Abstract

Recent progress is emerging on nondiffracting subwavelength fields propagating in complex plasmonic nanostructures. In this paper, we present a thorough discussion on diffraction-free localized solutions of Maxwell’s equations in a periodic structure composed of nanowires. This self-focusing mechanism differs from others previously reported, which lie on regimes with ultraflat spatial dispersion. By means of the Maxwell–Garnett model, we provide a general analytical expression of the electromagnetic fields that can propagate along the direction of the cylinder’s axis, keeping its transverse waveform unaltered. Numerical simulations based on the finite element method support our analytical approach. In particular, moderate filling fractions of the metallic composite lead to nonresonant-plasmonic spots of light propagating with a size that remains far below the limit of diffraction.

© 2013 Optical Society of America

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2013 (4)

2012 (3)

K. Dolgaleva and R. W. Boyd, “Local-field effects in nanostructured photonic materials,” Adv. Opt. Photon. 4, 1–77 (2012).
[CrossRef]

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, 093904 (2012).
[CrossRef]

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4229–4248 (2012).
[CrossRef]

2011 (4)

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, 116802 (2011).
[CrossRef]

J. J. Miret, D. Pastor, and C. J. Zapata-Rodríguez, “Subwavelength surface waves with zero diffraction,” J. Nanophoton. 5, 051801 (2011).
[CrossRef]

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, 3191–3193 (2011).
[CrossRef]

C. J. Zapata-Rodríguez, S. Vuković, M. R. Belić, D. Pastor, and J. J. Miret, “Nondiffracting Bessel plasmons,” Opt. Express 19, 19572–19581 (2011).
[CrossRef]

2010 (3)

J. J. Miret and C. J. Zapata-Rodríguez, “Diffraction-free propagation of subwavelength light beams in layered media,” J. Opt. Soc. Am. B 27, 1435–1445 (2010).
[CrossRef]

S. N. Kurilkina, V. N. Belyi, and N. S. Kazak, “Transformation of high-order Bessel vortices in one-dimensional photonic crystals,” J. Opt. 12, 015704 (2010).
[CrossRef]

C. López-Mariscal and J. C. Gutiérrez-Vega, “Observation of optical guiding using thermal light,” J. Opt. 12, 075702 (2010).
[CrossRef]

2009 (2)

2008 (1)

2007 (1)

2006 (5)

D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23, 391–403 (2006).
[CrossRef]

Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. 31, 1726–1728 (2006).
[CrossRef]

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73, 033108 (2006).
[CrossRef]

2005 (2)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett. 30, 2611–2613 (2005).
[CrossRef]

2004 (1)

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477–481 (2004).
[CrossRef]

2003 (2)

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175–183 (2003).
[CrossRef]

2002 (2)

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

1996 (1)

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[CrossRef]

1987 (2)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

Aiello, A.

Alessandri, K.

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

Arriaga, J.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Atrashchenko, A. V.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4229–4248 (2012).
[CrossRef]

Belic, M. R.

Belov, P. A.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4229–4248 (2012).
[CrossRef]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73, 033108 (2006).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Belyi, V. N.

S. N. Kurilkina, V. N. Belyi, and N. S. Kazak, “Transformation of high-order Bessel vortices in one-dimensional photonic crystals,” J. Opt. 12, 015704 (2010).
[CrossRef]

Bhuyan, M. K.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University, 1999).

Boyd, R. W.

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, 093904 (2012).
[CrossRef]

Chen, W.

Chen, Z.

Christodoulides, D. N.

Ciattoni, A.

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175–183 (2003).
[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, 093904 (2012).
[CrossRef]

Courvoisier, F.

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, 093904 (2012).
[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, 093904 (2012).
[CrossRef]

Dholakia, K.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Dolgaleva, K.

Drachev, V. P.

Dudley, A.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24, 22–29 (2013).
[CrossRef]

Dudley, J. M.

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Fagerholm, J.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[CrossRef]

Fahrbach, F. O.

