Abstract

Focusing light at the nanoscale has become a key factor in super-resolution applications. Dynamic control of this focusing can open new avenues in nanoelectronics and bioimaging, but it requires a platform that merges electronics with super-resolution capabilities. We present a planar metal–oxide–silicon (MOS) platform that allows us to shape, tune, and focus visible light at the nanoscale by compressing the wavelength of light fourfold, resulting in a scaled diffraction limit of 65 nm. We exemplify the control and flexibility by demonstrating nanovortex beams and short-wavelength super-oscillations of light that further enhance resolution toward 35 nm. Our platform achieves focusing strength similar to nanoantennas but without structural hotspots; hence it is possible to scan the focus via optical wavefront-shaping techniques. Super-resolution scanning without mechanical translations in a MOS platform can provide a building block for bioimaging, nanolithography, and lab-on-a-chip applications.

© 2015 Optical Society of America

Shaping, focusing, and controlling optical waves beyond their wavelength limit offers scientific challenges along with potential applications. Super-resolution microscopy techniques [1] carefully manage the photo-chemistry of labeling molecules to achieve optical resolution at tens of nanometers, while nanoantenna and nanofocusing elements utilize plasmonic resonance to confine light to specific predefined points [26], both breaking the so-called diffraction limit.

Recently, metasurfaces [710] and graphene plasmonics [11,12] achieved wave manipulation using ultrathin layers with partial control over the guided waves. However, dynamic manipulation of visible light at the nanoscale in a single all-inclusive platform is yet to be achieved. Silicon-based platforms make promising candidates because the high refractive index of Si can provide means for both super-resolution capabilities and dynamical control [1315]. Such platforms have been largely investigated for 1D systems in the IR regime (where optical absorption is low) toward applications in optical communications [16,17] and computing. Providing a silicon-based 2D platform with reduced losses for visible light can lead to novel on-chip applications for super-resolution imaging, nanolithography, and quantum optics.

Here we present nanoscale control of light propagating in ultrathin 2D silicon waveguides with mode wavelength compressed from 671 nm down to 184 nm. We control this short wavelength to demonstrate focusing to 65 nm FWHM (λ0/10) and nanovortices, along with super-oscillations in more complex waveguides that enhance the resolution to 35 nm. By reducing the dimensionality to 2D we relax the restrictions stemming from absorption in bulk silicon, while hybridizing photonic and plasmonic modes allows us to fully exploit its high refractive index. Phase-resolved near-field measurements prove super-resolution capabilities with unprecedented control over the optical wavelength, number of modes, shape, and brightness. Being homogeneous in 2D space makes this metal–oxide–silicon (MOS) platform compatible with wavefront shaping for dynamic focusing; hence it holds unique advantages for both lithography and microscopy on a chip, as well as for bioimaging.

Our super-resolution platform consists of transparent commercial Si membranes [Fig. 1(a)] coated on one side with a thin SiO2 and a thick metallic (silver or gold) layer. The structure supports hybrid photonic–plasmonic modes [18] of improved effective index (neff). The number of modes is determined by the Si membrane thickness, while the hybridization rate is controlled by the SiO2 layer: the thinner the layer, the stronger the hybridization and the plasmonic effect (see Supplement 1 for details). This geometry allows for single-mode operation with significant wavelength shortening in a 60-nm-thick Si waveguide. The Si extinction coefficient at 671 nm (k=0.014) plays a minor role in the overall absorption, being secondary to the Ohmic loss in the metal. Hence, this wavelength offers a good balance between resolution and losses.

 figure: Fig. 1.

Fig. 1. 2D silicon platform for nanoscale shaping and control of propagating waves. (a) The platform is based on transparent thin silicon membranes, in the format of microscope slides or chips. (b) Carefully designed slits provide coupling of light into the guided modes and their focusing. The measured focus of 65 nm is represented in 3D. (c) Side view showing the excitation, counterpropagation, and mode profile of the guided modes. Visible light (λ0=671nm) from underneath selectively excites short-wavelength modes (λSi=184nm) only at the slits. The counterpropagation (ultimately focusing) is mapped via the evanescent tail of the modes, which interacts with a scanning near-field probe.

