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Deep-subwavelength imaging of the modal dispersion of light


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.

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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.


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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.

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Authors and Affiliations



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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Correspondence to R. Sapienza.

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The authors declare no competing financial interests.

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

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