Propagable Optical Vortices with Natural Noninteger Orbital Angular Momentum in Free Space

Abstract

Light beams with optical vortices can propagate in free space only with integer orbital angular momentum. Herein, this scientific consensus theoretically and experimentally is upheaved by proposing light beams carrying natural noninteger orbital angular momentum. These peculiar vortex beams are unique solutions to the Helmholtz equation, which possesses optical vortices with topological charges of l + 0.5, where l is an integer. During propagation in free space, their amplitudes and vortex phases with noninteger topological charges can be maintained stably. The findings of this study provide an alternative state of optical vortices in physics, which can serve as basis for innovations in optics and related scientific fields.

Physical Essence of Propagable Fractional‐Strength Optical Vortices in Free Space

“…The stability of these unique vortex beams is dependent on the interaction between the vortex phase and the polarization of the fractional‐order VVB. [ 12 ] In the absence of both, the fractional‐order VVB and vortex beam with a noninteger topological charge cannot propagate individually in free space. However, it is unclear as to why does the middle state of a light beam exists naturally in free space.…”

“…The first is a vortex beam that possesses an optical vortex with a topological charge of ±0.5, in addition to a polarization state of an m + 0.5‐order VVB (see Equation ()); and the second is a vortex beam that has a constant polarization state, namely, a ±0.5‐order VVB, but an optical vortex with an arbitrary topological charge of l + 0.5 (see Equation ()). [ 12,13 ] …”

“…The first is a vortex beam that possesses an optical vortex with a topological charge of AE0.5, in addition to a polarization state of an m þ 0.5-order VVB (see Equation ( 13)); and the second is a vortex beam that has a constant polarization state, namely, a AE0.5-order VVB, but an optical vortex with an arbitrary topological charge of l þ 0.5 (see Equation ( 14)). [12,13]…”

“…Recently, we solved this problem by demonstrating a propagable vortex beam with a topological charge of l + 0.5. [ 12,13 ] It should be noted that this type of vortex beam is a solution to the wave function. That is, optical vortices with fractional topological charges naturally exist in free space.…”

“…[ 1,2 ] Unlike conventional vortices, fractional‐strength optical vortices have different carriers, namely, vector vortex beams (VVBs) with an order of m + 0.5. [ 12 ] Although a mathematical derivation for the generation of propagable fractional‐strength optical vortices was provided in our previous study, the physical essence of these unique vector beams is unclear. [ 12 ] It is unclear as to why the combination of both unstable states, namely, the m + 0.5 order VVB and vortex phase with topological charge of l + 0.5, can form a stable vortex beam with fractional‐order and fractional topological charges.…”