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Register a new userLinear and angular momentum of electromagnetic fields generated by an arbitrary distribution of charge and current densities at rest
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Starting from Stratton-Panofsky-Phillips-Jefimenko equations for the electric and magnetic fields generated by completely arbitrary charge and current density distributions at rest, we derive far-zone approximations for the fields, containing all components, dominant as well as sub-dominant. Using these approximate formulas, we derive general formulas for the total electromagnetic linear momentum and angular momentum, valid at large distances from arbitrary, non-moving charge and current sources.
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A decomposition of the angular momentum of the classical electromagnetic field into orbital and spin components that is manifestly gauge invariant and general has been obtained. This is done by decomposing the electric field into its longitudinal and transverse parts by means of the Helmholtz theorem. The orbital and spin components of the angular momentum of any specified electromagnetic field can be found from this prescription.
We develop a framework that provides a few-mode master equation description of the interaction between a single quantum emitter and an arbitrary electromagnetic environment. The field quantization requires only the fitting of the spectral density, obtained through classical electromagnetic simulations, to a model system involving a small number of lossy and interacting modes. We illustrate the power and validity of our approach by describing the population and electric field dynamics in the spontaneous decay of an emitter placed in a complex hybrid plasmonic-photonic structure.
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Robert N. C. Pfeifer
, Timo A. Nieminen
, Norman R. Heckenberg andn Halina Rubinsztein-Dunlop
2009
Almost a hundred years ago, two different expressions were proposed for the energy--momentum tensor of an electromagnetic wave in a dielectric. Minkowskis tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abrahams tensor predicted its decrease. Theoretical arguments were advanced in favour of both sides, and experiments proved incapable of distinguishing between the two. Yet more forms were proposed, each with their advocates who considered the form that they were proposing to be the one true tensor. This paper reviews the debate and its eventual conclusion: that no electromagnetic wave energy--momentum tensor is complete on its own. When the appropriate accompanying energy--momentum tensor for the material medium is also considered, experimental predictions of all the various proposed tensors will always be the same, and the preferred form is therefore effectively a matter of personal choice.
From electromagnetic wave equations, it is first found that, mathematically, any current density that emits an electromagnetic wave into the far-field region has to be differentiable in time infinitely, and that while the odd-order time derivatives of the current density are built in the emitted electric field, the even-order derivatives are built in the emitted magnetic field. With the help of Faradays law and Amperes law, light propagation is then explained as a process involving alternate creation of electric and magnetic fields. From this explanation, the preceding mathematical result is demonstrated to be physically sound. It is also explained why the conventional retarded solutions to the wave equations fail to describe the emitted fields.
It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the absence of electric and magnetic charge densities, these operators satisfy the canonical commutation relations for momentum and angular momentum. This confirms their validity as operators that can be used in quantum mechanical calculations of angular momentum.
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