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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 14270–14280
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The role of short and long range surface plasmons for plasmonic focusing applications

Avner Yanai and Uriel Levy  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 14270-14280 (2009)
http://dx.doi.org/10.1364/OE.17.014270


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Abstract

We propose and analyze a new plasmonic lens allowing the simultaneous focusing of both short and long range surface plasmons polaritons. The considered geometry is circularly symmetric and the SPP excitation is radially polarized. The long range and the short range modes are compared and found to have very different focusing properties. The trade-offs between the modes are discussed. The interplay between these two modes is used to demonstrate a practical focusing scenario providing a smaller spot size compared with previous version of plasmonic lenses, and a large depth of focus simultaneously.

© 2009 Optical Society of America

1. Introduction

Focusing of surface plasmon polaritons (SPPs) by plasmonic lenses (PLs) was shown to be useful in confining electromagnetic fields at the sub-wavelength scale [1

1. Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005). [CrossRef] [PubMed]

, 2

2. W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nature Nanotech. 3, 733–737 (2008). [CrossRef]

]. The combination of short SPP wavelength and planar focusing allows the realization of such lenses with effective numerical aperture (NA) larger than the refractive index of the surrounding dielectric material. The SPP wave is TM polarized and thus it becomes clear that the incident polarization plays a significant role, affecting the PL’s functionality . It was proposed [3

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

, 4

4. A. Yanai and U. Levy, “Plasmonic focusing with a coaxial structure illuminated by radially polarized light,” Opt. Express 17, 924–932 (2009). [CrossRef] [PubMed]

] and demonstrated [5

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

, 6

6. G. Lerman, A. Yanai, and U. Levy, “Demonstration of nano focusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9, 2139–2143 (2009). [CrossRef] [PubMed]

] that by illuminating the PL with radially polarized a stronger, tighter and circularly symmetric spot is obtained at the focus, compared with linear polarization illumination. It was also shown that the focusing efficiency could be enhanced by integrating Bragg reflectors and grating couplers into the device [4

4. A. Yanai and U. Levy, “Plasmonic focusing with a coaxial structure illuminated by radially polarized light,” Opt. Express 17, 924–932 (2009). [CrossRef] [PubMed]

].

Throughout the paper we consider circular symmetric PL structures and radial polarization illumination which was shown to provide advantages both in efficiency and in spot size. Thus, our problem in hand does not vary with the azimuthal angle θ.

2. SPP field distribution on a metallic circular disk

First, we express the SPP field components, resident on the surface of a metallic circular disk. The SPPs are excited by radially polarized light, and their propagation vector (β) is directed along the radial direction. The structure is depicted in Fig. 1. The decay constants into the metal and the dielectric are designated by ki where i=M,D stands for the metallic and dielectric regions respectively.

For our purposes, the relevant subset of Maxwell’s curl equations in cylindrical coordinates is:

ErzEzr=jωμHθ
(1)
1rHzθHθz=ε0εiEr
(2)
1rHθ+Hθr1rHrθ=ε0εiEz
(3)

The SPP is a TM mode, resulting:

Hr=Eθ=Hz=0
(4)

Assuming a bound SPP mode and no angular dependency (both the structure and the illumination have no angular variance) gives the following relations at z≥0:

z=kD,r=,θ=0,kD2=β2ω2ε0εDμ
(5)

Substituting Eq. (4) in Eqs. (2) and (3) results in:

Hθz=ε0εiEr
(6)
1rHθ+Hθr=ε0εiEz
(7)

The substitution of Eq. (1) in (7) gives:

1r[ErzEzr]+[ErzEzr]r=ω2με0εiEz
(8)

By eliminating Er from Eq. (8) with Eqs. (6) and (7) and then utilizing Eq. (5) we obtain:

