Laguerre-Gaussian mode sorter

Abstract

Exploiting a particular wave property for a particular application necessitates components capable of discriminating in the basis of that property. While spectral or polarisation decomposition can be straightforward, spatial decomposition is inherently more difficult and few options exist regardless of wave type. Fourier decomposition by a lens is a rare simple example of a spatial decomposition of great practical importance and practical simplicity; a two-dimensional decomposition of a beam into its linear momentum components. Yet this is often not the most appropriate spatial basis. Previously, no device existed capable of a two-dimensional decomposition into orbital angular momentum components, or indeed any discrete basis, despite it being a fundamental property in many wave phenomena. We demonstrate an optical device capable of decomposing a beam into a Cartesian grid of identical Gaussian spots each containing a single Laguerre-Gaussian component, using just a spatial light modulator and mirror.

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References 52

1. 1.

   Allen L, Beijersbergen MW, Spreeuw RJC, Woerdman JP. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A. 1992;45:8185-8189.

   Not in our library10.1103/physreva.45.8185 (opens in a new tab)

2. 2.

   Yao AM, Padgett MJ. Orbital angular momentum: origins, behavior and applications. Adv. Opt. Photonics. 2011;3:161-204.

   Not in our library10.1364/aop.3.000161 (opens in a new tab)

3. 3.

   Mair A, Vaziri A, Weihs G, Zeilinger A. Entanglement of the orbital angular momentum states of photons. Nature. 2001;412:313.

   Not in our library10.1038/35085529 (opens in a new tab)

4. 4.

   Uchida M, Tonomura A. Generation of electron beams carrying orbital angular momentum. Nature. 2010;464:737.

   Not in our library10.1038/nature08904 (opens in a new tab)

5. 5.

   He H, Friese MEJ, Heckenberg NR, Rubinsztein-Dunlop H. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 1995;75:826-829.

   Not in our library10.1103/physrevlett.75.826 (opens in a new tab)

6. 6.

   Franke-Arnold Sonja. Optical angular momentum and atoms. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2017;375(2087):20150435.

   Not in our library10.1098/rsta.2015.0435 (opens in a new tab)

7. 7.

   Allen L, Babiker M, Power WL. Azimuthal doppler shift in light beams with orbital angular momentum. Opt. Commun. 1994;112:141-144.

   Not in our library10.1016/0030-4018(94)00484-6 (opens in a new tab)

8. 8.

   Harwit M. Photon orbital angular momentum in astrophysics. Astrophys. J. 2003;597:1266.

   Not in our library10.1086/378623 (opens in a new tab)

9. 9.

   Wagner K, et al. Entangling the spatial properties of laser beams. Science. 2008;321:541-543.

   Not in our library10.1126/science.1159663 (opens in a new tab)

10. 10.

    Krenn, M., Malik, M., Erhard, M. & Zeilinger, A. Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.375, 20150442 (2017).

    Not in our library10.1098/rsta.2015.0442 (opens in a new tab)

11. 11.

    Sit A, et al. High-dimensional intracity quantum cryptography with structured photons. Optica. 2017;4:1006-1010.

    Not in our library10.1364/optica.4.001006 (opens in a new tab)

12. 12.

    Richardson DJ, Fini JM, Nelson LE. Space-division multiplexing in optical fibres. Nat. Photonics. 2013;7:354-362.

    Not in our library10.1038/nphoton.2013.94 (opens in a new tab)

13. 13.

    Zhao N, Li X, Li G, Kahn JM. Capacity limits of spatially multiplexed free-space communication. Nat. Photonics. 2015;9:822.

    Not in our library10.1038/nphoton.2015.214 (opens in a new tab)

14. 14.

    Gibson G, et al. Free-space information transfer using light beams carrying orbital angular momentum. Opt. Express. 2004;12:5448-5456.

    Not in our library10.1364/opex.12.005448 (opens in a new tab)

15. 15.

    Zeilinger MK, et al. Communication with spatially modulated light through turbulent air across Vienna. New J. Phys. 2014;16:113028.

