Plasmonics

, Volume 5, Issue 1, pp 57–62

Surface Plasmon Polariton Enhancement in Silver Nanowire–Nanoantenna Structure

Authors

  • Zheyu Fang
    • School of Physics, State Key Laboratory for Mesoscopic PhysicsPeking University
  • Yanwei Lu
    • School of Physics, State Key Laboratory for Mesoscopic PhysicsPeking University
  • Linran Fan
    • School of Physics, State Key Laboratory for Mesoscopic PhysicsPeking University
  • Chenfang Lin
    • School of Physics, State Key Laboratory for Mesoscopic PhysicsPeking University
    • School of Physics, State Key Laboratory for Mesoscopic PhysicsPeking University
    • National Center for Nanoscience and Technology
Article

DOI: 10.1007/s11468-009-9115-1

Cite this article as:
Fang, Z., Lu, Y., Fan, L. et al. Plasmonics (2010) 5: 57. doi:10.1007/s11468-009-9115-1
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Abstract

The surface plasmon polariton (SPP) coupling and enhancement in silver nanowire–nanoantenna structure is proposed and simulated by using finite difference time domain method. The results demonstrate that three-arm antenna can effectively enhance the coupling efficiency at the incident end and the SPP field intensity at the emission end. The enhancement factor, which is defined as the ratio of the SPP field intensity at the emission end with and without the three-arm antenna, for the various antenna arm lengths and incident wavelengths under different incident angles are calculated. The suggested structure can be served as an enhanced plasmonic waveguide for the nanophotonic and plasmonic circuits in the future.

Keywords

Surface plasmon polaritonWaveguideMetal opticsSubwavelength structure

Introduction

Surface plasmon polariton (SPP) as a hybrid mode of light field and collective electron oscillation is resonantly excited at the interfaces of metal and dielectric [1]. The fundamental SPP properties have been widely applied in many technique fields such as nanolithography [2, 3], plasmonic modulators [4, 5], plasmonic hyperlens [6], plasmonic trapping [7, 8], etc. Photonic elements based on SPP offer a solution to the nanoscale photonic and electronic integration for the ability to confine the light energy into the subwavelength structures [9, 10]. SPP waveguide, on the other hand, as one of the important topics in nanophotonics and photoelectronics has induced more concerns recently [1115]; however, for the Ohmic losses, SPP propagation length along the interfaces of metal and dielectric is still limited to the order of 10 μm in the case of noble metals [11].

Silver nanowire with an atomically smooth surface results in a lower propagation dissipation, which can be considered as an excellent SPP waveguide [16]. Recently, the silver nanowire with one end inserted perpendicularly to polymer waveguide is reported, which realizes the coupling of light into multiple nanowires at the same time [17]. However, the SPP propagation length (1.3 μm) for this structure is still limited by the low coupling efficiency at the incident end. On the other hand, nanoantenna structure can achieve electric filed enhancement by the collective electrons resonate at the gap area [18]. Previous works have reported that “bowtie”-shaped antennas, two metallic triangles facing tip to tip separated by a small gap, can enhance the electric field with hundreds of times [19, 20]. Metallic nanoparticles with sharp edges also can resonate the local electric fields for the same antenna enhancement effect [21]. To our knowledge, there are few reports on the combination of metallic nanowire and nanoantenna for the SPP propagation architecture.

In this paper, we report an SPP-enhanced structure by modeling nanoantenna at the incident end of a silver nanowire. With properly designed antennas, the coupling efficiency and SPP propagation can be effectively enhanced.