Forbes, A.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24, 22–29 (2013).
[CrossRef]

Friberg, A. T.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[CrossRef]

Furfaro, L.

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

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, 093904 (2012).
[CrossRef]

Ghosh, G.

E. D. Palik and G. Ghosh, The Electronic Handbook of Optical Constants of Solids (Academic, 1999).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill International Editions, 1996).

Gurchenkov, V.

Gutiérrez-Vega, J. C.

C. López-Mariscal and J. C. Gutiérrez-Vega, “Observation of optical guiding using thermal light,” J. Opt. 12, 075702 (2010).
[CrossRef]

Halevi, P.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Hao, Y.

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73, 033108 (2006).
[CrossRef]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Huttunen, J.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[CrossRef]

Inoue, T.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

Jacquot, M.

Janner, K.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477–481 (2004).
[CrossRef]

Janunts, N.

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, 116802 (2011).
[CrossRef]

Kazak, N. S.

S. N. Kurilkina, V. N. Belyi, and N. S. Kazak, “Transformation of high-order Bessel vortices in one-dimensional photonic crystals,” J. Opt. 12, 015704 (2010).
[CrossRef]

Kildishev, A. V.

Kim, D.

Kivshar, Y. S.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4229–4248 (2012).
[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, 116802 (2011).
[CrossRef]

Kizuka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

Klein, A. E.

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, 116802 (2011).
[CrossRef]

Krokhin, A. A.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Kurilkina, S. N.

S. N. Kurilkina, V. N. Belyi, and N. S. Kazak, “Transformation of high-order Bessel vortices in one-dimensional photonic crystals,” J. Opt. 12, 015704 (2010).
[CrossRef]

Lacourt, P.-A.

Laporta, P.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477–481 (2004).
[CrossRef]

Lavery, M.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24, 22–29 (2013).
[CrossRef]

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, 093904 (2012).
[CrossRef]

Liu, Y.

Longhi, S.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477–481 (2004).
[CrossRef]

López-Mariscal, C.

C. López-Mariscal and J. C. Gutiérrez-Vega, “Observation of optical guiding using thermal light,” J. Opt. 12, 075702 (2010).
[CrossRef]

Lu, C.

Manela, O.

Marques, R.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Maslovski, S. I.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Matsuoka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Minovich, A.

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, 116802 (2011).
[CrossRef]

Miret, J. J.

Morgan, D. P.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[CrossRef]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Nassoy, P.

Nefedov, I. S.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Neshev, D. N.

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, 116802 (2011).
[CrossRef]

Ornigotti, M.

Padgett, M.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24, 22–29 (2013).
[CrossRef]

Palik, E. D.

E. D. Palik and G. Ghosh, The Electronic Handbook of Optical Constants of Solids (Academic, 1999).

Palma, C.

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175–183 (2003).
[CrossRef]

Pastor, D.

J. J. Miret, D. Pastor, and C. J. Zapata-Rodríguez, “Subwavelength surface waves with zero diffraction,” J. Nanophoton. 5, 051801 (2011).
[CrossRef]

C. J. Zapata-Rodríguez, S. Vuković, M. R. Belić, D. Pastor, and J. J. Miret, “Nondiffracting Bessel plasmons,” Opt. Express 19, 19572–19581 (2011).
[CrossRef]

Pendry, J. B.

Pertsch, T.

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, 116802 (2011).
[CrossRef]

Podolskiy, V. A.

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Rohrbach, A.

Salomaa, M. M.

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[CrossRef]

Segev, M.

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Sihvola, A.

A. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, 1999).

Silveirinha, M.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Simovski, C. R.

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4229–4248 (2012).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Smith, D. R.

Sudhakaran, S.

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73, 033108 (2006).
[CrossRef]

Tretyakov, S. A.

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Vukovic, S.

Wang, S.

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University, 1999).

Yin, X.

Yoon, S. J.

Zapata-Rodrguez, C. J.

Zapata-Rodríguez, C. J.

Zhan, Q.

Zhang, P.

Zhang, X.

