Abstract

By analogy to the three dimensional optical bottle beam, we introduce the plasmonic bottle beam: a two dimensional surface wave which features a lattice of plasmonic bottles, i.e. alternating regions of bright focii surrounded by low intensities. The two-dimensional bottle beam is created by the interference of a non-diffracting beam, a cosine-Gaussian beam, and a plane wave, thus giving rise to a non-diffracting complex intensity distribution. By controlling the propagation constant of the cosine-Gauss beam, the size and number of plasmonic bottles can be engineered. The two dimensional lattice of hot spots formed by this new plasmonic wave could have applications in plasmonic trapping.

© 2013 OSA

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    [CrossRef]

2013 (3)

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated Plasmon Beam: Nondiffracting versus Linearly Focused,” Phys. Rev. Lett.110(4), 046807 (2013).
[CrossRef]

C. E. Garcia-Ortiz, V. Coello, Z. Han, and S. I. Bozhevolnyi, “Generation of diffraction-free plasmonic beams with one-dimensional Bessel profiles,” Opt. Lett.38(6), 905–907 (2013).
[CrossRef] [PubMed]

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics7(2), 123–127 (2013).
[CrossRef]

2012 (5)

C. J. Regan, L. Grave de Peralta, and A. A. Bernussi, “Two-dimensional Bessel-like surface plasmon-polariton beams,” J. Appl. Phys.112(10), 103107 (2012).
[CrossRef]

A. E. Klein, A. Minovich, M. Steinert, N. Janunts, A. Tünnermann, D. N. Neshev, Y. S. Kivshar, and T. Pertsch, “Controlling plasmonic hot spots by interfering Airy beams,” Opt. Lett.37(16), 3402–3404 (2012).
[CrossRef] [PubMed]

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett.109(16), 163903 (2012).
[CrossRef] [PubMed]

K. Wang and K. B. Crozier, “Plasmonic trapping with a gold nanopillar,” ChemPhysChem13(11), 2639–2648 (2012).
[CrossRef] [PubMed]

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss Plasmon beam: A localized long-range nondiffracting surface wave,” Phys. Rev. Lett.109(9), 093904 (2012).
[CrossRef] [PubMed]

2011 (6)

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011).
[CrossRef]

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun2, 469 (2011).
[CrossRef] [PubMed]

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B83(11), 115326 (2011).
[CrossRef]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett.36(16), 3191–3193 (2011).
[CrossRef] [PubMed]

2010 (3)

2009 (3)

2007 (1)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys.3(7), 477–480 (2007).
[CrossRef]

2006 (1)

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys.8(3), 43 (2006).
[CrossRef]

2005 (2)

2004 (2)

2003 (1)

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottle beams,” Opt. Commun.225(4-6), 215–222 (2003).
[CrossRef]

2002 (1)

2000 (1)

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Ahluwalia, B.

Arlt, J.

Bernussi, A. A.

C. J. Regan, L. Grave de Peralta, and A. A. Bernussi, “Two-dimensional Bessel-like surface plasmon-polariton beams,” J. Appl. Phys.112(10), 103107 (2012).
[CrossRef]

Bouchal, Z.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys.8(3), 43 (2006).
[CrossRef]

Bouma, B. E.

Bozhevolnyi, S. I.

Brzobohatý, O.

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics7(2), 123–127 (2013).
[CrossRef]

Capasso, F.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss Plasmon beam: A localized long-range nondiffracting surface wave,” Phys. Rev. Lett.109(9), 093904 (2012).
[CrossRef] [PubMed]

Chen, Z.

Christodoulides, D. N.

Chvátal, L.

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics7(2), 123–127 (2013).
[CrossRef]

Cižmár, T.

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics7(2), 123–127 (2013).
[CrossRef]

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys.8(3), 43 (2006).
[CrossRef]

Cluzel, B.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss Plasmon beam: A localized long-range nondiffracting surface wave,” Phys. Rev. Lett.109(9), 093904 (2012).
[CrossRef] [PubMed]

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B83(11), 115326 (2011).
[CrossRef]

Coello, V.

Cooper, J.

