1. Introduction

Surface plasmon polaritions (SPPs) are electro-magnetic excitations that propagate along a metal-dielectric surface with an exponentially decaying field in both neighboring media [1]. In recent years, there has been a renewed interest in SPPs [2–16] following the observation by Ebbesson et.al of the extraordinary enhancement of light transmission through subwavelength-size holes array perforated on thin metal film [5]. Moreover, it is found that SPPs have a potential to overcome the diffraction limit in conventional optics, which implies a variety of potential applications of nanoscaled photonic elements and devices such as metallic nanolens [6], nanoscale waveguide [7,8] and nanometric optical circuits [9], etc. However, the propagation of SPPs is usually accompanied with considerably great loss of energy, which greatly blocks its application. In this paper we propose a metal structure with Y-shaped air channels as a combiner of multiple SPPs like a conventional dielectric waveguide coupler. So the attenuation of SPPs passing through a narrow metallic guiding structure, such as a slit, can be compensated with increased intensity. Numerical simulation by finite difference time domain (FDTD) is given for the SPPs combination and shows its validity. The investigation of the dependence of the amplifying characteristic on the bend angle and the Fabry–Perot (F–P) cavity effect associated with the multiple reflections between slit openings is also performed.

2. SPP combination in Y-shaped metallic channels

 

Fig. 1. Dependence of complex propagation constant of SPPs in metallic channels on the channel width at the wavelength of 650 nm. The solid and dashed curves represent real and imaginary parts, respectively. The dotted curve corresponds to the propagation constant for the electromagnetic wave in a vacuum.

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Before we discuss the SPP combination in Y-shaped metallic channels, it is necessary to give a brief description of SPPs traveling in subwavelength channels sandwiched between two planar metal surfaces extended infinitely in the y-axis direction. In this paper, only the TM mode consisting of Ex, Ez, and Hy components (as shown in Fig. 2) is discussed due to its obvious plasmon excitation on a metal surface. It is known that a planar metallic-surface-neighboring dielectric medium sustains traveling SPPs with propagation constant $k_{\mathit{sp}}=k_0\sqrt{\frac{{\epsilon }_m{\epsilon }_d}{{\epsilon }_m+{\epsilon }_d}}$ [1], where k ₀ = 2π/λ is the free-space wave vector, ε_m and ε_d are the dielectric constants of metal and dielectric media, respectively. ε_m can be calculated from the Drude formalism ${\epsilon }_m\left(\omega \right)={\epsilon }_{\infty }-\frac{{\omega }_p^2}{\omega \left(\omega +\mathit{i\gamma }\right)}$, where ω_p is the plasma frequency, γ is the absorption, ω is the frequency and ε _∞ comes from the contribution of the bound electrons to the polarizability. For metal Ag used here, ω_p = 1.346×10¹⁶ Hz, γ = 9.617×10¹³ Hz and ε _∞ = 4.2. When two metallic surfaces are closely positioned, some guiding modes are produced in the air gap, in which the symmetric SPPs are the major components when the slit width is very small. In order to establish a quantitative understanding, Fig. 1 presents the propagation constant Re[β] as well as the loss Im[β] of the SPPs in metallic channels with different width w, where ε_d = 1 for air and ε_m = -17.36 + 0.72i for metal Ag at 650 nm wavelength. In narrow channels, both the real and imaginary parts of the SPP propagation constant increase greatly, implying the slowed propagation of SPPs as well as increased loss per unit length. For the channel width w = 30 nm, for instance, we can see from Fig. 1 that the real part of propagation constant Re[β] = 1.675k ₀ and the imaginary part Im[β] = 0.0134 k ₀, showing that slowed SPPs decay rapidly to 1/e intensity after traveling a length of about six wavelengths in air.

 

Fig. 2. The schematic of the Y-shaped metallic channel for SPP combination.

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As shown in Fig. 2, the structure of the SPPs combiner includes three channels in the shape of Y. The front two branch arms of the Y are connected with its stem branch. The arm and stem branches all have the same width of w. When the EM wave, TM polarized and propagating along the +z direction, approaches the openings of the two branch arms of Y, the SPPs will be excited by means of the end-fire excitation and travel along the air branches.

 

Fig. 3. Schematic of the cascaded Y-shaped metallic channels structure for four SPPs combined into one.

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As the SPPs from two arms reach the connection region, they are superimposed coherently with constructive interference and new SPP modes with intensified energy are excited in the following stem branch. Accompanied with the SPP combination, some reflection and scattering at bends and the entrances and exits of channels, which, together with the absorption in metal, lead to a great loss of EM energy.