Adv. Mater. (1)

C. R. Simovski, P. A. Belov, A. V. Atrashchenko, and Y. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mater. 24, 4229–4248 (2012).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. A (1)

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

J. Nanophoton. (1)

J. J. Miret, D. Pastor, and C. J. Zapata-Rodríguez, “Subwavelength surface waves with zero diffraction,” J. Nanophoton. 5, 051801 (2011).
[CrossRef]

J. Opt. (2)

S. N. Kurilkina, V. N. Belyi, and N. S. Kazak, “Transformation of high-order Bessel vortices in one-dimensional photonic crystals,” J. Opt. 12, 015704 (2010).
[CrossRef]

C. López-Mariscal and J. C. Gutiérrez-Vega, “Observation of optical guiding using thermal light,” J. Opt. 12, 075702 (2010).
[CrossRef]

J. Opt. B (1)

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477–481 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (3)

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Opt. Commun. (1)

A. Ciattoni and C. Palma, “Nondiffracting beams in uniaxial media propagating orthogonally to the optical axis,” Opt. Commun. 224, 175–183 (2003).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Opt. Photon. News (1)

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24, 22–29 (2013).
[CrossRef]

Phys. Rev. B (4)

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

P. A. Belov, Y. Hao, and S. Sudhakaran, “Subwavelength microwave imaging using an array of parallel conducting wires as a lens,” Phys. Rev. B 73, 033108 (2006).
[CrossRef]

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit (homogenization) for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Phys. Rev. E (1)

J. Fagerholm, A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, “Angular-spectrum representation of nondiffracting X waves,” Phys. Rev. E 54, 4347–4352 (1996).
[CrossRef]

Phys. Rev. Lett (1)

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, 116802 (2011).
[CrossRef]

Phys. Rev. Lett. (2)

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, 093904 (2012).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Science (1)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Other (6)

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

E. D. Palik and G. Ghosh, The Electronic Handbook of Optical Constants of Solids (Academic, 1999).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill International Editions, 1996).

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University, 1999).

A. E. Siegman, Lasers (University Science Books, 1986).

A. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, 1999).

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Figures (11)

Fig. 1.
Fig. 1.

Periodic array of nanowires made of a metal with dielectric constant ϵm, distributed in a squared lattice, and hosted in a dielectric medium with permittivity ϵd. The radius of the wires is r, and the lattice constant is a. Beam propagation is driven along the wire’s axis, which is the z axis.

Fig. 2.
Fig. 2.

(a) Conical distribution of wave vectors in agreement with the plane-wave Fourier expansion of BBs in effective uniaxial media. (b) Annular-shaped spectrum of TM BBs, P1(θ), and TE BBs, P2(θ). The arrows illustrate the angular dependence of the spectra.

Fig. 3.
Fig. 3.

Variation of ϵ and ϵ in terms of the filling fraction, by using the Maxwell–Garnett model, for silver wires hosted in alumina at λ0=700nm. Inset: Schematic illustration of the anisotropic medium that homogenizes the wire plasmonic crystal of Fig. 1.

Fig. 4.
Fig. 4.

Isofrequency curve in the βkt plane for TE and TM modes propagating in an Ag-wire medium hosted in alumina at λ0=700nm. Equations (6) and (12) are plotted for a filling fraction f=0.1 (ϵ=4.07 and ϵ=0.75) and for f=0.2 where ϵ=5.41 and ϵ=1.6. We also include a shaded area bounded by the isofrequency curve of Al2O3 (f=0) wherein diffraction-limited waves are included. Black dots represent frequencies used in Fig. 5 and succeeding figures.

Fig. 5.
Fig. 5.

Wave field |hx|2 for BBs associated with (a) e waves and (b) o waves propagating in a homogenized Ag-Al2O3 medium (f=0.1) provided that β=0.8k0. We represent the fields for B1=ZB=B1 and A1=i=A1, respectively. Box dimensions of the contour plots are 2μm×2μm.

Fig. 6.
Fig. 6.

