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Turbulence and periodic oscillations are easily seen with an optically bistable device with a delay in the feedback. The device is a hybrid, having both optical and electronic components. The details of the time-dependent output are investigated. In particular, as the input intensity is increased, the device output goes through a series of second-order nonequilibrium phase transitions or bifurcations. A truncated period-doubling sequence is observed prior to the onset of turbulence or chaos. The truncation is shown to be due to a noise-induced bifurcation gap. Within the chaotic regime, the device largely follows the reverse bifurcation scheme of Lorenz. In addition, there is a small domain of frequency-locked behavior that exists within the chaotic domain. These frequency-locked waveforms represent an alternate path to chaos. With the route to choas well understood, it remained to characterize the erratic motion itself. Dimension and correlation entropy are measured for various settings of our hybrid device. The measured dimension is found to be significantly less than dimensions consistent with a conjecture due to Kaplan and Yorke. The standard method of determining correlation entropy is shown to yield more than one value.

The switching energy and speed of a bistable GaAs etalon have been measured. At liquid nitrogen temperature, the switch-on was achieved by injecting a high density of carriers with an above-band-edge 600-nm external pulse. A minimum energy of 1 nJ was required. The measured switching time was 200 ps, limited by the detector response time. The switch-off was obtained by heating the device with a 300-nJ external pulse and consequently shifting the Fabry-Perot peak. Switch-off time was about 40 ns. Room-temperature bistability was first achieved in a GaAs-AlGaAs superlattice etalon. Switch-on by a near-band-edge 845-nm pulse of 10-pJ energy was observed.

An analog of an optically bistable device made constructed from both optical and electronic components is used to study chaos. This hybrid optically bistable system has a delay in the feedback so that the response time of the electronics is much faster than the feedback time. Such a system is unstable and shows pulsations and chaos. The character of the pulsations change as the gain of the amplifier or the input laser power is increased. These changes make up the period doubling route to chaos. Not all of the waveforms of an ideal period doubling sequence are observed. This truncation of the period-doubling sequence in the device is investigated as a function of the noise present in the system. Increasing the noise level decreases the number of period doublings observed. In the chaotic regime waveforms other than those predicted are observed. These waveforms are the frequency-locked waveforms seen in an earlier experiment which we find to be modified versions of the typical period-doubled waveforms. The transitions between these waveforms are discontinuous, and show hysteresis loops. By the introduction of an external locking signal, we are able to stabilize waveforms in the neighborhood of the discontinuous transitions. By so doing we show that the transitions among the branches are due to their lack of stability. The transitions are thus not strictly first-order nonequilibrium phase transitions, since in that case the branches cease to exist at the transition point. Since the path to chaos is nonunique, the types of chaos that are observable are also nonunique. To suggest a way to distinguish between different types of chaos and also to provide a tool for the study of chaos in other systems, we propose an operational test for chaos which leads to a straightforward experimental distinction between chaos and noise. We examine this test using the hybrid device to show that the method works. The test involves repeated measurement of the initial transient of a system whose initial condition is fixed. This method could be used to determine the existence of chaos in faster optical systems.

This dissertation presents the results of experimental research on the nonlinear refraction in InSb and the experimental demonstration of two nonlinear etalon devices using InSb as the active material. The first portion of the dissertation considers the Dynamic Burstein-Moss Shift model for nonlinearities in narrow-gap semiconductors. The physics and the equations are reviewed, and limitations in describing intensity dependent refraction in a semiconductor are considered. These limitations arise from the nonlinear dependence of charge carrier density upon irradiance. The second portion of the dissertation presents experimental measurements made on the nonlinear refraction of InSb at temperatures between 80 K and 182 K, for wavelengths from 5.75 μm to 6.10 μm, where the photon energy lay in the band tail below 100 cm⁻¹. Measurements of the linear absorption were first made with an infrared spectrometer for temperatures from 80 K to 300 K. The nonlinearity was measured by analyzing the transmission through InSb etalons. Nonlinear transmission curves were digitized and stored with an IBM PC-XT, then a curve fit was performed using the nonlinear refractive index as a fiting parameter. Observations are reported of increasing absorption, due in part to a thermal shift of the absorption edge. The second portion of the work presents the theory and demonstration of a bistable etalon using an edge-injected control beam. Plane-wave nonlinear etalon theory is used to describe the operation of such a device, illustrating the way in which switching and logic gate operation can be obtained. Two devices based on this concept are demonstrated: the 3-port device using a single control beam, and the 2SON gate using two control beams to perform two-input logic operation. The extension of the 2SON gate to an array of pixels, and some considerations for optimizing array performance, are considered. Two appendices follow the body of the dissertation, the first describing the preparation of the InSb etalon samples, and the second detailing several procedures for maintenance and operation of the CO laser used.

