## Nondiffracting Bessel plasmons |

Optics Express, Vol. 19, Issue 20, pp. 19572-19581 (2011)

http://dx.doi.org/10.1364/OE.19.019572

Acrobat PDF (2940 KB)

### Abstract

We report on the existence of nondiffracting Bessel surface plasmon polaritons (SPPs), advancing at either superluminal or subluminal phase velocities. These wave fields feature deep subwavelength FWHM, but are supported by high-order homogeneous SPPs of a metal/dielectric (MD) superlattice. The beam axis can be relocated to any MD interface, by interfering multiple converging SPPs with controlled phase matching. Dissipative effects in metals lead to a diffraction-free regime that is limited by the energy attenuation length. However, the ultra-localization of the diffracted wave field might still be maintained by more than one order of magnitude.

© 2011 OSA

## 1. Introduction

3. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature **419**(6903), 145–147 (2002). [CrossRef] [PubMed]

4. J. Jezek, T. Cizmar, V. Nedela, and P. Zemanek, “Formation of long and thin polymer fiber using nondiffracting beam,” Opt. Express **14**(19), 8506–8515 (2006). [CrossRef] [PubMed]

5. M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express **18**(2), 566–574 (2010). [CrossRef] [PubMed]

6. B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E **55**(3, Part B), 3539–3545 (1997). [CrossRef]

7. Y. Kartashov, V. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. **93**(9), 093904 (2004). [CrossRef] [PubMed]

8. M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E **68**, 016613 (2003). [CrossRef]

9. C. J. Zapata-Rodríguez and M. A. Porras, “X-wave bullets with negative group velocity in vacuum,” Opt. Lett. **31**(23), 3532–3534 (2006). [CrossRef] [PubMed]

10. T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. **70**, 1401–1404 (1993). [CrossRef] [PubMed]

11. L. Van Dao, K. B. Dinh, and P. Hannaford, “Generation of extreme ultraviolet radiation with a Bessel–Gaussian beam,” Appl. Phys. Lett. **95**(13) (2009). [CrossRef]

12. J. Fan, E. Parra, and H. Milchberg, “Resonant self-trapping and absorption of intense Bessel beams,” Phys. Rev. Lett. **84**(14), 3085–3088 (2000). [CrossRef] [PubMed]

13. P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive, and dissipative Kerr media,” Phys. Rev. Lett. **99**(22), 223902 (2007). [CrossRef]

14. D. Faccio and P. Di Trapani, “Conical-wave nonlinear optics: From Raman conversion to extreme UV generation,” Laser Phys. **18**(3), 253–262 (2008). [CrossRef]

*et al.*reported the first experimental result concerning an efficient excitation of local SPPs, by using the zeroth-order BB [15

15. H. Kano, D. Nomura, and H. Shibuya, “Excitation of surface-plasmon polaritons by use of a zeroth-order Bessel beam,” Appl. Opt. **43**(12), 2409–2411 (2004). [CrossRef] [PubMed]

16. K. J. Moh, X. C. Yuan, J. Bu, S. W. Zhu, and B. Z. Gao, “Radial polarization induced surface plasmon virtual probe for two-photon fluorescence microscopy,” Opt. Lett. **34**(7), 971–973 (2009). [CrossRef] [PubMed]

17. Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. **31**(11), 1726–1728 (2006). [CrossRef] [PubMed]

19. W. Chen and Q. Zhan, “Realization of an evanescent Bessel beam via surface plasmon interference excited by a radially polarized beam,” Opt. Lett. **34**(6), 722–724 (2009). [CrossRef] [PubMed]

20. A. Shaarawi, B. Tawfik, and I. Besieris, “Superluminal advanced transmission of X waves undergoing frustrated total internal reflection: the evanescent fields and the Goos–Hanchen effect,” Phys. Rev. E **66**(4, Part 2), 046626 (2002). [CrossRef]

27. G. Rui, Y. Lu, P. Wang, H. Ming, and Q. Zhan, “Evanescent Bessel beam generation through filtering highly focused cylindrical vector beams with a defect mode one-dimensional photonic crystal,” Opt. Commun. **283**(10), 2272–2276 (2010). [CrossRef]

