Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Deep-subwavelength imaging of the modal dispersion of light

Abstract

Numerous optical technologies and quantum optical devices rely on the controlled coupling of a local emitter to its photonic environment, which is governed by the local density of optical states (LDOS). Although precise knowledge of the LDOS is crucial, classical optical techniques fail to measure it in all of its frequency and spatial components. Here, we use a scanning electron beam as a point source to probe the LDOS. Through angular and spectral detection of the electron-induced light emission, we spatially and spectrally resolve the light wave vector and determine the LDOS of Bloch modes in a photonic crystal membrane at an unprecedented deep-subwavelength resolution (30–40 nm) over a large spectral range. We present a first look inside photonic crystal cavities revealing subwavelength details of the resonant modes. Our results provide direct guidelines for the optimum location of emitters to control their emission, and key fundamental insights into light–matter coupling at the nanoscale.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: High-resolution LDOS mapping on two-dimensional photonic crystals.
Figure 2: Momentum spectroscopy of a two-dimensional photonic crystal.
Figure 3: LDOS maps and momentum spectrum of a H1 photonic crystal cavity.
Figure 4: Mapping multiple cavity modes of an L3 photonic crystal cavity.
Figure 5: Resolution assessment.

Similar content being viewed by others

References

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

  2. John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).

    Article  CAS  Google Scholar 

  3. Garcia, P. D., Sapienza, R., Froufe-Pérez, L. & López, C. Strong dispersive effects in the light-scattering mean free path in photonic gaps. Phys. Rev. 79, 241109(R) (2009).

    Article  Google Scholar 

  4. Badolato, A. et al. Deterministic coupling of single quantum dots to single nanocavity modes. Science 308, 1158–1161 (2005).

    Article  CAS  Google Scholar 

  5. Englundet, D. et al. Controlling the spontaneous emission rate of single quantum dots in a 2D photonic crystal. Phys. Rev. Lett. 95, 013904 (2005).

    Article  Google Scholar 

  6. Curto, A. G. et al. Unidirectional emission of a quantum dot coupled to a nanoantenna. Science 329, 930–933 (2010).

    Article  CAS  Google Scholar 

  7. Akahane, Y., Asano, T., Song, B. & Noda, S. High-Q photonic nanocavity in a two-dimensional photonic crystal. Nature 425, 944–947 (2003).

    Article  CAS  Google Scholar 

  8. Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

    Article  CAS  Google Scholar 

  9. Michaelis, J., Hettich, C., Mlynek, J. & Sandoghdar, V. Optical microscopy using a single-molecule light source. Nature 405, 325–328 (2000).

    Article  CAS  Google Scholar 

  10. Kuehn, S., Hettich, C., Schmitt, C., Poizat, J-P. & Sandoghdar, V. Diamond colour centres as a nanoscopic light source for scanning near-field optical microscopy. J. Microsc. 202, 2–6 (2001).

    Article  Google Scholar 

  11. Frimmer, M., Chen, Y. & Koenderink, A. F. Scanning emitter lifetime imaging microscopy for spontaneous emission control. Phys. Rev. Lett. 107, 123602 (2011).

    Article  Google Scholar 

  12. Taminiau, T. H., Stefani, F. D., Segerink, F. B. & van Hulst, N. F. Optical antennas direct single-molecule emission. Nature Photon. 2, 234–237 (2008).

    Article  CAS  Google Scholar 

  13. Englund, D. et al. Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity. Nano Lett. 10, 3922–3926 (2010).

    Article  CAS  Google Scholar 

  14. Colas des Francs, G., Girard, C., Weeber, J. & Dereux, A. Relationship between scanning near-field optical images and local density of photonic states. Chem. Phys. Lett. 345, 512–516 (2001).

    Article  CAS  Google Scholar 

  15. Vignolini, S. et al. Polarization-sensitive near-field investigation of photonic crystal microcavities. Appl. Phys. Lett. 94, 163102 (2009).

    Article  Google Scholar 

  16. De Wilde, Y. et al. Thermal radiation scanning tunnelling microscopy. Nature 444, 740–743 (2006).

    Article  CAS  Google Scholar 

  17. Takeuchi, K. & Yamamoto, N. Visualization of surface plasmon polariton waves in two-dimensional plasmonic crystal by cathodoluminescence. Opt. Express 19, 12365–12374 (2011).