Nonlinear-optical switching and logic devices based on GaAs nonlinear Fabry-Perot etalons have been investigated theoretically and experimentally. The theoretical modeling has been performed with the first realistic and easily computed theory of GaAs nonlinear optical properties near the band edge. Both steady-state and dynamic calculations have been performed for optical bistability with GaAs etalons. High-transmission operation is predicted for certain etalon detunings from the excitation wavelength. Various logic-gate functions have simulated with the model. An investigation of differential energy gain in transient, one-wavelength operation was performed. The conclusion is that useful differential gain is not achievable in transient, one-wavelength operation if the pulse width is less than about ten times the carrier lifetime in the material. Waveguide structures with single-mode transverse confinement were designed and optical bistability was predicted for long GaAs etalons similar to cleaved waveguides. GaAs nonlinear optical devices were fabricated in forms of interest for application to optical parallel processing and guided wave signal processing. The fabrication work included etalon arrays and waveguide devices fabricated by reactive ion etching. The photolithography and reactive ion etching processes used and developed are described. Preliminary work on ultra-small quantum-confinement structures is described. Optical experiments were performed on the devices fabricated. The etalon arrays demonstrated extremely fast relaxation times for GaAs etalon devices, and demonstrated the ability to control material parameters through the fabrication process, by increasing the surface recombination rate of charge carriers. Fast optical bistability at low powers was also demonstrated in the array devices. Strip-loaded waveguides with cleaved ends were operated as optical bistable devices with conclusive evidence that the mechanism was electronic in origin. Nonlinear phase shifts of greater than $2\pi$ were observed in some waveguides. Such large nonlinear phase shifts are of great interest for the development of other nonlinear-optical waveguide devices.

The optical ring cavity has been studied for about ten years, both theoretically and experimentally. In these studies the uniform plane wave approximation has been used. In this work we investigate effects which result from the retention of the transverse diffraction. We establish that transverse structure is inevitable since plane wave fixed points are susceptible to transverse instabilities (modulational instability). We show that this instability is a universal mechanism for initiating various interesting and complicated, yet understandable, dynamical responses in a one and a two transverse dimensional cavity.

We analyze a dissipative map of the plane. The map was initially defined by Ikeda as a model for bistable behavior in an optical ring cavity. Our analysis is based upon an examination of attracting sets and basins of attraction. The primary tools utilized in the analysis are stable and unstable manifolds of fixed and periodic saddle points. These manifolds determine boundaries of basins of attraction, and the extent and evolution of attracting sets. We perform extensive numerical iterations of the map with a central focus on sudden changes in the topological nature of attractors and basins. Our analysis concentrates on the destruction of the lower branch attractor as a prominent example of attractor/basin interaction. This involves an examination of a possible link between two fixed points L and M, namely the heteroclinic connection Wᵘ(L) ∩ Wˢ(M) ≠ 0. We use two different methods to approach this question. Although the Ikeda map is used as the working model throughout, both of the techniques apply to a more general class of dissipative maps satisfying certain hypotheses. The first of these techniques analyzes Wˢ(M) when Wᵘ(M) ∩ Wˢ(M) ≠ 0, with the result that Wˢ(M) is found to invade some minimum limiting region for Wᵘ(M) ∩ Wˢ(M) ≠ 0 arbitrarily close to tangency. The second approach is more topological in nature. We define a mesh of subregions to bridge the spatial gap between the points L and M, and concentrate on the occurrence of Wᵘ(L) ∩ Wˢ(M) ≠ 0 (destruction of the attractor). The first main result is a necessary condition for the heteroclinic connection in terms of the behavior of the map on these subregions. The second result is a sequence of sufficient conditions for this link. There remains a gap between these two conditions, and in the final sections we present numerical investigations indicating that the concept of intersection links between subregions is useful to resolve cases near the boundary of the destruction region.

Entry into mitosis in eukaryotes depends on the activation of the Cyclin-dependent kinase 1 (Cdk1), which phosphorylates many mitotic protein substrates. Activation of Cdk1 requires formation of a complex with Cyclin B (CycB), which gradually rises in concentration during interphase. However, in most organisms Cdk1 activation is not gradual but switch-like, because phosphorylation of the Cdk1-CycB complex by the Wee1 kinase normally keeps Cdk1-CycB inactive during interphase. Mitotic entry is induced when rapid dephosphorylation of Cdk1-CycB by the Cdc25 phosphatase causes abrupt activation of Cdk1-CycB. Cdk1-CycB in turn phosphorylates both Wee1 and Cdc25 leading to Cdc25 activation and Wee1 inhibition. This regulation creates both a positive and a double-negative feedback loop in the system, which are thought to generate a sharp, bistable switch that controls mitotic entry. Bistability is known to require positive feedback and ultrasensitivity, however, how ultrasensitivity arises in the mitotic switch is subject to extensive research efforts both experimentally and theoretically. In this thesis I explore several possible sources of ultrasensitivity in the mitotic switch through mathematical modelling. Based on theoretical considerations and experimental evidence, I show that the existence of multiple positive feedback loops, multisite phosphorylation, and Cdk1-CycB-dependent regulation of Cdk1-counteracting phosphatase activity can all contribute to ultrasensitivity and bistability in the mitotic switch. I analyse models of the mitotic switch including these bistability-generating mechanisms, to simulate and explain experimental data and make testable predictions. I argue that it is unlikely that a single mechanism is responsible for ultrasensitivity in this system, and that bistability requires a combination of different sources, including the ones studied here and others such as enzyme saturation and sequestration effects. I also highlight the importance of network architecture and coherent regulation of opposing reactions in generating efficient biochemical switches. Finally, I draw on recent experimental evidence and ideas derived from this analysis to propose a revised network of the mitotic switch.

by Leung Pui-tang. / Parallel title in Chinese characters. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 92-94.