Rodney Loudon

Theory of the absorption edge in semiconductors in a high magnetic field

Abstract A theory based on the effective mass approximation is given for hole-electron pairs in a semiconductor in a magnetic field. The intensity of the absorption edge is determined by the wave function of relative motion of the pair, so that essentially it becomes necessary to solve the Schrodinger equation for a hydrogen atom in a magnetic field. This is done in an approximation valid in high fields which assumes that the Coulomb term affects only the motion along the field, and uses a potential form which allows the solutions to be written in terms of confluent hypergeometric functions. The results show that the main intensity in each magnetic sub-band transition is thrown into the lowest exciton line and that the absorption in the continuum is reduced to an insignificant shoulder. The peaks observed in the so-called magneto-optic effect will all be exciton peaks.

The enigma of optical momentum in a medium

It is 100 years since Minkowski and Abraham first gave rival expressions for the momentum of light in a material medium. At the single-photon level, these correspond, respectively, either to multiplying or dividing the free-space value () by the refractive index (n). The debate that this work started has continued till the present day, punctuated by the occasional publication of ‘decisive’ experimental demonstrations supporting one or other of these values. We review the compelling arguments made in support of the Minkowski and Abraham forms and are led to the conclusion that both momenta are correct. We explain why two distinct momenta are needed to describe light in a medium and why each appears as the natural, and experimentally observed, momentum in appropriate situations.

Polarization squeezing and continuous-variable polarization entanglement

A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.

Theory of infra-red and optical spectra of antiferromagnets

Abstract The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF2, FeF2 and CoF2. The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the...

Theory of fine structure on the absorption edge in semiconductors

Abstract General equations are derived for the details of the direct absorption edge in a semiconductor when the effects of excitons and of an applied external magnetic field are included. The effects produced by magnetic fields and excitons separately are readily derived as special cases and these are briefly reviewed with reference to work already published. The problem including both simultaneously could not be solved in general but expressions for the continuous absorption are obtained in an approximation valid in large magnetic fields. Simple spherical bands are assumed throughout and spin effects neglected.

Quantum theory of the lossless beam splitter

Abstract The electromagnetic fields associated with a beam splitter having two input arms and two output arms are quantized in terms of the spatial modes of the complete optical system. The continuum mode operators employed conveniently describe the flow of light through the beam splitter from sources to detectors. The formalism is used to determine the photocount fluctuations in difference detection of the two outputs, the effect of beam splitting on squeezed input light, and the distribution of output photocounts for a definite number of input quanta.

Decay of excited atoms in absorbing dielectrics

We present calculations of the rates of decay of an excited atom embedded in an absorbing dielectric. Decay can occur by spontaneous emission into transverse radiative modes of the electromagnetic field and by Joule heating via longitudinal coupling of the atom to the dielectric. The spontaneous emission (transverse) decay rate is modified in a dielectric, being the free-space rate multiplied by the real part of the refractive index at the transition frequency of the atom. There is a further modification due to the difference between the macroscopic dielectric field and the local field at the position of the atom. In addition there is a longitudinal decay rate which is proportional to the imaginary part of the dielectric constant and therefore vanishes in non-absorbing media. We derive expressions for each of these rates of decay and discuss the physical mechanisms leading to them.

On the electromagnetic force on a dielectric medium

The study of the mechanical effects of light on a dielectric medium has led to two quite distinct forms for the force density: one based on the microscopic distribution of charges and the other on the distribution of atomic dipoles. Both approaches are based directly on the Lorentz force, but it has been suggested that they lead, in a number of cases, to significantly different predictions. In this paper we address this paradoxical situation and show that in the majority of problems the force densities lead to identical results. Where the theories do differ we attempt to determine which of the two descriptions is the more reliable.

Theory of noise accumulation in linear optical-amplifier chains

The noise properties of the two main kinds of linear optical amplifier, phase-insensitive and phase-sensitive, are reviewed, with particular emphasis on their minimum-noise limits. An optical communications link is considered, in which identical sections of attenuating fiber alternate with identical linear amplifiers. The limits on the overall signal-to-noise ratios of such chains are derived. More attention is paid to the signal-to-noise ratio appropriate to phase-sensitive detection, but some results for direct detection are also given.

Theory of the radiation pressure on dielectric surfaces

The radiation pressures exerted by light beams incident normally on dielectric surfaces are calculated by evaluation of the quantum-mechanical Lorentz force. The free-space surface of an almost transparent dielectric and the interface of a lossy dielectric with a transparent medium are treated in detail. Light beams in the forms of a short single-photon pulse and a continuous-mode narrow-band coherent excitation are considered. The use of a pulse excitation enables discrimination of the surface and bulk contributions to the force. It is shown that the surface force is directed inwards to the dielectric for entrance and exit of the pulse from and to free space, contrary to the conclusions of some earlier work. For the interface of lossy and transparent dielectrics, it is shown that the high-reflectivity mirror modelled by an appropriate limit of the lossy dielectric experiences a force enhanced by the refractive index of the transparent medium, in agreement with experiments on a mirror suspended in liquid dielectrics. The results for the Lorentz force are used to identify the effective momenta of photons in dielectrics.