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Our experimental configuration is depicted in Fig. 1 and fully described in Supplement 1. We carve thin slits through the MOS platform, playing a dual role: their 50 nm width enables coupling of incident light into the short-wavelength modes, while their shape (circle or spiral) focuses these modes. The complex-valued electric field is mapped by a near-field optical microscope (Neaspec NeaSNOM). A nanosized probe scatters the local evanescent tail of the guided modes toward an interferometric detection scheme so as to provide both the amplitude and phase information. The full spatial maps are accumulated by raster scanning, and their spatial resolution is determined by the probe size (nearly 10 nm).

The ability to scale the diffraction limit in a controllable way via 2D silicon waveguides is displayed in Fig. 2, showing a spot of nearly λ0/10 size. The sharpest focus, obtained for a membrane–metal separation of 4 nm, is shown in Figs. 2(a) and 2(b). The focus is circularly symmetric in its amplitude and exhibits a standing phase pattern of short wavelength. Having both amplitude and phase information allows us to accurately calculate the 2D Fourier transform of the electric field to extract additional information. For example, the circle apparent in Fig. 2(c) corresponds to a single guided mode with wavelength of 184 nm (effective index neff=3.65), well separated from the background signal, and with equal contribution from all 2π angles (maximal numerical aperture).

 figure: Fig. 2.

Fig. 2. Focusing visible light in a 2D Si platform. Circularly polarized light is coupled into the waveguides and focused by an Archimedean spiral slit. (a)–(d) Focusing light within a Si-SiO2-Ag waveguide (thicknesses: 60 nm–4 nm–350 nm). The near-field maps of the measured amplitude (a) and phase (b) show symmetric focusing with a standing phase pattern. (c) The Fourier spectrum calculated from the mapped near field presents an uninterrupted circle yielding maximal numerical aperture for the focus. The radius, km=2π/λm, corresponds to a mode wavelength λm=184±5nm. (e)–(h) Tuning by few nm the SiO2 thickness (thicknesses: 60 nm–7 nm–350 nm) allows control over the wavelength, propagation length, and focal brightness. The newly measured focus is brighter, resulting in improved SNR. The improved brightness and propagation length (4.9 μm) are accompanied by a slightly longer wavelength λm=221±5nm. (d) and (h) We use the angular symmetry to angle-average the profile of the electric field. Such a profile fits the theoretical expectations of a J0 Bessel function, from which we establish (d) 65 nm and (h) 78 nm resolution for the 184 and 221 nm wavelength modes, respectively. The insets show close-up high-resolution scans of the focus (amplitude and phase).

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Figures 2(e)2(g) show the effect of increasing the separation to 7 nm, resulting in a brighter focus due to the increased propagation length. Ohmic loss, the dominant attenuation mechanism in this system, is reduced since a smaller portion of the mode resides in the metal (see Supplement 1). Controlling the hybridization of the mode therefore allows us to tune the contrast between brightness and resolution. The calculated Fourier transform shows a higher contrast between the outer ring and the inner spots, indicating improved signal to background ratio. This slightly coarser resolution is more robust to noise and therefore can be used, e.g., for fluorescence microscopy. The efficiency of the focusing lens and its field enhancement can be optimized to be comparable to that of plasmonic lenses, as discussed in Supplement 1. Averaging over all angles, we obtain a good fit with the zero-order Bessel function, J0(kmρ), which is the theoretical expectation for our 2D system [Figs. 2(d) and 2(h)]. The sizes of the focal spots, better appreciated in the close-up insets, are 65 and 78 nm, respectively. The images presented in Figs. 2(a) and 2(e) represent the point-spread functions (PSFs) of our scaled diffraction limit that will determine the best achievable resolution in future microscopy applications.

Not only can we control the resolution and brightness of our focus, we can also select its type and shape by properly designing the coupling slits, as shown in Fig. 3. Circular slits illuminated with circularly polarized light create a 2D vortex of electric field, U(ρ,θ)=exp(iθ)J1(kmρ), by means of optical spin-orbit coupling [19]. Such nanovortex exhibits doughnut-shaped intensity (dark focusing) and spiraling phase as is clearly visible in Figs. 3(a) and 3(b). The rotating phase (inset) holds nonzero angular momentum, while the averaged intensity profile [Fig. 3(c)] now corresponds to the intensity of the first-order Bessel function |J1|2. As expected for a mode wavelength of 184 nm, the first intensity maximum is 70 nm away from the center. While such wave patterns were demonstrated in optics [19] and acoustics [20], these are the first phase-resolved measurements at optical frequencies and, to the best of our knowledge, the smallest optical vortex ever measured. This nanovortex holds potential for particle trapping, spin-controlled manipulations, and light–matter interactions in miniature atomic systems.

 figure: Fig. 3.