2Ezr2+1rEzr+β2Ez=0
(9)
Fig. 1. Schematics of the cylindrical metallic disk and its resulting intensity patterns: (a) structure geometry. (b) Schematic pattern of ∣Ez2 corresponding to Eq. (11). (c) Schematic pattern of ∣Er2 corresponding to Eq. (12).
Er=jkDβ2Ezr
(10)

The solution for Eqs. (9) and (10) is given by:

Ez(r,z)=AJ0(βr)exp(kDz)
(11)
Er(r,z)=AjkDβJ1(βr)exp(kDz)
(12)

Eqs. (11) and (12) describe the electric field distribution that is bounded to the disk surface at the upper half plane (z≥0). Similar expressions can be written for the lower half plane (z≤0) by replacing kD with kM with the appropriate sign resulting in:

Ez(r,z)=BJ0(βr)exp(kMz)
(13)
Er(r,z)=BjkMβJ1(βr)exp(kMz)
(14)

Where A and B are arbitrary amplitude constants. From continuity of Er and εi Ez,i at z=0 one readily obtains that kD/kM = -εD/εM which is the same relation that holds for the standard 1D bi-layered plasmonic waveguide in Cartesian coordinates resulting in the well known characteristic equation β=k0εMεDεM+εD. Following the same procedure, it can be shown that the SPP characteristic equation of a multilayered disk (layered along the Z-direction) is the same as its 1D multilayered Cartesian equivalent.

As a final remark, we note the resemblance of the above derivation and Eqs. (11) and (12) to the TM01mode of a circular metallic waveguide propagating in the z direction.

3. Focusing characteristics for long and short range SPPs for a circular disk

When considering a symmetric insulator/metal/insulator (IMI) multilayer structure [7

7. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).

] two bounded modes can be excited, with symmetric and antisymmetric profiles of the electric field component along the propagation direction (i.e. Er) [8

8. D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981). [CrossRef]

, 9

9. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000). [CrossRef]

, 10

10. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005). [CrossRef] [PubMed]

, 11

11. A. Degiron and D. Smith, “Numerical simulations of long-range plasmons,” Opt. Express 14, 1611–1625 (2006). [CrossRef] [PubMed]

, 12

12. K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, “Long-range surface plasmon polariton nanowire waveguides for device applications,” Opt. Express 14, 314–319 (2006). [CrossRef] [PubMed]

]. The antisymmetric mode (or odd mode) is less confined compared with the symmetric (even) mode. It has a larger SPP wavelength and evolves it into the TEM mode of the surrounding dielectric as the metallic layer thickness decreases [9

9. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000). [CrossRef]

]. The symmetric mode shows the opposite trend: it gets more confined within the metal as the metal layer thickness decreases. This results in a shorter SPP wavelength, a shorter decay length into the surrounding dielectric, and a smaller propagation distance, due to enhancement of ohmic losses. Because of that, the antisymmetric mode is often termed a long range SPP (LRSPP) and the symmetric mode a short range SPP (SRSPP).

In this section, we will consider the focusing characteristics of both SPP modes for an IMI disk, layered along the Z-direction. Following the discussion in section 2, the characteristic equation of such disk is the same as that of the 1D IMI equivalent, which can be split into two equations, describing the LRSPP and SRSPP modes propagating along an IMI structure with metal thickness h (see ref. [7

7. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).

]):

tanh(12kMh)=kDεMkMεD
(15)
tanh(12kMh)=kMεDkDεM
(16)

Throughout this section, we will present analytic results that are calculated on the basis of Eqs. (11) - (16).

Fig. 2. SPP lateral field intensity distribution on the surface of the thin metallic disk embedded in a dielectric with n=1.33. The fields are calculated in the air. (a) SRSPP mode with metallic layer thickness h=15 nm. (b) SRSPP mode, h=10 nm. (c) LRSPP mode, h=15 nm.

