Photon-Like Solutions of Maxwell's Equations
| Scientific Paper | |
|---|---|
| Title | Photon-Like Solutions of Maxwell\'s Equations |
| Author(s) | John E Carroll |
| Keywords | Photon, Maxwell's Equations |
| Published | 2009 |
| Journal | None |
Abstract
Novel photon-like solutions of Maxwell's equations in free-space are constructed where transverse fields, propagating at frequency ? with phase (group) velocities vp (vg), possess local helical rotations at a frequency ? over the whole crosssection. These are referred to as distributed spin rotations. The frequencies ? and ? are independent with the helical modulation propagating at vg, unlike single frequency classical solutions with helical phase fronts. These novel solutions are accessible only with vector formalisms although the axial fields satisfy the standard scalar wave-equation. The theory is outlined using the compact Riemann Silberstein formulation of Maxwell's equations with a field vector F = E + icB. Light-cone coordinates facilitate a manifestly Lorentz invariant theory. Appropriately chosen distributed spin rotations provide a wide variety of Lorentz invariant packets that envelope the classical fields and contain energy that is proportional to the total helical rotation over the length of the packet. The requirement that both transverse and axial fields are enveloped together leads to quantisation of the rotational energy in integer units, N. Solutions with different N are orthogonal. Operators can be formed, which increase (decrease) the rate of helical rotation and hence increase (decrease) the energy, and behave as promotion and demotion operators of standard quantum theory supporting a view that these new solutions form a photon-analogue. The paper concludes with a review of single-photon experiments that are in keeping with this model. Appendices contain detailed mathematics, speculative material and theorise on quantum-like features of the photon-analogue with regard to interference, polarisation and entanglement.