28. C. J. Zapata-Rodríguez and J. J. Miret, “Diffraction-free beams in thin films,” J. Opt. Soc. Am. A **27**, 663–670 (2010). [CrossRef]

29. C. Zapata-Rodríguez and J. Miret, “Subwavelength nondiffractting beams in multilayered media,” Appl. Phys. A **103**, 699–702 (2011). [CrossRef]

30. S. Longhi and D. Janner, “X-shaped waves in photonic crystals,” Phys. Rev. B **70**, 235123 (2004). [CrossRef]

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

35. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. **35**, 2082–2084 (2010). [CrossRef] [PubMed]

## 2. High-order plasmonic modes

*m*= {1,2, ⋯ ,

*M*}. For convenience, we cast the magnetic field of each plasmonic mode as where

*k*is the wavenumber of the

_{m}*m*th-order surface mode and

*θ*determines its direction of propagation in the plane. The wavenumber

_{m}*k*is frequently given in terms of the plasmonic spatial frequency

_{m}*k*=

_{p}*c*/

*ω*. Furthermore, in order to excite surface resonances in the interfaces of our device,

_{p}*p*-polarized waves should be employed. Therefore, we consider TM waves whose magnetic field is confined in the

*xz*plane, that is

*h⃗*= (

_{m}*h*, 0,

_{xm}*h*). We point out that the magnetic field is solenoidal, leading to the equation

_{zm}*h*= −tan

_{zm}*θ*. We conclude that the problem may be fully described in terms of the scalar wavefield

_{m}h_{xm}*h*, from which other electromagnetic components may be derived.

_{xm}*h*(

_{xm}*y*) distributed inside our device. The general procedure may be followed from Ref. [33

33. J. J. Miret and C. J. Zapata-Rodríguez, “Diffraction-free propagation of subwavelength light beams in layered media,” J. Opt. Soc. Am. B **27**(7), 1435–1445 (2010). [CrossRef]

*N*of metallic strata, the periodic medium operates just as a photonic lattice whose unit cell translation matrix is here denoted by

*T*. The 2 × 2 matrix

*T*depends upon the wavenumber

*k*of the surface plasmon, but it is otherwise independent of the angular coordinate

_{m}*θ*. For an ideally unbounded photonic crystal, the values of

_{m}*k*are determined by the dispersion equation [36]: where

_{m}*L*=

*w*+

_{d}*w*is the period of the lattice and

_{m}*k*is a Bloch wavenumber. As a consequence, the values of

_{ym}*k*are restricted to allowed bands, which emerge when the trace of

_{m}*T*spans the region from −2 to 2, as depicted in Fig. 1(b). In the case presented we neglected material losses, by taking

*γ*= 0; thus

*T*became unimodular. Since the periodic structure is finite, solutions are derived from the equation [

*T*]

^{N}_{11}= 0, which is equivalent to [37

37. S. M. Vukovic, Z. Jaksic, and J. Matovic, “Plasmon modes on laminated nanomembrane-based waveguides,” J. Nanophoton. **4**, 041770 (2010). [CrossRef]

*N*= 11. Now, the wavenumbers

*k*form a discrete set of

_{m}*M*real numbers. This is shown in Fig. 1(b) where we obtained

*M*= 12 high-order SPPs. The modal field decays exponentially in the limit |

*y*| → ∞ and it may vary substantially within the stratified medium, as shown in Fig. 1(c). However, these surface waves are homogeneous in the

*xz*plane, as shown in Eq. (2). In general, the larger the number

*N*of layers, the higher the number

*M*= max(

*m*) of plasmonic modes sustainable in such a MD nanostructure.

