1. Introduction

A surface plasmon polariton (SPP) is a hybridized light-electron wave, or quasi-particle that propagates at the interface between a conductor and a dielectric material [1]. Due to its capability of confining light beyond the diffraction limit, it is believed by many as a potential building block for future subwavelength photonic circuits and devices [2]. In recent years, various types of plasmonic waveguide have been proposed, including long-range dielectric-loaded SPP waveguides [3, 4], metal-nanosphere chains [5, 6], sharp metal channels or wedges [7–9], metal nanowires [10], hybrid plasmonic waveguides with more than one dielectric layers adjacent to metal surface [11, 12], metal-slot waveguides [13, 14], etc. However, regardless of their cross-sectional configurations, once the waveguides have a sub-wavelength mode confinement their modal propagation length is counted only in micrometers; the high propagation loss is currently a key factor hindering the wide adoption of such waveguides. There are several possible approaches for reducing the loss without sacrificing mode confinement, such as by using gain dielectrics [15], by operating at a low temperature [16], by seeking new low-loss negative-permittivity materials [17], by improving the metal crystallinity [18] or by changing supporting substrate [19]. In this work, we first present our fabrication of a SPP waveguide that is reminiscent of the microstrip transmission line in microwave engineering. Its potential superiority over the slot waveguide will be briefly addressed. In addition, by thermally annealing the waveguide, we are able to reduce the propagation loss at 980 nm wavelength significantly.

2. Waveguide and the modes

The fabricated waveguide is schematically shown in Fig. 1(a). Basically it consists of two gold layers separated by a dielectric layer of Al₂O₃. Refer to the figure: the thicknesses of the three layers from top to bottom are h₁ = 80 nm, h₂ = 120 nm and h₃ = 100 nm respectively; the width of the top strip is w = 400 nm. The waveguide is sitting on a glass substrate. The gold and Al₂O₃ layers are deposited through electron-beam vaporization in a high vacuum at the same rate of 0.1 nm/s. The length of the waveguide (along z) is 30 μm. Patterning of the top-layer gold strip is achieved through electron-beam lithography. The top-view scanning-electron-microscope (SEM) image of the fabricated sample will be presented in Section 3.

 

Fig. 1 (a) Geometry of the waveguide under study. (b) Fundamental guided mode at 1550 nm. The color shading indicates the z-component of the Poynting vector, while the vectors show the transverse electric field. (c) The same but for a slot waveguide of similar size (see text).

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We focus on two experimentally available wavelengths, 980 nm and 1550 nm. We first numerically calculated, with COMSOL Multiphysics, the modal property of the waveguide. In our simulation, the permittivity of gold is acquired based on the Drude model from [20]. Al₂O₃ and the supporting dielectric substrate are assumed to have constant indices of 1.75 and 1.45 respectively. The simulation reveals that there are two modes guided in the waveguide both at 980 nm and 1550 nm. The fundamental mode has a propagation loss of 0.24 dB/μm at 980 nm and 0.20 dB/μm at 1550 nm; the higher-order mode is about 10% lossier. In Fig. 1(b) we illustrate the calculated mode profile at 1550 nm, which has an effective mode index n_eff = 1.9663 + 0.0057i. The waveguide can in fact be treated as a variant of the slot waveguide [13, 14], except with an extended bottom metal clad. In Fig. 1(c), we have shown the mode profile of a corresponding slot waveguide by narrowing the Al₂O₃ and gold layers to 400 nm in width. Here, in passing, we argue that our proposed waveguide is superior to the slot waveguide: firstly, simulations show that the slot equivalent has consistently a higher loss than the strip waveguide, though by only a few percent, owing to presence of additional metal corners; secondly, the experimental realization of our waveguide is easier as one only needs to pattern the top-layer gold. It is foreseeable that when the side surface roughness (due to lift-off in lithography process) is taken into account the slot waveguide would suffer even higher loss.

3. Experimental results and discussions

The measurement of its propagation loss is done in a way similar to the cut-back method in the fiber-optics community. A tapered fiber tip is used to excite the waveguide from its side; the output light intensity scattered from the end of waveguide is captured by a CCD camera, while the excitation spot is carefully varied along the waveguide. The propagation loss can then be extracted by fitting the light output versus propagation distance to an exponentially decaying function [21, 22]. The error in propagation loss from repeated measurements, even with different fiber tips, is well within 10%. The measured output intensity (I₀) of the waveguide at 980 nm is shown by the black squares in Fig. 2(a). A least-square curve fitting suggests that the waveguide has a propagation loss of 0.45 dB/μm. Similarly at 1550 nm the output is recorded by the black squares in Fig. 2(b), and the fitted loss is 0.31 dB/μm. The experimentally obtained propagation loss values are higher than those calculated based on the Drude model pamameter data [20], but the difference is acceptable. Besides, it can introduce some difference to the gold parameters due to different sample preparation methods. In Fig. 2(c) we show 9 snapshots for the coupling experiment at 980 nm at various excitation spots. The SPP waveguide and the fiber tip are clearly seen in the top bright-field image.

