Control of semiconductor emitter frequency by increasing polariton momenta

A Publisher Correction to this article was published on 16 July 2018

This article has been updated


Light emission and absorption is fundamentally a joint property of both an emitter and its optical environment. Nevertheless, because of the much smaller momenta of photons compared with electrons at similar energies, the optical environment typically modifies only the emission/absorption rates, leaving the emitter transition frequencies practically an intrinsic property. We show here that surface polaritons, exemplified by graphene plasmons, but also valid for other types of polariton, enable substantial and tunable control of the transition frequencies of a nearby quantum well, demonstrating a sharp break with the emitter-centric view. Central to this result is the large momenta of surface polaritons that can approach the momenta of electrons and impart a pronounced non-local behaviour to the quantum well. This work facilitates non-vertical optical transitions in solids and empowers ongoing efforts to access such transitions in indirect-bandgap materials, such as silicon, as well as enriching the study of non-locality in photonics.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Illustration of the coupling of graphene plasmon polaritons to a quantum well.
Fig. 2: Control of the emission and absorption frequencies of a quantum well by tuning the graphene Fermi energy.
Fig. 3: Confinement factor effect on plasmonic transitions.
Fig. 4: Doppler effect in plasmonic transitions.

Change history

  • 16 July 2018

    In the version of this Article originally published, there were errors in equations (1), (3b) and (6), as well as in the equation in the sentence beginning “The results presented are normalized to yield...”, in addition, equation (5) wasn’t numbered as such; the details are shown in the correction notice. These errors have now been corrected online.


  1. 1.

    Yariv, A. Quantum Electronics 3rd edn (Wiley, New York, NY, 1989).

  2. 2.

    Schubert, E. F. Light Emitting Diodes (Cambridge Univ. Press, Cambridge, 2006).

  3. 3.

    Theuwissen, A. J. P. Solid-State Imaging with Charge-Coupled Devices Vol. 1 (Kluwer Academic, Boston, MA, 1995).

  4. 4.

    Green, M. A. Solar Cells: Operating Principles, Technology and System Applications (Univ. New South Wales, Sydney, 1998).

  5. 5.

    Purcell, E. M. Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681–681 (1946).

    Article  Google Scholar 

  6. 6.

    Kleppner, D. Inhibited spontaneous emission. Phys. Rev. Lett. 47, 233–236 (1981).

    Article  ADS  Google Scholar 

  7. 7.

    Pelton, M. Modified spontaneous emission in nanophotonic structures. Nat. Photon. 9, 427–435 (2015).

    Article  ADS  Google Scholar 

  8. 8.

    Vats, N., John, S. & Busch, K. Theory of fluorescence in photonic crystals. Phys. Rev. A 65, 043808 (2002).

    Article  ADS  Google Scholar 

  9. 9.

    Neogi, A. et al. Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling. Phys. Rev. B 66, 153305 (2002).

    Article  ADS  Google Scholar 

  10. 10.

    Lamb, W. E. & Retherford, R. C. Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72, 241–243 (1947).

    Article  ADS  Google Scholar 

  11. 11.

    Bethe, H. A. The electromagnetic shift of energy levels. Phys. Rev. 72, 339 (1947).

    Article  MATH  ADS  Google Scholar 

  12. 12.

    Wylie, J. M. & Sipe, J. E. Quantum electrodynamics near an interface. Phys. Rev. A 30, 1185–1193 (1984).

    Article  ADS  Google Scholar 

  13. 13.

    Khitrova, G., Gibbs, H. M., Kira, M. S., Koch, W. & Scherer, A. Vacuum Rabi splitting in semiconductors. Nat. Phys. 2, 81–90 (2006).

    Article  Google Scholar 

  14. 14.

    Zhang, Y. et al. Sub-nanometre control of the coherent interaction between a single molecule and a plasmonic nanocavity. Nat. Commun. 8, 15225 (2017).

    Article  ADS  Google Scholar 

  15. 15.

    Chang, C. H., Rivera, N., Joannopoulos, J. D., Soljačić, M. & Kaminer, I. Constructing ‘designer atoms’ via resonant graphene-induced lamb shifts. ACS Photon. 4, 3098–3105 (2017).

    Article  Google Scholar 

  16. 16.

    Cohen-Tannoudji, C., Dupont-Roc, J. & Grynberg, G. Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, New York, NY, 1989).

  17. 17.

    Scholl, J. A., Koh, A. L. & Dionne, J. A. Quantum plasmon resonances of individual metallic nanoparticles. Nature 483, 421–427 (2012).

    Article  ADS  Google Scholar 

  18. 18.

    Raza, S. et al. Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS. Nanophotonics 2, 131–138 (2013).

    Article  ADS  Google Scholar 

  19. 19.

    Jin, D. et al. Quantum-spillover-enhanced surface-plasmonic absorption at the interface of silver and high-index dielectrics. Phys. Rev. Lett. 115, 193901 (2015).

    Article  ADS  Google Scholar 

  20. 20.

