Charles Thompson

Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses

A comprehensive model is developed for focused pulse propagation in water. The model incorporates self-focusing, group velocity dispersion, and laser-induced breakdown in which an electron plasma is generated via cascade and multiphoton ionization processes. The laser-induced breakdown is studied first without considering self-focusing to give a breakdown threshold of the light intensity, which compares favorably with existing experimental results. The simple study also yields the threshold dependence on pulse duration and input spot size, thus providing a framework to view the results of numerical simulations of the full model. The simulations establish the breakdown threshold in input power and reveal qualitatively different behavior for picoand femto-second pulses. For longer pulses, the cascade process provides the breakdown mechanism, while for shorter pulses the cooperation between the self-focusing and the multiphoton plasma generation dominates the breakdown threshold.

Laser induced bubble formation in the retina

The immediate thermodynamic effects of absorption of a laser pulse in the retina are theoretically studied to understand underlying physical damage mechanisms at threshold fluences. Damage is most likely to occur at threshold levels in the retinal pigment epithelium due to the strong absorption by the melanosomes.

Melanin granule model for laser-induced thermal damage in the retina

An analytical model for thermal damage of retinal tissue due to absorption of laser energy by finite-sized melanin granules is developed. Since melanin is the primary absorber of visible and near-IR light in the skin and in the retina, bulk heating of tissue can be determined by superposition of individual melanin granule effects. Granules are modeled as absorbing spheres surrounded by an infinite medium of water. Analytical solutions to the heat equation result in computations that are quick and accurate. Moreover, the model does not rely on symmetric beam profiles, and so arbitrary images can be studied. The important contribution of this model is to provide a more accurate biological description of sub-millisecond pulse exposures than previous retinal models, while achieving agreement for longer pulses. This model can also be naturally extended into the sub-microsecond domain by including vaporization as a damage mechanism. It therefore represents the beginning of a model which can be applied across the entire pulse duration domain.

Finite Population Model for Performance Evaluation Between Narrowband and Wideband Users in the Shared Radio Spectrum

In this paper a theoretical evaluation of channel access availability of narrow and wideband users occupying a common range of frequencies in the radio spectrum is presented. User inter-request and call duration times are taken to be random and exponentially distributed. The number of available frequency channels is fixed. The differentiating feature between narrow and wideband users is the number of frequency channels required by each user to transmit their data. The probability of a given user being blocked from acquiring a spectral channel is determined. It is shown that the degree of blocking experienced by narrowband users can only be maintained by either throttling the offered load or limiting population size of wideband users requesting channel access.

Performance models for wireless spectrum shared by wideband and narrowband sources

This work examines the blocking performance of narrow-band (NB) and wideband (WB) sources that access a shared pool of wireless channels. The NB sources utilize a single channel, whereas WB sources access simultaneously a larger group of channels. This system is analyzed in the context of maximizing the utilization of spectrum that is allocated to the WB system by allowing NB sources random access to the same spectrum. The performance measure to be controlled is the blocking experienced by WB sources. A queueing model of this system is proposed that allows evaluation of the impact of NB sources on WB performance. Assuming Poisson arrival process models and negative exponential distributions for the channel holding times, the dependence of the blocking probability of the WB source is derived as a function of the NB utilization factor. In an uncontrolled NB access scheme, the WB blocking is lower bounded by the blocking probability experienced by NB sources. The performance improvement afforded by adding extra NB channels and by controlling the access rates of the NB source for finite population WB sources is presented. The analysis presented here provides an assessment of some of the emerging paradigms for adaptive spectrum allocation. Of particular interest are the criteria under which spectrum agile, cognitive and software radios functioning in an opportunistic fashion can access unused spectrum allocated to a primary system without adversely affecting the performance of the primary system

Coupled-wave analysis of apodized volume gratings

This work presents the use of longitudinal refractive index modulation (apodization) in photosensitive glass for improved sidelobe suppression in volume holographic optical elements. We develop a numerical model for both uniform and apodized volume holograms based on rigorous coupled-wave analysis. We validate the model by comparison with a transmissive 1.55- mum uniform volume grating in photothermorefractive glass. We then apply our numerical model to calculate the spectral response of apodized gratings. The numerical results demonstrate that apodization of the refractive index modulation envelope improves spectral selectivity and reduces first and second-order side-lobe peaks by up to 33 and 65 dB, respectively. We suggest a method for creating apodization in volume holograms with approximately Gaussian spatial refractive index profile.

Transition to chaos in acoustically driven flows

In this paper, a model describing the process of transition to chaotic fluid motion in an acoustically driven fluid is presented. The nonlinear interaction between the Stokes boundary layer and linearly unstable three‐dimensional vortical disturbances is examined. Special consideration is given to the amplitude range above which these disturbances bifurcate from linear stability. It is found that oscillatory modulation present in the basic‐flow results in successive period‐doubling bifurcations of the three‐dimensional vortical disturbances. It is shown that these bifurcations result in the disturbance amplitude becoming chaotic.

On the acoustics of a coupled space

An examination of acoustic wave propagation in a coupled space is presented. The analysis presented is limited to the first two longitudinal modes of the cavity. It is shown that the spacial behavior of the modes of vibration in the cavity is affected by the coupling discontinuity. The degree with which the discontinuity influences the pressure variation is parametrized by a single small parameter e, where e is the ratio of the typical cavity height, H0 to the cavity length L0. An approximate solution for the pressure in the space is obtained using the method of matched asymptotic expansions. Experimental results are also presented as verification of the theoretical results.

Characterizing spatial correlation in indoor channels

The spatial correlation features of channel impulse responses for an indoor environment are presented. The wide-hand impulse responses of a rectangular enclosure are calculated using the method of images. Bandpass representations of the non line-of-sight multipath responses are obtained for 2.4 GHz ISM band and their spatial cross correlation estimated for various positions of the transmitter and receiver arrays. The receiver and transmitter correlations are shown to exhibit periodic features and a spatial dependence in the decay rate. The correlation minima decreases with transmitter-receiver (T-R) separation and peak-to-peak correlation amplitude exhibits larger values when the transmitter and receivers are positioned close to the corners of the room. The oscillatory features in the spatial correlation may be attributed to the distribution of multipath clusters in time. For certain configurations of the T-R arrays the clusters are well separated resulting in a slower rate of oscillation at the inter-cluster time scale. In the short or intra-cluster time-scale, the correlation can exhibit a slow decay rate. At the corners, these clusters appear at faster rate and individual clusters are of a shorter duration. This feature leads to a faster and more structured oscillation in the correlation features. These observations are important considerations in design and evaluation of the performance of multiple-output multiple-input wireless communications systems.

ABR traffic control in ATM networks using optimal control theory

In this work we examine the problem of regulating available bit rate (ABR) traffic in an ATM network. The issue of providing control signals to throttled sources at distant locations from a bottlenecked node is of particular interest. The process of modeling and design of the controller is outlined. A linear quadratic tracker is used to provide the appropriate control signal to each source. It is shown that designing the controller for minimum error energy resulted in the best tracking performance. However this result is obtained at the expense of VC buffer time delays. This situation is remedied by the addition of a simple regulator. Using a regulator one can obtain low buffer overshoot in the transient period while maintaining the good link utilization in the steady-state period.