Laguerre-Gaussian modes become elegant after an azimuthal phase modulation

TL;DR

This paper reveals that Laguerre-Gaussian modes, after azimuthal phase modulation, are actually elegant LG modes with modified quantum numbers, offering a new perspective on their propagation and structure.

Contribution

It demonstrates that phase-only azimuthal modulation transforms LG modes into elegant LG modes with altered quantum numbers, clarifying their propagation characteristics.

Findings

Modulated beams have the angular spectrum of elegant LG modes.

The fields acquire new OAM and radial quantum numbers.

Beams map back to LG-type modes after modulation.

Abstract

Laguerre-Gaussian (LG) modes are solutions of the paraxial Helmholtz equation in cylindrical coordinates and are associated with light fields carrying orbital angular momentum (OAM). It is customary to modulate such beams using phase-only vortex profiles, for example, when increasing (laddering up) or decreasing (laddering down) the OAM content of some given LG mode. However, the resulting beams have been shown to be hypergeometric-Gaussian modes, due to the changing radial amplitudes on propagation. In this work, we show that these beams in fact have the angular spectrum of elegant Laguerre-Gaussian (eLG) modes, and therefore map back to LG-type modes. Accordingly, the fields obtain new OAM and radial quantum numbers that depend on the initial OAM and additional OAM gained during modulation.