## 3. Diffraction-free sinusoidal beams

*k*is governed by the MD multilayer. However, we may modify ad lib the spatial frequency

_{m}*β*≥ 0 along the beam axis of a nondiffracting SPP, here taken to be the

*z*axis, provided

*β*≤

*k*. For that purpose we consider the superposition of two homogeneous surface plasmons of the same wavenumber

_{m}*k*, but different directions of propagation, given by the angles +

_{m}*θ*and −

_{m}*θ*, respectively, as shown in Fig. 2(a). The projections of the wave vectors onto the

_{m}*z*axis coincide with

*β*=

*k*cos

_{m}*θ*leading to a phase front advancing at a velocity

_{m}*v*=

_{p}*ω*/

*β*along such a direction. Assuming additionally that both plasmonic modes become equal in strength |

*h*|, the net flux of power along the

_{xm}*x*axis is zero. The resultant field

*H*=

_{xm}*h*(

_{xm}*y*)exp (

*iβz*)cos (

*k*+

_{xm}x*φ*) yields Young fringes whose maxima are controlled by the spatial frequency

_{m}*k*=

_{xm}*k*sin

_{m}*θ*and the dephasing

_{m}*φ*of the surface plasmons [see Fig. 2(b)].

_{m}*n*=

_{m}*k*/

_{m}*k*

_{0}, where

*k*

_{0}= 2

*π*/

*λ*

_{0}. In other words, the sinusoidal SPP runs faster than a single-mode SPP. In general,

*β*= 6.12

*μ*m

^{−1}which, in practical terms, is associated with a luminal effective-mode index

## 4. Ultra-confined modes

35. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. **35**, 2082–2084 (2010). [CrossRef] [PubMed]

*m*of the mode. Therefore, we may conceive a coherent superposition of plasmonic cosine waves exhibiting the same propagation constant

*β*along the

*z*axis, provided that

*β*≤

*k*for all

_{m}*m*involved. This condition fixes the values of

*θ*, as outlined in Fig. 2(c) for the twelve distinct SPPs. Moreover, localization around the beam axis, set on a given MD interface

_{m}*y*=

*y*

_{0}at

*x*= 0, is achieved by adapting the individual dephases such that

*φ*= 0, giving

_{m}*h*(

_{xm}*y*

_{0}) in order to match their phases at the beam axis. Furthermore, we seek for values of

*h*(

_{xm}*y*

_{0}) leading to a field

*H*(

_{x}*x*,

*y*

_{0}, 0) to trace a Bessel profile. We may express the zeroth-order Bessel function as where

*k*

_{⊥}is higher than any

*k*involved. Our procedure is based on the fact that the integral (7) approaches the series expansion (6) given at (

_{xm}*x*,

*y*

_{0}, 0) by means of a numerical quadrature with preassigned nodes

*k*[38]. The solutions

_{xm}*h*(

_{xm}*y*

_{0}) =

*f*(

*k*

_{⊥},

*k*) ∫

_{xm}*L*(

_{m}*k*)

_{x}*dk*of the quadrature, expressed in terms of the Lagrange polynomials

_{x}*L*, provide a wave field through Eq. (6) whose intensity on the MD interface is approximately

_{m}*M*= 12 modes involved at

*λ*

_{0}= 1.55

*μ*m. The central part of the waveform is accurately represented by the Bessel function, whose highest main peak has an intensity FWHM Δ

*= 0.38*

_{x}*μ*m. The error visible in the wings comes from difference between the finite series expansion and the integral involving Bessel function.

*β*close to

*k*

_{1}= min (

*k*), causing the coefficients

_{m}*h*(

_{xm}*y*

_{0}) ≥ 0 to be in phase. If the number

*M*of modes becomes large, we may conveniently break up the integral (7) into several parts, leading to the well-known compound rules [38]. Occasionally, we may disregard some modal solutions in Eq. (6), without significant loss of accuracy. Finally, the error term of the quadrature formula decreases for

*k*

_{⊥}approaching the maximum value of all

*k*involved, that is

_{xm}*k*.