    Raza, S. et al. Multipole plasmons and their disappearance in few-nanometre silver nanoparticles. Nat. Commun. 6, 8788 (2015).

    Article  Google Scholar 

  21. 21.

    Raza, S., Bozhevolnyi, S. I., Wubs, M. & Mortensen, N. A. Nonlocal optical response in metallic nanostructures. J. Phys. Condens. Matter 27, 183204 (2014).

    Article  ADS  Google Scholar 

  22. 22.

    Christensen, T. From Classical to Quantum Plasmonics in Three and Two Dimensions (Springer, New York, NY, 2017).

  23. 23.

    Varas, A., Garcia-Gonzalez, P., Feist, J., Garcia-Vidal, F. J. & Rubio, A. Quantum plasmonics: from jellium models to ab initio calculations. Nanophotonics 5, 409–426 (2016).

    Article  Google Scholar 

  24. 24.

    Zhu, W. et al. Quantum mechanical effects in plasmonic structures with subnanometre gaps. Nat. Commun. 7, 11495 (2016).

    Article  ADS  Google Scholar 

  25. 25.

    Fitzgerald, J. M., Narang, P., Craster, R. V., Maier, S. A. & Giannini, V. Quantum plasmonics. Proc. IEEE 104, 2307–2322 (2016).

    Article  Google Scholar 

  26. 26.

    Lundeberg, M. et al. Turning quantum non-local effects in graphene plasmonics. Science 357, 187–191 (2017).

    Article  ADS  Google Scholar 

  27. 27.

    Ginzburg, P. et al. Spontaneous emission in non-local materials. Light Sci. Appl. 6, e16273 (2017).

    Article  Google Scholar 

  28. 28.

    Garcia de Abajo, F. J. Graphene plasmonics: challenges and opportunities. ACS Photon. 1, 135–152 (2014).

    Article  Google Scholar 

  29. 29.

    Jablan, M., Buljan, H. & Soljacic, M. Plasmonics in graphene at infrared frequencies. Phys. Rev. B 80, 245435 (2009).

    Article  ADS  Google Scholar 

  30. 30.

    Jablan, M., Soljacic, M. & Buljan, H. Plasmons in graphene: fundamental properties and potential applications. Proc. IEEE 101, 1689–1704 (2013).

    Article  Google Scholar 

  31. 31.

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

    Article  ADS  Google Scholar 

  32. 32.

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

    Article  ADS  Google Scholar 

  33. 33.

    Woessner, A. et al. Highly confined low-loss plasmons in graphene–boron nitride heterostructures. Nat. Mater. 14, 421–425 (2014).

    Article  ADS  Google Scholar 

  34. 34.

    Rivera, N., Kaminer, I., Zhen, B., Joannopoulos, J. D. & Soljačić, M. Shrinking light to allow forbidden transitions on the atomic scale. Science 353, 263–269 (2016).

    MathSciNet  Article  MATH  ADS  Google Scholar 

  35. 35.

    Hillenbrand, R., Taubner, T. & Keilmann, F. Phonon-enhanced light–matter interaction at the nanometre scale. Nature 418, 159–162 (2002).

    Article  ADS  Google Scholar 

  36. 36.

    Taubner, T., Korobkin, D., Urzhumov, Y., Shvets, G. & Hillenbrand, R. Near-field microscopy through a SiC superlens. Science 313, 1595 (2006).

    Article  Google Scholar 

  37. 37.

    Dai, S. et al. Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride. Science 343, 1125–1129 (2014).

    Article  ADS  Google Scholar 

  38. 38.

    Basov, D. N., Fogler, M. M. & Garcia de Abajo, F. J. Polaritons in van der Waals materials. Science 354, aag1992 (2016).

    Article  Google Scholar 

  39. 39.

    Low, T. et al. Polaritons in layered two-dimensional materials. Nat. Mater. 16, 182–194 (2017).

    Article  ADS  Google Scholar 

  40. 40.

    Lin, X. et al. All-angle negative refraction of highly squeezed plasmon and phonon polaritons in graphene–boron nitride heterostructures. Proc. Natl Acad. Sci. USA 114, 6717–6721 (2017).

    ADS  Google Scholar 

  41. 41.

    Thongrattanasiri, S., Koppens, F. H. L. & Garcia de Abajo, F. J. Complete optical absorption in periodically patterned graphene. Phys. Rev. Lett. 108, 047401 (2012).

    Article  ADS  Google Scholar 

  42. 42.

    Brar, V. W., Jang, M. S., Sherrott, M., Lopez, J. J. & Atwater, H. A. Highly confined tunable mid-infrared plasmonics in graphene nanoresonators. Nano Lett. 13, 2541–2547 (2013).

    Article  ADS  Google Scholar 

  43. 43.

    Coldren, L. A. & Corzine, S. W. Diode Lasers and Photonic Integrated Circuits (Wiley, New York, NY, 2012).

  44. 44.

    Griffiths, D. Introduction to Quantum Mechanics (Pearson Prentice Hall, Upper Saddle River, NJ, 1995).