Fig. 3. Nanovortex in 2D Si platform. Guided modes (λm=184nm) are focused into a dark spot via a circular slit and circularly polarized light. (a) and (b) Near-field maps of intensity and phase show dark focusing with spiraling phase, respectively. This focus holds nonzero angular momentum. (c) The angle-averaged intensity profile is fitted with the intensity of the first-order Bessel function (J12). High-resolution close-up images of the intensity and phase of the focus are shown in the insets.

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Increasing the Si thickness to above 100 nm results in dual-mode performance, where the interplay between the metallic and two dielectric constituents provides additional degrees of freedom to manipulate the guided modes (see Supplement 1). Engineering the two modes independently offers control over the super-position of the short-wavelength modes, synergizing the individual properties of each mode with the other’s. Super-oscillations are an excellent example for such a synergy, as the coherent super-position of the interfering waves of different wavelengths results in spatial oscillations smaller than any of the propagating waves [2123].

We locally create super-oscillations in a dual-mode waveguide by controlling the amplitude and phase relations between the two short-wavelength modes around a common zero-crossing point. This is achieved by illuminating a carefully designed circular slit (see Supplement 1) such that both modes focus to a dark spot (zero crossing) with equal amplitudes and opposite phases. Figures 4(a)4(d) show the super-position of two distinguishable wavelengths λm,1=200nm and λm,2=282nm, resulting in a beating pattern with rapid changes of amplitude and phase in the center of the interference pattern. These super-oscillations are clearly better resolved in the high-res scans shown in the insets and the cross sections [Fig. 4(d)]. The visibility is further improved by applying a band-pass filter on the calculated Fourier transform, enabled by the fact that the guided modes and the background are well separated. The Fourier filter removes the background and high-frequency noise, thereby improving the signal-to-noise ratio (SNR) in the filtered real-space image [Figs. 4(e)4(h)]. The linecuts of the filtered amplitude and phase clearly reveal super-oscillations having a FWHM of 35 nm.

 figure: Fig. 4.

Fig. 4. Super-oscillations of two short-wavelength modes. Linearly polarized light is coupled into the two propagating modes of a Si-SiO2-Au waveguide (thicknesses: 160 nm–22 nm–170 nm). (a) and (b) The measured amplitude and phase, respectively, show the interference between modes. High-resolution amplitude and phase close-ups (insets) show super-oscillations faster than any propagating Fourier component. (c) The calculated Fourier spectrum of the field shows two waveguide modes of wavelengths λm,1=200±5nm and λm,2=282±5nm, and far-field background (the inner ring). (d) The averaged amplitude (black) and phase (red) profiles show 70 nm zero crossings of amplitude and phase. (e)–(h) A Fourier band-pass filter improves the visibility of the super-oscillations in both (e) amplitude and (f) phase. (g) The filtered Fourier spectrum contains only guided mode components. (l) The linecuts show amplitude features of FWHM=35nm and phase flips of nearly 70 nm—clear signatures of super-oscillations. (i)–(k) Calculated near-field amplitude, phase, Fourier spectrum, and linecuts, respectively. The calculation well describes the measurement of super-oscillations.

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We presented a silicon-based platform for super-resolution control over propagating waves, shortening a 671 nm illumination wavelength to 184 nm—shorter than that of excimer lasers, which are widely used for optical nanolithography. We showed focusing into a bright spot and a dark nanovortex below 70 nm, i.e., λ0/10, without breaking the diffraction limit. We utilized the level of control over the propagating modes to further demonstrate 35 nm sized super-oscillations between two short wavelengths, breaking the already-scaled diffraction limit of the system.

In providing resolution comparable to the state-of-the-art methods while keeping the simplicity and flexibility of a diffraction-limited system, we offer the potential to develop a simple, easy-to-fabricate microscopy platform, compatible with the mature silicon industry. The homogeneous 2D platform presented allows for a dynamic focusing, i.e., the ability to change the position of the focal spot using a spatial light modulator [13,24], in contrast to focusing by a nanoantenna that requires mechanical scanning. Controlling the resolution, shape, type, and brightness of a focal spot, combined with future demonstration of subwavelength position control [25], could be manifested in super-resolution microscopy, nanolithography, and particle trapping with enhanced field-of-view relative to plasmonic systems at this scale.

Funding

ICORE Excellence Center “Circle of Light”; Israel Science Foundation (ISF) (1457/11); European Union’s Seventh Framework Programme (FP7) (626812).

