title: The quantum theory of optical bistability in nonlinear systems

authors: Steyn-Ross, Moira L.

abstract: This thesis is concerned with the investigation of the behaviour of various nonlinear systems when excited by a coherent light-field. 

Of particular interest to us is the possibility of observing optical bistability in these systems.

In Chapter One we introduce the general theoretical methods we employ to perform all investigations.

In Chapters Two and Three we develop a quantum theory of the interaction of light with a variety of different systems, i.e. Raman active media, the parametric oscillator, the two-photon absorber and a system of three-level atoms.

In each case, a master equation, containing all statistical information about the system, is derived. This enables the systematic inclusion of a damping mechanism into each model.

Discussion is limited to the steady state behaviour of the systems, and in general we assume the deterministic limit in which we ignore quantum fluctuations in the field variables. It is then possible to factorise the steady state expectation values of these variables. 

Steady state calculations indicate that each system may exhibit optical bistability in output field/intensity dependent on input field/intensity.

To determine whether a system will display optical bistability, it is necessary to perform a stability analysis. Where possible, such analytical calculations are performed. However, in certain cases the complexity of the highly nonlinear systems results in these calculations becoming extremely difficult. In such cases, conclusions relating to the stability of the system are drawn from graphical plots of its steady state behaviour.

Chapters Four to Eight are devoted to a study of the intracavity interaction of coherent radiation with semiconductors.

As explained in Chapter Four (of an introductory nature), this work was prompted by two recent experiments which indicated the existence of optical bistability in semiconductors. Although both experiments used semiconductors as the nonlinear material, the mechanism proposed to produce the observed bistability in each case was vastly different.

In Chapter Eight we discuss one of these mechanisms – interband excitation. We present a very simple theory of this effect and show that in essence it is equivalent to the theory of optical bistability in two-level systems. However, we stress that our theory is only approximate and relies on the validity of several simplifying assumptions.

Chapters Five and Six concern the other form of semiconductor optical bistability - arising from the interaction between a light field and excitons comprising the semiconductor.

In order to develop a quantum theory of this system using master equation techniques, it is necessary to transform the fermion system to a boson system. Bosonisation transformations required to effect this are developed in Chapter Five. 

In Chapter Six we present a fully quantum mechanical theory of optical bistability in excitonic systems. Two types of bistability are found: bistability in output intensity and also exciton number, dependent on input intensity.

In Chapter Seven we investigate the effects of quantum fluctuations in a low density exciton system, by considering its Fokker-Planck equation. We discuss in detail the adiabatic elimination of stochastic variables with regard to the system’s Fokker-Planck equation.

text: The quantum theory of optical bistability in nonlinear systems This thesis is concerned with the investigation of the behaviour of various nonlinear systems when excited by a coherent light-field. 

Of particular interest to us is the possibility of observing optical bistability in these systems.

In Chapter One we introduce the general theoretical methods we employ to perform all investigations.

In Chapters Two and Three we develop a quantum theory of the interaction of light with a variety of different systems, i.e. Raman active media, the parametric oscillator, the two-photon absorber and a system of three-level atoms.

In each case, a master equation, containing all statistical information about the system, is derived. This enables the systematic inclusion of a damping mechanism into each model.

Discussion is limited to the steady state behaviour of the systems, and in general we assume the deterministic limit in which we ignore quantum fluctuations in the field variables. It is then possible to factorise the steady state expectation values of these variables. 

Steady state calculations indicate that each system may exhibit optical bistability in output field/intensity dependent on input field/intensity.

To determine whether a system will display optical bistability, it is necessary to perform a stability analysis. Where possible, such analytical calculations are performed. However, in certain cases the complexity of the highly nonlinear systems results in these calculations becoming extremely difficult. In such cases, conclusions relating to the stability of the system are drawn from graphical plots of its steady state behaviour.

Chapters Four to Eight are devoted to a study of the intracavity interaction of coherent radiation with semiconductors.

As explained in Chapter Four (of an introductory nature), this work was prompted by two recent experiments which indicated the existence of optical bistability in semiconductors. Although both experiments used semiconductors as the nonlinear material, the mechanism proposed to produce the observed bistability in each case was vastly different.

In Chapter Eight we discuss one of these mechanisms – interband excitation. We present a very simple theory of this effect and show that in essence it is equivalent to the theory of optical bistability in two-level systems. However, we stress that our theory is only approximate and relies on the validity of several simplifying assumptions.

Chapters Five and Six concern the other form of semiconductor optical bistability - arising from the interaction between a light field and excitons comprising the semiconductor.

