Phase conjugation via four-wave mixing in a resonant medium

This thesis describes the theoretical solution and experimental verification of phase conjugation via nondegenerate four-wave mixing in resonant media. The theoretical work models the resonant medium as a two-level atomic system with the lower state of the system being the ground state of the atom. Working initially with an ensemble of stationary atoms, the density matrix equations are solved by third-order perturbation theory in the presence of the four applied electro-magnetic fields which are assumed to be nearly resonant with the atomic transition. Two of the applied fields are assumed to be non-depleted counterpropagating pump waves while the third wave is an incident signal wave. The fourth wave is the phase conjugate wave which is generated by the interaction of the three previous waves with the nonlinear medium. The solution of the density matrix equations gives the local polarization of the atom. The polarization is used in Maxwell's equations as a source term to solve for the propagation and generation of the signal wave and phase conjugate wave through the nonlinear medium. Studying the dependence of the phase conjugate signal on the various parameters such as frequency, we show how an ultrahigh-Q isotropically sensitive optical filter can be constructed using the phase conjugation process.

In many cases the pump waves may saturate the resonant medium so we also present another solution to the density matrix equations which is correct to all orders in the amplitude of the pump waves since the third-order solution is correct only to first-order in each of the field amplitudes. In the saturated regime, we predict several new phenomena associated with degenerate four-wave mixing and also describe the ac Stark effect and how it modifies the frequency response of the filtering process. We also show how a narrow bandwidth optical filter with an efficiency greater than unity can be constructed.

In many atomic systems the atoms are moving at significant velocities such that the Doppler linewidth of the system is larger than the homogeneous linewidth. The latter linewidth dominates the response of the ensemble of stationary atoms. To better understand this case the density matrix equations are solved to third-order by perturbation theory for an atom of velocity v. The solution for the polarization is then integrated over the velocity distribution of the macroscopic system which is assumed to be a gaussian distribution of velocities since that is an excellent model of many real systems. Using the Doppler broadened system, we explain how a tunable optical filter can be constructed whose bandwidth is limited by the homogeneous linewidth of the atom while the tuning range of the filter extends over the entire Doppler profile.

Since it is a resonant system, sodium vapor is used as the nonlinear medium in our experiments. The relevant properties of sodium are discussed in great detail. In particular, the wavefunctions of the 3S and 3P states are analyzed and a discussion of how the 3S-3P transition models a two-level system is given.

Using sodium as the nonlinear medium we demonstrate an ultrahigh-Q optical filter using phase conjugation via nondegenerate four-wave mixing as the filtering process. The filter has a FWHM bandwidth of 41 MHz and a maximum efficiency of 4 x 10^-3. However, our theoretical work and other experimental work with sodium suggest that an efficient filter with both gain and a narrower bandwidth should be quite feasible.

Criterio para análisis de fatiga con tensiones aleatorias

[ES]El trabajo que aquí se presenta tiene como principal objetivo comprobar la validez del método de Osgood, que es una particularización del método de Palmgren-Miner, que se emplea cuando un punto de una pieza está sometido a tensiones aleatorias. Se quiere comprobar su validez en situaciones reales en las que no se cumplen algunas de sus hipótesis de partida. En concreto en este trabajo se va a analizar la validez del método en dos casos: cuando el registro de tensiones aplicado sobre la pieza es alterno pero no sigue una distribución Gaussiana y cuando ni es Gaussiano ni alterno. Los resultados obtenidos empleando el método de Osgood en ambos casos se compararán con el daño obtenido para el mismo registro de tensiones empleando un método de daño lineal como es el método de Palmgren-Miner. Para llevar a cabo esta comprobación se va a hacer uso del programa Excel, mediante el cual se generarán los registros de tensiones aleatorias con los que se va a trabajar.

Continuous stochastic processes

A general review of stochastic processes is given in the introduction; definitions, properties and a rough classification are presented together with the position and scope of the author's work as it fits into the general scheme.

The first section presents a brief summary of the pertinent analytical properties of continuous stochastic processes and their probability-theoretic foundations which are used in the sequel.

The remaining two sections (II and III), comprising the body of the work, are the author's contribution to the theory. It turns out that a very inclusive class of continuous stochastic processes are characterized by a fundamental partial differential equation and its adjoint (the Fokker-Planck equations). The coefficients appearing in those equations assimilate, in a most concise way, all the salient properties of the process, freed from boundary value considerations. The writer’s work consists in characterizing the processes through these coefficients without recourse to solving the partial differential equations.