Acknowledgment

The fabrication in this work was supported by the Russell Berrie Nanotechnology Institute (RBNI) and the Micro Nano Fabrication Unit (MNFU) at the Technion. B. G. acknowledges: The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013]) under grant agreement n° 626812 – MC--MultiSPLASH.

 

See Supplement 1 for supporting content.

REFERENCES

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4. M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004). [CrossRef]  

5. E. Verhagen, A. Polman, and L. K. Kuipers, Opt. Express 16, 45 (2008). [CrossRef]  

6. H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012). [CrossRef]  

7. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013). [CrossRef]  

8. N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014). [CrossRef]  

9. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013). [CrossRef]  

10. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014). [CrossRef]  

11. A. Vakil and N. Engheta, Science 332, 1291 (2011). [CrossRef]  

12. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

13. B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013). [CrossRef]  

14. B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014). [CrossRef]  

15. H. Yilmaz, E. G. van Putten, J. Bertolotti, A. Lagendijk, W. L. Vos, and A. P. Mosk, Optica 2, 424 (2015). [CrossRef]  

16. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010). [CrossRef]  

17. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004). [CrossRef]  

18. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008). [CrossRef]  

19. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008). [CrossRef]  

20. T. Brunet, J.-L. Thomas, and R. Marchiano, Phys. Rev. Lett. 105, 034301 (2010). [CrossRef]  

21. M. V. Berry and S. Popescu, J. Phys. A 39, 6965 (2006). [CrossRef]  

22. E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012). [CrossRef]  

23. E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. G. Makris, and M. Segev, Opt. Express 21, 13425 (2013). [CrossRef]  

24. M. I. Stockman, D. J. Bergman, and T. Kobayashi, Phys. Rev. B 69, 054202 (2004). [CrossRef]  

25. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012). [CrossRef]  

References

  • View by:

  1. S. W. Hell, Science 316, 1153 (2007).
    [Crossref]
  2. L. Novotny and N. van Hulst, Nat. Photonics 5, 83 (2011).
    [Crossref]
  3. G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, Nano Lett. 9, 3608 (2009).
    [Crossref]
  4. M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
    [Crossref]
  5. E. Verhagen, A. Polman, and L. K. Kuipers, Opt. Express 16, 45 (2008).
    [Crossref]
  6. H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
    [Crossref]
  7. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
    [Crossref]
  8. N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
    [Crossref]
  9. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
    [Crossref]
  10. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
    [Crossref]
  11. A. Vakil and N. Engheta, Science 332, 1291 (2011).
    [Crossref]
  12. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).
  13. B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
    [Crossref]
  14. B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
    [Crossref]
  15. H. Yilmaz, E. G. van Putten, J. Bertolotti, A. Lagendijk, W. L. Vos, and A. P. Mosk, Optica 2, 424 (2015).
    [Crossref]
  16. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
    [Crossref]
  17. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
    [Crossref]
  18. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008).
    [Crossref]
  19. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
    [Crossref]
  20. T. Brunet, J.-L. Thomas, and R. Marchiano, Phys. Rev. Lett. 105, 034301 (2010).
    [Crossref]
  21. M. V. Berry and S. Popescu, J. Phys. A 39, 6965 (2006).
    [Crossref]
  22. E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
    [Crossref]
  23. E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. G. Makris, and M. Segev, Opt. Express 21, 13425 (2013).
    [Crossref]
  24. M. I. Stockman, D. J. Bergman, and T. Kobayashi, Phys. Rev. B 69, 054202 (2004).
    [Crossref]
  25. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
    [Crossref]

2015 (1)

2014 (3)

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
[Crossref]

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[Crossref]

B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
[Crossref]

2013 (4)

E. Greenfield, R. Schley, I. Hurwitz, J. Nemirovsky, K. G. Makris, and M. Segev, Opt. Express 21, 13425 (2013).
[Crossref]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
[Crossref]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
[Crossref]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

2012 (4)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
[Crossref]

2011 (2)

L. Novotny and N. van Hulst, Nat. Photonics 5, 83 (2011).
[Crossref]

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[Crossref]

2010 (2)

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
[Crossref]

T. Brunet, J.-L. Thomas, and R. Marchiano, Phys. Rev. Lett. 105, 034301 (2010).
[Crossref]

2009 (1)

G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, Nano Lett. 9, 3608 (2009).
[Crossref]

