Nanofocusing of Surface Plasmon Polaritons by partially metal- coated dielectric conical probe: Optimal asymmetric distance.

Ngo Thi Thu,(1),* Kazuo Tanaka,(1) Masahiro Tanaka,(1) and Dao Ngoc Chien(2)

(1) Department of Electronics and Computer Engineering, Gifu University, Yanagido 1-1, Gifu City, Japan 501-1193

(2)Faculty of Electronics and Telecommunications, Hanoi University of Science and Technology, 1-DaiCoViet, HaiBaTrung, Hanoi City, Vietnam

Abstract: Nanometric superfocusing of optical intensity near the tip of partially metal- coated dielectric conical probe of the convergent surface plasmon polariton wave is investigated by the volume integral equation method. It is possible to perform nanofocusing using this probe by using linearly polarized Gaussian beam as the incident wave. Strongly localized and enhanced optical near-fields can be created on the tip of this probe for both linearly and radially polarized Gaussian beams.

Keywords: (230.7370) Waveguide; (240.6680) Surface plasmons; (260.2110) Electromagnetic theory

  1. Introduction

A very promising perspective for future nano-optics is the possiblility to create the localized and enhanced optical near-field due to resonant properties of metal nanosystems. Recent theoretical and experimental studies of nanometric integrated optical circuits that employ surface plasmon polaritons (SPPs) have shown that functional devices utilizing SPPs have been proposed and are expected to play an important role in future of nanometric integrated optical circuit [1-12]. However the diffraction limit of light makes it difficult to construct optical devices with dimensions that are much smaller than optical wavelengths and that have much higher integration densities than current optical integrated circuits. In order to overcome this difficulty, a technique using metal-coated dielectric conical probe supporting SPPs has been proposed to create the significantly localized near-fields in the nanosized region on the tip [3-6]. This focusing technique is often called SPP superfocusing or nanofocusing so far [3, 4, 6-12]. By using the focusing technique, optical waveguides based on SPPs can be miniaturized much further than conventional diffraction-limited optical waveguides [1-12], opening up the possibility of developing nanometric integrated optical circuits. However, the original symmetric metal-coated conical probe is valid only for the incident radially polarized (RP) beam and is not valid for the incident linearly polarized (LP) beam.

It is possible to achieve SPP nanofocusing for the incident LP beam by breaking the symmetric structure of the probe. The authors have proposed an idea of using metal-coated dielectric probe of tilted shape and have shown that it is valid for both incident LP and RP beams [4]. In this paper, in order to achieve the SPP superfocusing for the case of incident LP beam by the conical probe, we examine another asymmetric structure of the probe, i.e., the partially metal-coated dielectric probe.

In the present study, the volume integral equations (VIE) method is used to simulate the problem numerically [1, 2, 4-6]. Based on the VIE method we show that the probe proposed can achieve the SPP superfocusing for both incident LP and RP beams.

  1. Geometry of the partially metal-coated dielectric probe

We consider the partially metal-coated dielectric probe shown in Fig. 1. The conical dielectric probe has a base radius R and is made of a dielectric with a permittivity ε_1 fabricated in the (x, y, z) coordinate system shown in Fig. 1. The surrounding free space has a permittivity ε_0. The conical probe has a height of h. The side of conical dielectric probe is partially coated with the metal with a permittivity ε_2 and thickness of d.

Figure 1. Geometry of the partially metal-coated conical dielectric probe. (a) The conical structure The cross sections of the asymmetric probe are shown on (b) z-y plane, (c) z-x plane and (d) x-y plane.

In Fig. 1, we can see that the probe consists of two parts i.e., the dielectric with covered metal-coated layer and the original dielectric without coating metal. We notice that the shape of the partially metal-coated conical dielectric probe is rotationally symmetric about z-axis in Fig. 1. However, the distribution of the dielectric permittivity is not rotationally symmetric due to the partial metal-coating.

We consider that the metal-coating is cut by a plane parallel to the y-z plane (cut plane) shown in Fig. 1. In order to define the degree of the asymmetry of the partially metal-coated probe, we use the ratio between l, which is the distance between the cut plane and the z-axis shown in Fig. 1(a), (c) and (d), and base radius R, i.e., l/R. The case of l/R=1 corresponds to the fully metal-coated symmetric probe, the case of l/R=0 corresponds to the half metal-coated asymmetric probe and other cases of 0 < l/R< 1 correspond to the partially metal-coated asymmetric probes.

We first divide three dimensional models of the probe into tiny cubes having dimensions ofto solve the scattering problem shown in Fig. 1 by the VIE method [1, 3]. Then we discretize the VIE by the moment-method and finally solve the resultant system of linear equationsnumerically by generalized minimum residual method with fast Fourier transformation.In this paper, the wavelength (λ) is 633 nm and δ is given by δ=0.05 (δ=5nm). The metal coating is gold (Au) whose relative permittivity is given by 2 /0=-13.8-j1.08 and that of the dielectric is given by 1/0= 2.25. The beam spot size is given by w=λ at z=0 and the thickness is given by d=0.27 (d=27.4 nm).

