Experimental proposal of a mode sorter for vector vortex beams of arbitrary order

TL;DR

The paper introduces an experimental scheme to sort vector vortex beams of arbitrary order $m$ using three resonant triangular cavities and a Profile Rotator (PR) that rigidly rotates the beam profile via a K-mirror and a Faraday rotator. By exploiting symmetry under horizontal flips and carefully aligning parity axes, the scheme demultiplexes the four basis states $(\Psi^+_m,\Psi^-_m,\Phi^0_m,\Phi^-_m)$ while preserving polarization, enabling high-dimensional mode separation. The authors extend the approach to arbitrary $m$ by analyzing symmetry axes and showing how odd orders can be sorted with a $\pi/4$ profile rotation, and proposing q-plate preprocessing for even orders to convert to odd. This framework connects mode-symmetry theory with a practical, potentially scalable sorter, with applications in quantum information, optical communications, and structured-light manipulation.

Abstract

We propose an experimental scheme for sorting vector vortex beams using a system of three optical cavities. The method targets the separation of the four vector vortex modes of a given order m by exploiting their symmetry properties with respect to radial axes. The first cavity separates the modes into two pairs, one symmetric and one antisymmetric under horizontal flip, by transmitting one pair and reflecting the other. Each output is then directed into a second cavity, which further resolves the pairs into individual modes based on their parity. A key element between the cavities is a novel system introduced in this work, the Profile Rotator (PR), which rigidly rotates the beam profile (including its polarization structure) using an appropriately calibrated K-mirror and a Faraday rotator. The theoretical framework is based on the analysis of mode symmetries and their interaction with cavity boundary conditions. This work lays the groundwork for experimental implementations of efficient mode sorting, with potential applications in high-dimensional quantum information processing, optical communications, and structured light manipulation.

Figures (4)

• Figure 1: Representation of the ring-shaped intensity profile and inhomogeneous polarization of Vector Vortex Beam bases for (a) $m=1$ and (b) $m=2$. From left to right: $\Psi^+_m$, $\Psi^-_m$, $\Phi^+_m$, and $\Phi^-_m$.
• Figure 2: Proposed experimental setup. Any linear combination of the four elements of the vector mode basis can be sorted by a set of three cavities. Cavity-resonant modes are fully transmitted and non-resonant modes are fully reflected, provided the plane cavity mirrors have the same reflectivity and the concave mirror is highly reflective. PR = $\pi/4$ profile rotator: rigidly rotates the beam profile (including polarization pattern) by an angle of $\pi/4$ before cavities 2 and 3. FR = $\pi/2$ Faraday rotator: locally rotates the polarization vectors by $\pi/2$ all over the beam profile.
• Figure 3: Schematic of the proposed Profile Rotator (PR), showing its effect on the polarization profile of $m = 1$ vector vortex beams after each component. The K-mirror is set to a rotation angle $\beta = \pi/8$, and the Faraday rotator applies a uniform polarization rotation of $\pi/4$ radians. All angles are measured counterclockwise from the vertical.
• Figure 4: Representation of the symmetry (red lines) and antisymmetry (blue dashed lines) axes for (a) $m=2$ and (b) $m=3$ VVBs. The axes are described by the angle $\alpha$ they make with the vertical direction, measured counterclockwise.