_{xM}*x*= 0 on the MD surface

*y*=

*y*

_{0}. Under ordinary conditions it will not be found at a point out of the beam axis, where such a phase matching holds. As a consequence, a strong confinement of the plasmonic BB is expected to occur around (

*x*,

*y*) = (0,

*y*

_{0}). Note, however, that nonlocality of high-order SPPs [39

39. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. **90**(19), 191109 (2007). [CrossRef]

*k*

_{2}= 6.16

*μ*m

^{−1}. We conclude that it is propitious for a phase matching at the cladding boundaries, but it leads to spurious sidelobes in the case when the beam axis is set around the center of the layered waveguide. Contrarily, the SPP of

*k*

_{12}= 8.45

*μ*m

^{−1}enhances the field in the central part of the metal-dielectric structure, which benefits the bright spots traveling on a MD interface near the midpoint. We point out that some SPPs will be useful for both cases, as displayed for

*k*

_{6}= 7.36

*μ*m

^{−1}, but others like

*k*

_{11}= 8.38

*μ*m

^{−1}might disable light confinement in the mentioned regions.

*H*|

_{x}^{2}derived from Eq. (6) when the phase matching is boosted at different surfaces of the metal-dielectric nanostructure. In Fig. 3(a) the phase matching is accomplished on the interface that belongs to the central silver film. For convenience we discarded 5 plasmonic modes with indices

*m*= {1,2,7,9,11}, which induced a field localization out of the beam axis. The numerical quadrature was set for the BB that has a transverse frequency

*k*

_{⊥}= 5.90

*μ*m

^{−1}. The anisotropic spot displays a sub-wavelength FWHM Δ

*y*= 160 nm along the

*y*axis, and an in-plane FWHM Δ

*x*= 416 nm. In Fig. 3(b) the beam axis is relocated on the boundary of the MD device and the cladding. In this case we employed 8 different surface modes (from

*m*= 1 to

*m*= 8) for the Bessel quadrature, with

*k*

_{⊥}= 5.20

*μ*m

^{−1}. As a consequence, the FWHM Δ

*x*= 430 nm results in a slightly higher value than that obtained above, otherwise Δ

*y*= 113 nm. This is also illustrated in Fig. 3(c) by means of the full 3D arrangement. Note that the transverse wave field in (a) is essentially different from (b), in spite of using roughly the same in-plane Bessel distribution.

*xz*plane, however, out-of-plane intensity is determined by the geometry and materials composing the multilayered waveguide. The Bessel-like distribution along the

*x*axis cannot be maintained in other directions, due to the intrinsic anisotropy of the stratified medium. Moreover, the field of the Bessel plasmon is enhanced along distinctive paths in the transverse

*xy*plane. These characteristic directions are usually associated with those of the energy flow [40]. To obtain the lengthwise paths where the field is confined near the beam axis, we calculate the Poynting vector for each homogeneous SPP. This procedure is rendered possible by the following important result: The group velocity

*u⃗*=

_{m}*dω*/

*dk⃗*represents the average Poynting vector in the

_{tm}*xy*plane divided by the average energy density for every Bloch mode of the MD lattice, where

*k⃗*= (

_{tm}*k*,

_{xm}*k*). Accordingly, the energy flux of the nondiffracting Bessel plasmon travels normally to the beam axis along the gradients provided from the dispersion contour.

_{ym}*ω*= 0.0942

*ω*, that corresponds to the vacuum wavelength

_{p}*λ*

_{0}= 1.55

*μ*m. The photonic band structure of this 1D MD crystal can be calculated numerically using Eq. (3). For each plasmonic Bloch mode we present a straight line whose slope

*s*is governed by the gradient computed from the dispersion contour, that is the direction of the vector

_{m}*u⃗*, as

_{m}*s*= [

_{m}*u⃗*]

_{m}*/[*

_{y}*u⃗*]

_{m}*. Note that the 1st- and 2nd-order SPPs are located in the bandgap of the periodic MD medium and therefore are excluded from the present analysis. The strongly scattering MD lattice modifies the dispersion relation of light so much that the dispersion contour is far from being circular. As a result, the velocities*

_{x}*u⃗*involved are clumped into two classes, including low numerical aperture wavevectors whose slopes ±

_{m}*s*do not differ substantially. In Fig. 4(b) we represent the straight lines intersecting on the beam axis where the phase matching is accomplished, as shown in Fig. 3(b). We verify that light is bounded primarily at regions marked by the streamlines of the Poynting vectors associated with each plasmonic mode.

