Scott Glasgow

Complete integrability of the reduced Maxwell—Bloch equations with permanent dipole

Abstract We obtain the Lax pair, hierarchy of commuting flows and Backlund transformations for a reduced Maxwell–Bloch (RMB) system. This system is of particular interest for the description of unipolar, nonoscillating electromagnetic solitons (also called “electromagnetic bubbles” ).

Role of group velocity in tracking field energy in linear dielectrics.

A new context for the group delay function (valid for pulses of arbitrary bandwidth) is presented for electromagnetic pulses propagating in a uniform linear dielectric medium. The traditional formulation of group velocity is recovered by taking a narrowband limit of this generalized context. The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points consists of two parts: a spectral superposition of group delays and a delay due to spectral reshaping via absorption or amplification. The use of the new context is illustrated for pulses propagating both superluminally and subluminally. The inevitable transition to subluminal behavior for any initially superluminal pulse is also demonstrated.

Energy transport in linear dielectrics

We examine the energy exchanged between an electromagnetic pulse and a linear dielectric medium in which it propagates. While group velocity indicates the presence of field energy (the locus of which can move with arbitrary speed), the velocity of energy transport maintains strict luminality. This indicates that the medium treats the leading and trailing portions of the pulse differently. The principle of causality requires the medium to respond to the instantaneous spectrum, the spectrum of the pulse truncated at each new instant as a given locale in the medium experiences the pulse.

Role of the instantaneous spectrum on pulse propagation in causal linear dielectrics.

A model-independent theorem demonstrates how a causal linear dielectric medium responds to the instantaneous spectrum, that is, the spectrum of the electric field pulse that is truncated at each new instant (as a given locale in the medium experiences the pulse). This process leads the medium to exchange energy with the front of a pulse differently than with the back as the instantaneous spectrum laps onto or off of nearby resonances. So-called superluminal pulse propagation in either absorbing or amplifying media as well as highly subluminal pulse propagation are understood qualitatively and quantitatively within this context.

Spontaneous emission in the near-resonant Kapitza-Dirac effect

We study the influence of spontaneous emission on atom diffraction by a standing wave laser field. We characterize, analytically, the major regimes of the near-resonant Kapitza-Dirac effect and study, numerically, the influence of spontaneous emission. In particular, we discuss in some detail two important classes of two-beam resonances which are major candidates to develop effective atom beam splitters, the so-called Bragg and Doppleron resonances.

Acceleration of Free Electrons in a Symmetric Evanescent Wave

The possibility of accelerating free electrons in a vacuum gap between closely spaced dielectric materials is explored. Plane waves impinging symmetrically on the gap from either side at oblique incidence produce an evanescent wave with net electric field along the direction of propagation. Near the critical angle, the evanescent wave propagates at the vacuum speed of light. A theoretical development and numerical simulations show that free electrons in the gap can be accelerated and accumulate energy indefinitely. This approach lies outside the purview of the Lawson-Woodward theorem, which does not apply in the vicinity of a medium. Damage thresholds of materials restrict the light intensity to far below that achievable by current high-power lasers. This limits the particle energy that might be achieved from an accelerator based on this approach.

Quantum fluctuations in the dressed vacuum of a bosonic model system

Quantum fluctuations and the polarizability of the vacuum state are sometimes interpreted in terms of virtual particles that come into and out of existence for a limited amount of time. We study the spatial and temporal properties of these auxiliary particles on a numerical space-time grid for a one-dimensional model system. This approach permits us to compute the average distance between virtual particles and their lifetime. The creation dynamics of the virtual particles from the bare vacuum state is also examined.

Optimal electromagnetic energy transmission and real-time dissipation in extended media

Pulse reshaping effects that give rise to fast and slow light phenomena are inextricably linked to the dynamics of energy exchange between the pulse and the propagation medium. Energy that is dissipated from the pulse can no longer participate in this exchange process, but previous methods of calculating real-time dissipation are not valid for extended propagation media. We present a method for calculating real-time dissipation that is valid for electromagnetic pulse propagation in extended media. This method allows one to divide the energy stored in an extended medium into the portion that can be later transmitted out of the medium, and that portion which must be lost to either dissipation or reflection.

Probability Density of the CIR Model

We present an alternative derivation of the transition density in the Cox-Ingersoll-Ross (CIR) model. Applying methods developed in elementary quantum mechanics we show that the transition density can be determined from the eigenvalue problem of a second order differential operator with continuous spectrum. The operator turns out to be the stochastic analogue of the time-dependent quantum mechanical position operator in one dimension. Finally, to demonstrate the applicability of this technique to other one-dimensional diffusion problems, we re-derive the familiar transition densities of the Vasicek and Black-Scholes models and write down the equations of motion for the relevant operators in the Courtadon interest rate model.

Scattering of a Strong Laser Field by an Electron Wave Packet

Quantum electrodynamics indicates that an electron scatters light independent of its wave-packet size, even when larger than the stimulating wavelength. We highlight this theoretical conclusion and give a progress report on experimental validation.