Abstract

Ring-core optical fibers have been designed to carry orbital angular momentum modes. We demonstrate the imaging of these modes, individually identifying modes separated temporally by only 30 ps. A single-pixel camera operating in the short-wave infrared detection range is used to image the 1550 nm wavelength optical modes. With this technique, examination of these optical modes can be performed with significantly higher temporal resolution than is possible with conventional imaging systems, such that the imaging of modes separated by spin-orbit coupling is achieved and evaluated. Deconvolution is required to separate the instrument response from the optical mode signal, increasing the clarity and temporal resolution of the measurement system.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. A. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).
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    [Crossref]

2019 (3)

C. P. Bradley, S. S. Mukherjee, A. D. Reinhardt, P. F. McManamon, A. O. Lee, and V. Dhulla, “3D imaging with $128\times 128$128×128 eye safe InGaAs p-i-n lidar camera,” Proc. SPIE 11005, 1100510 (2019).
[Crossref]

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

S. D. Johnson, D. B. Phillips, Z. Ma, S. Ramachandran, and M. J. Padgett, “A light-in-flight single-pixel camera for use in the visible and short-wave infrared,” Opt. Express 27(7), 9829–9837 (2019).
[Crossref]

2018 (2)

2017 (1)

D. L. P. Vitullo, C. C. Leary, P. Gregg, R. A. Smith, D. V. Reddy, S. Ramachandran, and M. G. Raymer, “Observation of interaction of spin and intrinsic orbital angular momentum of light,” Phys. Rev. Lett. 118(8), 083601 (2017).
[Crossref]

2016 (1)

2015 (4)

2014 (1)

2013 (2)

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5-6), 455–474 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

2012 (1)

R.-J. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

2011 (1)

2009 (2)

S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett. 34(16), 2525–2527 (2009).
[Crossref]

C. C. Leary, M. G. Raymer, and S. J. van Enk, “Spin and orbital rotation of electrons and photons via spin-orbit interaction,” Phys. Rev. A 80(6), 061804 (2009).
[Crossref]

2008 (1)

2005 (1)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

1969 (1)

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57(1), 58–68 (1969).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Altmann, Y.

Andrews, H. C.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57(1), 58–68 (1969).
[Crossref]

Barankov, R. A.

Barré, N.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Bradley, C. P.

C. P. Bradley, S. S. Mukherjee, A. D. Reinhardt, P. F. McManamon, A. O. Lee, and V. Dhulla, “3D imaging with $128\times 128$128×128 eye safe InGaAs p-i-n lidar camera,” Proc. SPIE 11005, 1100510 (2019).
[Crossref]

Bramerie, L.

Buller, G. S.

X. Ren, P. W. R. Connolly, A. Halimi, Y. Altmann, S. McLaughlin, I. Gyongy, R. K. Henderson, and G. S. Buller, “High-resolution depth profiling using a range-gated CMOS SPAD quanta image sensor,” Opt. Express 26(5), 5541–5557 (2018).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Chen, H.

Connolly, P. W. R.

Demas, J.

Denolle, B.

Dhulla, V.

C. P. Bradley, S. S. Mukherjee, A. D. Reinhardt, P. F. McManamon, A. O. Lee, and V. Dhulla, “3D imaging with $128\times 128$128×128 eye safe InGaAs p-i-n lidar camera,” Proc. SPIE 11005, 1100510 (2019).
[Crossref]

Dimarcello, F. V.

Edgar, M. P.

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

Esmaeelpour, M.

Essiambre, R.-J.

R.-J. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

Faccio, D.

D. Faccio and A. Velten, “A trillion frames per second: the techniques and applications of light-in-flight photography,” Rep. Prog. Phys. 81(10), 105901 (2018).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Fleming, J.

Fontaine, N. K.

Gariepy, G.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Ghalmi, S.

Gibson, G. M.

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

Gnauck, A. H.

Golowich, S.

Golowich, S. E.

Gregg, P.

Guan, B.

Gyongy, I.

Halimi, A.

Henderson, R.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Henderson, R. K.

Heshmat, B.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Huang, B.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Insou, X.

Jian, P.

Johnson, S. D.

Kane, J.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57(1), 58–68 (1969).
[Crossref]

Koonen, A.

Kristensen, P.

Krstajic, N.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Labroille, G.

Leach, J.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Leary, C. C.