2008 (3)

E. Verhagen, A. Polman, and L. K. Kuipers, Opt. Express 16, 45 (2008).
[Crossref]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008).
[Crossref]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

2007 (1)

S. W. Hell, Science 316, 1153 (2007).
[Crossref]

2006 (1)

M. V. Berry and S. Popescu, J. Phys. A 39, 6965 (2006).
[Crossref]

2004 (3)

M. I. Stockman, D. J. Bergman, and T. Kobayashi, Phys. Rev. B 69, 054202 (2004).
[Crossref]

M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
[Crossref]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
[Crossref]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
[Crossref]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

Aulbach, J.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
[Crossref]

Bartal, G.

B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
[Crossref]

Bergman, D. J.

M. I. Stockman, D. J. Bergman, and T. Kobayashi, Phys. Rev. B 69, 054202 (2004).
[Crossref]

Berry, M. V.

M. V. Berry and S. Popescu, J. Phys. A 39, 6965 (2006).
[Crossref]

Bertolotti, J.

Blau, Y.

B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
[Crossref]

Bokor, J.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
[Crossref]

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
[Crossref]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
[Crossref]

Brunet, T.

T. Brunet, J.-L. Thomas, and R. Marchiano, Phys. Rev. Lett. 105, 034301 (2010).
[Crossref]

Cabrini, S.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
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Chen, J.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, Nano Lett. 9, 3608 (2009).
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H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
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B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
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de Abajo, F. J. G.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
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A. Vakil and N. Engheta, Science 332, 1291 (2011).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
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A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
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G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008).
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Gjonaj, B.

B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
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B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
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Godignon, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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Hasman, E.

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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
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Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
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S. W. Hell, Science 316, 1153 (2007).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

Hurwitz, I.

Huth, F.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
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Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
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M. I. Stockman, D. J. Bergman, and T. Kobayashi, Phys. Rev. B 69, 054202 (2004).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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Kuipers, L. K.

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B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
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A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
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A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
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E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
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V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
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T. Brunet, J.-L. Thomas, and R. Marchiano, Phys. Rev. Lett. 105, 034301 (2010).
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G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
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H. Yilmaz, E. G. van Putten, J. Bertolotti, A. Lagendijk, W. L. Vos, and A. P. Mosk, Optica 2, 424 (2015).
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B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
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A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
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Niv, A.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
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L. Novotny and N. van Hulst, Nat. Photonics 5, 83 (2011).
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B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008).
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
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V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008).
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Polman, A.

Popescu, S.

M. V. Berry and S. Popescu, J. Phys. A 39, 6965 (2006).
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G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, Nano Lett. 9, 3608 (2009).
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G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
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E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
[Crossref]

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E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
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E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
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Schley, R.

Schuck, P. J.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
[Crossref]

Segev, M.

Seok, T. J.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
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A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
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Staffaroni, M.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
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M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
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M. I. Stockman, D. J. Bergman, and T. Kobayashi, Phys. Rev. B 69, 054202 (2004).
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Thomas, J.-L.

T. Brunet, J.-L. Thomas, and R. Marchiano, Phys. Rev. Lett. 105, 034301 (2010).
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Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
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Thongrattanasiri, S.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

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A. Vakil and N. Engheta, Science 332, 1291 (2011).
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van Hulst, N.

L. Novotny and N. van Hulst, Nat. Photonics 5, 83 (2011).
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van Putten, E. G.

Veksler, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
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Verhagen, E.

Volpe, G.

G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, Nano Lett. 9, 3608 (2009).
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Vos, W. L.

Wu, M. C.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
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Yablonovitch, E.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
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Yilmaz, H.

Yu, N.

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
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Yulevich, I.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
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Zhang, X.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008).
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Zheludev, N. I.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
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Zurutuza Elorza, A.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

J. Phys. A (1)

M. V. Berry and S. Popescu, J. Phys. A 39, 6965 (2006).
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Nano Lett. (2)

G. Volpe, S. Cherukulappurath, R. Juanola Parramon, G. Molina-Terriza, and R. Quidant, Nano Lett. 9, 3608 (2009).
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B. Gjonaj, A. David, Y. Blau, G. Spektor, M. Orenstein, S. Dolev, and G. Bartal, Nano Lett. 14, 5598 (2014).
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Nat. Mater. (2)

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
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E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, Nat. Mater. 11, 432 (2012).
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Nat. Photonics (5)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photonics 2, 496 (2008).
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A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
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L. Novotny and N. van Hulst, Nat. Photonics 5, 83 (2011).
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G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Nat. Photonics 4, 518 (2010).
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H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, Nat. Photonics 6, 838 (2012).
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Nature (2)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, Nature 487, 77 (2012).