Courtial, J.

Crozier, K. B.

K. Wang and K. B. Crozier, “Plasmonic trapping with a gold nanopillar,” ChemPhysChem13(11), 2639–2648 (2012).
[CrossRef] [PubMed]

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun2, 469 (2011).
[CrossRef] [PubMed]

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Scannable plasmonic trapping using a gold stripe,” Nano Lett.10(9), 3506–3511 (2010).
[CrossRef] [PubMed]

Dally, A.

Daria, V.

de Fornel, F.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss Plasmon beam: A localized long-range nondiffracting surface wave,” Phys. Rev. Lett.109(9), 093904 (2012).
[CrossRef] [PubMed]

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B83(11), 115326 (2011).
[CrossRef]

Dellinger, J.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss Plasmon beam: A localized long-range nondiffracting surface wave,” Phys. Rev. Lett.109(9), 093904 (2012).
[CrossRef] [PubMed]

Dholakia, K.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottle beams,” Opt. Commun.225(4-6), 215–222 (2003).
[CrossRef]

Dumas, C.

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B83(11), 115326 (2011).
[CrossRef]

Eriksen, R.

Garcia-Ortiz, C. E.

Genevet, P.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss Plasmon beam: A localized long-range nondiffracting surface wave,” Phys. Rev. Lett.109(9), 093904 (2012).
[CrossRef] [PubMed]

Girard, C.

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys.3(7), 477–480 (2007).
[CrossRef]

Glueckstad, J.

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Grave de Peralta, L.

C. J. Regan, L. Grave de Peralta, and A. A. Bernussi, “Two-dimensional Bessel-like surface plasmon-polariton beams,” J. Appl. Phys.112(10), 103107 (2012).
[CrossRef]

Grier, D. G.

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett.109(16), 163903 (2012).
[CrossRef] [PubMed]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Han, Z.

He, X.

Huang, L.

Isenhower, L.

Janunts, N.

A. E. Klein, A. Minovich, M. Steinert, N. Janunts, A. Tünnermann, D. N. Neshev, Y. S. Kivshar, and T. Pertsch, “Controlling plasmonic hot spots by interfering Airy beams,” Opt. Lett.37(16), 3402–3404 (2012).
[CrossRef] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Jordan, P.

Juan, M. L.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011).
[CrossRef]

Karásek, V.

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics7(2), 123–127 (2013).
[CrossRef]

Kivshar, Y. S.

A. E. Klein, A. Minovich, M. Steinert, N. Janunts, A. Tünnermann, D. N. Neshev, Y. S. Kivshar, and T. Pertsch, “Controlling plasmonic hot spots by interfering Airy beams,” Opt. Lett.37(16), 3402–3404 (2012).
[CrossRef] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Klein, A. E.

A. E. Klein, A. Minovich, M. Steinert, N. Janunts, A. Tünnermann, D. N. Neshev, Y. S. Kivshar, and T. Pertsch, “Controlling plasmonic hot spots by interfering Airy beams,” Opt. Lett.37(16), 3402–3404 (2012).
[CrossRef] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Kollárová, V.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys.8(3), 43 (2006).
[CrossRef]

Lalouat, L.

L. Lalouat, B. Cluzel, C. Dumas, L. Salomon, and F. de Fornel, “Imaging photoexcited optical modes in photonic-crystal cavities with a near-field probe,” Phys. Rev. B83(11), 115326 (2011).
[CrossRef]

Li, L.

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated Plasmon Beam: Nondiffracting versus Linearly Focused,” Phys. Rev. Lett.110(4), 046807 (2013).
[CrossRef]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

Li, T.

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated Plasmon Beam: Nondiffracting versus Linearly Focused,” Phys. Rev. Lett.110(4), 046807 (2013).
[CrossRef]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

Lin, J.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss Plasmon beam: A localized long-range nondiffracting surface wave,” Phys. Rev. Lett.109(9), 093904 (2012).
[CrossRef] [PubMed]

Lindquist, N. C.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science325(5940), 594–597 (2009).
[CrossRef] [PubMed]

Liu, X. Y.