D. L. P. Vitullo, C. C. Leary, P. Gregg, R. A. Smith, D. V. Reddy, S. Ramachandran, and M. G. Raymer, “Observation of interaction of spin and intrinsic orbital angular momentum of light,” Phys. Rev. Lett. 118(8), 083601 (2017).
[Crossref]

C. C. Leary, M. G. Raymer, and S. J. van Enk, “Spin and orbital rotation of electrons and photons via spin-orbit interaction,” Phys. Rev. A 80(6), 061804 (2009).
[Crossref]

Lee, A. O.

C. P. Bradley, S. S. Mukherjee, A. D. Reinhardt, P. F. McManamon, A. O. Lee, and V. Dhulla, “3D imaging with $128\times 128$128×128 eye safe InGaAs p-i-n lidar camera,” Proc. SPIE 11005, 1100510 (2019).
[Crossref]

Lenglé, K.

Li, C.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Lingle, R.

Love, J.

A. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

Ma, Z.

McLaughlin, S.

McManamon, P. F.

C. P. Bradley, S. S. Mukherjee, A. D. Reinhardt, P. F. McManamon, A. O. Lee, and V. Dhulla, “3D imaging with $128\times 128$128×128 eye safe InGaAs p-i-n lidar camera,” Proc. SPIE 11005, 1100510 (2019).
[Crossref]

Monberg, E.

Mukherjee, S. S.

C. P. Bradley, S. S. Mukherjee, A. D. Reinhardt, P. F. McManamon, A. O. Lee, and V. Dhulla, “3D imaging with $128\times 128$128×128 eye safe InGaAs p-i-n lidar camera,” Proc. SPIE 11005, 1100510 (2019).
[Crossref]

Nicholson, J. W.

Padgett, M. J.

Phillips, D. B.

Pratt, W. K.

W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard transform image coding,” Proc. IEEE 57(1), 58–68 (1969).
[Crossref]

Ramachandran, S.

S. D. Johnson, D. B. Phillips, Z. Ma, S. Ramachandran, and M. J. Padgett, “A light-in-flight single-pixel camera for use in the visible and short-wave infrared,” Opt. Express 27(7), 9829–9837 (2019).
[Crossref]

D. L. P. Vitullo, C. C. Leary, P. Gregg, R. A. Smith, D. V. Reddy, S. Ramachandran, and M. G. Raymer, “Observation of interaction of spin and intrinsic orbital angular momentum of light,” Phys. Rev. Lett. 118(8), 083601 (2017).
[Crossref]

P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air-core optical fibers,” Optica 2(3), 267–270 (2015).
[Crossref]

S. Ramachandran, P. Gregg, P. Kristensen, and S. E. Golowich, “On the scalability of ring fiber designs for OAM multiplexing,” Opt. Express 23(3), 3721–3730 (2015).
[Crossref]

J. Demas and S. Ramachandran, “Sub-second mode measurement of fibers using C2 imaging,” Opt. Express 22(19), 23043–23056 (2014).
[Crossref]

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5-6), 455–474 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

D. N. Schimpf, R. A. Barankov, and S. Ramachandran, “Cross-correlated (C2) imaging of fiber and waveguide modes,” Opt. Express 19(14), 13008–13019 (2011).
[Crossref]

S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett. 34(16), 2525–2527 (2009).
[Crossref]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16(10), 7233–7243 (2008).
[Crossref]

S. Ramachandran, S. Golowich, M. F. Yan, E. Monberg, F. V. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting polarization degeneracy of modes by fiber design: a platform for polarization-insensitive microbend fiber gratings,” Opt. Lett. 30(21), 2864–2866 (2005).
[Crossref]

Randel, S.

Raskar, R.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Raymer, M. G.

D. L. P. Vitullo, C. C. Leary, P. Gregg, R. A. Smith, D. V. Reddy, S. Ramachandran, and M. G. Raymer, “Observation of interaction of spin and intrinsic orbital angular momentum of light,” Phys. Rev. Lett. 118(8), 083601 (2017).
[Crossref]

C. C. Leary, M. G. Raymer, and S. J. van Enk, “Spin and orbital rotation of electrons and photons via spin-orbit interaction,” Phys. Rev. A 80(6), 061804 (2009).
[Crossref]

Reddy, D. V.

D. L. P. Vitullo, C. C. Leary, P. Gregg, R. A. Smith, D. V. Reddy, S. Ramachandran, and M. G. Raymer, “Observation of interaction of spin and intrinsic orbital angular momentum of light,” Phys. Rev. Lett. 118(8), 083601 (2017).
[Crossref]

Reinhardt, A. D.