Fig. 2 shows the electrical energy density components obtained by the excitation of a thin layer of silver (εM = -13.9 + 0.65i) embedded in a dielectric environment with refractive index n=1.33 (this environment will be later used in section 4). The excitation wavelength is λ 0 =600 nm. Fig.2(a) and 2(b) show the results of the SRSPP mode for layer thickness of 15 and 10 nm respectively. A smaller central lobe is obtained for the 10 nm thick layer, indicating a shorter SPP wavelength. In addition, the contribution of the radial field becomes more significant as the layer thickness decreases (this will be further discussed in section 3.2). From Fig. 2(b), one can notice that at the edges of the PL the energy density decreases towards the middle of the structure. This is because of the very significant propagation losses for a 10 nm thick layer. A turning point is obtained around r=500 nm, where the focusing overcomes this loss. Finally, Fig.2(c) shows the result of a LRSPP mode for layer thickness of 15 nm. The Er component is seen to be negligible, indicating that the SPP wavelength of this mode is very similar to the vacuum wavelength. Further decrease of the layer has a negligible effect on the LRSPP mode.

3.1. Figures of merit

To evaluate the performance of the PL, we consider four figures of merit (FOM). The first two are the spot size (SPSZ) and the depth of focus (DOF), previously defined for a plasmonic lens in [4

4. A. Yanai and U. Levy, “Plasmonic focusing with a coaxial structure illuminated by radially polarized light,” Opt. Express 17, 924–932 (2009). [CrossRef] [PubMed]

] as the FWHM of the electric energy density along the radial direction and the distance along the z direction for which the electric energy density drops by a factor of two, respectively. The other two FOMs are the effective numerical aperture defined as NA eff = λ 0/(λSPP × nD) (this criterion represents the improvement factor of the PL’s NA compared to that of a dielectric lens with a nearly zero focal length, i.e. having the highest possible NA for a given nD) and the propagation length L = 1/(2×Im[β ]). Fig. 3 presents these FOMs versus the excitation wavelength for a circular silver disk with metal thickness h=15 nm embedded in a dielectric medium. We vary the refractive index of the dielectric between nD = 1 and nD = 1.5. The results show the trade-off between the FOMs obtained by the LRSPP and the SRSPP modes. The SRSPP mode possesses a smaller SPP wavelength and therefore a smaller SPSZ at the cost of a smaller DOF due to tighter confinement to the interface. The LRSPP however, exhibits the opposite behavior. The effective NA provides an interesting comparison between the PL and a standard dielectric lens. Since the LRSPP evolves into the TEM mode of the surrounding dielectric as the metallic layer thickness decreases [9

9. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000). [CrossRef]

], NA eff approaches the value of unity. For the SRSPP mode however, NA eff grows significantly as the dielectric index or the optical frequency increase because of its highly dispersive nature. Unfortunately, the improvement in NA is coupled to higher loss. Nevertheless, an improvement factor of ≈ 1.5 is achievable with moderate loss.

Fig. 3. FOMs of the PL. The left and the right columns correspond to LRSPP and SRSPP excitations respectively. (a)-(e) λSPP, SPSZ, DOF, NA eff and the propagation length respectively, as a function of the excitation wavelength λ 0. (f) Legend for (a)-(e) specifying the refractive index nD surrounding the metal.
Fig. 4. (a) SPSZ Normalized by (λ 0/nD) as a function of the metal thickness. (b) SPSZ Normalized by (λSPP/nD) as a function of the metal thickness. (c) Legend for (a)-(b) specifying the refractive index nD surrounding the metal.

To summarize, the two modes offer two distinct and possibly useful focusing characteristics: The SRSPP provides a very high numerical aperture lens, but with fast decaying energy, both in the z and in the propagation direction (r). The LRSPP, because of its large DOF (that can be of the order of the free space optical wavelength) provides a slowly decaying “light bullet” in the z direction. Unfortunately, the improvement in the resulting NA is smaller in this case. A combination of the two modes may become useful, as discussed in section 4.