First, a class of coefficients leading to a unique, continuous process is presented, and several facts are proven to show why this class is restricted. Then, in terms of the coefficients, the unconditional statistics are deduced, these being the mean, variance and covariance. The most general class of coefficients leading to the Gaussian distribution is deduced, and a complete characterization of these processes is presented. By specializing the coefficients, all the known stochastic processes may be readily studied, and some examples of these are presented; viz. the Einstein process, Bachelier process, Ornstein-Uhlenbeck process, etc. The calculations are effectively reduced down to ordinary first order differential equations, and in addition to giving a comprehensive characterization, the derivations are materially simplified over the solution to the original partial differential equations.

In the last section the properties of the integral process are presented. After an expository section on the definition, meaning, and importance of the integral process, a particular example is carried through starting from basic definition. This illustrates the fundamental properties, and an inherent paradox. Next the basic coefficients of the integral process are studied in terms of the original coefficients, and the integral process is uniquely characterized. It is shown that the integral process, with a slight modification, is a continuous Markoff process.

The elementary statistics of the integral process are deduced: means, variances, and covariances, in terms of the original coefficients. It is shown that an integral process is never temporally homogeneous in a non-degenerate process.

Finally, in terms of the original class of admissible coefficients, the statistics of the integral process are explicitly presented, and the integral process of all known continuous processes are specified.

Measuring temporal fluctuation on femtosecond scale in a random medium

We report an observation of femtosecond optical fluctuations of transmitted light when a coherent femtosecond pulse propagates through a random medium. They are a result of random interference among scattered waves coming from different trajectories in the time domain. Temporal fluctuations are measured by using cross-correlated frequency optical gating. It is shown that a femtosecond pulse will be broadened and distorted in pulse shape while it is propagating in random medium. The real and imaginary components of transmitted electric field are also distorted severely. The average of the fluctuated transmission pulses yields a smooth profile, probability functions show good agreement with Gaussian distribution. (c) 2007 Elsevier B.V. All rights reserved.

二元振幅型面板用于光束空间整形

为了提高高功率激光系统的整体效率和充分利用光能,需要对前端注入的高斯光束进行空间整形,实现驱动器终端激光的均匀化输出。采用振幅型二元面板对激光光束进行空间强度整形,利用误差扩散法进行了理论设计,数值摸拟了整形效果,同时讨论了面板加工误差以及空间滤波器的小孔大小等因素带来的影响。根据理论设计,分别加工了反高斯透射率分布和抛物线透射率分布的二元面板,并进行了整形实验,实现了各自的整形功能,并做了误差分析。实验证明二元面板能对激光光束的空间强度分布实现了精确的整形。

A stochastic model of temporal variations in monthly temperature, precipitation, snowfall, and resulting snowpack

We report a Monte Carlo representation of the long-term inter-annual variability of monthly snowfall on a detailed (1 km) grid of points throughout the southwest. An extension of the local climate model of the southwestern United States (Stamm and Craig 1992) provides spatially based estimates of mean and variance of monthly temperature and precipitation. The mean is the expected value from a canonical regression using independent variables that represent controls on climate in this area, including orography. Variance is computed as the standard error of the prediction and provides site-specific measures of (1) natural sources of variation and (2) errors due to limitations of the data and poor distribution of climate stations. Simulation of monthly temperature and precipitation over a sequence of years is achieved by drawing from a bivariate normal distribution. The conditional expectation of precipitation. given temperature in each month, is the basis of a numerical integration of the normal probability distribution of log precipitation below a threshold temperature (3°C) to determine snowfall as a percent of total precipitation. Snowfall predictions are tested at stations for which long-term records are available. At Donner Memorial State Park (elevation 1811 meters) a 34-year simulation - matching the length of instrumental record - is within 15 percent of observed for mean annual snowfall. We also compute resulting snowpack using a variation of the model of Martinec et al. (1983). This allows additional tests by examining spatial patterns of predicted snowfall and snowpack and their hydrologic implications.