Simulation method

The SPP dispersion at interfaces of semi-infinite dielectric and metal can be expressed as [1],
$$ {k_{\text{sp}}} = \frac{\omega }{c}{\left[ {\frac{{{\varepsilon_{\text{d}}}{\varepsilon_{\text{m}}}}}{{{\varepsilon_{\text{d}}} + {\varepsilon_{\text{m}}}}}} \right]^{1/2}} $$
(1)
where ksp is the SPP wave vector and εd and εm are the permittivities of the dielectric and metal, respectively. Since ksp is larger than the light wave vector under the same frequency, momentum compensation should be necessary for the SPP excitation. Apart from the momentum compensation, another necessary condition to excite SPP by light is that the electric field of the incident light must have the component parallel to the metallic plane. Sharp edges, such as the end face of nanowire and the tip of antenna, can be used to realize the SPP excitation [11]. The compensation of SPP momentum with scattered wave vector component will be automatically selected at the incident spot, and the local electric field can be enhanced [22].
The SPP coupling efficiency and enhancement factor in silver nanowire, nanoantenna, and their combination structure are investigated by using finite difference time domain (FDTD) method. The simulations are performed by commercial software XFDTD (Remcom, Inc.). Silicon dioxide as the substrate material with a permittivity of 2.127 [23] is used in our model. By utilizing the modified Debye model [24] and the Drude model [25], the complex silver permittivity ε(ω) can be derived as
$$ \varepsilon \left( \omega \right) = 1 + \frac{{{\varepsilon_{\text{s}}} - {\varepsilon_\infty }}}{{1 + i\omega \tau }} - \frac{{{\varepsilon_{\text{s}}} - {\varepsilon_\infty }}}{{i\omega \tau }} $$
(2)
where \( {\varepsilon_\infty } = 1 \) is the infinite frequency permittivity, εs is the static permittivity at zero frequency, and τ is the relaxation time.
First, the SPP propagation along the silver nanowire is simulated. The 10.5-μm long p-polarized laser’s focus point is set on the incident end of a 80-nm-diameter silver nanowire, and the incident angle is set to be 5°. From the propagation area of Fig. 1, it can be seen that a standing plasmon waves along the nanowire (Y-axis) are excited, which consists with the experimental observation as SPP Fabry–Perot resonators [26]. SPP modes generated by the scattering light at the input end of nanowire will propagate at the incident vector and be reflected by the output end [16, 26]. The interference of incident and reflected SPP modes can generate standing plasmon waves on the nanowire surface. For the little energy dissipation during the wave propagation, silver nanowire can be served as an excellent SPP transport element in subwavelength optoelectronics. Inset is the schematic of simulation silver nanowire with the notations of SPP coupling and propagation areas.
https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig1_HTML.gif
Fig. 1

The curve of electric field distribution along the silver nanowire surface. Energy dissipation occurs at the incident end with standing SPP waves along the propagation area. Inset is the schematic of the simulation model with a p-polarized laser illuminating the coupling area under 5° incident angle. The xy-plane is parallel to the silicon substrate with y direction along the generatrix of the nanowire, and the original point is the farthest point from the silicon substrate in the incident plane of the nanowire

Two- and three-arm triangle nanoantennas with a 130-nm gap are also simulated for the comparison of electric field enhancement. The antenna is designed with a 540 nm arm length, 80 nm width, and 65 nm cutoff (see Fig. 2a, c). This antenna architecture can be used to hold various scale nanowires in the gap area. During the simulation, the p-polarized laser with 5° incident angle is focused on the gap. The average electric filed intensity for two- and three-arm antenna structure is about 1.54 and 10.8 times in comparison with the background (without antenna). The electric field distributions corresponding to the same area of Fig. 2a, c are shown in Fig. 2b, d.
https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig2_HTML.gif
Fig. 2

a, c Architectures of two- and three-arm antenna with 540 nm arm length illuminated by p-polarized laser under the 5° incident angle, respectively. b, d Electric field distributions for plane Z = −40 nm corresponding to the same area of a and c, respectively

Geometry optimization

In the following simulations, various three-arm antennas with 53° apex angle are designed at the input end of a silver nanowire (80 nm diameter, 10.5 μm long), as shown in Fig. 3a. The antenna structure can be used to modify the coupling direction and intensity of SPP field by using different antenna arm lengths, incident wavelengths, and incident angles.
https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig3_HTML.gif
Fig. 3

a Schematic of the three-arm triangle antenna and silver nanowire. P-polarized light illuminates the input end under the 5° incident angle. b Simulation mesh grids for the wire–antenna structure and SPP propagation space. Average electric field intensities of areas A and B are calculated for the enhancement factors

Figure 3b shows the simulation mesh of the nanowire–nanoantenna structure. The average electric field intensity (|E|2) in regions A (Iin) and B (Iout) are calculated for the enhancement factors. To minimize the numerical errors, distinguished simulation cell grids are applied in different areas. Grid of 2×3 nm is utilized in the antenna gap area of antennas, and grid of 10 nm is used to mesh the other simulation space.