  1. Optical intensity distribution

The geometry of the partially metal-coated dielectric probe shown in Fig. 1 has been considered an idealized mathematical model of typical conical structure that has an apex 37 degrees and a base radius given by (R=712nm).The conical dielectric probe has a height h. We first use the height h for probe 1 given by (h=1652 nm). Meanwhile, the whole structure is discretized using cubes arranged in 328 layers parallel to the x-y plane. Figure 2 shows the arrangement of the cubes in the top 14 layers. The inset shows the tiny cubes having dimensions ofto solve the scattering problem shown in Fig. 1 by the VIE method.

Fig. 2. The arrangement of cubes in the top 14 layers of probe 1 (). The inset shows the tiny cubewith dimensions.
(a) / (b) / (c)
Fig. 3. Distributions of optical intensity in the x-z plane for probe 1 in asymmetric structure (a) with , (b) with and in symmetric structure (c) with . The coating metal is Au(). The dielectric is glass ().

Figure 3 present numerical results how a LP beam is focused into the partially conical metal-coated dielectric probe and show how a highly confined electric field is generated. The results in Fig. 3 indicate that, SPPs are excited along the metal coating. Figures 3(a) and 3(b) show the results of optical intensities for the asymmetric cases of and in the x-z plane for probe 1 (as Fig.2), respectively.In Figs. 3(a) and (b), we can see that in the partially metal-coated dielectric probes, the optical intensity for incident LP beam is focused and enhanced on the tip. Contrast to the results in Fig. 3 (a) and (b), the result in Fig. 3(c) for the symmetric probe indicates that SPP excited along the metal coating is suppressed on the probe tip. It means that the original symmetric metal-coated conical probe is not valid for the incident LP beam.

  1. Dependence of maximum optical intensities on the distance l/R

The dependence of the maximum enhanced optical intensity at the tip on the distance l/R is shown in Fig. 4.In Fig. 4, the distance l/R is changed from 0 to 1 while keeping the other parameters of dielectric conical probe. The results shown in Fig. 4 reveal that the maximum optical intensity strongly depends on the distance l/Rfor both LP and RP incident beams. In Fig. 4, while fully metal-coated conventional probe is the optimum shape for incident RP beam, it is interesting that the optimum value of l/R=0.41 can be obtained for incident LP beam.

Fig. 4. The maximum of optical intensity at the tipfor incident RP beam and incident LP beam. The ordinates mean results for the incident LP beam (left) and the incident RP beam (right)

CONCLUSION.

For the purpose of development of surface plasmon polariton (SPP) nanofocusing probe that is valid for linearly polarized incident waves, we examined the partially metal-coated dielectric probe in this paper. The basic characteristics of the maximum optical intensity on the tip created by SPP nanofocusing in the probe are investigated by the volume integral equation. We considered the cases of incident linearly polarized (LP) and radially polarized (RP) Gaussian beams. The intensity distributions of various structure of the probe are investigated. Although the intensities of enhanced fields on the tip for incident LP beams are smaller than those obtained by the incident RP beams, it is found that the partially metal-coated dielectric probe can create the localized and enhances intensity on the tip that is 103 times larger than that of incident wave for incident LP waves.

ACKNOWLEDGMENT

Numerical simulations were performed by the supercomputer of The Information Technology Center of Nagoya University.

REFERENCES

  1. Handbook of Nanophysics: Nanoelectronics and Nanophotonics edited by Klaus D. Sattler
  2. T. T. Minh, K. Tanaka and M. Tanaka, “Analysis Propagation Characteristics of the Surface Plasmon Polariton Trench Waveguides by Method of Lines,” PIERS Proceedings, Cambridge, USA, July 5–8, 2010
  3. K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett, vol. 82, No. 8, pp. 1158-1160, 2003.
  4. N. T. Thu, K. Tanaka, M. Tanaka and D. N. Chien, “Superfocusing of surface plasmon plaritons by metal-coated dielectric probe of tilted conical shape,” J. Opt. Soc. Am. A, vol. 30, No. 6, pp. 1113-1118, 2013
  5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature, vol.424, no. 6950, pp. 824-830, 2003.
  6. Kazuo Tanaka, Kiyofumi Katayama, and Masahiro Tanaka, “Optical field characteristics of nanofocusing by conical metal-coated dielectric probe,” Opt. Express, vol. 19, No. 21, pp. 21028-21037, 2011.
  7. K. Tanaka, G. W. Burr, T. Grosjean, T. Maletzky, and U. C. Fischer, “Superfocussing in a metal-coated tetrahedral tip by dimensional reduction of surfac-to edge-plasmon modes,” Appl. Phys. B 93, 257-266, 2008.
  8. K. Tanaka, K. Katayama, and M. Tanaka, “Nanofocusing of surface plasmon polaritons by a pyramidal structure on an aperture,” Opt. Express 18, 787-798, 2010.
  9. Mark I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” PhysRevLett 93, pp. 74041, 2004.
  10. N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun 253(1-3), 118–124, 2005.
  11. W. Ding, S. R. Andrews, and S. A. Maier, “Internal excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Phys. Rev. A 75, 063822, 2007.
  12. Wei Liu, Dragomir N. Neshev, Andrey E. Miroshnichenko, Ilya V. Shadrivov, and Yuri S. Kivshar, “Polychromatic nanofocusing of surface plasmon polaritons,” Phys. Rev. B 83, 073404, 2011.