Abstract
"The "focused doughnut", a single-cycle electromagnetic perturbation of toroidal topology with inseparable time and spatial dependencies propagates at the speed of light in vacuum, as was shown by Hellwarth and Nouchi in 1996. While normal incidence reflection and refraction of conventional electromagnetic pulses in isotropic media do not lead to polarization changes, "focused doughnut" pulses undergo complex field transformations owing to the toroidal field structure and the presence of longitudinal components. We also demonstrate that "focused doughnuts" can interact strongly with structured media exciting dominant dynamic toroidal dipoles in spherical dielectric particles."
Highlights
The homogeneous Maxwell’s equations describe the behavior of electromagnetic radiation in free space
We demonstrate that due to the toroidal field configuration of the FD pulses, even reflection from dielectric and metallic interfaces can lead to complex field transformations
Longitudinal fields shown at two times – one prior to incidence on the boundary (t1) and one after the pulse has been reflected and transmitted (t2). In both polarisation cases the toroidal topology of the pulse is maintained after being transmitted though the dielectric interface and it undergoes the expected increase in momentum within the medium as for conventional electromagnetic pulses
Summary
The homogeneous Maxwell’s equations describe the behavior of electromagnetic radiation in free space. Pulse solutions to the homogeneous Maxwell’s equations i.e. representing localised propagation of finite electromagnetic energy, are significantly less well analyzed. FWMs were required to meet six criteria: 1) satisfy the homogeneous Maxwells equations, 2) be continuous and non-singular, 3) have a three-dimensional pulse structure, 4) be non-dispersive for all time, 5) move at light velocity c along straight lines, and 6) carry finite electromagnetic energy. The original FWMs were subsequently shown to violate the sixth criterion [3,4,5], the finite energy requirement was satisfied by utilizing superpositions of the FWMs over carefully chosen weighting functions [6, 7] These superpositions are termed as electromagnetic directed energy pulse trains (EDEPTs) and can be tailored so as to give localized propagation of electromagnetic energy in space and time.
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Published Version
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