Exponential beams of electromagnetic radiation

Abstract

We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of rho. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker representation of the solutions of the Maxwell equations in terms of just one complex function. The connection between the Bessel beams and the exponential beams is made explicit by constructing the exponential beams as wave packets of Bessel beams.

Dedicated to the memory of Edwin Power

Cited by in corpus (7)

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• The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism
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• Gravitational waves carrying orbital angular momentum
• Quantum-mechanical description of optical beams
• Backflow in relativistic wave equations
• Quantum numbers and spectra of structured light