J. X. Pu, X. Y. Liu, and S. Nemoto, “Partially coherent bottle beams,” Opt. Commun.252(1-3), 7–11 (2005).
[CrossRef]

Liu, Y.

Lu, C.

Maerkl, S. J.

Martin, O. J.

McGloin, D.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottle beams,” Opt. Commun.225(4-6), 215–222 (2003).
[CrossRef]

Melville, H.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottle beams,” Opt. Commun.225(4-6), 215–222 (2003).
[CrossRef]

Minovich, A.

A. E. Klein, A. Minovich, M. Steinert, N. Janunts, A. Tünnermann, D. N. Neshev, Y. S. Kivshar, and T. Pertsch, “Controlling plasmonic hot spots by interfering Airy beams,” Opt. Lett.37(16), 3402–3404 (2012).
[CrossRef] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Nagpal, P.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science325(5940), 594–597 (2009).
[CrossRef] [PubMed]

Nemoto, S.

J. X. Pu, X. Y. Liu, and S. Nemoto, “Partially coherent bottle beams,” Opt. Commun.252(1-3), 7–11 (2005).
[CrossRef]

Neshev, D. N.

A. E. Klein, A. Minovich, M. Steinert, N. Janunts, A. Tünnermann, D. N. Neshev, Y. S. Kivshar, and T. Pertsch, “Controlling plasmonic hot spots by interfering Airy beams,” Opt. Lett.37(16), 3402–3404 (2012).
[CrossRef] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Norris, D. J.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science325(5940), 594–597 (2009).
[CrossRef] [PubMed]

Oh, S.-H.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science325(5940), 594–597 (2009).
[CrossRef] [PubMed]

Padgett, M.

Padgett, M. J.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Pertsch, T.

A. E. Klein, A. Minovich, M. Steinert, N. Janunts, A. Tünnermann, D. N. Neshev, Y. S. Kivshar, and T. Pertsch, “Controlling plasmonic hot spots by interfering Airy beams,” Opt. Lett.37(16), 3402–3404 (2012).
[CrossRef] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Piestun, R.

Pu, J. X.

J. X. Pu, X. Y. Liu, and S. Nemoto, “Partially coherent bottle beams,” Opt. Commun.252(1-3), 7–11 (2005).
[CrossRef]

Quidant, R.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011).
[CrossRef]

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys.3(7), 477–480 (2007).
[CrossRef]

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D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett.109(16), 163903 (2012).
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[CrossRef] [PubMed]

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L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated Plasmon Beam: Nondiffracting versus Linearly Focused,” Phys. Rev. Lett.110(4), 046807 (2013).
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L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
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ChemPhysChem (1)

K. Wang and K. B. Crozier, “Plasmonic trapping with a gold nanopillar,” ChemPhysChem13(11), 2639–2648 (2012).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

C. J. Regan, L. Grave de Peralta, and A. A. Bernussi, “Two-dimensional Bessel-like surface plasmon-polariton beams,” J. Appl. Phys.112(10), 103107 (2012).
[CrossRef]

Nano Lett. (1)

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Scannable plasmonic trapping using a gold stripe,” Nano Lett.10(9), 3506–3511 (2010).
[CrossRef] [PubMed]

Nat Commun (1)

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat Commun2, 469 (2011).
[CrossRef] [PubMed]

Nat. Photonics (2)

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[CrossRef]

O. Brzobohatý, V. Karásek, M. Šiler, L. Chvátal, T. Čižmár, and P. Zemánek, “Experimental demonstration of optical transport, sorting and self-arrangement using a ‘tractor beam’,” Nat. Photonics7(2), 123–127 (2013).
[CrossRef]

Nat. Phys. (1)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys.3(7), 477–480 (2007).
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New J. Phys. (1)

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys.8(3), 43 (2006).
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Phys. Rev. B (1)

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[CrossRef]

Phys. Rev. Lett. (5)

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett.109(16), 163903 (2012).
[CrossRef] [PubMed]

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L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated Plasmon Beam: Nondiffracting versus Linearly Focused,” Phys. Rev. Lett.110(4), 046807 (2013).
[CrossRef]