_{m}## 5. Dissipation effects

*γ*= 0. Excitations of free electrons of real metals however suffer damping. Therefore, we consider now the case when

*γ*in Eq. (1) is no longer zero and with it the SPP propagation constant

*k*becomes complex. The traveling SPPs are damped with an energy attenuation length

_{m}*l*= [2Im (

_{m}*k*)]

_{m}^{−1}. As a consequence, the nondiffracting nature of plasmonic BBs is preserved, but each

*m*th-order SPP contributing in the summation of Eq. (6) runs a distance shorter than its propagation length

*l*. This effect is illustrated in Fig. 5(a). The phase fronts of the field

_{m}*H*advance with a constant velocity, provided

_{x}*β*= Re (

*k*) cos

_{m}*θ*is conserved. The modal angle

_{m}*θ*brings to effect that each causal plasmonic signal travels its own distance

_{m}*l*, to reach the beam axis at the

_{m}*z*axis coordinate

*l*/ cos

_{m}*θ*. In our numerical simulation

_{m}*l*

_{1}= 267

*μ*m,

*l*

_{2}= 45.0

*μ*m, and

*l*decreases fast at higher

_{m}*m*, up to

*l*

_{11}= 3.09

*μ*m and

*l*

_{12}= 3.06

*μ*m; however

*θ*≪ 1 leading to an incessant drop of higher

_{m}*m*th-order terms taking part in the summation in Eq. (6). Consequently, the on-axis intensity is reduced by a factor 1/

*e*at

*z*= 6.8

*μ*m, as shown in Fig. 5(b), which is primarily determined by the energy attenuation lengths of the highest-order SPPs. Fig. 5(c) elucidates how the Bessel profile of the nondiffracting plasmon evolves toward a cosine amplitude distribution. This evidences that the 1st-order sinusoidal SPP contributes exclusively to the wave superposition (6) at sufficiently long distances.

## 6. Conclusions

*L*= 0.30

*μ*m. We have analyzed a device including 11 nanomembranes of 10 nm each, operating at telecom wavelength

*λ*

_{0}= 1.55

*μ*m. A Bessel wave field with intensity FWHM Δ

*= 0.38*

_{x}*μ*m is guided along the metal/dielectric flat interface at a propagation constant

*β*= 6.12

*μ*m

^{−1}, leading to a luminal phase velocity

*v*= 0.66

_{p}*c*. The origin of this interesting phenomenon lies in the phase-matched excitation of superlattice of high-order SPPs. Dissipative effects in silver leads to a diffraction-free regime that is limited by energy attenuation length of

*l*= 6.8

*μ*m. However, localization about the beam axis is maintained along a range which is higher than

*l*by more than one order of magnitude.

## Acknowledgments

## References and links

1. | J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A |

2. | J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. |

3. | V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature |

4. | J. Jezek, T. Cizmar, V. Nedela, and P. Zemanek, “Formation of long and thin polymer fiber using nondiffracting beam,” Opt. Express |

5. | M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express |

6. | B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E |

7. | Y. Kartashov, V. Vysloukh, and L. Torner, “Rotary solitons in Bessel optical lattices,” Phys. Rev. Lett. |

8. | M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E |

9. | C. J. Zapata-Rodríguez and M. A. Porras, “X-wave bullets with negative group velocity in vacuum,” Opt. Lett. |

10. | T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. |

11. | L. Van Dao, K. B. Dinh, and P. Hannaford, “Generation of extreme ultraviolet radiation with a Bessel–Gaussian beam,” Appl. Phys. Lett. |

12. | J. Fan, E. Parra, and H. Milchberg, “Resonant self-trapping and absorption of intense Bessel beams,” Phys. Rev. Lett. |

13. | P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of conical waves in focusing, dispersive, and dissipative Kerr media,” Phys. Rev. Lett. |