3.2. Longitudinal and transverse electric components, and their effect on the spot size

4. Numerical analysis of a focusing scheme

In this section we propose a circular wedge configuration for realizing a PL that exhibits a combination of LRSPP and SRSPP. Fig. 5 shows the cross-section and 3-D view of the proposed structure. As can be seen, the structure combines a central section made of a plain circular metallic layer with radius f and thickness h, surrounded by an outer wedge-like circular section with initial thickness w. The overall radius of the structure is d. The focusing is obtained at the center of the structure (r=0). Wedge-like and adiabatic structures attract much interest in plasmonic research, primarily for confinement of electromagnetic waves [13

13. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404(2004). [CrossRef] [PubMed]

, 14

14. D. K. Gramotnev and K. C. Vernon, “Adiabatic nano-focusing of plasmons by sharp metallic wedges,” Appl. Phys. B Lasers Opt. 86, 7–17 (2007).

, 15

15. D. Gramotnev, M. Vogel, and M. Stockman, “Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods,” J. Appl. Phys. 104, 034311 (2008). [CrossRef]

, 16

16. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons,” Phys. Rev. Lett. 100, 023901-1-4 (2008). [CrossRef] [PubMed]

, 17

17. K. Kurihara, K. Yamamoto, J. Takahara, and A. Otomo,“Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables,” J. Phys. A Math. Theor. 41295401 (2008). [CrossRef]

, 18

18. E. Verhagen, A. Polman, and L. Kuipers, “Nanofocusing in laterally taperd plasmonic waveguides,” Opt. Express 16, 45–57 (2008). [CrossRef] [PubMed]

, 19

19. L. Feng, D. Van Orden, M. Abashin, Q. Wang, Y. Chen, V. Lomakin, and Y. Fainman, “Nanoscale optical field localization by resonantly focused plasmons,” Opt. Express 17, 4824–4832 (2009). [CrossRef] [PubMed]

]. Here we use the wedge-like structure for adiabatic shrinkage of the metallic layer thickness, and because the wide edges and their sharp corners are suitable for excitation of SPPs. The adiabatic structure is important to obtain the thin metallic layer needed, with as small as possible back-reflections due to mode mismatch. The wedge is placed on top of a Cytop layer. To cope with bio-imaging applications, the focal region is embedded in water based liquid. Both Cytop and the water based liquid have a refractive index n ≈ 1.33, ensuring the symmetry needed for LRSPP and SRSPP.

Fig. 5. (a) Schematic diagram of the cross-section of the circular wedge (b) 3-D view of the circular wedge

Fig. 6 shows the focusing of the two distinct modes, as calculated by FDTD. For our calculations we use Meep [20

20. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006). [CrossRef] [PubMed]

], a free-software FDTD package available at [21]. First, we investigate the structure by the excitation of pure symmetric and anti-symmetric modes. These modes are excited by sources with the corresponding symmetry. The excitation vacuum wavelength is λ 0 = 600 nm. The geometrical parameters are w=70 nm, d=4200 nm, f=2100 nm, and h=15 nm and computational cell resolution of 2 nm. Fig. 6 shows the resulting electric energy density patterns for both pure modes. It is apparent that in Fig. 6(a) that the energy density comprises of two contributions: 1 - contribution from the SRSPP mode that is bounded to the surface and 2 - contribution due to diffraction of light from the edges of the sample. Diffraction exists also in Fig. 6(b), but is less apparent because of the existence of the slowly decaying LRSPP mode.

