Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium

We investigate the influence of ionization on the propagation and spectral effects of a few-cycle ultrashort laser pulse in a two-level medium. It is found that when the fractional ionization is weak, the production of higher spectral components makes no difference. However, when the two states are essentially depleted before the peak of the laser pulse, the impact of ionization on the higher spectral components is very significant.

Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation

Nonlinear propagation of fs laser pulses in liquids and the dynamic processes of filamentation such as self-focusing, intensity clamping, and evolution of white light production have been analyzed by using one- and two-photon fluorescence. The energy losses of laser pulses caused by multiphoton absorption and conical emission have been measured respectively by z-scan technique. Numerical simulations of fs laser propagation in water have been made to explain the evolution of white light production as well as the small-scale filaments in liquids we have observed by a nonlinear fluorescence technique. (c) 2005 Optical Society of America.

Effects of Lorentz local field correction on propagation properties of few-cycle pulse in dense Λ-type atomic medium

By solving numerically the full Maxwell-Bloch equations without the slowly varying envelope approximation and the rotating-wave approximation, we investigate the effects of Lorentz local field correction (LFC) on the propagation properties of few-cycle laser pulse in a dense A-type three-level atomic medium. We find that: when the area of the input pulse is larger, split of pulse occurs and the number of the sub-pulses with LFC is larger than that without LFC; at the same distance, the time interval between the first sub-pulse and the second sub-pulse in the case without LFC is longer than that with LFC, the time of pulse appearing in the case without LFC is later than that in the case with LFC, and the two phenomena are more obvious with propagation distance increasing; time evolution rules of the populations of levels vertical bar 1 >, vertical bar 2 > and vertical bar 3 > in the two cases with and without LFC are much different. When the area of the input pulse is smaller, effects of LFC on time evolutions of the pulse and populations are remarkably smaller than those in the case of larger area pulse. (c) 2008 Elsevier B.V. All rights reserved.

Controlling wave propagation through nonlinear engineered granular systems

We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave guiding chains to control the acoustic wave transmission. The rapid wave front amplitude decay exhibited by these granular networks makes them highly attractive for impact mitigation applications. The agreement between experiments, numerical simulations, and applicable theoretical predictions validates the wave guiding capabilities of these engineered granular crystals and networks and opens a wide range of possibilities for the realization of increasingly complex granular material design.

Generation of intense extreme supercontinuum radiation via resonant propagation effects

Confinement of electromagnetic energy into a single well-controlled oscillation of light is very important for generation of intense supercontinuum radiation. We find that the pulse breakup of few-cycle ultrashort laser pulses via resonant propagation effects can achieve this aim. By extracting such pulses and then focusing them to drive the He atoms, about 200 eV intense supercontinuum radiation can be generated, which is capable of supporting similar to 20 attosecond isolated pulse generation.

Self-induced transmission on intersubband resonance in multiple quantum wells

We investigate the nonlinear propagation of ultrashort pulses on resonant intersubband transitions in multiple semiconductor quantum wells. It is shown that the nonlinearity rooted from electron-electron interactions destroys the condition giving rise to self-induced transparency. However, by adjusting the area of input pulse, we find the signatures of self-induced transmission due to a full Rabi flopping of the electron density, and this phenomenon can be approximately interpreted by the traditional standard area theorem via defining the effective area of input pulse.

Seismic reflection experiments imaging the physical nature of crustal structures in southern California

Seismic reflection methods have been extensively used to probe the Earth's crust and suggest the nature of its formative processes. The analysis of multi-offset seismic reflection data extends the technique from a reconnaissance method to a powerful scientific tool that can be applied to test specific hypotheses. The treatment of reflections at multiple offsets becomes tractable if the assumptions of high-frequency rays are valid for the problem being considered. Their validity can be tested by applying the methods of analysis to full wave synthetics.

Three studies illustrate the application of these principles to investigations of the nature of the crust in southern California. A survey shot by the COCORP consortium in 1977 across the San Andreas fault near Parkfield revealed events in the record sections whose arrival time decreased with offset. The reflectors generating these events are imaged using a multi-offset three-dimensional Kirchhoff migration. Migrations of full wave acoustic synthetics having the same limitations in geometric coverage as the field survey demonstrate the utility of this back projection process for imaging. The migrated depth sections show the locations of the major physical boundaries of the San Andreas fault zone. The zone is bounded on the southwest by a near-vertical fault juxtaposing a Tertiary sedimentary section against uplifted crystalline rocks of the fault zone block. On the northeast, the fault zone is bounded by a fault dipping into the San Andreas, which includes slices of serpentinized ultramafics, intersecting it at 3 km depth. These interpretations can be made despite complications introduced by lateral heterogeneities.

