Few-cycle Electromagnetic Pulses with Finite Energy and Bounded Angular Momentum: Analysis of the Skyrmionic Texture at Focal Plane

Abstract

Exact solutions to Maxwell equations with topological charge based on a modification to Brittingham's single cycle pulses are analyzed demonstrating that they have finite values of energy, momentum, and angular momentum. Moreover, the ratio of angular momentum to energy is bounded due to the dependence of the mean frequency on topological charge. We have also analyzed the skyrmionic texture of the electric and magnetic fields showing that it is possible to obtain skyrmionic numbers higher than the one for the magnetic field by means of a superposition of pulses with different topological charges and null skyrmionic number.

Electromagnetic Pulses: A Novel Framework for Helicity, Chirality, and Their Flows

“…( 4), ( 5), ( 6), ( 7), ( 8) and ( 9)). To do this, we are going to use the electromagnetic pulses with finite energy and momentum generated through the potential proposed by Ziolkowsky [16] with the parameters analyzed by Hellwarth and Nouchi [14], which have analytical solutions for the volume integrals [14], [17]. The starting point is the following scalar potential which is a solution to the wave equation…”

“…( 18), ( 19) and (20) provide the spectral density of the three scalar properties for any type of electromagnetic pulse as a function of the asymptotic behavior of the electric field and the magnetic field, in such a way that the property can be obtained by means of the integral over all frequencies of the respective spectral density according to Eq. (17). It is noteworthy that the sole distinction between the spectral density of helicity and chirality lies in a scaling factor applied to the power of ω and a constant c.…”

Electromagnetic Pulses: A Novel Framework for Helicity, Chirality and Their Flows

“…). To do this, we are going to use the electromagnetic pulses with finite energy and momentum generated through the potential proposed by Ziolkowsky [14] with the parameters analyzed by Hellwarth and Nouchi [13], which have analytical solutions for the volume integrals [13,15].…”