Abstract

Modulating the amplitude and phase of light is at the heart of many applications such as wavefront shaping1, transformation optics2,3, phased arrays4, modulators5 and sensors6. Performing this task with high efficiency and small footprint is a formidable challenge7,8. Metasurfaces5,9 and plasmonics10 are promising, but metals exhibit weak electro-optic effects. Two-dimensional materials, such as graphene, have shown great performance as modulators with small drive voltages11,12. Here, we show a graphene plasmonic phase modulator that is capable of tuning the phase between 0 and 2π in situ. The device length of 350 nm is more than 30 times shorter than the 10.6 μm free-space wavelength. The modulation is achieved by spatially controlling the plasmon phase velocity in a device where the spatial carrier density profile is tunable. We provide a scattering theory for plasmons propagating through spatial density profiles. This work constitutes a first step towards two-dimensional transformation optics3 for ultracompact modulators7 and biosensing13.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from $8.99

All prices are NET prices.

References

  1. 1.

    Laser Beam Shaping: Theory and Techniques (CRC, 2014).

  2. 2.

    , & Controlling electromagnetic fields. Science 312, 1780–1782 (2006).

  3. 3.

    & Transformation optics using graphene. Science 332, 1291–1294 (2011).

  4. 4.

    , , , & Large-scale nanophotonic phased array. Nature 493, 195–199 (2013).

  5. 5.

    & Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).

  6. 6.

    , & Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J. Opt. Soc. Am. 72, 156–160 (1982).

  7. 7.

    , , & Silicon optical modulators. Nat. Photon. 4, 518–526 (2010).

  8. 8.

    , , & Review and perspective on ultrafast wavelength-size electro-optic modulators. Laser Photon. Rev. 9, 172–194 (2015).

  9. 9.

    , & Planar photonics with metasurfaces. Science 339, 1232009 (2013).

  10. 10.

    , , & PlasMOStor: a metal-oxide-Si field effect plasmonic modulator. Nano Lett. 9, 897–902 (2009).

  11. 11.

    et al. Experimental verification of electro-refractive phase modulation in graphene. Sci. Rep. 5, 10967 (2015).

  12. 12.

    , & Optical modulators with 2D layered materials. Nat. Photon. 10, 227–238 (2016).

  13. 13.

    et al. Mid-infrared plasmonic biosensing with graphene. Science 349, 165–168 (2015).

  14. 14.

    et al. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 487, 82–85 (2012).

  15. 15.

    et al. Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012).

  16. 16.

    et al. Highly confined low-loss plasmons in graphene–boron nitride heterostructures. Nat. Mater. 14, 421–425 (2015).

  17. 17.

    , , & Graphene plasmonic lens for manipulating energy flow. Sci. Rep. 4, 1–7 (2014).

  18. 18.

    et al. Electronic and plasmonic phenomena at graphene grain boundaries. Nat. Nanotech. 8, 821–825 (2013).

  19. 19.

    et al. Strong plasmon reflection at nanometer-size gaps in monolayer graphene on SiC. Nano Lett. 13, 6210–6215 (2013).

  20. 20.

    et al. Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns. Science 344, 1369–1373 (2014).

  21. 21.

    , , , & Direct measurement of optical phase in the near field. Appl. Phys. Lett. 76, 541–543 (2000).

  22. 22.

    , , & Local observations of phase singularities in optical fields in waveguide structures. Phys. Rev. Lett. 85, 294–297 (2000).

  23. 23.

    et al. Plasmonic metasurfaces to steer infrared light. Sci. Rep. 5, 12423 (2015).

  24. 24.

    et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

  25. 25.

    , , & Near-field imaging of mid-infrared surface phonon polariton propagation. Appl. Phys. Lett. 87, 16–18 (2005).

  26. 26.

    & Principles of Optics (Cambridge Univ. Press, 1999).

  27. 27.

    Theory of carrier density in multigated doped graphene sheets with quantum correction. Phys. Rev. B 87, 125427 (2013).

  28. 28.

    et al. Plasmons and the spectral function of graphene. Phys. Rev. B 77, 081411 (2008).

  29. 29.