Structured precision modelling with Cholesky basis superposition for speech recognition

Structured precision modelling is an important approach to improve the intra-frame correlation modelling of the standard HMM, where Gaussian mixture model with diagonal covariance are used. Previous work has all been focused on direct structured representation of the precision matrices. In this paper, a new framework is proposed, where the structure of the Cholesky square root of the precision matrix is investigated, referred to as Cholesky Basis Superposition (CBS). Each Cholesky matrix associated with a particular Gaussian distribution is represented as a linear combination of a set of Gaussian independent basis upper-triangular matrices. Efficient optimization methods are derived for both combination weights and basis matrices. Experiments on a Chinese dictation task showed that the proposed approach can significantly outperformed the direct structured precision modelling with similar number of parameters as well as full covariance modelling. © 2011 IEEE.

Satellite formation in drop-on-demand printing of polymer solutions

High speed photographic images of jets formed from dilute solutions of polystyrene in diethyl phthalate ejected from a piezoelectric drop-on-demand inkjet head have been analyzed in order to study the formation and distribution of drops as the ligament collapses. Particular attention has been paid to satellite drops, and their relative separation and sizes. The effect of polymer concentration was investigated. The distribution of nearest-neighbour centre spacing between the drops formed from the ligament is better described by a 2-parameter modified gamma distribution than by a Gaussian distribution. There are (at least) two different populations of satellite size relative to the main drop size formed at normal jetting velocities, with ratios of about three between the diameters of the main drop and the successive satellite sizes. The distribution of the differences in drop size between neighbouring drops is close to Gaussian, with a small non-zero mean for low polymer concentrations, which is associated with the conical shape of the ligament prior to its collapse and the formation of satellites. Higher polymer concentrations result in slower jets for the same driving impulse, and also a tendency to form ligaments with a near-constant width. Under these conditions the mean of the distribution of differences in nearest-neighbour drop size was zero.

Metastability mechanisms in thin film transistors quantitatively resolved using post-stress relaxation of threshold voltage

A new approach is presented to resolve bias-induced metastability mechanisms in hydrogenated amorphous silicon (a-Si:H) thin film transistors (TFTs). The post stress relaxation of threshold voltage (V(T)) was employed to quantitatively distinguish between the charge trapping process in gate dielectric and defect state creation in active layer of transistor. The kinetics of the charge de-trapping from the SiN traps is analytically modeled and a Gaussian distribution of gap states is extracted for the SiN. Indeed, the relaxation in V(T) is in good agreement with the theory underlying the kinetics of charge de-trapping from gate dielectric. For the TFTs used in this work, the charge trapping in the SiN gate dielectric is shown to be the dominant metastability mechanism even at bias stress levels as low as 10 V.

Scalar and its dissipation in the near field of turbulent lifted jet flame

In this study various scalar dissipation rates and their modelling in the context of partially premixed flame are investigated. A DNS dataset of the near field of a turbulent hydrogen lifted jet flame is processed to analyse the mixture fraction and progress variable dissipation rates and their cross dissipation rate at several axial positions. It is found that the classical model for the passive scalar dissipation rate ε{lunate}̃ZZ gives good agreement with the DNS, while models developed based on premixed flames for the reactive scalar dissipation rate ε{lunate}̃cc only qualitatively capture the correct trend. The cross dissipation rate ε{lunate}̃cZ is mostly negative and can be reasonably approximated at downstream positions once ε{lunate}̃ZZ and ε{lunate}̃cc are known, although the sign cannot be determined. This approach gives better results than one employing a constant ratio of turbulent timescale and the scalar covariance c'Z'̃. The statistics of scalar gradients are further examined and lognormal distributions are shown to be very good approximations for the passive scalar and acceptable for the reactive scalar. The correlation between the two gradients increases downstream as the partially premixed flame in the near field evolves ultimately to a diffusion flame in the far field. A bivariate lognormal distribution is tested and found to be a reasonable approximation for the joint PDF of the two scalar gradients. © 2011 The Combustion Institute.

