Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

Ultrafast electronic excitation in CaF2 crystals

A new pump and probe experimental system was developed, the pump pulse duration of which is stretched and is much longer than that of the probe pulse. Using this system, time-resolved electronic excitation processes and damage mechanisms in CaF2 crystals were studied. The measured reflectivity of the probe pulse begins to increase at the peak of the pump pulse and increases rapidly in the latter half of the pump pulse, when the pump pulse duration is stretched to 580fs. Our experimental results indicate that both multiphoton ionization and impact ionization play important roles in the generation of conduction band electrons, at least they do so when the pump pulse durations are equal to or longer than 580fs.

Alignment of nanoparticles formed on the surface of 6H-SiC crystals irradiated by two collinear femtosecond laser beams

Nanoripples with periods of 150 and 80 nm are formed on the surface of 6H-SiC crystals irradiated by the p-polarized 800 nm and the s-polarized 400 nm femtosecond lasers, respectively. When both of the two collinear laser beams focus simultaneously on the sample surface, nanoparticles are formed on the whole ablation area, and they array in parallel lines. We propose and confirm that the second harmonics in the sample surface excited by the incident lasers plays an important role in the formation of nanostructures.

Comparison of laser performances of 5at.% Yb : Gd2xY2(1-x)SiO5 crystals between different cutting directions

We investigate the laser actions of 5at.% Yb:Gd2xY2(1-x)SiO5 (Yb:GYSO; x = 0.1) crystals with different cutting directions, parallel and vertical to the growth axis. Our results show that the cutting direction of the sample plays an astonished role in the laser operation. The sample cut vertically to the growth axis possesses the favourable lasing characteristics. Its output power reaches 3.13W at 1060nm with a slope efficiency of 44.68% when the absorbed pump power is 8.9 W. In contrast, the sample cut parallel reaches only 1.65 W at 1044 nm with a slope elLiciency of 33.76% with absorbed pump power of 7.99 W. The absorption and emission spectra of the two samples are examined and the merit factor M is calculated. Our analysis is in agreement well with the experimental results. The wavelength tuning range of the superior sample covers from 1013.68 nm to 1084.82 nm.

Three-dimensional self-assembly of brush block copolymers to photonic crystals

The development of Ring Opening Metathesis Polymerization has allowed the world of block copolymers to expand into brush block copolymers. Brush block copolymers consist of a polymer backbone with polymeric side chains, forcing the backbone to hold a stretched conformation and giving it a worm-like shape. These brush block copolymers have a number of advantages over tradition block copolymers, including faster self-assembly behavior, larger domain sizes, and much less entanglement. This makes them an ideal candidate in the development of a bottom-up approach to forming photonic crystals. Photonic crystals are periodic nanostructures that transmit and reflect only certain wavelengths of light, forming a band gap. These are used in a number of coatings and other optical uses. One and two dimensional photonic crystals are commercially available, though are often expensive and difficult to manufacture. Previous work has focused on the creation of one dimensional photonic crystals from brush block copolymers. In this thesis, I will focus on the synthesis and characterization of asymmetric brush block copolymers for self-assembly into two and three dimensional photonic crystals. Three series of brush block copolymers were made and characterized by Gel Permeation Chromatography and Nuclear Magnetic Resonance spectroscopy. They were then made into films through compressive thermal annealing and characterized by UV-Vis Spectroscopy and Scanning Electron Microscopy. Evidence of non-lamellar structures were seen, indicating the first reported creation of two or three dimensional photonic crystals from brush block copolymers.

Transmission spectrum of a double quantum-dot-nanocavity system in photonic crystals

We investigate the optical transmission properties of a combined system which consists of two quantum-dot-nanocavity subsystems indirectly coupled to a waveguide in a planar photonic crystal. A Mollow-like triplet and the growth of sidebands are found, reflecting intrinsic optical responses in the complex microstructure.

Theoretical and experimental study on femtosecond laser induced damage in CaF2 crystals

We report on the damage threshold in CaF2 crystals induced by femtosecond laser at wavelengths of 800 nm and 400 nm, respectively. The dependences of ablation depths and ablation volumes on laser fluences are also presented. We investigate theoretically the coupling constants between phonon and conduction band electrons (CBE), and calculate the rates of CBE absorbing laser energy. A theoretical model including CBE production, laser energy deposition, and CBE diffusion is applied to study the damage mechanisms. Our results indicate that energy diffusion greatly influences damage threshold and ablation depth.

