NONLINEAR EFFECTS IN MAGNETIC GARNET FILMS AND NONRECIPROCAL OPTICAL BLOCH OSCILLATIONS IN WAVEGUIDE ARRAYS

This dissertation presents detailed experimental and theoretical investigations of nonlinear and nonreciprocal effects in magnetic garnet films. The dissertation thus comprises two major sections. The first section concentrates on the study of a new class of nonlinear magneto-optic thin film materials possessing strong higher order magnetic susceptibility for nonlinear optical applications. The focus was on enlarging the nonlinear performance of ferrite garnet films by strain generation and compositional gradients in the sputter-deposition growth of these films. Under this project several bismuth-substituted yttrium iron garnet (Bi,Y) 3 (Fe,Ga)5 O12(acronym as Bi:YIG) films have been sputter-deposited over gadolinium gallium garnet (Gd 3 Ga5 O12 ) substrates and characterized for their nonlinear optical response. One of the important findings of this work is that lattice mismatch strain drives the second harmonic (SH) signal in the Bi:YIG films, in agreement with theoretical predictions; whereas micro-strain was found not to correlate significantly with SH signal at the micro-strain levels present in these films. This study also elaborates on the role of the film's constitutive elements and their concentration gradients in nonlinear response of the films. Ultrahigh sensitivity delivered by second harmonic generation provides a new exciting tool for studying magnetized surfaces and buried interfaces, making this work important from both a fundamental and application point of view. The second part of the dissertation addresses an important technological need; namely the development of an on-chip optical isolator for use in photonic integrated circuits. It is based on two related novel effects, nonreciprocal and unidirectional optical Bloch oscillations (BOs), recently proposed and developed by Professor Miguel Levy and myself. This dissertation work has established a comprehensive theoretical background for the implementation of these effects in magneto-optic waveguide arrays. The model systems we developed consist of photonic lattices in the form of one-dimensional waveguide arrays where an optical force is introduced into the array through geometrical design turning the beam sideways. Laterally displaced photons are periodically returned to a central guide by photonic crystal action. The effect leads to a novel oscillatory optical phenomenon that can be magnetically controlled and rendered unidirectional. An on-chip optical isolator was designed based on the unidirectionality of the magneto-opticBloch oscillatory motion. The proposed device delivers an isolation ratio as high as 36 dB that remains above 30 dB in a 0.7 nm wavelength bandwidth, at the telecommunication wavelength 1.55 μm. Slight modifications in isolator design allow one to achieve an even more impressive isolation ratio ~ 55 dB, but at the expense of smaller bandwidth. Moreover, the device allows multifunctionality, such as optical switching with a simultaneous isolation function, well suited for photonic integrated circuits.

Tunable single- and dual-wavelength SHG from diode-pumped PPKTP waveguides

A compact, all-room-temperature, widely tunable, continuous wave laser source in the green spectral region (502.1–544.2 nm) with a maximum output power of 14.7 mW is demonstrated. This was made possible by utilizing second-harmonic generation (SHG) in a periodically poled potassium titanyl phosphate (PPKTP) crystal waveguide pumped by a quantum-well external-cavity fiber-coupled diode laser and exploiting the multimode-matching approach in nonlinear crystal waveguides. The dual-wavelength SHG in the wavelength region between 505.4 and 537.7 nm (with a wavelength difference ranging from 1.8 to 32.3 nm) and sum-frequency generation in a PPKTP waveguide is also demonstrated.

Chiroptical spectroscopy of biomolecules using chiral plasmonic nanostructures

This thesis explores the potential of chiral plasmonic nanostructures for the ultrasensitive detection of protein structure. These nanostructures support the generation of fields with enhanced chirality relative to circularly polarised light and are an extremely incisive probe of protein structure. In chapter 4 we introduce a nanopatterned Au film (Templated Plasmonic Substrate, TPS) fabricated using a high through-put injection moulding technique which is a viable alternative to expensive lithographically fabricated nanostructures. The optical and chiroptical properties of TPS nanostructures are found to be highly dependent on the coupling between the electric and magnetic modes of the constituent solid and inverse structures. Significantly, refractive index based measurements of strongly coupled TPSs display a similar sensitivity to protein structure as previous lithographic nanostructures. We subsequently endeavour to improve the sensing properties of TPS nanostructures by developing a high through-put nanoscale chemical functionalisation technique. This process involves a chemical protection/deprotection strategy. The protection step generates a self-assembled monolayer (SAM) of a thermally responsive polymer on the TPS surface which inhibits protein binding. The deprotection step exploits the presence of nanolocalised thermal gradients in the water surrounding the TPS upon irradiation with an 8ns pulsed laser to modify the SAM conformation on surfaces with high net chirality. This allows binding of biomaterial in these regions and subsequently enhances the TPS sensitivity levels. In chapter 6 an alternative method for the detection of protein structure using TPS nanostructures is introduced. This technique relies on mediation of the electric/magnetic coupling in the TPS by the adsorbed protein. This phenomenon is probed through both linear reflectance and nonlinear second harmonic generation (SHG) measurements. Detection of protein structure using this method does not require the presence of fields of enhanced chirality whilst it is also sensitive to a larger array of secondary structure motifs than the measurements in chapters 4 and 5. Finally, a preliminary investigation into the detection of mesoscale biological structure is presented. Sensitivity to the mesoscale helical pitch of insulin amyloid fibrils is displayed through the asymmetry in the circular dichroism (CD) of lithographic gammadions of varying thickness upon adsorption of insulin amyloid fibril spherulites and fragmented fibrils. The proposed model for this sensitivity to the helical pitch relies on the vertical height of the nanostructures relative to this structural property as well as the binding orientation of the fibrils.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Third harmonic generation of the surface wave in the semiconductor-metal slowing-down structure

A nonlinear process is considered of the surface wave third harmonics generation in a slowing-down semiconductor-metal structure. The process is conditioned by non-parabolicity of the charge carrier dispersion law. It is shown that in narrow-gap semiconducting materials it is necessary to account for the process together with the surface wave second harmonics generation conditioned by nonlinearity of quasi-hydrodynamics and the Maxwell equations. The conclusion is made that the third harmonies amplitude in narrow-gap semiconductors may exceed substantially the signal amplitude at the 3w frequency in a gas plasma and be of the same order with the surface waves second harmonies amplitude.

