Deep-subwavelength imaging of the modal dispersion of light

Journal name:
Nature Materials
Year published:
Published online


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.

At a glance


  1. High-resolution LDOS mapping on two-dimensional photonic crystals.
    Figure 1: High-resolution LDOS mapping on two-dimensional photonic crystals.

    a, Sketch of the experimental set-up: an electron beam is incident on the sample surface, generating optical radiation that is collected by the mirror placed above the sample and sent to an optical spectrometer or to an imaging CCD (charge-coupled device) camera. Scanning of the electron beam allows for deep-subwavelength spatial mapping of the LDOS. b,c, LDOS maps of a photonic crystal Si3N4 membrane with a lattice constant a  =  400 nm and a hole diameter of 230 nm in the high-energy bands at a wavelength of 500 nm (a/λ  =  0.8) and 590 nm (a/λ  =  0.68), respectively. The Bloch mode is visible in its periodic LDOS modulation, it is delocalized over the full crystal and has the same symmetry as the lattice. d, LDOS spectrum taken in the centre between three holes, normalized by the cathodoluminescence emission from an unstructured membrane reference. The Bloch modes modulate the LDOS by 30%. The LDOS maps are the raw data without any background subtraction, corrected only for system response and are integrated over a 9 nm bandwidth.

  2. Momentum spectroscopy of a two-dimensional photonic crystal.
    Figure 2: Momentum spectroscopy of a two-dimensional photonic crystal.

    Angular emission patterns from a photonic crystal at different wavelengths (collected bandwidth ~40 nm) by exciting the photonic crystal in the symmetry point between three holes. The images at a wavelength of 500 and 600 nm correspond to the spatial LDOS maps in Fig. 1b,c. Azimuthal ( ) and polar (θ) angles are indicated. The hexagonal symmetry is clearly visible as well as an increasing number of polar peaks for higher energies. The black area at the top and the black circle in the centre of the images correspond to angular ranges that are not collected by the mirror.

  3. LDOS maps and momentum spectrum of a H1 photonic crystal cavity.
    Figure 3: LDOS maps and momentum spectrum of a H1 photonic crystal cavity.

    a, Secondary electron microscopy image of a photonic crystal membrane with a hole defect (H1 cavity) with a lattice constant a  =  330 nm and a hole diameter of 230 nm. The area outlined is shown in b. b, LDOS image of the cavity at a wavelength of 650 nm, with a bandwidth of 9 nm. c, Angular emission pattern when the cavity is excited in its centre (collection bandwidth ~40 nm). The hexagonal momentum distribution shows a maximum around k  =  0 and a hexagonal pattern of lobes.

  4. Mapping multiple cavity modes of an L3 photonic crystal cavity.
    Figure 4: Mapping multiple cavity modes of an L3 photonic crystal cavity.

    a,b, Measured LDOS maps of an L3 photonic crystal cavity (lattice period a  =  330 nm, hole diameter d  =  230 nm) at the frequency of the two cavity modes, 649 and 681 nm, respectively, with a bandwidth of 9 nm. c, Measured cavity resonance spectrum measured in the centre of the cavity normalized to the spectrum of an unstructured membrane. The cavity modes exhibit an increase of LDOS of a factor of ~2 at the resonance location. d,e, Measured angular emission patterns at the two resonance frequencies. The long axis of the cavity is parallel to the horizontal direction along 90° and 270°. The cavities exhibit clear directional emission peaks, at 90° and 270° for both wavelengths. f, The vague circular pattern in the background is attributed to the interference of light emitted from the cavity with light reflected by the silicon substrate, as also observed for a reference unstructured membrane. g,h, Calculated LDOS maps for the same experimental parameters (see Methods). The theoretical maps exhibit the same symmetry and similar LDOS distribution as in the experiments. i, The LDOS spectra calculated in the middle of the cavity; two peaks are visible, at around 600 and 680 nm. The vertical dotted lines in c and i indicate the position of the LDOS maps shown above.

  5. Resolution assessment.
    Figure 5: Resolution assessment.

    ac, Line-scans over a 150 nm square hole in a silicon membrane. b shows the line-cut of the LDOS at the wavelength of 600 nm as compared with the SEM topology line-cut. CL, cathodoluminescence. The LDOS signal drops from 10% to 90% in 33 nm, following the topology, which drops from 10% to 90% in 21 nm. df, Plots of the measurements performed on the opposite geometry of a silicon membrane nanostrip. Such a system supports sharp spectral resonances that are spatially localized at the edges of the strip. These sharp features are compared in e to the SEM topology image. Their width at half-maximum is 48 nm. In b,e the open dots are the measured data, and the solid lines are the result of the fit. The blue vertical lines show the 90–10% signal drop. In a,c,d,f the white dotted line shows the spectral and spatial position of the line-cut. Measurements were made using 3 nm steps in the electron beam position.


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Author information


  1. ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain

    • R. Sapienza,
    • J. Renger,
    • M. Kuttge &
    • N. F. van Hulst
  2. Department of Physics, Kings College London, Strand, London WC2R 2LS, UK

    • R. Sapienza
  3. Center for Nanophotonics, FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands

    • T. Coenen &
    • A. Polman
  4. ICREA-Institució Catalana de Recerca i Estudis Avançats, 08015 Barcelona, Spain

    • N. F. van Hulst


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.

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