Ultraviolet-infrared femtosecond laser-induced damage in fused silica and CaF2 crystals

The damage in fused silica and CaF2 crystals induced by wavelength tunable femtosecond lasers is studied. The threshold fluence is observed to increase rapidly with laser wavelength lambda in the region of 250-800 nm, while it is nearly a constant for 800

Crystal Coulomb energies: I. Organic donor-acceptor complexes--a review. II. Classical Ewald calculations of the Coulomb binding energy of four donor-acceptor crystals and Wurster's blue perchlorate. III. A rapid-convergence quantum-mechanical formalism for crystal electronic energies

Chapter I

Theories for organic donor-acceptor (DA) complexes in solution and in the solid state are reviewed, and compared with the available experimental data. As shown by McConnell et al. (Proc. Natl. Acad. Sci. U.S., 53, 46-50 (1965)), the DA crystals fall into two classes, the holoionic class with a fully or almost fully ionic ground state, and the nonionic class with little or no ionic character. If the total lattice binding energy 2ε₁ (per DA pair) gained in ionizing a DA lattice exceeds the cost 2ε_o of ionizing each DA pair, ε₁ + ε_o less than 0, then the lattice is holoionic. The charge-transfer (CT) band in crystals and in solution can be explained, following Mulliken, by a second-order mixing of states, or by any theory that makes the CT transition strongly allowed, and yet due to a small change in the ground state of the non-interacting components D and A (or D⁺ and A^-). The magnetic properties of the DA crystals are discussed.

Chapter II

A computer program, EWALD, was written to calculate by the Ewald fast-convergence method the crystal Coulomb binding energy E_C due to classical monopole-monopole interactions for crystals of any symmetry. The precision of E_C values obtained is high: the uncertainties, estimated by the effect on E_C of changing the Ewald convergence parameter η, ranged from ± 0.00002 eV to ± 0.01 eV in the worst case. The charge distribution for organic ions was idealized as fractional point charges localized at the crystallographic atomic positions: these charges were chosen from available theoretical and experimental estimates. The uncertainty in E_C due to different charge distribution models is typically ± 0.1 eV (± 3%): thus, even the simple Hückel model can give decent results.

E_C for Wurster's Blue Perchl orate is -4.1 eV/molecule: the crystal is stable under the binding provided by direct Coulomb interactions. E_C for N-Methylphenazinium Tetracyanoquino- dimethanide is 0.1 eV: exchange Coulomb interactions, which cannot be estimated classically, must provide the necessary binding.

EWALD was also used to test the McConnell classification of DA crystals. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine: 7,7,8,8-Tetracyanoquinodimethan) E_C = -4.0 eV while 2ε_o = 4.6₅ eV: clearly, exchange forces must provide the balance. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine:para-Chloranil) E_C = -4.4 eV, while 2ε_o = 5.0 eV: again EC falls short of 2ε₁. As a Gedankenexperiment, two nonionic crystals were assumed to be ionized: for (1:1)-(Hexamethyl- benzene:para-Chloranil) E_C = -4.5 eV, 2ε_o = 6.6 eV; for (1:1)- (Napthalene:Tetracyanoethylene) E_C = -4.3 eV, 2ε_o = 6.5 eV. Thus, exchange energies in these nonionic crystals must not exceed 1 eV.

Chapter III

A rapid-convergence quantum-mechanical formalism is derived to calculate the electronic energy of an arbitrary molecular (or molecular-ion) crystal: this provides estimates of crystal binding energies which include the exchange Coulomb inter- actions. Previously obtained LCAO-MO wavefunctions for the isolated molecule(s) ("unit cell spin-orbitals") provide the starting-point. Bloch's theorem is used to construct "crystal spin-orbitals". Overlap between the unit cell orbitals localized in different unit cells is neglected, or is eliminated by Löwdin orthogonalization. Then simple formulas for the total kinetic energy Q^(XT)_λ, nuclear attraction [λ/λ]^XT, direct Coulomb [λλ/λ'λ']^XT and exchange Coulomb [λλ'/λ'λ]^XT integrals are obtained, and direct-space brute-force expansions in atomic wavefunctions are given. Fourier series are obtained for [λ/λ]^XT, [λλ/λ'λ']^XT, and [λλ/λ'λ]^XT with the help of the convolution theorem; the Fourier coefficients require the evaluation of Silverstone's two-center Fourier transform integrals. If the short-range interactions are calculated by brute-force integrations in direct space, and the long-range effects are summed in Fourier space, then rapid convergence is possible for [λ/λ]^XT, [λλ/λ'λ']^XT and [λλ'/λ'λ]^XT. This is achieved, as in the Ewald method, by modifying each atomic wavefunction by a "Gaussian convergence acceleration factor", and evaluating separately in direct and in Fourier space appropriate portions of [λ/λ]^XT, etc., where some of the portions contain the Gaussian factor.