 

Fig. 2 Output intensity v.s. propagation distance measured at 980 nm (a) and 1550 nm (b) before (black squares) and after (red circles) annealing. The black and red lines are the fitted curves for the decaying light intensity in the waveguide before and after annealing, respectively. (c) Bright- and dark-field images for coupling at 980 nm recorded by a CCD camera.

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It has already been known that thermal annealing can significantly change the quality of a gold film, by increasing the grain size and flatting the film surface, which was previously confirmed by examining SEM images [23, 24], TEM images and X-ray diffraction analysis [25, 26]. Here we demonstrate the effect of thermal annealing on light propagation in our fabricated plasmonic waveguide, as a consequence of the change in gold quality. The annealing treatments were done in a temperature-controlled oven at atmospheric pressure. First, the sample was heated to 300 °C from room temperature (25 °C) and the temperature was maintained for 18 hours before cooling. The heating and cooling rates are about 1.5 and 0.5 °C/min, respectively; they are slow enough so no thermal shocks are induced. The propagation losses at 980 and 1550 nm are then measured using the same technique described above. The output intensity measurements are shown by the red circles in Fig. 2(a) and 2(b). By curve fitting, we obtain the propagation losses at 980 nm and 1550 nm as 0.20 dB/μm and 0.28 dB/μm respectively.

Quite surprisingly, the propagation loss at 980 nm has been decreased by more than 50% (from 0.45 to 0.20 dB/μm). We attribute the reduction of the propagation loss to the structural improvement in the gold strip and possibly also in the bottom gold film. Indeed the top-view SEM images of the waveguide before and after annealing (Fig. 3) show clear difference: before annealing (Fig. 3(a)) the surface of gold strip appear grainy with grain sizes in 15–30 nm; after annealing (Fig. 3(b)) the strip surface as well as its sides appear much smoother, and the grain sizes also increase, which agree well with the result achieved in paper [23–26]. Apart from the surface, the possible change in the inner structure of the gold parts may also have contributed to the improvement of propagation.

 

Fig. 3 (a) SEM images of a section of the fabricated waveguide. (b) The waveguide after thermal annealing at 300 °C.

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As described earlier, the gold layers in our sample are deposited onto the substrate by electron-beam evaporation, and the deposition can be divided into several stages [25, 27]. Firstly, individual gold nuclei grows on the substrate. Further deposition renders the nuclei into larger islands by means of surface diffusion or impingement of single atoms. With certain nuclei density and substrate condition, liquid-like coalescence of individual islands becomes the dominant growth process in the next stage for the discontinuous film. Finally with the increase of the thickness of the gold layer, the islands are large enough to make metallic contact with one another and an electrically continuous film come into exist. During the thermal annealing at 300 °C, we believe that “coalescence” among the grains is further enforced [24, 28, 29]. Upon heating, two grains (clusters) touch or collide and merge to form into one bigger grain (cluster) mainly by surface diffusion. The driving force of this phenomenon is the minimization of surface free energy of the system. Coalescence leads to the enlargement of grain size, which can reduce the roughness of surface in some extent. As a result, the quality of gold layer can be improved [23–26].This agrees in general with our SEM observations.

We also notice that the propagation loss at 1550nm only decreases by ∼10% (from 0.31 to 0.28 dB/μm) after annealing. This can be qualitatively explained by the fact that a lower portion of the electric field intensity is located in the metal regions of the waveguide at 1550 nm compared to at 980 nm. Indeed, from our numerical modal calculation, it is found that only about 0.4% of the modal electric field intensity for the fundamental mode is in the metal at 1550 nm; whereas at 980 nm it’s 1.1%. The difference for the second-order mode is similar, at 0.4% and 1.2% respectively.

To further investigate the effect of annealing temperature, we put the same waveguide back to the oven and heated it at 400 °C again for 18 hours. Compared to what we have obtained for 300 °C, no obvious difference is found, both from the top-view SEM image of the waveguide and from the measured propagation losses at the two wavelengths. Then we pushed the annealing temperature to 500 °C (also 18 hours). The top gold strip then undergoes severe distortion: the width of the gold strip at different positions experiences shrinking by different degrees. The nonuniformity of the width leads to increased propagation losses at both 980 and 1550 nm.

4. Conclusion

In conclusion, we have fabricated a plasmonic waveguide that resembles the microstrip transmission line. Though it can be treated as a variant of the metal-slot waveguide, it is potentially less lossy and has the advantage of simpler fabrication procedure. By using thermal annealing we are able to reduce the propagation loss of the waveguide by more than 50% at 980 nm. At 1550 nm, the effect of thermal annealing in reducing the loss is not significant, which can be explained by the lower portion of the modal electrical field located in the metal parts.