The harmonic torsional oscillations of a thin disk submerged in a fluid with a surfactant surface layer

A formulation in terms of a Fredholm integral equation of the first kind is given for the axisymmetric problem of a disk oscillating harmonically in a viscous fluid whose surface is contaminated with a surfactant film. The equation of the first kind is converted to a pair of coupled integral equations of the second kind, which are solved numerically. The resistive torque on the disk is evaluated and surface velocity profiles are computed for varying values of the ratio of the coefficient of surface shear viscosity to the coefficient of viscosity of the substrate fluid, and the depth of the disk below the surface.

Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Harmonic Analysis of Advanced Bus-Clamping PWM Techniques

Special switching sequences can be employed in space-vector-based generation of pulsewidth-modulated (PWM) waveforms for voltage-source inverters. These sequences involve switching a phase twice, switching the second phase once, and clamping the third phase in a subcycle. Advanced bus-clamping PWM (ABCPWM) techniques have been proposed recently that employ such switching sequences. This letter studies the spectral properties of the waveforms produced by these PWM techniques. Further, analytical closed-form expressions are derived for the total rms harmonic distortion due to these techniques. It is shown that the ABCPWM techniques lead to lower distortion than conventional space vector PWM and discontinuous PWM at higher modulation indexes. The findings are validated on a 2.2-kW constant $V/f$ induction motor drive and also on a 100-kW motor drive.

Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.

I. Site effects and exciton structure in molecular crystals - Benzene. II. The first and second triplet states of solid benzene

The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C₆H₆, C₆H₅D, m-C₆H₄D₂, p-C₆H₄D₂, sym-C₆H₃D₃, C₆D₅H, and C₆D₆ in either a C₆H₆ or C₆D₆ host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C₆H₆, C₆D₆, and sym-C₆H₃D₃; c) the orientational effect for the isotopes without a trigonal axis in both the ¹B_2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be^-Cr - A/r⁶ ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (³B_1u and ³E_1u) is given.

Development of Swept Frequency Method for Measuring Frequency Response of Photodetectors Based on Harmonic Analysis

We develop a swept frequency method for measuring the frequency response of photodetectors; (PDs) based on harmonic analysis. In this technique, a lightwave from a laser source is modulated by a radio-frequency (RF) signal via a Mach-Zehnder LiNbO3 modulator, and detected by a PD under test. The measured second-order harmonic of the RF signal contains information of the frequency responses and nonlinearities of the RF source, modulator, and PD. The frequency response of the PD alone is obtained by deducting the known frequency responses and nonlinearities of the RF source and modulator. Compared with the conventional swept frequency method, the measurement frequency range can be doubled using the proposed method. Experiment results show a good agreement between the measured results and those obtained using other techniques.

Harmonic mode-locked ytterbium-doped fibre ring laser

We demonstrate a harmonic mode-locked ytterbium-doped fibre ring laser, which consists of a polarization-sensitive isolator, two polarization controllers, two 976 nm laser diodes as the pump source and a two-segment ytterbium-doped fibre. Utilizing an additive pulse mode-locked technique based on nonlinear polarization evolution, the ytterbium-doped fibre laser can operate in mode-locked state by adjusting the position of polarization controllers. The cavity fundamental repetition rate is 23.78 MHz. We also observe the second- and third-harmonic mode locking in the normal dispersion region, and their repetition rates are 47.66 MHz and 71.56 MHz, respectively. Over-driving of the saturable absorber in the harmonic mode-locking pulse is analysed and discussed in detail.

High-order harmonic generation and multi-photon ionization of Na-2 in laser fields

In this paper high-order harmonic generation (HHG) spectra and the ionization probabilities of various charge states of small cluster Na-2 in the multiphoton regimes are calculated by using time-dependent local density approximation (TDLDA) for one-colour (1064 nm) and two-colour (1064 nm and 532 nm) ultrashort (25 fs) laser pulses. HHG spectra of Na2 have not the large extent of plateaus due to pronounced collective effects of electron dynamics. In addition, the two-colour laser field can result in the breaking of the symmetry and generation of the even order harmonic such as the second order harmonic. The results of ionization probabilities show that a two-colour laser field can increase the ionization probability of higher charge state.

Inverse Class-E Amplifier With Transmission-Line Harmonic Suppression

This paper reports on the design methodology and experimental characterization of the inverse Class-E power amplifier. A demonstration amplifier with excellent second and third harmonic-suppression levels has been designed, constructed, and measured. The circuit fabricated using a 1.2-min gate-width GaAs MESFET is shown to be able to deliver 22-dBm output power at 2.3 GHz. The amplifier achieves a peak power-added efficiency of 64 % and drain efficiency of 69 %, and exhibits 11.6 dB power gain when operated from a 3-V supply voltage. Comparisons of simulated and measured results are given with good agreement between them being obtained. Experimental results are presented for the amplifier's response to Gaussian minimum shift keying modulation, where a peak error vector modulation value of 0.6% is measured.