C. P. Bradley, S. S. Mukherjee, A. D. Reinhardt, P. F. McManamon, A. O. Lee, and V. Dhulla, “3D imaging with $128\times 128$128×128 eye safe InGaAs p-i-n lidar camera,” Proc. SPIE 11005, 1100510 (2019).
[Crossref]

Ren, X.

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Ryf, R.

Schimpf, D. N.

Shubochkin, R.

Smith, R. A.

D. L. P. Vitullo, C. C. Leary, P. Gregg, R. A. Smith, D. V. Reddy, S. Ramachandran, and M. G. Raymer, “Observation of interaction of spin and intrinsic orbital angular momentum of light,” Phys. Rev. Lett. 118(8), 083601 (2017).
[Crossref]

Snyder, A.

A. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Sun, Y.

Thomson, R. R.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Tkach, R. W.

R.-J. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012).
[Crossref]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

van Enk, S. J.

C. C. Leary, M. G. Raymer, and S. J. van Enk, “Spin and orbital rotation of electrons and photons via spin-orbit interaction,” Phys. Rev. A 80(6), 061804 (2009).
[Crossref]

Velten, A.

D. Faccio and A. Velten, “A trillion frames per second: the techniques and applications of light-in-flight photography,” Rep. Prog. Phys. 81(10), 105901 (2018).
[Crossref]

Vitullo, D. L. P.

D. L. P. Vitullo, C. C. Leary, P. Gregg, R. A. Smith, D. V. Reddy, S. Ramachandran, and M. G. Raymer, “Observation of interaction of spin and intrinsic orbital angular momentum of light,” Phys. Rev. Lett. 118(8), 083601 (2017).
[Crossref]

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Wisk, P.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Yablon, A. D.

Yan, M. F.

Yoo, S.

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref]

Nanophotonics (1)

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5-6), 455–474 (2013).
[Crossref]

Nat. Commun. (1)

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6(1), 6021 (2015).
[Crossref]

Nat. Photonics (1)

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

Opt. Express (8)

S. D. Johnson, D. B. Phillips, Z. Ma, S. Ramachandran, and M. J. Padgett, “A light-in-flight single-pixel camera for use in the visible and short-wave infrared,” Opt. Express 27(7), 9829–9837 (2019).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. The layout of the optical fiber and single-pixel camera. The pulsed laser is incident on a spatial light modulator (SLM) to precisely adjust the coupling into the optical fiber. The light is coupled into and travels through the ring-core fiber, and the collimated output is incident on a digital micromirror device (DMD). The signal reflected by each mask displayed on the DMD is measured by a fiber-coupled high-speed photodetector via a multimode fiber (MMF). The signal is measured by an oscilloscope triggered from the laser; data is transferred to the PC for analysis.
Fig. 2.
Fig. 2. Example of the deconvolution process. Using the data set presented later in Fig. 3c) an example of the deconvolution is shown. The raw data (a) is deconvolved with the measured impulse response (b), producing the resulting signal (c). The signal is then Gaussian smoothed to produce the final signal (d).
Fig. 3.
Fig. 3. Measurement of the optical modes. Each data set is shown with the total signal measured over time and the modes present for the peaks indicated by the arrows. (a) shows the full measurement of all present modes. The modes associated with single OAM are shown below the time series (modes $L=\pm 1$ to $L=\pm 7$), other modes are shown above. The image (b) is the summed signal for all time bins, showing similar signal to (c), an image recorded by a Goldeye P-008 SWIR camera with an InGaAs sensor. (d) shows the first modes where there is strong coupling between the fundamental Gaussian and SOa$_{0,1}$ and SOaa$_{0,1}$ modes. (e) shows the SOa$_{3,2}$/SOaa$_{3,2}$ and SOa$_{4,1}$/SOaa$_{4,1}$ modes. The interference of the $+L$ and $-L$ modes produce the petal pattern as shown in the image.
Fig. 4.
Fig. 4. Dependence on the relative arrival times on the mode order $L$. Through the analysis of the propagation times measured in Fig. 3a) for the modes $L=\pm 4$ to $L=\pm 7$, where the time delay between the SOa and SOaa modes is larger than the temporal resolution of our experiment, the relation between the time delay difference and the square of the mode order $L$ is shown to be linear.

Equations (3)

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I2D(t)=i=1NM(t)iHi,
δβ=Lka2nco20|E(r)|2Δn(r)rdr
δng=cdδβdω=c2Lω2a2nco2(0|E(r)|2Δn(r)rdrωddω0|E(r)|2Δn(r)rdr)