  45. 45.

    Glauber, R. J. & Lewenstein, M. Quantum optics of dielectric media. Phys. Rev. A 43, 467–491 (1991).

    Article  ADS  Google Scholar 

  46. 46.

    Scheel, S. & Buhmann, S. Y. Macroscopic QED—concepts and applications. Acta Phys. Slov. 58, 675–809 (2008).

    ADS  Google Scholar 

  47. 47.

    Bitan, G. Energy Distribution of Single and Two Photon Emitters in Plasmonic Environments. MSc thesis, Technion IIT Department of Electrical Engineering (2014).

  48. 48.

    Kaminer, I. et al. Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene. Nat. Commun. 7, 11880 (2016).

    Article  ADS  Google Scholar 

  49. 49.

    Koppens, F. H. L., Chang, D. E. & Garcia de Abajo, F. J. Graphene plasmonics: a platform for strong light–matter interactions. Nano Lett. 11, 3370–3377 (2011).

    Article  ADS  Google Scholar 

  50. 50.

    Rivera, N., Rosolen, G., Joannopoulos, J. D., Kaminer, I. & Soljačić, M. Making two-photon processes dominate one-photon processes using mid-IR phonon polaritons. Proc. Natl Acad. Sci. USA 114, 13607 (2017).

    Article  ADS  Google Scholar 

  51. 51.

    Landau, L. D., Lifshitz, E. M. & Pitaevskii, L. P. Electrodynamics of Continuous Media Vol. 8 (Elsevier, New York, NY, 2008).

  52. 52.

    Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotech. 7, 699–712 (2012).

    Article  ADS  Google Scholar 

  53. 53.

    McGill, T. C. & Collins, D. A. Prospects for the future of narrow bandgap materials. Semicond. Sci. Technol. 8, S1 (1993).

    Article  ADS  Google Scholar 

  54. 54.

    Sloan, J., Rivera, N., Soljačić, M. & Kaminer, I. Tunable UV-emitters through graphene plasmonics. Nano Lett. 18, 308–313 (2017).

    Article  ADS  Google Scholar 

  55. 55.

    Törmä, P. & Barnes, W. L. Strong coupling between surface plasmon polaritons and emitters: a review. Rep. Prog. Phys. 78, 013901 (2014).

    Article  Google Scholar 

  56. 56.

    Jung, J. et al. Dyadic Green’s functions of thin films: applications within plasmonic solar cells. Phys. Rev. B 83, 085419 (2011).

    Article  ADS  Google Scholar 

  57. 57.

    Trolle, M. L. & Pedersen, T. G. Indirect optical absorption in silicon via thin-film surface plasmon. J. Appl. Phys. 112, 043103 (2012).

    Article  ADS  Google Scholar 

  58. 58.

    Tongay, S. et al. Thermally driven crossover from indirect toward direct bandgap in 2D semiconductors: MoSe2 versus MoS2. Nano Lett. 12, 5576–5580 (2012).

    Article  ADS  Google Scholar 

  59. 59.

    Zhang, Y. et al. Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2. Nat. Nanotech. 9, 111–115 (2014).

    Article  ADS  Google Scholar 

  60. 60.

    Malý, P. et al. Picosecond and millisecond dynamics of photoexcited carriers in porous silicon. Phys. Rev. B 54, 7929–7936 (1996).

    Article  ADS  Google Scholar 

  61. 61.

    Tan, Y. W. et al. Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 99, 246803 (2007).

    Article  ADS  Google Scholar 

Download references


The authors thank M. Hoffman for the illustration in Fig. 1a and R. Tenne for his advice. The research of J.D.J. and M.S. was supported as part of the Army Research Office through the Institute for Soldier Nanotechnologies under contract no. W911NF-18-2-0048 (photon management for developing nuclear-TPV and fuel-TPV mm-scale-systems), and also supported as part of the S3TEC, an Energy Frontier Research Center funded by the US Department of Energy under grant no. DE-SC0001299 (for fundamental photon transport related to solar TPVs and solar-TEs). The research of M.O. was supported by the the Israeli ICore Excellence Center ‘Circle of Light’. N.R. was supported by Department of Energy Fellowship DE-FG02-97ER25308. T.C. acknowledges support from the Danish Council for Independent Research (grant no. DFF–6108-00667). I.K. was supported by the Azrieli foundation as an Azrieli Fellow, and was partially supported by the Seventh Framework Programme of the European Research Council (FP7-Marie Curie IOF) under grant no. 328853-MC-BSiCS.

Author information




All authors made significant contributions to writing the manuscript.

Corresponding authors

Correspondence to Yaniv Kurman or Ido Kaminer.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary discussion, derivations and data; Supplementary Figures 1–9; Supplementary References 1–12.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kurman, Y., Rivera, N., Christensen, T. et al. Control of semiconductor emitter frequency by increasing polariton momenta. Nature Photon 12, 423–429 (2018).

Download citation

Further reading


Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing