Abstract

It has been recently shown that specially engineered light beams have the remarkable ability to propagate along curved trajectories in vacuum. Current methods for generating accelerating beams use phase modulators and lenses, leading to length scales on the order of tens of centimeters or larger. This poses constraints and severely limits their applicability inside materials. Here, we accelerate light inside glass using a metasurface consisting of plasmonic nanoantennas. Highly bending beams with radii of curvature on the order of a hundred micrometers were generated, and the imaged intensities agree well with theory. Our approach for generating accelerating beams allows for their integration into on-chip photonic systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, Science 352, 1190 (2016).
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2015 (6)

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, Nano Lett. 15, 5358 (2015).
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F. Diebel, B. M. Bokić, D. V. Timotijević, D. M. Jović Savić, and C. Denz, Opt. Express 23, 24351 (2015).
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2014 (3)

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, Nano Lett. 14, 2491 (2014).
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J. Lee, M. Tymchenko, C. Argyropoulos, P. Chen, F. Lu, F. Demmerle, G. Boehm, M. Amann, A. Alù, and M. A. Belkin, Nature 511, 65 (2014).
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I. Epstein and A. Arie, Phys. Rev. Lett. 112, 023903 (2014).
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2013 (4)

X. Ni, A. V. Kildishev, and V. M. Shalaev, Nat. Commun. 4, 2807 (2013).
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C. Pfeiffer and A. Grbic, Phys. Rev. Lett. 110, 197401 (2013).
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A. Mathis, F. Courvoisier, R. Giust, L. Furfaro, M. Jacquot, L. Froehly, and J. M. Dudley, Opt. Lett. 38, 2218 (2013).
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2012 (8)

F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, Opt. Lett. 37, 1736 (2012).
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I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[Crossref]

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[Crossref]

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[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[Crossref]

2011 (7)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[Crossref]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
[Crossref]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 2883 (2011).
[Crossref]

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, Opt. Lett. 36, 3191 (2011).
[Crossref]

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[Crossref]

2010 (3)

A. Salandrino and D. N. Christodoulides, Opt. Lett. 35, 2082 (2010).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[Crossref]

D. G. Papazoglou, S. Suntsov, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 81, 061807(R) (2010).
[Crossref]

2009 (3)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref]

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[Crossref]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[Crossref]

2008 (2)

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[Crossref]

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[Crossref]

2007 (4)

L. Novotny, Phys. Rev. Lett. 98, 266802 (2007).
[Crossref]

R. Merlin, Science 317, 927 (2007).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[Crossref]

2003 (1)

C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, and H. E. Hernández-Figueroa, Opt. Commun. 222, 75 (2003).
[Crossref]

1997 (1)

D. M. Pozar, S. D. Targonski, and H. D. Syrigos, IEEE Trans. Antennas Propag. 45, 287 (1997).
[Crossref]

1987 (2)

J. Durnin and J. J. Miceli, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref]

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[Crossref]

1979 (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[Crossref]

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[Crossref]

D. G. Papazoglou, S. Suntsov, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 81, 061807(R) (2010).
[Crossref]

Aieta, F.

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, Nano Lett. 15, 5358 (2015).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Alù, A.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Chen, F. Lu, F. Demmerle, G. Boehm, M. Amann, A. Alù, and M. A. Belkin, Nature 511, 65 (2014).
[Crossref]

Amann, M.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Chen, F. Lu, F. Demmerle, G. Boehm, M. Amann, A. Alù, and M. A. Belkin, Nature 511, 65 (2014).
[Crossref]

Argyropoulos, C.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Chen, F. Lu, F. Demmerle, G. Boehm, M. Amann, A. Alù, and M. A. Belkin, Nature 511, 65 (2014).
[Crossref]

Arie, A.

I. Epstein and A. Arie, Phys. Rev. Lett. 112, 023903 (2014).
[Crossref]

I. Dolev, I. Epstein, and A. Arie, Phys. Rev. Lett. 109, 203903 (2012).
[Crossref]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[Crossref]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[Crossref]

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[Crossref]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[Crossref]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Belkin, M. A.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Chen, F. Lu, F. Demmerle, G. Boehm, M. Amann, A. Alù, and M. A. Belkin, Nature 511, 65 (2014).
[Crossref]

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[Crossref]

Boehm, G.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Chen, F. Lu, F. Demmerle, G. Boehm, M. Amann, A. Alù, and M. A. Belkin, Nature 511, 65 (2014).
[Crossref]

Boguslawski, M.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

Bokic, B. M.

Boltasseva, A.

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, Nano Lett. 14, 2491 (2014).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Science 335, 427 (2012).
[Crossref]

Boulesbaa, A.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentin, Nano Lett. 15, 7388 (2015).
[Crossref]

Briggs, D. P.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentin, Nano Lett. 15, 7388 (2015).
[Crossref]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[Crossref]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[Crossref]

Capasso, F.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, Science 352, 1190 (2016).
[Crossref]

M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, Nano Lett. 15, 5358 (2015).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[Crossref]

Cheah, K. W.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, Nat. Mater. 14, 607 (2015).
[Crossref]

Chen, P.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Chen, F. Lu, F. Demmerle, G. Boehm, M. Amann, A. Alù, and M. A. Belkin, Nature 511, 65 (2014).
[Crossref]

Chen, S.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. H. Wong, E. Y. B. Pun, K. W. Cheah, T. Zentgraf, and S. Zhang, Nat. Mater. 14, 607 (2015).
[Crossref]

Chen, W. T.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, Science 352, 1190 (2016).
[Crossref]

Chen, Z.

Christodoulides, D. N.

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 2883 (2011).
[Crossref]

A. Salandrino and D. N. Christodoulides, Opt. Lett. 35, 2082 (2010).
[Crossref]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[Crossref]

Courvoisier, F.

Dartora, C. A.

C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, and H. E. Hernández-Figueroa, Opt. Commun. 222, 75 (2003).
[Crossref]

Demmerle, F.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Chen, F. Lu, F. Demmerle, G. Boehm, M. Amann, A. Alù, and M. A. Belkin, Nature 511, 65 (2014).
[Crossref]

Denz, C.

F. Diebel, B. M. Bokić, D. V. Timotijević, D. M. Jović Savić, and C. Denz, Opt. Express 23, 24351 (2015).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

Devlin, R. C.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, Science 352, 1190 (2016).
[Crossref]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[Crossref]

Diebel, F.

F. Diebel, B. M. Bokić, D. V. Timotijević, D. M. Jović Savić, and C. Denz, Opt. Express 23, 24351 (2015).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
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Other (4)

The spacing a between the centers of two adjacent pixels is either 20 or 12.5 μm for the LCOS SLM models made by Hamamatsu, and 6.4 and 3.74 μm for, respectively, the LETO and GAEA 4K SLMs made by Holoeye Photonics AG. For 800 nm light, normally incident upon a slit array of period d=2a, the first-order diffraction angles are <7°. Also at 800 nm, the linear series SLM made by Meadowlark Optics has a 1.6 μm pixel spacing, which gives a first-order diffraction angle of nearly 15°.

Light focused by an objective lens with a numerical aperture of 0.95 refracts inside glass with refractive index n=1.45 at a maximum angle of 41°.

E. Hecht, Optics, 4th ed. (Pearson, 2002), pp. 107–109.

E. Hecht, Optics, 4th ed. (Pearson, 2002), pp. 273–276.

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Figures (3)

Fig. 1.
Fig. 1. (a) Nanoantenna geometry. Incident light polarized at 45° relative to the orthogonal symmetric (S) and antisymmetric (AS) axes results in the excitation of both antenna modes and a cross-polarized scattered field. (b) Two-dimensional contour plot showing the calculated light intensity before and after traversing the metasurface at z=0. Illumination at 45° allows for spatial separation of the unperturbed and accelerating beams, which are readily observed at z>0. (c) Calculated phase shift produced by the metasurface. The discontinuity in the phase gradient near x=135  μm has a very minor effect on the beam properties.
Fig. 2.
Fig. 2. Schematics of the experimental setup and images of the metasurface. (a) Optical microscope image (green) showing the large-scale pattern of the antenna array, which modulates the incident field along the x axis. Individual antennas are resolved in the SEM image. (b) Schematics describing the metasurface illumination and setup used for imaging the accelerating beams. The beam reflected by the metasurface has been omitted. The first lens (L1) collects light from the accelerating beam scattered from defects in the glass, and the second lens (L2) images the collected light onto the CCD. The gray area indicates the image plane.
Fig. 3.
Fig. 3. (a), (c) Experimental and (b), (d) calculated intensity plots for the 400 and 100 μm radius of curvature metasurfaces, respectively. To highlight the beam acceleration, a dotted line was added tracing circular trajectories of the same radius of curvature.

Equations (5)

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E(z0,x)=exp(αx)Jβ(kx+β)Θ(x+βk).
E(0,x)=A(x)exp[iϕ(x)]=2E(z0,x)z0G(z0,xx)dx,
G(z,x)=(i/4)H0(2)(kz2+x2)
E(z,x)=2E(0,x)zG+(z,xx)dx,
G+(z,x)=(i/4)H0(1)(kz2+x2)

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