of various types of collision processes on these decay rates.

A study of nonlinear phenomena in the propagation of electromagnetic waves in a weakly ionized gas

This thesis is a study of nonlinear phenomena in the propagation of electromagnetic waves in a weakly ionized gas externally biased with a magnetostatic field. The present study is restricted to the nonlinear phenomena rising from the interaction of electromagnetic waves in the ionized gas. The important effects of nonlinearity are wave-form distortion leads to cross modulation of one wave by a second amplitude-modulated wave.

The nonlinear effects are assumed to be small so that a perturbation method can be used. Boltzmann’s kinetic equation with an appropriate expression for the collision term is solved by expanding the electron distribution function into spherical harmonics in velocity space. In turn, the electron convection current density and the conductivity tensors of the nonlinear ionized gas are found from the distribution function. Finally, the expression for the current density and Maxwell’s equations are employed to investigate the effects of nonlinearity on the propagation of electromagnetic waves in the ionized gas, and also on the reflection of waves from an ionized gas of semi-infinite extent.

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19A degrees 35'N, 112A degrees E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

Nonlinear Dynamics of Semiconductor LasersControl and Synchronization of Chaos:

Nonlinear dynamics of laser systems has become an interesting area of research in recent times. Lasers are good examples of nonlinear dissipative systems showing many kinds of nonlinear phenomena such as chaos, multistability and quasiperiodicity. The study of these phenomena in lasers has fundamental scientific importance since the investigations on these effects reveal many interesting features of nonlinear effects in practical systems. Further, the understanding of the instabilities in lasers is helpful in detecting and controlling such effects. Chaos is one of the most interesting phenomena shown by nonlinear deterministic systems. It is found that, like many nonlinear dissipative systems, lasers also show chaos for certain ranges of parameters. Many investigations on laser chaos have been done in the last two decades. The earlier studies in this field were concentrated on the dynamical aspects of laser chaos. However, recent developments in this area mainly belong to the control and synchronization of chaos. A number of attempts have been reported in controlling or suppressing chaos in lasers since lasers are the practical systems aimed to operated in stable or periodic mode. On the other hand, laser chaos has been found to be applicable in high speed secure communication based on synchronization of chaos. Thus, chaos in laser systems has technological importance also. Semiconductor lasers are most applicable in the fields of optical communications among various kinds of laser due to many reasons such as their compactness, reliability modest cost and the opportunity of direct current modulation. They show chaos and other instabilities under various physical conditions such as direct modulation and optical or optoelectronic feedback. It is desirable for semiconductor lasers to have stable and regular operation. Thus, the understanding of chaos and other instabilities in semiconductor lasers and their xi control is highly important in photonics. We address the problem of controlling chaos produced by direct modulation of laser diodes. We consider the delay feedback control methods for this purpose and study their performance using numerical simulation. Besides the control of chaos, control of other nonlinear effects such as quasiperiodicity and bistability using delay feedback methods are also investigated. A number of secure communication schemes based on synchronization of chaos semiconductor lasers have been successfully demonstrated theoretically and experimentally. The current investigations in these field include the study of practical issues on the implementations of such encryption schemes. We theoretically study the issues such as channel delay, phase mismatch and frequency detuning on the synchronization of chaos in directly modulated laser diodes. It would be helpful for designing and implementing chaotic encryption schemes using synchronization of chaos in modulated semiconductor laser

Nonlinear Dynamics of Multiple Quantum Well Lasers: Chaos and Multistability

This thesis presents analytical and numerical results from studies based on the multiple quantum well laser rate equation model. We address the problem of controlling chaos produced by direct modulation of laser diodes. We consider the delay feedback control methods for this purpose and study their performance using numerical simulation. Besides the control of chaos, control of other nonlinear effects such as quasiperiodicity and bistability using delay feedback methods are also investigated.A number of secure communication schemes based on synchronization of chaos semiconductor lasers have been successfully demonstrated theoretically and experimentally. The current investigations in these field include the study of practical issues on the implementations of such encryption schemes. We theoretically study the issues such as channel delay, phase mismatch and frequency detuning on the synchronization of chaos in directly modulated laser diodes. It would be helpful for designing and implementing chaotic encryption schemes using synchronization of chaos in modulated semiconductor lasers.

Identification of nonlinear structures using discrete-time Volterra series

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear angle control of a sectioned airfoil by using shape memory alloys

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)