    , , , & Lippmann-Schwinger theory for two-dimensional plasmon scattering. Preprint at (2017).

  30. 30.

    , & Scattering of graphene plasmons by defects in the graphene sheet. ACS Nano 7, 4988–4994 (2013).

  31. 31.

    et al. All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale. Nat. Photon. 9, 525–528 (2015).

  32. 32.

    , , & Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator. Opt. Express 15, 17106–17113 (2007).

  33. 33.

    et al. Large optical spectral range dispersion engineered silicon-based photonic crystal waveguide modulator. Opt. Express 20, 12318–12325 (2012).

  34. 34.

    et al. Experimental demonstration of graphene plasmons working close to the near-infrared window. Opt. Lett. 41, 5345–5348 (2016).

  35. 35.

    & Graphene-based plasmonic switches at near infrared frequencies. Opt. Express 21, 15490–15504 (2013).

Download references

Acknowledgements

We thank A. J. Huber, K.-J. Tielrooij, I. Epstein and W. Heni for fruitful discussions, and D. Davydovskaya and G. Navickaite for assistance in the clean room. Open source software was used (www.matplotlib.org, www.python.org, www.inkscape.org). F.H.L.K. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522), support by Fundacio Cellex Barcelona, the ERC starting grant (307806, CarbonLight), the Government of Catalonia through the SGR grant (2014-SGR-1535), the Mineco grants Ramón y Cajal (RYC-2012-12281) and Plan Nacional (FIS2013-47161-P), and project GRASP (FP7-ICT-2013-613024-GRASP). F.H.L.K. and R.H. acknowledge support by the EC under Graphene Flagship (contract no. CNECT-ICT-696656). Y.G. and J.H. acknowledge support from the US Office of Naval Research N00014-13-1-0662. M.P. is extremely grateful for the financial support granted by the ICFO during a visit in August 2016 and acknowledges Fondazione Istituto Italiano di Tecnologia. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and JSPS KAKENHI grant numbers JP26248061, JP15K21722 and JP25106006.

Author information

Author notes

    • Achim Woessner
    •  & Yuanda Gao

    These authors contributed equally to this work.

Affiliations

  1. ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

    • Achim Woessner
    • , Mark B. Lundeberg
    •  & Frank H. L. Koppens
  2. Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA

    • Yuanda Gao
    • , Cheng Tan
    •  & James Hone
  3. NEST, Scuola Normale Superiore, I-56126 Pisa, Italy

    • Iacopo Torre
  4. Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy

    • Iacopo Torre
    •  & Marco Polini
  5. National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

    • Kenji Watanabe
    •  & Takashi Taniguchi
  6. CIC nanoGUNE and UPV/EHU, 20018 Donostia-San Sebastian, Spain

    • Rainer Hillenbrand
  7. IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain

    • Rainer Hillenbrand
  8. ICREA – Institució Catalana de Recerça i Estudis Avancats, 08010 Barcelona, Spain

    • Frank H. L. Koppens

Authors

  1. Search for Achim Woessner in:

  2. Search for Yuanda Gao in:

  3. Search for Iacopo Torre in:

  4. Search for Mark B. Lundeberg in:

  5. Search for Cheng Tan in:

  6. Search for Kenji Watanabe in:

  7. Search for Takashi Taniguchi in:

  8. Search for Rainer Hillenbrand in:

  9. Search for James Hone in:

  10. Search for Marco Polini in:

  11. Search for Frank H. L. Koppens in:

Contributions

A.W., M.B.L. and F.H.L.K. conceived the experiment. A.W. performed the experiments and simulations, analysed the data and wrote the manuscript. Y.G. and C.T. fabricated the devices. I.T. and M.P. developed the LS-RPA. M.B.L. helped with simulations and data analysis. K.W. and T.T. synthesized the h-BN. R.H., J.H. and F.H.L.K. supervised the work. All authors contributed to the scientific discussion and manuscript revisions.

Competing interests

R.H. is co-founder of Neaspec GmbH, a company producing scattering-type scanning near-field optical microscope systems such as the ones used in this study. All other authors declare no competing financial interests.

Corresponding author

Correspondence to Frank H. L. Koppens.

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphoton.2017.98