The enhancement factor of wire–antenna structure with various arm lengths is investigated with 1.55-μm wavelength under 5° incident angle. For the condition of 140 nm arm length, the SPP field distribution of the top layer (Z = 0, interfaces of silver and air) is shown in Fig. 4. The simulation geometry is indicated as the inset. In Table 1, the field intensities of both input (Iin) and output (Iout) ends as well as the enhancement factor for different arm lengths (from 140 nm to 1.14 μm) are calculated and compared with the single silver nanowire (arm length = 0). The maximum enhancement factor 1.82 is obtained for the arm length of 140 nm.
https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig4_HTML.gif
Fig. 4

Simulation geometry and electric field distribution (layer Z = 0) of three-arm antenna (140 nm) and silver nanowire structure at the 1.55-μm wavelength under 5° incident angle

Table 1

Intensities for different arm lengths at input (Iin) and output (Iout) ends

Arm length (μm)

Iin (a.u.)

Iout (a.u.)

Enhancement factor

0.00

34.82

4.857

1

0.14

36.09

8.824

1.816

0.34

43.67

8.519

1.754

0.54

51.85

7.587

1.562

0.74

54.95

7.131

1.468

0.94

64.05

6.541

1.347

1.14

89.30

6.161

1.268

Figure 5 reflects the trade-off between SPP propagation field and the arm length of the antenna structure. With the increase of arm length, the SPP field intensity enhances at the incident region, which can be explained by the tip enhancement effect at the gap area [17]. However, for the output end, the SPP field intensity behaves in the opposite way but has a maximum magnitude at the arm length of 140 nm. We suppose that with the extending of antenna arm length, the local electric field is enhanced, but the strong field localization will limit the SPP coupling from the antenna gap to the silver nanowire. Thus, the simulation result shows that 140 nm for antenna arm length is the optimal size for the wire–antenna structure to obtain a maximum enhancement factor with 1.55-μm incident wavelength under 5° incident angle.
https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig5_HTML.gif
Fig. 5

Electric field intensity curves of input and output ends with respect to the different antenna arm lengths

The enhancement factor is also related to the wavelength of incident laser. Electric field intensities of the wire–antenna structure under distinctive wavelengths from visible to infrared range are analyzed by using 140-nm three-arm antenna structure under 5° incident angle. The simulation geometry is shown in Fig. 6a, which is the same as the inset of Fig. 4. Figure 6a–c gives the electric field distribution of the top layer (z = 0) under the wavelengths of 1, 2, and 4 μm. Standing plasmon waves are generated between the input and output end planes. From these steady-state images, it can be found that the SPP wavelength is close to the incident laser wavelength, i.e., λSPP ≈ λin.
https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig6_HTML.gif
Fig. 6

a–c Simulation of electric field distributions in layer Z = 0 under 1-, 2-, and 4-μm wavelengths at 5° incident angle, using the antenna–wire structure (140 nm) as shown in the insert of a

Table 2 shows the calculation data of the SPP field intensities both input (Iin) and output (Iout) ends as well as its enhancement factor. With the incident wavelength changing from 1 to 2 and 4 μm, the field intensity at the output end increases from 0.273 to 3.238 and 4.818. Comparing with the results of the silver nanowire without antenna, the maximum enhancement factor 2.33 can be achieved at the 2-μm incident wavelength.
Table 2

Intensities for different wavelengths at input (Iin) and output (Iout) ends

Wavelength (μm)

Iin (a.u.) without antenna

Iin (a.u.) with antenna

Iout (a.u.) without antenna

Iout (a.u.) with antenna

Enhancement factor

0.60

0.076

0.056

0.012

0.013

1.123

1.03

1.398

2.304

0.371

0.273

0.736

2.00

4.511

5.175

1.394

3.238

2.332

3.10

12.24

16.09

1.627

2.760

1.696

4.13

19.66

22.28

3.088

4.818

1.560

5.00

34.82

39.19

4.857

8.567

1.764

Figure 7 reflects the dependence between SPP field intensity and incident wavelength. For the incident range less than 1 μm, there is nearly no difference of the output intensity for the structure with and without antenna. This can be explained by the huge dissipation of the SPP field caused by the Ohmic loss of silver layer at visible range. It also can be found that with the increase of incident wavelength, the SPP field intensity at both input and output ends are enhanced. However, the ratio of the emission SPP field with and without antenna gives the maximum enhancement factor 2.33 at the 2-μm incident wavelength, which indicates that for the structure of 140-nm arm length antenna and 80-nm-diameter silver nanowire, SPP modes can be resonantly excited with 2-μm incident wavelength under 5° incident angle. The suggested architecture has potential applications for SPP enhancement transmission, processing, and integration circuits in the near-infrared wavelengths. Moreover, for the property of monotone increasing at infrared range, this nanowire–nanoantenna structure can also be served as the wavelength division multiplexing in the future.
https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig7_HTML.gif
Fig. 7

