Mode density of orbital angular momentum modes in a cylindrical cavity and in free space

TL;DR

This paper derives an approximate expression for the mode density of orbital angular momentum modes in large cylindrical cavities and shows their convergence to free space modes, confirming that mode density is independent of OAM.

Contribution

It provides a new approximate formula for OAM mode density in large cavities and compares it to free space, extending understanding of mode distributions.

Findings

Mode density converges to free space modes in large cavities.

Mode density is independent of orbital angular momentum.

Derived expression aligns with Weyl's law.

Abstract

In this short note we derive an approximate expression for the mode density of modes carrying orbital angular momentum (OAM) in a cylindrical cavity which is large compared to the inverse wavevector in any direction. We argue that in the large cavity limit the modes asymptotically converges to the corresponding OAM modes in free space. We compare the result to Weyl's law. It is found, as expected, that the mode density does not depend on whether or not the modes carry OAM.