Two-component model for the interstellar scattering in direction to the Vela pulsar

This paper discusses a rigorous treatment of the refractive scintillation of pulsar PSR B0833-45 caused by a two-component interstellar scattering medium. It is assumed that the interstellar scattering medium is composed of a thin screen ISM and an extended interstellar medium. We consider that the scattering of the thin screen concentrates in a thin layer presented by a delta function distribution and that the scattering density of the extended irregular medium satisfies the Gaussian distribution. We investigate and develop equations for the flux density structure function corresponding to this two-component ISM geometry in the scattering density distribution and compare our result with that of the Vela pulsar observations. We conclude that the refractive scintillation caused by this two-component ISM scattering gives a more satisfactory explanation for the observed flux density variation of the Vela pulsar than does the single extended medium model. The level of refractive scintillation is strongly sensitive to the distribution of scattering material along the line of sight. The logarithmic slope of the structure function is sensitive to thin screen location and is relatively insensitive to the scattering strength of the thin screen medium. Therefore, the proposed model can be applied to interpret the structure function of flux density observed in pulsar PSR B0833-45. The result suggests that the medium consists of a discontinuous distribution of plasma turbulence embedded in the Vela supernova remnant. Thus our work provides some insight into the distribution of the scattering along the line of sight to the Vela pulsar.

GROWTH INTERRUPTION INDUCED INTERFACE MICROROUGHNESS IN SINGLE QUANTUM-WELLS

Growth interruption-induced microroughness is studied by photoluminescence (PL) of single quantum wells with different well widths and interruption times. Analysis of the peak splitting in the PL spectra shows that the adjacent peak splittings correspond to well width differences smaller than one monolayer. The number of split peaks increases with increasing well width, saturating when the well width exceeds 11 monolayers. This trend correlates well with the decrease in the lateral dimension of the exciton, which corresponds roughly to the minimum optically sampled area of the interface. For a given quantum well, a plot of the normalized integrated intensities of the split PL peaks versus the well width fluctuation is well described by a Gaussian distribution with an average fluctuation smaller than one monolayer. These results are consistent with the microroughness model.

Dynamics of morphological changes for mitochondrial fission and fusion

Mitochondria experience continuous fusion and fission in a living cell, but their dynamics remains poorly quantified. Here a theoretical model was developed, upon a simplified population balance equation (PBE), to predict the morphological changes induced by mitochondrial fission and fusion. Assuming that both fission and fusion events are statistically independent, the survival probability of mitochondria staying in the fission or fusion state was formulated as an exponentially-decayed function with time, which depended on the time-dependent distribution of the mitochondrial volume and the fission and fusion rates. Parametric analysis was done for two typical volume distributions. One was Gamma distribution and the other was Gaussian distribution, derived from the measurements of volume distribution for individual mitochondria in a living cell and purified mitochondria in vitro. The predictions indicated that the survival probability strongly depended on morphological changes of individual mitochondria and was inversely correlated to the fission and fusion rates. This work provided a new insight into quantifying the mitochondrial dynamics via monitoring the evolution of the mitochondrial volume.

Non-reproducibility of the cross sections of the products induced from dissipative reaction of F-19+Al-27

The differential cross sections of the dissipative products B, Q N, O, F, Ne, Na and Mg induced from the reactions of F-19+Al-27 at two incident energies have been measured at the HI-13 tandem accelerator, Beijing. In the case of a fixed beam incident energy 114MeV or 118.75MeV respectively, identical reaction system and the same detection system, 20 target points in steps of 2mm on(.)a 10mmx50mm rectangular Al foil have been bombarded. The experimental results indicate that the probability distribution of the cross sections is much wider than a standard Gaussian distribution. This non-reproducibility of the cross sections can't be interpreted by the statistical property of a finite count rate.

How Well Can TCP Infer Network State?

The Transmission Control Protocol (TCP) has been the protocol of choice for many Internet applications requiring reliable connections. The design of TCP has been challenged by the extension of connections over wireless links. We ask a fundamental question: What is the basic predictive power of TCP of network state, including wireless error conditions? The goal is to improve or readily exploit this predictive power to enable TCP (or variants) to perform well in generalized network settings. To that end, we use Maximum Likelihood Ratio tests to evaluate TCP as a detector/estimator. We quantify how well network state can be estimated, given network response such as distributions of packet delays or TCP throughput that are conditioned on the type of packet loss. Using our model-based approach and extensive simulations, we demonstrate that congestion-induced losses and losses due to wireless transmission errors produce sufficiently different statistics upon which an efficient detector can be built; distributions of network loads can provide effective means for estimating packet loss type; and packet delay is a better signal of network state than short-term throughput. We demonstrate how estimation accuracy is influenced by different proportions of congestion versus wireless losses and penalties on incorrect estimation.