Dependence of input and output intensities with the incident wavelength from 1 to 5 μm for structures with and without antenna (140 nm) under 5° incident angle

This simulation is also concerned about the enhancement factor of 140-nm triangle antenna with 2-μm incident wavelength under different incident angles from 5° to 85°. Figure 8 shows the steady-state electric field distribution of the layer (z = 0) with the incident and reflected SPP waves interfering on the silver nanowire surface under 5°, 45°, and 85° incident angles, respectively.
https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig8_HTML.gif
Fig. 8

Electric field distributions for layer Z = 0 under indent angle 5°, 45°, and 85°

Table 3 gives out the calculated data of SPP field intensity in structures with and without antennas for both input and output ends. The maximum enhancement factor 2.33 under the 5° incident angle is obtained in comparison with the other angles. This result confirms that the optimal SPP resonant condition for the 80-nm-diameter silver nanowire–antenna structure is the 140 nm arm length with 2-μm incident wavelength under 5° incident angle.

Figure 9 shows that with the incident angle changing from 5° to 85°, the SPP field will experience first increase (5° to 25°) then decrease (25° to 85°) and with a maximum output intensity around 25° incident angle.
Table 3

Intensities for different angles at input (Iin) and output (Iout) ends

Angle (deg)

Iin (a.u.) without antenna

Iin (a.u.) with antenna

Iout (a.u.) without antenna

Iout (a.u.) with antenna

Enhancement factor

5

4.511

5.175

1.394

3.238

2.332

25

1.891

2.554

4.486

5.640

1.257

45

3.735

3.586

2.309

2.100

0.910

65

1.861

1.768

0.725

0.579

0.799

85

0.902

0.225

0.067

0.034

0.503

https://static-content.springer.com/image/art%3A10.1007%2Fs11468-009-9115-1/MediaObjects/11468_2009_9115_Fig9_HTML.gif
Fig. 9

Comparison of input and output SPP intensities for different incident angles from 5° to 85° using the simulation geometry with and without antenna structure (140 nm arm length)

From the data of 25°, it also can be seen that the average SPP field intensity at the output end (Iout) is larger than the input end (Iin) and with a ratio about 9:4 (see Table 3). This can be explained by calculating the energy flux Sin and Sout with the Poynting vector \( S = \left( {E \times B} \right) \times {\mu^{ - 1}} \), which presents the local electromagnetic energy. Since the magnetic field at the input end is about ten times to the output, the ratio for the energy flux at the input and output ends can be estimated about 20:3, which dominates that with a different magnetic field, the electric field at the output end can have the possibility larger than the input end. In case of the incident angle larger than 40°, there is nearly no enhancement effect for the structures with and without triangle antennas, as shown in the curves of Fig. 9.

Conclusion

In conclusion, an enhanced SPP propagation structure based on silver nanowire–nanoantenna combination is proposed and simulated by using FDTD method. By comparing with the single silver nanowire, three-arm triangle antenna plays a role to enhance the SPP coupling efficiency at the incident end and SPP field intensity at the emission end. The enhancement factors for the various antenna arm lengths and incident wavelengths under different incident angles are calculated. For the trade-off between these parameters and SPP enhancement factor, the antenna with arm length of 140 nm under 2-μm wavelength, 5° incident angle is the optimal condition for the maximum SPP coupling efficiency. The suggested approach has potential applications for the plasmonic and photoelectronic circuits at near-infrared and infrared wavelength.

Acknowledgments

The work is supported by National Science Foundation of China (10574002), National Basic Research Program of China (973 Program; 2007CB936800), and Undergraduate Scientific Training Program Funding of Peking University.

Copyright information

© Springer Science+Business Media, LLC 2009