In Fig. 7(a) one can see an FDTD calculation showing the electric energy density resulting from an illumination function having the following parameters: λ 0 = 600 nm, α = 0.1[μm-1], and r 0 = 200 nm. The geometrical parameters are the same as those used for Fig. 6. The thin wedge is better observed in Fig. 7(b) which provides a zoom near the focal region. In a practical illumination scenario (as the one described above), the two modes (symmetric and anti-symmetric) are excited simultaneously. In order to evaluate the symmetry of the field at the focus, we define a function that measures the excited mode parity. The function compares the sign of the SPP magnetic component (H ϕ) at two points on both sides of the metallic layer (z=±h/2, r=0) at each time step of the FDTD solver, and accumulates the sign comparisons over a single time period of the optical frequency. At each time step, in case the sign is equal, the function adds -1 to the accumulation. Otherwise, it adds +1. This can be formulated as: S = (Δt/T)∑Tt n=1 Neq[sgn(H ϕ (P 1)),sgn(H ϕ(P 2))] where “S” is the symmetry measurement function, Δt is the time interval of the FDTD solver, T is the time period, “Neq[x,y]” is a function that returns -1 if x=y and +1 otherwise, and “sgn“ is the sign function. P1 and P2 are two measurement points at r=0 and z=±h/2. The normalization factor Δt/T ensures that S returns a value in the range [-1,+1], where the cases S=-1 and S=+1 correspond to pure anti-symmetric and symmetric modes respectively.

Fig. 6. FDTD simulation showing the total electric energy density (logarithmic color scaling) for: (a) excitation of a pure symmetric mode. The region designated by the purple rectangle is dominated by the energy density of the SRSPP. The region designated by the white rectangle is dominated by energy density originated from diffraction and radiation from the wedge. (b) excitation of a pure anti-symmetric mode
Fig. 7. (a) Electric energy density (logarithmic color scaling) resulted by excitation of LRSPP and SRSPP modes using radially polarized light illumination. (b) Zoom of Fig. 7(a) in the vicinity of the focal region (c) The resulting SPSZ as a function of the distance (along the z axis) from the center of the metallic layer. (d) The normalized electric energy density at the center as a function of the distance from the metallic surface.

The symmetry function returned a value of 0.697 indicating that mostly SRSPP are excited. Indeed, it can be observed in Fig. 7(c) that the SPSZ in the vicinity of the surface is 124 nm, which is close to the analytically expected value for the SRSPP mode (125.5 nm). Around z=220 nm the SPSZ reaches the value of 160 nm, whereas 162 nm is the analytically expected value of the SPSZ due to LRSPP. The SPSZ continues to grow with Z. This can be explained by the contribution of free space modes originating from diffraction and radiation from the wedge. The 4 nm discontinuities in Fig. 7(c) are due to the 2 nm resolution used in the FDTD calculation.

A different approach to try to understand the contribution of the various modes along the Z-axis, is by looking at the normalized electric energy at the center as a function of Z (Fig. 7(d)). A linear fit is able to reveal the SPP decay constants (mind the semi-logarithmic scale). In Fig. 7(d), the red line shows the linear fit preformed near the surface, indicating a decay constant of 0.031 [1/nm], whereas the analytic value for the energy decay factor of the SRSPP mode is 0.035 [1/nm]. The region where the SRSPP have decayed enough and therefore is dominated by LRSPP, is harder to localize because the contribution of non-SPP waves originating from diffraction and radiation grows with Z. However, at Z=200 nm the fit (green line) that indicated a decay constant of 0.0036 [1/nm], (analytic expected value for the LRSPP is 0.0032 [1/nm]). We also note that in this region the SPSZ is identical to the theoretical expected value resulting from LRSPP excitation. The increase in energy density that is observed at higher Z-values is attributed to diffraction and radiation from the edges of the sample. Further investigation is needed, in order to understand the contribution of the various modes more thoroughly.

5. Conclusions

Acknowledgments

The authors are grateful to Mark I. Stockman for fruitful discussions and would like to acknowledge the support of the Israeli Science Foundation, the Israeli Ministry of Science and the Peter Brojde Center for Innovative Engineering and Computer Science.

References and links

1.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005). [CrossRef] [PubMed]

2.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nature Nanotech. 3, 733–737 (2008). [CrossRef]

3.

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

4.

A. Yanai and U. Levy, “Plasmonic focusing with a coaxial structure illuminated by radially polarized light,” Opt. Express 17, 924–932 (2009). [CrossRef] [PubMed]

5.