14. | D. Faccio and P. Di Trapani, “Conical-wave nonlinear optics: From Raman conversion to extreme UV generation,” Laser Phys. |

15. | H. Kano, D. Nomura, and H. Shibuya, “Excitation of surface-plasmon polaritons by use of a zeroth-order Bessel beam,” Appl. Opt. |

16. | K. J. Moh, X. C. Yuan, J. Bu, S. W. Zhu, and B. Z. Gao, “Radial polarization induced surface plasmon virtual probe for two-photon fluorescence microscopy,” Opt. Lett. |

17. | Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. |

18. | A. Bouhelier, F. Ignatovich, A. Bruyant, C. Huang, G. C. d. Francs, J.-C. Weeber, A. Dereux, G. P. Wiederrecht, and L. Novotny, “Surface plasmon interference excited by tightly focused laser beams,” Opt. Lett. |

19. | W. Chen and Q. Zhan, “Realization of an evanescent Bessel beam via surface plasmon interference excited by a radially polarized beam,” Opt. Lett. |

20. | A. Shaarawi, B. Tawfik, and I. Besieris, “Superluminal advanced transmission of X waves undergoing frustrated total internal reflection: the evanescent fields and the Goos–Hanchen effect,” Phys. Rev. E |

21. | S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B |

22. | W. Williams and J. Pendry, “Generating Bessel beams by use of localized modes,” J. Opt. Soc. Am. A |

23. | C. J. Zapata-Rodríguez, M. T. Caballero, and J. J. Miret, “Angular spectrum of diffracted wave fields with apochromatic correction,” Opt. Lett. |

24. | A. V. Novitsky and L. M. Barkovsky, “Total internal reflection of vector Bessel beams: Imbert-Fedorov shift and intensity transformation,” J. Opt. A |

25. | V. N. Belyi, N. S. Kazak, S. N. Kurilkina, and N. A. Khilo, “Generation of TE- and TH-polarized Bessel beams using one-dimensional photonic crystal,” Opt. Commun. |

26. | D. Mugnai and P. Spalla, “Electromagnetic propagation of Bessel-like localized waves in the presence of absorbing media,” Opt. Commun. |

27. | G. Rui, Y. Lu, P. Wang, H. Ming, and Q. Zhan, “Evanescent Bessel beam generation through filtering highly focused cylindrical vector beams with a defect mode one-dimensional photonic crystal,” Opt. Commun. |

28. | C. J. Zapata-Rodríguez and J. J. Miret, “Diffraction-free beams in thin films,” J. Opt. Soc. Am. A |

29. | C. Zapata-Rodríguez and J. Miret, “Subwavelength nondiffractting beams in multilayered media,” Appl. Phys. A |

30. | S. Longhi and D. Janner, “X-shaped waves in photonic crystals,” Phys. Rev. B |

31. | O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett. |

32. | J. J. Miret and C. J. Zapata-Rodríguez, “Diffraction-free beams with elliptic Bessel envelope in periodic media,” J. Opt. Soc. Am. B |

33. | J. J. Miret and C. J. Zapata-Rodríguez, “Diffraction-free propagation of subwavelength light beams in layered media,” J. Opt. Soc. Am. B |

34. | J. J. Miret, D. Pastor, and C. J. Zapata-Rodriguez, “Subwavelength surface waves with zero diffraction,” J. Nanophoton. |

35. | A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. |

36. | P. Yeh, |

37. | S. M. Vukovic, Z. Jaksic, and J. Matovic, “Plasmon modes on laminated nanomembrane-based waveguides,” J. Nanophoton. |

38. | H. M. Antia, |

39. | J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. |

40. | J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(350.5500) Other areas of optics : Propagation

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: July 28, 2011

Revised Manuscript: September 2, 2011

Manuscript Accepted: September 2, 2011

Published: September 22, 2011

**Citation**

Carlos J. Zapata-Rodríguez, Slobodan Vuković, Milivoj R. Belić, David Pastor, and Juan J. Miret, "Nondiffracting Bessel plasmons," Opt. Express **19**, 19572-19581 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19572

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### References

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