    Not in our library10.1088/1367-2630/16/11/113028 (opens in a new tab)

16. 16.

    Nicolas A, et al. A quantum memory for orbital angular momentum photonic qubits. Nat. Photonics. 2014;8:234.

    Not in our library10.1038/nphoton.2013.355 (opens in a new tab)

17. 17.

    CaiLabs. Canunda Application Note (2016).

    Not in our library

18. 18.

    Hell SW, Wichmann J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy. Opt. Lett. 1994;19:780-782.

    Not in our library10.1364/ol.19.000780 (opens in a new tab)

19. 19.

    Fürhapter S, Jesacher A, Bernet S, Ritsch-Marte M. Spiral phase contrast imaging in microscopy. Opt. Express. 2005;13:689-694.

    Not in our library10.1364/opex.13.000689 (opens in a new tab)

20. 20.

    Foo G, Palacios DM, Swartzlander GA. Optical vortex coronagraph. Opt. Lett. 2005;30:3308-3310.

    Not in our library10.1364/ol.30.003308 (opens in a new tab)

21. 21.

    Heckenberg NR, McDuff R, Smith CP, White AG. Generation of optical phase singularities by computer-generated holograms. Opt. Lett. 1992;17:221-223.

    Not in our library10.1364/ol.17.000221 (opens in a new tab)

22. 22.

    Forbes A, Dudley A, McLaren M. Creation and detection of optical modes with spatial light modulators. Adv. Opt. Photonics. 2016;8:200-227.

    Not in our library10.1364/aop.8.000200 (opens in a new tab)

23. 23.

    Turnbull GA, Robertson DA, Smith GM, Allen L, Padgett MJ. The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate. Opt. Commun. 1996;127:183-188.

    Not in our library10.1016/0030-4018(96)00070-3 (opens in a new tab)

24. 24.

    Yan Y, et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing. Nat. Commun. 2014;5:4876.

    Not in our library10.1038/ncomms5876 (opens in a new tab)

25. 25.

    Peele AG, et al. Observation of an x-ray vortex. Opt. Lett. 2002;27:1752-1754.

    Not in our library10.1364/ol.27.001752 (opens in a new tab)

26. 26.

    Hefner BT, Marston PL. An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems. J. Acoust. Soc. Am. 1999;106:3313-3316.

    Not in our library10.1121/1.428184 (opens in a new tab)

27. 27.

    Grillo V, et al. Measuring the orbital angular momentum spectrum of an electron beam. Nat. Commun. 2017;8:15536.

    Not in our library10.1038/ncomms15536 (opens in a new tab)

28. 28.

    Clark CW, et al. Controlling neutron orbital angular momentum. Nature. 2015;525:504.

    Not in our library10.1038/nature15265 (opens in a new tab)

29. 29.

    Plick WN, Krenn M. Physical meaning of the radial index of Laguerre–Gauss beams. Phys. Rev. A. 2015;92:063841.

    Not in our library10.1103/physreva.92.063841 (opens in a new tab)

30. 30.

    Karimi E, Santamato E. Radial coherent and intelligent states of paraxial wave equation. Opt. Lett. 2012;37:2484-2486.

    Not in our library10.1364/ol.37.002484 (opens in a new tab)

31. 31.

    Karimi E, et al. Exploring the quantum nature of the radial degree of freedom of a photon via Hong–Ou–Mandel interference. Phys. Rev. A. 2014;89:013829.

    Not in our library10.1103/physreva.89.013829 (opens in a new tab)

32. 32.

    Leach J, et al. Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon. Phys. Rev. Lett. 2004;92:013601.

    Not in our library10.1103/physrevlett.92.013601 (opens in a new tab)

33. 33.

    Berkhout GCG, Lavery MPJ, Courtial J, Beijersbergen MW, Padgett MJ. Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett. 2010;105:153601.

    Not in our library10.1103/physrevlett.105.153601 (opens in a new tab)

34. 34.

    Mirhosseini M, Malik M, Shi Z, Boyd RW. Efficient separation of the orbital angular momentum eigenstates of light. Nat. Commun. 2013;4:2781.