I. Spectroscopic evidence for slow vibrational relaxation in excited electronic states of diatomics in rare gas solids. II. Static crystal field effects in the electronic spectra of isotopically mixed benzene crystals

Part I

Studies of vibrational relaxation in excited electronic states of simple diatomic molecules trapped in solid rare-gas matrices at low temperatures are reported. The relaxation is investigated by monitoring the emission intensity from vibrational levels of the excited electronic state to vibrational levels of the ground electronic state. The emission was in all cases excited by bombardment of the doped rare-gas solid with X-rays.

The diatomics studied and the band systems seen are: N₂, Vegard-Kaplan and Second Positive systems; O₂, Herzberg system; OH and OD, A ²Σ⁺ - X²II_i system. The latter has been investigated only in solid Ne, where both emission and absorption spectra were recorded; observed fine structure has been partly interpreted in terms of slightly perturbed rotational motion in the solid. For N₂, OH, and OD emission occurred from v' > 0, establishing a vibrational relaxation time in the excited electronic state of the order, of longer than, the electronic radiative lifetime. The relative emission intensity and decay times for different v' progressions in the Vegard-Kaplan system are found to depend on the rare-gas host and the N₂ concentration, but are independent of temperature in the range 1.7°K to 30°K.

Part II

Static crystal field effects on the absorption, fluorescence, and phosphorescence spectra of isotopically mixed benzene crystals were investigated. Evidence is presented which demonstrate that in the crystal the ground, lowest excited singlet, and lowest triplet states of the guest deviate from hexagonal symmetry. The deviation appears largest in the lowest triplet state and may be due to an intrinsic instability of the ³B_1u state. High resolution absorption and phospho- rescence spectra are reported and analyzed in terms of site-splitting of degenerate vibrations and orientational effects. The guest phosphorescence lifetime for various benzene isotopes in C₆D₆ and sym-C₆H₃D₃ hosts is presented and discussed.

Design of adjustable superresolving filters based on birefringent crystals

A two-mode adjustable superresolving filter based on a birefringent filter is proposed. This kind of filter has superresolution in two modes of adjustment. One is rotation of the binary pupil filter on the optical axis of the system and the other is the tilt of the filter away from the pupil plane on axis parallel or perpendicular to the optical axis of the crystal. The filters act as complex amplitude filters in the former mode, and as pure phase filters in the latter. By analyzing two superresolving parameters, we obtain the optimal design parameters that ensure a large field of view, a large superresolving range, and a high setting accuracy. This kind of filter can provide more flexibility in practical applications. (c) 2006 Optical Society of America.

Study of noncollinear quasi-phase matching optical parametric amplification with group-velocity matching based on periodically poled crystals

The properties of noncollinear optical parametric amplification (NOPA) based on quasi-phase matching of periodically poled crystals are investigated, under the condition that the group velocity matching (GVM) of the signal and idler pulses is satisfied. Our study focuses on the dependence of the gain spectrum upon the noncollinear angle, crystal temperature, and crystal angle with periodically poled KTiOPO4 (PPKTP), periodically poled LiNbO3 (PPLN), and periodically poled LiTaO3 (PPLT), and the NOPA gain properties of the three crystals are compared. Broad gain bandwidth exists above 85 nm at a signal wavelength of 800 nm with a 532 nm pump pulse, with proper noncollinear angle and grating period at a fixed temperature for GVM. Deviation from the group-velocity-matched noncollinear angle can be compensated by accurately tuning the crystal angle or temperature with a fixed grating period for phase matching. Moreover, there is a large capability of crystal angle tuning.

Effects of gamma-irradiation on Al2O3 crystals grown under reducing atmosphere

Gamma-ray irradiation-induced color centers in Al2O3 crystals grown by temperature gradient techniques (TGT) under a strongly reducing atmosphere were studied. The transition F+ -> F takes place during the irradiation process. Glow discharge mass spectroscopy (GDMS) and annealing treatments show that Fe3+ impurity ions are present in the crystals. A composite (F+-Fe3+) defect was presented to explain the origin of the 255 nm band absorption in the TGT-Al2O3 crystals. (C) 2006 Elsevier B.V. All rights reserved.

Femtosecond laser ablation of crystals SiO2 and YAG

Damage threshold of crystals SiO2 and YAG against 60-900 fs, 800 nm laser pulses are reported. The breakdown mechanisms were discussed based on the double-flux model and Keldysh theory. We found that impact ionization plays the important role in the femtosecond laser-induced damage in crystalline SiO2, while the roles of photoionization and impact ionization in YAG crystals depend on the laser pulse durations. (C) 2007 Elsevier B.V. All rights reserved.