In 1985 the Calcrust consortium designed a survey in the eastern Mojave desert to image structures in both the shallow and the deep crust. Preliminary field experiments showed that the major geophysical acquisition problem to be solved was the poor penetration of seismic energy through a low-velocity surface layer. Its effects could be mitigated through special acquisition and processing techniques. Data obtained from industry showed that quality data could be obtained from areas having a deeper, older sedimentary cover, causing a re-definition of the geologic objectives. Long offset stationary arrays were designed to provide reversed, wider angle coverage of the deep crust over parts of the survey. The preliminary field tests and constant monitoring of data quality and parameter adjustment allowed 108 km of excellent crustal data to be obtained.

This dataset, along with two others from the central and western Mojave, was used to constrain rock properties and the physical condition of the crust. The multi-offset analysis proceeded in two steps. First, an increase in reflection peak frequency with offset is indicative of a thinly layered reflector. The thickness and velocity contrast of the layering can be calculated from the spectral dispersion, to discriminate between structures resulting from broad scale or local effects. Second, the amplitude effects at different offsets of P-P scattering from weak elastic heterogeneities indicate whether the signs of the changes in density, rigidity, and Lame's parameter at the reflector agree or are opposed. The effects of reflection generation and propagation in a heterogeneous, anisotropic crust were contained by the design of the experiment and the simplicity of the observed amplitude and frequency trends. Multi-offset spectra and amplitude trend stacks of the three Mojave Desert datasets suggest that the most reflective structures in the middle crust are strong Poisson's ratio (σ) contrasts. Porous zones or the juxtaposition of units of mutually distant origin are indicated. Heterogeneities in σ increase towards the top of a basal crustal zone at ~22 km depth. The transition to the basal zone and to the mantle include increases in σ. The Moho itself includes ~400 m layering having a velocity higher than that of the uppermost mantle. The Moho maintains the same configuration across the Mojave despite 5 km of crustal thinning near the Colorado River. This indicates that Miocene extension there either thinned just the basal zone, or that the basal zone developed regionally after the extensional event.

The propagation and deposition of fast muons in dense DT mixture

The propagation of the fast muon population mainly due to collisional effect in a dense deuterium-tritium (DT for short) mixture is investigated and analysed within the framework of the relativistic Fokker-Planck equation. Without the approximation that the muons propagate straightly in the DT mixture, the muon penetration length, the straggling length, and the mean transverse dispersion radius are calculated for different initial energies, and especially for different densities of the densely compressed DT mixture in our suggested muon-driven fast ignition (FI). Unlike laser-driven FI requiring super-high temperature, muons can catalyze DT fusion at lower temperatures and may generate an ignition sparkle before the self-heating fusion follows. Our calculation is important for the feasibility and the experimental study of muon-driven FI.

Propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems

We investigate the propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems using an iterative predictor-corrector finite-difference time-domain method. It is shown that when the initial effective area is equal to 2 pi, the effective area will remain invariant during the course of propagation, and a complete Rabi oscillation can be achieved. However, for an elliptically polarized few-cycle ultrashort laser pulse, polarization conversion can occur. Eventually, the laser pulse will evolve into two separate circularly polarized laser pulses with opposite helicities.

Propagation of a few-cycle laser pulse in a V-type three-level system

Propagation of a few-cycle laser pulse in a V-type three-level system (fine structure levels of rubidium) is investigated numerically. The full three-level Maxwell-Bloch equations without the rotating wave approximation and the standing slowly varying envelope approximation are solved by using a finite-difference time-domain method. It is shown that, when the usual unequal oscillator strengths are considered, self-induced transparency cannot be recovered and higher spectral components can be produced even for small-area pulses. (c) 2005 Pleiades Publishing, Inc.

Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium

We theoretically investigate carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium. Our results show that a soliton pulse can be generated during the two-photon resonant propagation of few-cycle pulse in the polar molecule medium. Moreover, the main features of the soliton pulse, such as pulse duration and intensity, depend crucially on the carrier-envelope phase of the incident pulse, which could be utilized to determine the carrier-envelope phase of a few-cycle ultrashort laser pulse from a mode-locked oscillator.