M. Babiker

THE ORBITAL ANGULAR MOMENTUM OF LIGHT

Publisher Summary This chapter discusses the orbital angular momentum of light, outlines the theoretical basis for the orbital angular momentum of beams within the paraxial approximation, and indicates the unapproximated theory, based on the full set of Maxwell equations. The chapter discusses the problems associated with the separation and identification of spin and orbital contributions to the angular momentum properties of a field, the properties of Laguerre–Gaussian beams, which are physically realizable in the laboratory, and the ways in which the beams may be generated. It reviews the phenomenological behavior of beams possessing orbital angular momentum and their interaction with matter in bulk. The chapter also describes the measurement of the rotational Doppler shift, which arises when beams possessing orbital and spin angular momenta are rotated. The dipole-interaction of atoms with the orbital angular momentum of light beams is considered. The roles of spin and orbital angular momentum are also compared and contrasted.

Longitudinal polar optical modes in semiconductor quantum wells

A continuum theory is employed for investigating the longitudinal optical (LO) modes in polar semiconductor heterostructures. Particular emphasis is laid on the symmetric double heterostructure (DHS) such as occurs in a semiconductor quantum well. The existence of two-dimensional (2D) bulk-type double-interface-type and guided-type LO modes is examined for this case and their characteristic dispersion relations derived. It is shown with reference to a typical GaAs quantum well that the presence of at most two double-interface modes and a finite number of guided LO modes depends on the difference between the squares of the limiting bulk LO frequencies of the two materials. The implications of the results for light scattering experiments and for the properties of electrons confined in quantum wells are pointed out and discussed.

AZIMUTHAL DOPPLER SHIFT IN LIGHT BEAMS WITH ORBITAL ANGULAR MOMENTUM

Abstract We show that an atom moving in a light beam with orbital angular momentum experiences an azimuthal shift in the resonant frequency in addition to the usual axial Doppler and recoil shifts. For a Laguerre-Gaussian beam characterised by an orbital angular momentum quantum number l , the shift is lV φ / r where r is the radial atomic position and V φ the azimuthal component of velocity. The predicted shift could play a significant role in interactions between atoms and standing light fields in cooling experiments as well as in ion traps.

Effective-mass eigenfunctions in superlattices and their role in well-capture

Abstract The rate of capture into the wells of a superlattice is calculated using the effective-mass eigenfunctions and the superlattice folded spectrum of polar optical phonons. The dependence on well-width is followed for the specific case of 100A barriers. A general trend of diminishing rate with diminishing well-width is obtained, but superimposed on this is a resonance structure (periodic in well-width) associated with ‘nearly’ bound states. The results are significantly different from other published work, principally because the latter has been hitherto on the bulk-phonon spectrum, and on single wells.

A quantum electrodynamics framework for the nonlinear optics of twisted beams

A theory is presented for the detailed formulation of the nonlinear optics of laser beams endowed with orbital angular momentum. Following an introductory excursion into the general principles of such twisted beams, a quantum electrodynamical formulation is developed for representing the photonics of their interaction with matter. Detailed results are given for Laguerre–Gaussian beams in the large-Rayleigh-range limit. Utilization of the theory in nonlinear optics is illustrated by application to second-harmonic generation.

On a Generalization of the Power-Zienau-Woolley Transformation in Quantum Electrodynamics and Atomic Field Equations

A canonical transformation is performed on the conventional Hamiltonian for the electromagnetic radiation field and an assemblage of neutral molecules in interaction. The new Hamiltonian has interaction energies expressed in terms of the electromagnetic fields alone and these energies have direct physical significance. The terms linear in e are the multipole interactions, both electric and magnetic, and the term quadratic in e is a generalization of the elementary diamagnetic energy shift. The intermolecular Coulomb energies have cancelled with transverse polarization fields in the new Hamiltonian, although the intramolecular Coulomb potentials are left unaffected. The equations of motion that follow from the new Hamiltonian are deduced. They are the so-called atomic-field equations for the Maxwell fields and Schrödinger equation for an electron wave in a transverse electromagnetic field. The former are the microscopic analogues of Maxwell’s equations in a medium (not restricted to dipole polarization fields) and the latter are dependent on the field strengths alone (not explicit functions of the vector potential).

Quantized orbital angular momentum transfer and magnetic dichroism in the interaction of electron vortices with matter.

Following the very recent experimental realization of electron vortices, we consider their interaction with matter, in particular, the transfer of orbital angular momentum in the context of electron energy-loss spectroscopy, and the recently observed dichroism in thin film magnetized iron samples. We show here that orbital angular momentum exchange does indeed occur between electron vortices and the internal electronic-type motion, as well as center-of-mass motion of atoms in the electric dipole approximation. This contrasts with the case of optical vortices where such transfer only occurs in transitions involving multipoles higher than the dipole. The physical basis of the observed dichroism is explained.

MULTISUBBAND HOT-ELECTRON TRANSPORT IN GAN-BASED QUANTUM WELLS

A simple rigorous analytical theory of two-dimensional (2D) nonequilibrium electrons occupying an arbitrary number of subbands in a quantum well is developed. The electric-field dependence of electron mobility and the average kinetic energy for AlN/GaN quantum wells are presented. At temperatures below 200 K the electron mobility is controlled mainly by the acoustic phonon scattering and it is a nonmonotonous function of the electric field, which has a maximum. At room and higher temperatures the interaction with both acoustic and polar optical phonons determine the hot-electron mobility and it depends very weakly on the electric field. Both the mobility and average energy of 2D electrons are smaller than that for three-dimensional (3D) electrons in the bulk semiconductor. Our theory provides a self-consistent transition from the 2D to the 3D regime of electron transport with increasing electric field accompanied by the occupation of an increasingly large number of subbands by the electrons.

Derivation of the Power-Zienau-Woolley Hamiltonian in quantum electrodynamics by gauge transformation

The different forms of Hamiltonian for the coupled system consisting of the electromagnetic field and a non-relativistic charged particle are considered in the context of gauge-transformation theory. The conventional Lagrangian of the system in an arbitrary gauge is converted to a new form by transformation to another arbitrary gauge, and a new formulation of the theory is obtained by expressing the new Lagrangian in terms of the initial potentials. Thus different gauge transformations produce different momenta ∏ conjugate to the initial vector potential A, and hence different forms of Hamiltonian. The transformations that produce the Coulomb-gauge and Power-Zienau-Woolley (P. Z. W.) Hamiltonians are considered in detail. It is shown that ∏ is transverse in both cases and only the transverse part of A is accordingly involved in the field quantization; neither the longitudinal part of A nor the scalar potential appears explicitly, the instantaneous Coulomb energies being included via an electronic polarization determined by the gauge generator. The transformations between gauges are illustrated by simple diagrammatic representations of A and ∏. Compararison with the commonly used unitary transformation derivation of the P. Z. W. Hamiltonian emphasizes the need for a careful reinterpretation of the physical significance of ∏ after the unitary transformation has been made.

A new resonance phenomenon associated with electron transitions in superlattices and single quantum wells

Abstract The rate of capture of electrons into the quantum wells of a superlattice and the rate of intersub-band transition within the wells are shown to vary resonantly with well-width. In addition to the well-known electron-state resonances which enhance capture, quite new phonon resonances arise when there is confinement of a new guided mode into the GaAs well. In providing an enhanced possibility of transition within the barrier, these phonon resonances tend to counteract the effect of electron resonances on capture.