Electromagnetic radiation

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Radiation ◽  
Magnetic Dipole ◽  
Antenna Arrays ◽  
Electric Dipole ◽  
Free Electron ◽  
Vector Potential ◽  
Electric Quadrupole ◽  
Multipole Expansion ◽  
Multipole Moments

This chapter begins by expressing the multipole expansion of the dynamic vector potential A ( r, t) in terms of electric and magnetic multipole moments. Differentiation of A ( r, t) leads directly to the fields E ( r, t) and B ( r, t), which have a component transporting energy away from the sources to infinity. This component is called electromagnetic radiation and it arises only when electric charges experience an acceleration. A range of questions deal with the various types of radiation, including electric dipole and magnetic dipole–electric quadrupole. Larmor’s formula is applied in both its non-relativistic and relativistic forms. Also considered are some applications involving antennas, antenna arrays and the scattering of radiation by a free electron.

Fields in Terms of the Multipole Moments of the Source

2019 ◽  
pp. 85-110
Author(s):  
Richard Freeman ◽  
James King ◽  
Gregory Lafyatis
Keyword(s):  
Magnetic Fields ◽  
Magnetic Dipole ◽  
Vector Potential ◽  
Electric Quadrupole ◽  
Multipole Expansion ◽  
Source Location ◽  
Source Distribution ◽  
Multipole Moments ◽  
Electric And Magnetic Fields ◽  
Radiation Zone

Many if not most evaluations of electric and magnetic fields arising from source configurations are performed using multipole moments of the source distribution. As an example, Jefimenko’s equations are evaluated in the radiation zone by expansion of the charge and current distributions in their lowest order moments. The important moments, electric and magnetic dipole, and the electric quadrupole are examined in detail. The electric and magnetic fields for all regions of space relative to the source location (near, intermediate, and radiation) are evaluated using the multipole expansion of the vector potential in terms of these moments. Finally, the power radiated by the multipole moments of the source is presented.

Forbidden transitions in molecular vibrational-rotational spectroscopy

1989 ◽  
Vol 54 (10) ◽  
pp. 2555-2630 ◽  
Author(s):  
Dušan Papoušek
Keyword(s):  
Magnetic Dipole ◽  
Electric Dipole ◽  
Dipole Moments ◽  
Physical Nature ◽  
Electric Quadrupole ◽  
Rotational Spectroscopy ◽  
Quadrupole Moments ◽  
Electric Dipole Moments ◽  
Selection Rules ◽  
Rotational States

A review is given of the forbidden ( more precisely: perturbation allowed) transistions between molecular vibrational-rotational states including transistions which are induced by the electric dipole and quadrupole moments and the magnetic dipole moment. The basic theory of these transistions is outlined starting with the overall symmetry selection rules, followed by the discussion of the spin statistics isomers, approximate selection rules for the usual vibrational-rotational transistions, and forbidden transistions induced by the electric quadrupole and magnetic dipole moments. Forbidden transistions due to the vibrationally and rotationally induced electric dipole moments are the discussed in detail for symmetric top and spherical top molecules with the emphasis on the physical nature of the various phenomena leading to these transistions. A summary is also given of the most important experimental work on the forbidden transistions in diatomic molecules and polar as well as nonpolar polyatomics.

The electromagnetic potentials

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Radiation ◽  
Gauge Transformation ◽  
Vector Potential ◽  
Point Charge ◽  
Wave Equations ◽  
Multipole Expansion ◽  
Inhomogeneous Wave ◽  
Electromagnetic Potentials ◽  
Starting Point

This chapter expresses the fields E ( r, t) and B ( r, t) in terms of the electromagnetic potentials Ф( r, t) and A ( r, t), and shows that these potentials are defined only up to a gauge transformation. This leads the reader naturally to the Coulomb and Lorenz gauges which are usually encountered in textbooks. The inhomogeneous wave equations whose solutions are the retarded electromagnetic potentials are also considered, as well as the Lienard–Wiechert potentials for an arbitrarily moving point charge. A few questions are included in which the Lagrangian and Hamiltonian of a point charge are expressed in terms of Ф and A. The chapter concludes by deriving a multipole expansion for the dynamic vector potential which will provide the starting point in our treatment of electromagnetic radiation later on in Chapter 11

Light propagation in cubic and other anisotropic crystals

1990 ◽  
Vol 430 (1880) ◽  
pp. 593-614 ◽  
Keyword(s):  
Optical Activity ◽  
Electric Dipole ◽  
Light Propagation ◽  
Light Wave ◽  
Electric Quadrupole ◽  
Dipole Approximation ◽  
Multipole Moments ◽  
Magnetic Dipoles ◽  
Cubic Crystals

A consistent multipole theory is presented to describe light propagation in non-absorbing non-magnetic crystals. Although valid for the 32 crystal classes, the theory is applied here to all except the five members of the triclinic and monoclinic systems. To account for the birefringence that has been observed in certain cubic crystals and also for the predicted Jones birefringence, the theory has to allow for electric octopoles and magnetic quadrupoles induced by the light wave. At the earlier stage of electric quadrupoles and magnetic dipoles, it is able to describe optical activity in crystals. An expression for this is derived which, when electric quadrupole contributions are omitted, yields the familiar Nye result. As a criterion for the correct inclusion in the theory of all relevant induced multipole moments, tensor expressions for observables are shown to be independent of the choice of origin. Finally, the concepts of O-ray and E-ray are found to break down beyond the electric dipole approximation and alternatives are proposed.

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