    Article  CAS  Google Scholar 

  18. García de Abajo, F. J. Optical excitations in electron microscopy. Rev. Mod. Phys. 82, 209–275 (2010).

    Article  Google Scholar 

  19. Kuttge, M. et al. Local density of states, spectrum, and far-field interference of surface plasmon polaritons probed by cathodoluminescence. Phys. Rev. B 79, 113405 (2009).

    Article  Google Scholar 

  20. Coenen, T., Vesseur, E. J. R. & Polman, A. Angle-resolved cathodoluminescence spectroscopy. Appl. Phys. Lett. 99, 143103 (2011).

    Article  Google Scholar 

  21. Kuttge, M., García de Abajo, F. J. & Polman, A. Ultrasmall mode volume plasmonic nanodisk resonators. Nano Lett. 10, 1537–1541 (2009).

    Article  Google Scholar 

  22. Yamamoto, N., Ohtani, S. & García de Abajo, F. J. Gap and Mie plasmons in individual silver nanospheres near a silver surface. Nano Lett. 11, 91–95 (2011).

    Article  CAS  Google Scholar 

  23. Bashevoy, M. V., Jonsson, F., MacDonald, K. F., Chen, Y. & Zheludev, N. I. Hyperspectral imaging of plasmonic nanostructures with nanoscale resolution. Opt. Exp. 15, 11313–11320 (2007).

    Article  CAS  Google Scholar 

  24. Vesseur, E. J. R. & Polman, A. Plasmonic whispering gallery cavities as optical nanoantennas. Nano Lett. 11, 5524–5530 (2011).

    Article  CAS  Google Scholar 

  25. López-García, M. et al. Enhancement and directionality of spontaneous emission in hybrid self-assembled photonic-plasmonic crystals. Small 6, 1757–1761 (2010).

    Article  Google Scholar 

  26. Notomi, M. Manipulating light with strongly modulated photonic crystals. Rep. Prog. Phys. 73, 096501 (2010).

    Article  Google Scholar 

  27. Vučković, J., Lončar, M., Mabuchi, H. & Scherer, A. Optimization of the Q factor in photonic crystal microcavities. IEEE J. Quantum Electron. 38, 850–856 (2002).

    Article  Google Scholar 

  28. Taminiau, T. H., Stefani, F. D. & van Hulst, N. F. Optical nanorod antennas modeled as cavities for dipolar emitters: Evolution of sub- and super-radiant modes. Nano Lett. 11, 1020–1024 (2011).

    Article  CAS  Google Scholar 

  29. Coenen, T., Vesseur, E. J. R. & Polman, A. Deep subwavelength spatial characterization of angular emission from single-crystal Au plasmonic ridge nanoantennas. ACS Nano 6, 1742–1750 (2012).

    Article  CAS  Google Scholar 

  30. Kuttge, M. Cathodoluminescence Plasmon Microscopy, Utrecht University, PhD thesis (2009).

Download references

Acknowledgements

We wish to thank P. de Roque, K. Kuipers, L. Novotny and J. García de Abajo for fruitful discussions and C. Dominguez for the growth of the Si3N4 membranes. This research was financially supported by the MICINN, programmes FIS2009-08203, CONSOLIDER CSD2007-046, RyC, Integrated nano and microfabrication Clean Room ICTS project, Fundació CELLEX, and the EU Project ERC and FP7 People. The work is part of the research programme of FOM, financially supported by NWO, and of the research programme NanoNextNL, funded by the Dutch Ministry of Economic Affairs.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed extensively to the work presented in this paper. R.S. conceived the idea to carry out cathodoluminescence to probe the LDOS in photonic crystals; T.C. developed the angle-resolved cathodoluminescence imaging spectroscopy instrument. R.S. and T.C. performed the experiments. J.R., M.K. and R.S. fabricated the samples; R.S., T.C. and M.K. analysed the data; R.S. and M.K. performed the theoretical calculations. All authors contributed to the manuscript. N.F.v.H. and A.P. gave overall supervision.

Corresponding author

Correspondence to R. Sapienza.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 317 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sapienza, R., Coenen, T., Renger, J. et al. Deep-subwavelength imaging of the modal dispersion of light. Nature Mater 11, 781–787 (2012). https://doi.org/10.1038/nmat3402

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat3402

This article is cited by

Search

Quick links

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