Optical Vortex emitted by Classical Radiation Dumping due to Classical Van Hove singularity near Cut-off frequency of a Waveguide

Classical radiation dumping has been a controversial subject because of an acausal solution of the Lorentz-Abraham (LA) equation that involves the third derivative in time. This is in contrast with quantum mechanics where the second quantization formulation on the radiation process due to the quantum transition of a charged particle has been exactly solved without any contradiction to the fundamental laws of physics in the well-known Friedrichs-Lee model. We have shown that the classical radiation dumping is also analyzed without any contradiction to the fundamental laws by classicizing the commutation relation of the annihilation and creation operators to the Poisson bracket of the normal modes of the classical field [1]. In this talk we apply this classical formulation to the emission process of an optical vortex with an angular momentum from a cyclotron motion of an electron in a cylindrical waveguide. The optical vortex from a cyclotron radiation has been experimentally observed [2]. We will show an interesting mechanism of emission of the optical vortex due to the Van Hove singularity of the density of state of the classical electro-magnetic field appearing at the cut-off frequencies of the waveguide. This new mechanism of emission process cannot be described in terms of the LA equation, because one cannot use the perturbation analysis performed in the LA equation, due to the Van Hove singularity.

[1] T. Petrosky et al, Phys. Rev. A 68 (2003) 022107.

[2] M. Katoh et al, Phys. Rev. Lett. 118 (2017) 094801-1–5.