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
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Opt. Express (2)

Optica (1)

Phys. Rev. B (1)

M. I. Stockman, D. J. Bergman, and T. Kobayashi, Phys. Rev. B 69, 054202 (2004).
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Phys. Rev. Lett. (4)

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
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T. Brunet, J.-L. Thomas, and R. Marchiano, Phys. Rev. Lett. 105, 034301 (2010).
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B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
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M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
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Science (5)

S. W. Hell, Science 316, 1153 (2007).
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, Science 340, 724 (2013).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, Science 345, 298 (2014).
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A. Vakil and N. Engheta, Science 332, 1291 (2011).
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A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 339, 1232009 (2013).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. 2D silicon platform for nanoscale shaping and control of propagating waves. (a) The platform is based on transparent thin silicon membranes, in the format of microscope slides or chips. (b) Carefully designed slits provide coupling of light into the guided modes and their focusing. The measured focus of 65 nm is represented in 3D. (c) Side view showing the excitation, counterpropagation, and mode profile of the guided modes. Visible light (λ0=671nm) from underneath selectively excites short-wavelength modes (λSi=184nm) only at the slits. The counterpropagation (ultimately focusing) is mapped via the evanescent tail of the modes, which interacts with a scanning near-field probe.
Fig. 2.
Fig. 2. Focusing visible light in a 2D Si platform. Circularly polarized light is coupled into the waveguides and focused by an Archimedean spiral slit. (a)–(d) Focusing light within a Si-SiO2-Ag waveguide (thicknesses: 60 nm–4 nm–350 nm). The near-field maps of the measured amplitude (a) and phase (b) show symmetric focusing with a standing phase pattern. (c) The Fourier spectrum calculated from the mapped near field presents an uninterrupted circle yielding maximal numerical aperture for the focus. The radius, km=2π/λm, corresponds to a mode wavelength λm=184±5nm. (e)–(h) Tuning by few nm the SiO2 thickness (thicknesses: 60 nm–7 nm–350 nm) allows control over the wavelength, propagation length, and focal brightness. The newly measured focus is brighter, resulting in improved SNR. The improved brightness and propagation length (4.9 μm) are accompanied by a slightly longer wavelength λm=221±5nm. (d) and (h) We use the angular symmetry to angle-average the profile of the electric field. Such a profile fits the theoretical expectations of a J0 Bessel function, from which we establish (d) 65 nm and (h) 78 nm resolution for the 184 and 221 nm wavelength modes, respectively. The insets show close-up high-resolution scans of the focus (amplitude and phase).
Fig. 3.
Fig. 3. Nanovortex in 2D Si platform. Guided modes (λm=184nm) are focused into a dark spot via a circular slit and circularly polarized light. (a) and (b) Near-field maps of intensity and phase show dark focusing with spiraling phase, respectively. This focus holds nonzero angular momentum. (c) The angle-averaged intensity profile is fitted with the intensity of the first-order Bessel function (J12). High-resolution close-up images of the intensity and phase of the focus are shown in the insets.
Fig. 4.
Fig. 4. Super-oscillations of two short-wavelength modes. Linearly polarized light is coupled into the two propagating modes of a Si-SiO2-Au waveguide (thicknesses: 160 nm–22 nm–170 nm). (a) and (b) The measured amplitude and phase, respectively, show the interference between modes. High-resolution amplitude and phase close-ups (insets) show super-oscillations faster than any propagating Fourier component. (c) The calculated Fourier spectrum of the field shows two waveguide modes of wavelengths λm,1=200±5nm and λm,2=282±5nm, and far-field background (the inner ring). (d) The averaged amplitude (black) and phase (red) profiles show 70 nm zero crossings of amplitude and phase. (e)–(h) A Fourier band-pass filter improves the visibility of the super-oscillations in both (e) amplitude and (f) phase. (g) The filtered Fourier spectrum contains only guided mode components. (l) The linecuts show amplitude features of FWHM=35nm and phase flips of nearly 70 nm—clear signatures of super-oscillations. (i)–(k) Calculated near-field amplitude, phase, Fourier spectrum, and linecuts, respectively. The calculation well describes the measurement of super-oscillations.

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