Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics I. Theory

The quasi mode theory of macroscopic quantization in quantum optics and cavity QED developed by Dalton, Barnett and Knight is generalized. This generalization allows for cases in which two or more quasi permittivities, along with their associated mode functions, are needed to describe the classical optics device. It brings problems such as reflection and refraction at a dielectric boundary, the linear coupler, and the coupling of two optical cavities within the scope of the theory. For the most part, the results that are obtained here are simple generalizations of those obtained in previous work. However the coupling constants, which are of great importance in applications of the theory, are shown to contain significant additional terms which cannot be 'guessed' from the simpler forms. The expressions for the coupling constants suggest that the critical factor in determining the strength of coupling between a pair of quasi modes is their degree of spatial overlap. In an accompanying paper a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary is given as an illustration of the generalized theory. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics II. Application to reflection and refraction at a dielectric interface

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.

Observation of bound states of solitons in a passively mode-locked fiber laser

We report on an experimental observation of bound states of solitons in a passively mode-locked fiber soliton ring laser. The observed bound solitons are stable and have discrete, fixed soliton separations that are independent of the experimental conditions.

Fitting a mixture model to three-mode three-way data with missing information

When the data consist of certain attributes measured on the same set of items in different situations, they would be described as a three-mode three-way array. A mixture likelihood approach can be implemented to cluster the items (i.e., one of the modes) on the basis of both of the other modes simultaneously (i.e,, the attributes measured in different situations). In this paper, it is shown that this approach can be extended to handle three-mode three-way arrays where some of the data values are missing at random in the sense of Little and Rubin (1987). The methodology is illustrated by clustering the genotypes in a three-way soybean data set where various attributes were measured on genotypes grown in several environments.

Theory of a mode-locked atom laser with toroidal geometry

We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to (h) over bar /2. It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.

Near-resonant holographic interferometry of hypersonic flow

Near-Resonant Holographic Interferometry is a powerful technique which extends the established advantages of conventional holographic interferometry by allowing a species-specific number density to be determined. It has been tested in the harsh flow conditions generated in a high enthalpy facility yielding information about the shock shape on a cylindrical body and on the distribution of a trace species seeded into the flow.

Stochastic Schrodinger equation approach to quantum noise in resonant tunneling current

We apply the quantum trajectory method to current noise in resonant tunneling devices. The results from dynamical simulation are compared with those from unconditional master equation approach. We show that the stochastic Schrodinger equation approach is useful in modeling the dynamical processes in mesoscopic electronic systems.

Are pioneer axons guided by regulatory gene expression domains in the zebrafish forebrain? High-resolution analysis of the patterning of the zebrafish brain during axon tract formation

Although the principles of axon growth are well understood in vitro the mechanisms guiding axons in vivo are less clear. It has been postulated that growing axons in the vertebrate brain follow borders of neuroepithelial cells expressing specific regulatory genes. In the present study we reexamined this hypothesis by analysing the earliest growing axons in the forebrain of embryonic zebrafish. Confocal laser scanning microscopy was used to determine the spatiotemporal relationship between growing axons and the expression pattern of eight regulatory genes in zebrafish brain. Pioneer axons project either longitudinally or dorsoventrally to establish a scaffold of axon tracts during this developmental period. Each of the regulatory genes was expressed in stereotypical domains and the borders of some were oriented along dorsoventral and longitudinal planes. However, none of these borders clearly defined the trajectories of pioneer axons. In two cases axons coursed in proximity to the borders of shh and pax6, but only for a relatively short portion of their pathway. Only later growing axons were closely apposed to the borders of some gene expression domains. These results suggest that pioneer axons in the embryonic forebrain do not follow continuous pathways defined by the borders of regulatory gene expression domains, (C) 2000 Academic Press.

Determination of eutectic solidification mode in Sr-modified hypoeutectic Al-Si alloys by EBSD

The effect of eutectic modification by strontium on nucleation and growth of the eutectic in hypoeutectic Al-Si foundry alloys has been investigated by electron back-scattering diffraction (EBSD) mapping. Specimens were prepared from three hypoeutectic AlSi base alloys with 5, 7 and 10 mass%Si and with different strontium contents up to 740 ppm for modification of eutectic silicon. By comparing the orientation of the aluminium in the eutectic to that of the surrounding primary aluminium dendrites? the growth mode of the eutectic could be determined. The mapping results indicate that the eutectic grew from the primary phase in unmodified alloys. When the eutectic was modified by strontium, eutectic grains nucleated separately from the primary dendrites. However, in alloys with high strontium levels, the eutectic again grew from the primary phase. These observed effects of strontium additions on the eutectic solidification mode are independent of silicon content in the range between 5 and 10 mass%Si.

Eutectic growth mode in strontium, antimony and phosphorus modified hypoeutectic Al-Si foundry alloys

The effect of strontium (Sr), antimony (Sb) and phosphorus (P) on nucleation and growth mode of the eutectic in hypoeutectic Al-10 mass%Si alloys has been investigated by electron back-scattering diffraction (EBSD) mapping. Specimens were prepared from a hypoeutectic Al-10 mass%Si base alloy, adding different levels of strontium, antimony and phosphorus for modification of eutectic silicon. By comparing the orientation of the aluminium in the eutectic to that of the surrounding primary aluminium dendrites, the solidification mode of the eutectic could be determined. The results of these studies show that the eutectic nucleation mode, and subsequent growth mode, is strongly dependent on additive elements. The EBSD mapping results indicate that the eutectic grew from the primary phase in unmodified and phosphorus-containing alloys. When the eutectic was modified by strontium or antimony, eutectic grains nucleated and grew separately from the primary dendrites.

Eutectic solidification mode in sodium modified Al-7 mass %Si-3.5 mass %Cu-0.2 mass %Mg casting alloys

The influence of sodium (Na) on nucleation and growth of the Al-Si eutectic in a commercial hypoeutectic Al-Si-Cu-Mg foundry alloy has been investigated. The microstructural evolution during eutectic solidification was studied by a quenching technique. By comparing the orientation of the aluminium in the eutectic to that of the surrounding primary aluminium dendrites by EBSD, the eutectic solidification mode could be determined. The results show that the eutectic solidification starts near the mould wall and evolves with front growth opposite the thermal gradient on a macro-scale, and on a micro-scale with independent heterogeneous nucleation of eutectic grains in interdendritic spaces. Na-modified alloys therefore behave significantly differently from those modified by other elemental additions.