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arXiv:2604.14119

Single Plane Spatial Mode Sorter

Khen Cohen, Yoav Yosif-Or, Yaron Oz, Ady Arie

physics.opticseess.SPphysics.app-phquant-phSubmitted Apr 15, 2026• Announced Apr 16, 2026
arXivHTMLPDF

Abstract

A mode sorter separates a set of M orthogonal spatial modes in a shared input channel into M different output channels. Here we present an analytic derivation and experimental validation of a single plane device for sorting spatial modes from a diverse variety of mode families, including Hermite-Gaussian (HG), Laguerre-Gaussian (LG), Bessel-Gaussian (BG), with almost no cross-talk. This sorting capability is required for a wide range of applications that employ classical or quantum light. We also show that applying this design in order to sort a set of Orbital Angular Momentum (OAM) modes with zero radial index reproduces the well-known Fork grating configuration. Furthermore, by taking the limit of M -> inf, we present an analytical expression for sorting all the modes of a given family. By operating this device in reverse, it can be used to generate arbitrary modes, by illuminating it with a Gaussian beam. The power transmission coefficient for this sorter goes as 1/M and we provide a mathematical proof that this is optimal for any typical arrangement of the detector positions. We further study the sorter sensitivity to wavelength and random phase noise.

Journal reference
Opt. Express 34, 1837-1849 (2026)
DOI
10.1364/OE.584001
Comments
29 pages, 17 figures. Published in Opt. Express 34, 1837-1849 (2026)

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A mode sorter separates a set of M orthogonal spatial modes in a shared input channel into M different output channels. Here we present an analytic derivation and experimental validation of a single plane device for sorting spatial modes from a diverse variety of mode families, including Hermite-Gaussian (HG), Laguerre-Gaussian (LG), Bessel-Gaussian (BG), with almost no cross-talk. This sorting capability is required for a wide range of applications that employ classical or quantum light. We also show that applying this design in order to sort a set of Orbital Angular Momentum (OAM) modes with zero radial index reproduces the well-known Fork grating configuration. Furthermore, by taking the limit of M -> inf, we present an analytical expression for sorting all the modes of a given family. By operating this device in reverse, it can be used to generate arbitrary modes, by illuminating it with a Gaussian beam. The power transmission coefficient for this sorter goes as 1/M and we provide a mathematical proof that this is optimal for any typical arrangement of the detector positions. We further study the sorter sensitivity to wavelength and random phase noise.
Sorting spatial optical modes is a key challenge that underpins many applications from superresolved imaging to high-dimensional quantum key distribution. However, to date, implementations of optical mode sorters only operate on specific sets of modes, such as those carrying orbital angular momentum, and therefore lack versatility with respect to operation with an arbitrary spatial basis. Here we demonstrate an arbitrary spatial mode sorter by harnessing the random mode mixing process occurring during light propagation in a multimode fiber by wave-front shaping. By measuring the transmission matrix of the fiber, we show sorting of up to 25 transverse spatial modes of the Fourier, Laguerre-Gaussian, and random basis to an arbitrary set of positions at the output. Our approach provides a spatial mode sorter that is compact, easy to fabricate, programable, and usable with any spatial basis, which is promising for quantum and classical information science.
We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG(nm) input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG(l)(p) modes depending upon whether they have an even or odd value of their orbital angular momentum l. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m = 1) spatial states, covering the entire Poincar e sphere of first-order transverse modes.
The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a paraxial photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field.
Photons were generated possessing orbital angular momentum (OAM) in the form of Laguerre-Gaussian (LG) laser modes. Three Mach-Zehnder interferometer systems, with the use of Dove prisms, were constructed to sort and detect the LG modes based on their OAM state. Successful generating, sorting, and detecting of LG modes is the first step towards information encoding and decoding via lasers. It is possible to generate many LG modes, which can be orthogonally decoded. With many modes to encode information with it is possible to transfer more than one bit of information with a single photon using LG encoding. An experimental test of this concept was performed by demonstrating the generation and sorting of LG modes with attenuated intensities averaging below one photon passing through the system at a time. In summary, generating, sorting, and low-power detecting of specific LG modes were all demonstrated.
The dimension of the state space for information encoding offered by the transverse structure of light is usually limited by the finite size of apertures. The widely used orbital angular momentum (OAM) number of Laguerre-Gaussian (LG) modes in free-space communications cannot achieve the theoretical maximum transmission capacity unless the radial degree of freedom is multiplexed into the protocol. While the methodology to sort the radial quantum number has been developed, the application of radial modes in quantum communications requires an additional ability to efficiently measure the superposition of LG modes in the mutually unbiased basis. Here we develop and implement a generic mode sorter that is capable of sorting the superposition of LG modes through the use of a mode converter. As a consequence, we demonstrate an 8-dimensional quantum key distribution experiment involving all three transverse degrees of freedom: spin, azimuthal, and radial quantum numbers of photons. Our protocol presents an important step towards the goal of reaching the capacity limit of a free-space link and can be useful to other applications that involve spatial modes of photons.
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) -- which direct photons according to their polarization -- and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any ddd-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation.