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arXiv:2004.05585 · Physical Review A

Arbitrary spatial mode sorting in a multimode fiber

Hugo Defienne, Daniele Faccio

Published Jun 24, 2020• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.101.063830

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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.
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.
The need to increase data transfer rates constitutes a key challenge in modern information-driven societies. Taking advantage of the transverse spatial modes of light to encode more information is a promising avenue for both classical and quantum photonics. However, to ease access to the encoded information, it is essential to be able to sort spatial modes into different output channels. Here, we introduce a way to customize the sorting of arbitrary spatial light modes. Our method relies on the high degree of control over random scattering processes by preshaping of the phase structure of the incident light. We demonstrate experimentally that various sets of modes, irrespective of their specific modal structure, can be transformed to a broad range of output channel arrangements. Thus, our method enables full access to all of the information encoded in the transverse structure of the field; for example, azimuthal and radial modes. We also demonstrate that coherence is retained in this complex mode transformation, which opens up applications in quantum and classical information science.
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.
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.