(a) Isofrequency curve for the Ag-wire medium hosted in Al2O3 (f=0.1 and d=5nm) assuming β=0.8k0. The insets illustrate the angular dependence of the two branches. (b) Normalized intensity of the x component of the field hkB for Bloch modes pointed as A, B, and C in the isofrequency curve. Units are set in dB. (c) Field intensity |hxq|2 resulting from Eq. (25) for nondiffracting beams associated with e waves (q=1) and o waves (q=2).

Fig. 7.
Fig. 7.

(a) Isofrequency curve for a metallic compound of f=0.2 and a wire diameter of d=5nm. Again the propagation constant is β=0.8k0. The inset illustrates the angular dependence of the single branch. (b) Wave field |hx2|2 corresponds to a nondiffracting beam that gets connected with the TE BB in the EMA.

Fig. 8.
Fig. 8.

(a) Isofrequency curve for the Ag-Al2O3 compound at a propagation constant β=0.8k0. The case of a wire diameter d=50nm (dashed lines) is compared with EMA estimations (solid lines). (b) Intensity |x·hkB|2 for Bloch modes at wave vectors set by the points A, B, and C. Scaling is set in dB.

Fig. 9.
Fig. 9.

Transverse profile of the intensity |hxq|2 corresponding to a nondiffracting beam of β=0.8k0 propagating in a wire medium of f=0.1 with cylinder diameter d=50nm in the cases: (a) q=1 and (b) q=2.

Fig. 10.
Fig. 10.

Intensity |hx2|2 of diffraction-free beams propagating at an on-axis spatial frequency β=0.8k0 in a Ag-Al2O3 compound of metal diameter d=50nm and filling fraction f=0.2. The origin r=(0,0) of the coordinate systems is set (a) at the center of a cylinder and (b) at midpoint of two adjacent wires. The field profile near the beam axis is scaled for the sake of clarity.

Fig. 11.
Fig. 11.

(a) Normalized on-axis intensity if silver losses are included in the numerical simulation. In this case, β=0.8k0 in a Ag-Al2O3 compound of metal diameter d=50nm and filling fraction f=0.2. (b) Transverse profile of the wave field as the beam propagates along the z axis.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

×(ϵ1×H)=k02H,
(ϵk02β2+t2)ht=ϵ1tϵ×(t×ht),
ϵ=[(1+f)ϵm+(1f)ϵd]ϵd(1f)ϵm+(1+f)ϵd,
ϵ=fϵm+(1f)ϵd,
(kt2+t2)hz=0,
kto=ϵk02β2,
hzo(r,ϕ)=ktoβm=Amψmo(r,ϕ),
ψmo(r,ϕ)=exp(imϕ)Jm(ktor),
ψmo(r,ϕ)=(i)m02πexp(imθ)exp(iktor)dθ.
hto=12m=Am[i(ψm+1oψm1o)x+(ψm+1o+ψm1o)y].
(ϵk02β2+ϵϵt2)ht=iβ(1ϵϵ)thz,
kte=ϵk02β2ϵ/ϵ,
(ϵk02β2+ϵϵt2)ez=0
eze(r,ϕ)=kteβm=Bmψme(r,ϕ),
hte=+12ZBm=Bm[(ψm+1e+ψm1e)x+i(ψm+1e+ψm1e)y],
F{g}(kt)=g(r)exp(iktr)d2r.
F{ψm(r,ϕ)}=(2π)2kt1(i)mexp(imθ)δ(kt|kt|),
0f<ϵdϵdϵm.
0f<ϵm+ϵdϵmϵd.
hxo(r,ϕ)=02πP2(θ)exp(iktor)dθ,
P2(θ)=1+cos2θ,
P1(θ)=1cos2θ,
HkB=hkB(r)exp(ikBr)exp(iβziωt),
a/2a/2dxa/2a/2dy|x·hkB(x,y)|2=1,
hxq(r)=02π[x·hkBq(r)]Pq(θ)exp(ikBqr)dθ,

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