In order to develop a quantum theory of this system using master equation techniques, it is necessary to transform the fermion system to a boson system. Bosonisation transformations required to effect this are developed in Chapter Five. 

In Chapter Six we present a fully quantum mechanical theory of optical bistability in excitonic systems. Two types of bistability are found: bistability in output intensity and also exciton number, dependent on input intensity.

In Chapter Seven we investigate the effects of quantum fluctuations in a low density exciton system, by considering its Fokker-Planck equation. We discuss in detail the adiabatic elimination of stochastic variables with regard to the system’s Fokker-Planck equation.

year: 1981

title: How an exchange of perspectives led to tentative ethical guidelines for visual ethnography

authors: Pope, Clive C.

subjects: visual ethics

abstract: Qualitative research, especially visual ethnography, is an iterative not a linear process, replete with good intentions, false starts, mistaken assumptions, miscommunication and a continually revised statement of the problem. That the camera freezes everything and everyone in the frame only complicates ethical considerations. This work, jointly authored by the researcher, the Research Ethics Committee (REC) chair and an informed outsider, walks the reader through the ethical challenges the researcher experienced seeking REC approval to conduct a visual ethnography of a secondary school's rowing event. Eventually, the researcher found the challenges and ambiguities of informed consent indicative of the current issues facing many researchers working with the visual medium. The account fleshes out a procedural ethics and ethics in practice dichotomy and ends with the researcher and REC chair retrospectively contemplating the iterative ethics of visual ethnography. We conclude our conversation by proposing five tentative guidelines for visual ethnography researchers and their research ethics committees.

text: How an exchange of perspectives led to tentative ethical guidelines for visual ethnography Qualitative research, especially visual ethnography, is an iterative not a linear process, replete with good intentions, false starts, mistaken assumptions, miscommunication and a continually revised statement of the problem. That the camera freezes everything and everyone in the frame only complicates ethical considerations. This work, jointly authored by the researcher, the Research Ethics Committee (REC) chair and an informed outsider, walks the reader through the ethical challenges the researcher experienced seeking REC approval to conduct a visual ethnography of a secondary school's rowing event. Eventually, the researcher found the challenges and ambiguities of informed consent indicative of the current issues facing many researchers working with the visual medium. The account fleshes out a procedural ethics and ethics in practice dichotomy and ends with the researcher and REC chair retrospectively contemplating the iterative ethics of visual ethnography. We conclude our conversation by proposing five tentative guidelines for visual ethnography researchers and their research ethics committees.

year: 2010

title: A late-Holocene and prehistoric record of environmental change from Lake Waikaremoana, New Zealand

authors: Newnham, Rewi M.

subjects: Palynology

abstract: Further evidence in support of a late pre-European (Polynesian) settlement of New Zealand is provided by an 1850-year-long tephropalynological record from a remote region in New Zealand's North Island. The earliest unequivocally anthropogenic forest clearance is estimated from sedimentation rates to have occurred c. 375 14C years BP (c. ad 1523–1631), although the radiocarbon chronology, shown by tephrochron ology to be erroneous due to hard-water effects, suggested this occurred c. 900 years earlier. Delineation of the anthropogenic era, and the distinction between human activity and other agents of environmental change in the pollen/spore diagram, are supported by cluster analysis and detrended correspondence analysis. Two distinct phases of forest clearance are evident during the pre-European era, reflecting local changes either in population pressure or settlement patterns. We note that the lull between the two phases of forest clearance coincides with the maximum of the ‘Little Ice Age’ within the period c. late ad 1600s to early 1800s.

text: A late-Holocene and prehistoric record of environmental change from Lake Waikaremoana, New Zealand Further evidence in support of a late pre-European (Polynesian) settlement of New Zealand is provided by an 1850-year-long tephropalynological record from a remote region in New Zealand's North Island. The earliest unequivocally anthropogenic forest clearance is estimated from sedimentation rates to have occurred c. 375 14C years BP (c. ad 1523–1631), although the radiocarbon chronology, shown by tephrochron ology to be erroneous due to hard-water effects, suggested this occurred c. 900 years earlier. Delineation of the anthropogenic era, and the distinction between human activity and other agents of environmental change in the pollen/spore diagram, are supported by cluster analysis and detrended correspondence analysis. Two distinct phases of forest clearance are evident during the pre-European era, reflecting local changes either in population pressure or settlement patterns. We note that the lull between the two phases of forest clearance coincides with the maximum of the ‘Little Ice Age’ within the period c. late ad 1600s to early 1800s.

year: 1998