Optical Thomas-Reiche-Kuhn sum rules

The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region

Theory of radiation pressure on magneto–dielectric materials

We present a classical linear response theory for a magneto–dielectric material and determine the polariton dispersion relations. The electromagnetic field fluctuation spectra are obtained and polariton sum rules for their optical parameters are presented. The electromagnetic field for systems with multiple polariton branches is quantized in three dimensions and field operators are converted to 1–dimensional forms appropriate for parallel light beams. We show that the field–operator commutation relations agree with previous calculations that ignored polariton effects. The Abraham (kinetic) and Minkowski (canonical) momentum operators are introduced and their corresponding single–photon momenta are identified. The commutation relations of these and of their angular analogues support the identification, in particular, of the Minkowski momentum with the canonical momentum of the light. We exploit the Heaviside–Larmor symmetry of Maxwell's equations to obtain, very directly, the Einsetin–Laub force density for action on a magneto–dielectric. The surface and bulk contributions to the radiation pressure are calculated for the passage of an optical pulse into a semi–infinite sample

Polarization squeezing and continuous-variable polarization entanglement

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. The use of pairs of primary polarization-squeezed light beams leads to substantially increased entanglement and to the generation of EPR-entangled light beams. 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.Comment: 27 pages, including 10 figure

The theory of the absorption edge in semiconductors

The thesis is concerned with optical absorption by a semiconductor due to the excitation of electrons from the valence band to the conduction band giving rise to the phenomenon of the absorption edge. In treating the final state of the semiconductor in such an absorption process it is shewn that the system Bay be considered as a two particle one in which the excited electron in the conduction band is bound to the hole left behind in the valence band, which behaves in many ways like a positively charged particle. A bound system of this type is called an exciton. The theory of the exciton is developed in some detail in the effective mass approximation for the case of a semiconductor with spherical energy bands. The effect of an externally applied uniform magnetic field is calculated. Using the exciton wave-function derived in this way, a general expression for the absorption coefficient due to exciton creation in a magnetic field is obtained. The evaluation of this formula requires a knowledge of the wave-functions of the hydrogen atom in a magnetic field. For special cases, e.g. zero magnetic field it is shewn how the general absorption coefficient formula leads to expressions previously derived by other authors. The ware-equation for the hydrogen atom in a magnetic field in solved by a perturbation theory approach for the case where the magnetic field energy is larger than the Coulomb energy, a case of some importance in semiconductors since the Coulomb interaction is reduced by the dielectric constant and the electron or hole effective masses are usually small. Both bound and free states of the exciton are considered, and formal expressions for f-values and absorption coefficients are presented. These formal expressions are evaluated numerically for some important cases. The positions and intensities of the lowest observable absorption lines are calculated when the electronic transition from the valence band to the conduction band is either allowed or forbidden, and the values of the absorption coefficients close to the absorption edge are determined. Finally the accuracy of the perturbation theory method used is assessed and recent experimental work on the absorption edge is discussed

The theory of the absorption edge in semiconductors

The thesis is concerned with optical absorption by a semiconductor due to the excitation of electrons from the valence band to the conduction band giving rise to the phenomenon of the absorption edge. In treating the final state of the semiconductor in such an absorption process it is shewn that the system Bay be considered as a two particle one in which the excited electron in the conduction band is bound to the hole left behind in the valence band, which behaves in many ways like a positively charged particle. A bound system of this type is called an exciton. The theory of the exciton is developed in some detail in the effective mass approximation for the case of a semiconductor with spherical energy bands. The effect of an externally applied uniform magnetic field is calculated. Using the exciton wave-function derived in this way, a general expression for the absorption coefficient due to exciton creation in a magnetic field is obtained. The evaluation of this formula requires a knowledge of the wave-functions of the hydrogen atom in a magnetic field. For special cases, e.g. zero magnetic field it is shewn how the general absorption coefficient formula leads to expressions previously derived by other authors. The ware-equation for the hydrogen atom in a magnetic field in solved by a perturbation theory approach for the case where the magnetic field energy is larger than the Coulomb energy, a case of some importance in semiconductors since the Coulomb interaction is reduced by the dielectric constant and the electron or hole effective masses are usually small. Both bound and free states of the exciton are considered, and formal expressions for f-values and absorption coefficients are presented. These formal expressions are evaluated numerically for some important cases. The positions and intensities of the lowest observable absorption lines are calculated when the electronic transition from the valence band to the conduction band is either allowed or forbidden, and the values of the absorption coefficients close to the absorption edge are determined. Finally the accuracy of the perturbation theory method used is assessed and recent experimental work on the absorption edge is discussed.</p