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

6.

G. Lerman, A. Yanai, and U. Levy, “Demonstration of nano focusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9, 2139–2143 (2009). [CrossRef] [PubMed]

7.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).

8.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981). [CrossRef]

9.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000). [CrossRef]

10.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005). [CrossRef] [PubMed]

11.

A. Degiron and D. Smith, “Numerical simulations of long-range plasmons,” Opt. Express 14, 1611–1625 (2006). [CrossRef] [PubMed]

12.

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, “Long-range surface plasmon polariton nanowire waveguides for device applications,” Opt. Express 14, 314–319 (2006). [CrossRef] [PubMed]

13.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404(2004). [CrossRef] [PubMed]

14.

D. K. Gramotnev and K. C. Vernon, “Adiabatic nano-focusing of plasmons by sharp metallic wedges,” Appl. Phys. B Lasers Opt. 86, 7–17 (2007).

15.

D. Gramotnev, M. Vogel, and M. Stockman, “Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods,” J. Appl. Phys. 104, 034311 (2008). [CrossRef]

16.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons,” Phys. Rev. Lett. 100, 023901-1-4 (2008). [CrossRef] [PubMed]

17.

K. Kurihara, K. Yamamoto, J. Takahara, and A. Otomo,“Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables,” J. Phys. A Math. Theor. 41295401 (2008). [CrossRef]

18.

E. Verhagen, A. Polman, and L. Kuipers, “Nanofocusing in laterally taperd plasmonic waveguides,” Opt. Express 16, 45–57 (2008). [CrossRef] [PubMed]

19.

L. Feng, D. Van Orden, M. Abashin, Q. Wang, Y. Chen, V. Lomakin, and Y. Fainman, “Nanoscale optical field localization by resonantly focused plasmons,” Opt. Express 17, 4824–4832 (2009). [CrossRef] [PubMed]

20.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31, 2972–2974 (2006). [CrossRef] [PubMed]

21.

http://ab-initio.mit.edu/meep/

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(310.2790) Thin films : Guided waves
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optoelectronics

History
Original Manuscript: May 21, 2009
Revised Manuscript: July 5, 2009
Manuscript Accepted: July 5, 2009
Published: July 31, 2009

Citation
Avner Yanai and Uriel Levy, "The role of short and long range surface plasmons for plasmonic focusing applications," Opt. Express 17, 14270-14280 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-14270


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References

  1. Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with a plasmonic lens," Nano Lett. 5, 1726-1729 (2005). [CrossRef] [PubMed]
  2. W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008). [CrossRef]
  3. Q. Zhan, "Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam," Opt. Lett. 31, 1726-1728 (2006). [CrossRef] [PubMed]
  4. A. Yanai and U. Levy, "Plasmonic focusing with a coaxial structure illuminated by radially polarized light," Opt. Express 17, 924-932 (2009). [CrossRef] [PubMed]
  5. W. Chen and Q. Zhan, "Realization of an evanescent Bessel beam via surface plasmon interference excited by a radially polarized beam," Opt. Lett. 34, 722-724 (2009). [CrossRef] [PubMed]
  6. G. Lerman, A. Yanai and U. Levy, "Demonstration of nano focusing by the use of plasmonic lens illuminated with radially polarized light," Nano Lett. 9, 2139-2143 (2009). [CrossRef] [PubMed]
  7. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).
  8. D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981). [CrossRef]
  9. P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000). [CrossRef]
  10. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express 13, 977-984 (2005). [CrossRef] [PubMed]
  11. A. Degiron and D. Smith, "Numerical simulations of long-range plasmons," Opt. Express 14, 1611-1625 (2006). [CrossRef] [PubMed]
  12. K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, "Long-range surface plasmon polariton nanowire waveguides for device applications," Opt. Express 14, 314-319 (2006). [CrossRef] [PubMed]
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