In order to get stronger SPP intensity, a multilevel structure that has several Y shaped waveguides is introduced. For example, three Y units are connected in form of Y like a tree, as shown in Fig. 3. Similarly, the combined SPPs from the first two Y stems will meet and unite at the third Y’s connection, and SPPs can be further intensified.

3. Numerical simulation through FDTD

FDTD simulation of Y branches is performed to further study numerically its optical property. The metal material here is Ag and the light source is at a wavelength of 650 nm. The parameters of the channel are as follows: channel width w = 30 nm, channel length of two arms and stem of Y is 150 nm. The length and width of the combiner are about 600 nm and 330 nm, smaller than the traveling space of light in air in one oscillation period.

 

Fig. 4. FDTD simulation result of Poynting vector Sz of the combination structure shown in Fig. 3 for λ = 650 nm and w= 30 nm.

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Fig. 4 presents the time-averaged Poynting vector Sz of our simulation, which indicates the magnitude of energy flow along the z direction. When the incident light reached the entrance, a high density of charge was generated at the corner as a result of the abrupt change of dielectric constant there, so the corner played a role much like a pin end, where the SPPs can be excited. It can be seen from the picture that the energy is much larger at the corner. The SPPs propagate along the surface of the slit and its intensity increase greatly around the junction of arms and stem branches due to constructive interference superimposing [10]. Although the loss in the bend should not be ignored and the attenuation of the metal is large, the intensity of the SPPs is enhanced greatly at the exit port compared with the one for a single channel. In addition, SPPs in the junction of the two arms are increased furthermore by means of the same reason as given above, which helps to increase the final light output.

4. Loss analysis and F–P cavity effect

 

Fig. 5. Output intensity of the Y combiner of 2 to 1 with a different bend angle. The two arms are 150 nm long and the total length of the combiner is set to 400 nm. Channel width and wavelength are the same as in Fig. 4.

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The greatest disadvantage associated with nanometric metallic channels may be their considerably high energy loss, originating mainly from metallic absorption and scattering at bends. As metal absorption has been presented in Fig. 1, only bend loss is discussed here. A set of simulations was performed for a combiner of 2 to 1 with different bend (angle between the two arms of Y) ranging from 40° to 180°. The values of Sz at the export of the last stem branches are plotted in Fig. 5. As expected, sharp bends (large angle) bring higher loss as well as lower export intensity and slight bends (small angle) ensure low loss and great output of light. In addition, it is worth noting that the Y branch still works as a SPP combiner even with a 180° bend. This phenomenon, distinguished greatly from conventional dielectric wave guiding optics, preludes its privilege and potential of constructing nano-size photonic devices.

Another feature of metallic channel we are interested in is its F–P cavity effect as SPPs travel in metallic branches with finite length. The cavity effect can be viewed as multiple light reflections occurring at any openings of branches due to impedance mismatch between channels and free space. To give a numerical understanding of this effect, we simply calculate the output intensity of the Y combiner of 2 to 1 with variant length of the stem branch. As clearly shown in Fig. 6, the output SPPs intensity oscillates regularly with stem length and the oscillation period 200nm shown in the figure coincides with a half of SPPs wavelength in the branch which can be determined by ${\lambda }_{\mathit{spp}}=\frac{{\lambda }_0}{\mathrm{Re}\left(\frac{\beta }{k_0}\right)}$, referring to the Fig. 1. However the amplitude monotonically decreases with the increase of the stem length, which we believe comes from increased metal absorption.

 

Fig. 6. Output intensity for the Y combiner of 2 to 1 with different length of the stem channel. The bend angle here is 60° and arms length is 150 nm. Channels width and wavelength are as stated in Fig. 4.

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4. Conclusion

In conclusion, a Y-shaped metallic channel is proposed as a structure for implementing the combination of SPPs 2 to 1. By cascading multiple Y-shaped channels, an N-to-1 SPP combiner can be readily obtained. Numerical simulation of 4-to-1 structures is performed through the FDTD method and illustrates its validity. Moreover, the loss of the EM wave traveling in this structure with variant bend angle and length of stem branch is discussed numerically by investigating the output intensity of the final Y stem branch. We also found that the metallic channels with finite length display strong F–P cavity effect due to reflections of the SPPs at branch openings. These results would help to find applications of SPPs in plasmonics and nanotechnology where great SPPs are required, such as the high-intensity SPP source, nano-SPP circuit, optical storage, etc.

Other aspects of the proposed structure, such as the impacts of the slit width on the final light output, and how many channels can work efficiently considering the loss, deserve further investigation in the future.

This work was supported by the Chinese Nature Science Grant (60507014/F05), the Innovation Grant of the Chinese Academy of Science, and the Open Project (KFS4) from the State Key Laboratory of Optical Technologies for Microfabrication, Institute of Optics and Electronics, Chinese Academy of Sciences.