Orbital angular momentum mode sorting based on a hybrid radial-angular hybrid lens

Abstract

Orbital angular momentum (OAM) modes have their phase distribution as exp (jlθ), which resembles the plane wave in the Cartesian coordinates. Like the traditional lens, which can focus the plane wave on the focal plane, the angular lens can focus the OAM beam in the angular domain, albeit with a relatively long tail due to the unsatisfied angular focal condition for the non-ring shape beams. In this paper, a hybrid lens in the angular domain and the radial domain is proposed. The radial lens with the specific radially distributed phase guarantees the angular focal condition is met for the beams with an arbitrary beam waist or radial field distribution, which significantly improves the performance for the OAM modes sorting by the angular lens. The discrimination of the different OAM modes can be achieved efficiently based on such a single optical component, i.e., the proposed hybrid radial-angular lens, with the OAM modes inter-mode crosstalk as 3.7% when the topological charge difference is 3.

Efficient Angular Separation of the Dense Orbital Angular Momentum of Light

“…Hence, more efficient angular separation of neighboring OAM modes (spacing of 1) can be achieved by combining the hybrid lens with a higher-fold OAM multiplier. In summary, we have achieved the hypothesis in [34] and proposed a scheme that can angularly sort the dense OAM modes while reasonably maintaining the simplicity of the setup. This scheme may find applications in OAM-based communication systems and open up new opportunities for sorting the OAM of light.…”

“…The phase of the pure radial lens can be expressed as Ω radical false( r false) = − k 2 f true( r − r 0 2 r ) 2 with the same focal length f = k r 0 2 / l 0 , where r denotes the polar coordinates defined as x 2 + y 2 , r 0 is a constant related to the satisfaction of the focusing condition. By combining the advantages of radial lenses and angular lenses, the phase of the hybrid lens in the angular domain and radial domain is mathematically represented as follows: Ω 3 false( r , θ false) = − l 0 2 θ 2 − k 2 f false( r − r 0 2 r ) 2 − β r where β is the radial correction factor for the hybrid lens.…”

“…In this letter, in order to address the above issues and indeed improve sorting performance, the OAM multiplier technique 38 is introduced and combined with the hybrid lens 34 to efficiently achieve angular separation of the adjacent OAM modes. We distinguish our sorting scheme from the above techniques, as they only implement a single photonic momentum transformation and do not involve the multiplication operation of photonic momentum.…”

“…Meanwhile, it was proposed to combine the quadratic phase of the angular lens with metasurface techniques to achieve simultaneous detection of OAM and spin angular momentum (SAM). , Nevertheless, unlike the conventional lens, the pure angular lens mainly results in unavoidable side lobes in the focal plane. Hence, a hybrid lens in the angular and radial domains is proposed to improve sorting performance in both free space and fiber-integrated systems . However, such a hybrid lens still cannot distinguish neighboring OAM modes as shown in Figure a, an identical issue faced in the previous transverse separation .…”

Vortex grating-encrypted orbital angular momentum multiplexed holography

“…Furthermore, counting the number of fringes were inefficient for the detection of various possible OAM modes, especially for high-order OAMs. Another common method is the coordinate transformation and the astigmatic transformation which aim to transferring the input OAM mode with annular shape into a linear-shaped mode [22][23][24]. These techniques generally require two or more optical devices and have a high requirement for the alignment of optical path.…”