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Science (1)

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Other (1)

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Supplementary Material (1)

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Figures (3)

Fig. 1
Fig. 1

(a) The Cosine Gauss Beam (CGB) is formed by interfering two plane waves propagating at an angle. Its wavevector, k x CGB , is therefore strictly smaller than the plane waves wavevector k spp . Two different methods to generate plasmonic bottle beams: (b) due to the wavevector mismatch between different CGBs ( θ 1 = 10 o and θ 2 = 20 o )interference effects will produce an in-plane intensity modulation along the propagation direction; (c) the same type of wavevector mismatch occurs when a CGB ( θ 1 = 10 o ) is superposed onto a co-propagating plane wave. The bottom figures show the near-field intensity distribution (electric field component normal to the plane) obtained from analytical calculations. In (b) the amplitudes of the two CGBs are equal. In (c), since these two surface waves have different propagation constant, and therefore different propagation losses, we control the amplitude of the electric field of the plane wave (term B in Eq. (3), scaled down to 1/1400 of that of the CGB, i.e. B = A/1400) to maximize the number of bottles. The parameters used in the calculations are: k spp = 8.7.10 6 +i1.7 10 4 m 1 , corresponding to SPPs excited by free space wavelength of about 730 nm [25] and W 0 = 8.10 6 . The dashed colored curves and the black curve locate the position of the intensity cross sections plotted in Fig. 2.

Fig. 2
Fig. 2

(a) Theoretical calculation of the length and width of the near-field bottles with respect to the half angle   θ between the two plane waves creating the Cosine-Gauss beam. The length and width are calculated by considering the distance between two consecutive minima along x and y respectively. (b) shows the normalized near-field intensity along the propagation axis x, for y = 0, as illustrated by the black curve in Fig. 1(c). The red, green and blue curves in (c) indicate intensity distribution after several propagation distances x (respectively x = 0, 25, 50 μm) (also indicated in Fig. 1(c) by the dashed lines normal to the propagation direction). The parameters used in the calculations are the same as those used in Fig. 1.

Fig. 3
Fig. 3

(a) Scanning electron micrograph of the plasmonic bottle beam coupler. The beam is formed by illuminating three gratings etched on the surface of a gold film. We designed the period of these gratings (fixed at 710nm) to match the wavelength of SPPs, in order to resonantly excite SPPs with illumination at normal incidence. Two of the gratings offset from each other by an angle, launch plane wave surface plasmons (blue lines) which interfere with each other along the symmetry axis to form the propagating Cosine-Gauss beam. An additional grating is then used to excite an on-axis surface plasmon plane wave (red lines), which in turn interferes with the cosine Gauss beam. The resulting interference pattern results in a periodic modulation of the intensity along the propagation direction,the bottle beam, as illustrated by the dashed black arrow. (b) Sketch of the near-field scanning optical microscope (NSOM) experimental configuration. The light is focused from the glass substrate side onto the gratings. The gratings launch the surface waves and the two dimensional near-field distribution is collected using the NSOM [26]. (c) Near-field scanning optical microscope (NSOM) images showing the in-plane intensity of several plasmonic bottle beams. By increasing the angle between the CGB couplers, we can excite bottle beams with different beating periods. Scanning electron micrograph of the corresponding grating couplers are also presented on the right part of the NSOM images. The bottle waves are created on the leftmost part of the devices, i.e. where all the waves overlap. From the NSOM images, we can also appreciate the non-diffracting character of the beams which preserve the size and the shape of the intensity pattern throughout the propagation distance (estimated at 30μm for an air/Au interface for an incident wavelength λ0 = 735 nm).

Equations (4)

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2 E z + ε d k 0 2 E z =0
k sp 2 = k x 2 + k y 2 = α 2 + ε d k 0 2 = k 0 2 ε d ε m ε d + ε m
E CGB z =A.f(x).exp(j k x x)cos( k y y)exp( y 2 w 0 2 )exp(αz)
E z =[ A.f(x).exp(j k x CGB x)cos( k y CGB y)+Bexp(j k sp x) ]exp( y 2 w 0 2 )exp(αz)

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