    Not in our library10.1038/ncomms3781 (opens in a new tab)

35. 35.

    Zhou Y, et al. Sorting photons by radial quantum number. Phys. Rev. Lett. 2017;119:263602.

    Not in our library10.1103/physrevlett.119.263602 (opens in a new tab)

36. 36.

    Gu X, Krenn M, Erhard M, Zeilinger A. Gouy phase radial mode sorter for light: concepts and experiments. Phys. Rev. Lett. 2018;120:103601.

    Not in our library10.1103/physrevlett.120.103601 (opens in a new tab)

37. 37.

    Dudley A, et al. Efficient sorting of Bessel beams. Opt. Express. 2013;21:165-171.

    Not in our library10.1364/oe.21.000165 (opens in a new tab)

38. 38.

    Liu C, et al. Discrimination of orbital angular momentum modes of the terahertz vortex beam using a diffractive mode transformer. Opt. Express. 2016;24:12534-12541.

    Not in our library10.1364/oe.24.012534 (opens in a new tab)

39. 39.

    Morizur JF, et al. Programmable unitary spatial mode manipulation. J. Opt. Soc. Am. A. 2010;27:2524-2531.

    Not in our library10.1364/josaa.27.002524 (opens in a new tab)

40. 40.

    Fontaine, N. K. et al. Design of high order mode-multiplexers using multiplane light conversion. in Proc. European Conference on Optical Communication (ECOC) (2017).

    Not in our library

41. 41.

    Sakamaki Y, Saida T, Hashimoto T, Takahashi H. New optical waveguide design based on wavefront matching method. J. Light. Technol. 2007;25:3511-3518.

    Not in our library10.1109/jlt.2007.906798 (opens in a new tab)

42. 42.

    Piggott AY, et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nat. Photonics. 2015;9:374.

    Not in our library10.1038/nphoton.2015.69 (opens in a new tab)

43. 43.

    Hughes TW, Minkov M, Shi Y, Fan S. Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica. 2018;5:864-871.

    Not in our library10.1364/optica.5.000864 (opens in a new tab)

44. 44.
    Laguerre-Gaussian mode sorter · 2019

    No notice
45. 45.

    Yang G, Dong B, Gu B, Zhuang J, Ersoy OK. Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison. Appl. Opt. 1994;33:209-218.

    Not in our library10.1364/ao.33.000209 (opens in a new tab)

46. 46.

    Goodman JW, Lawrence RW. Digital image formation from electronically detected holograms. Appl. Phys. Lett. 1967;11:77-79.

    Not in our library10.1063/1.1755043 (opens in a new tab)

47. 47.

    Carpenter, J., Eggleton, B. J. & Schröder, J. Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre. Nat. Photonics9, 751–757 (2015).

    Not in our library

48. 48.

    Fontaine, N. K. et al. Characterization of space-division multiplexing systems using a swept-wavelength interferometer. in Proc. Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013 OW1K.2 (Optical Society of America, 2013). 10.1364/OFC.2013.OW1K.2.

    Not in our library

49. 49.

    Carpenter J, Eggleton BJ, Schröder J. Complete spatiotemporal characterization and optical transfer matrix inversion of a 420 mode fiber. Opt. Lett. 2016;41:5580-5583.

    Not in our library10.1364/ol.41.005580 (opens in a new tab)

50. 50.

    Carpenter J, Eggleton BJ, Schröder J. Comparison of principal modes and spatial eigenmodes in multimode optical fibre. Laser Photonics Rev. 2016;11:1600259.

    Not in our library10.1002/lpor.201600259 (opens in a new tab)

51. 51.
    Laguerre-Gaussian mode sorter · 2019

    No notice
52. 52.

    Lu T, Pivnenko M, Robertson B, Chu D. Pixel-level fringing-effect model to describe the phase profile and diffraction efficiency of a liquid crystal on silicon device. Appl. Opt. 2015;54:5903-5910.

    Not in our library10.1364/ao.54.005903 (opens in a new tab)

Cited by papers we hold 2

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