1. Introduction

Miniaturization of optical circuits and dense integration of optical devices remain major tasks in micro and nanotechnology. One of the promising approaches for downscaling optical components is to use surface plasmon-polaritons (SPPs) [1,2]. These are electromagnetic excitations supported by metallic structures that offer subwavelength light confinement in the direction perpendicular to the metallic-dielectric interface [1,2]. Various geometries have been proposed and experimentally studied to demonstrate subwavelength confinement and efficient guiding of the plasmon-polariton modes including metal strips with nm-scale thickness [3–5], subwavelength nanowires [6,7] and metal gap waveguides [8,9]. Among the studied geometries, a V-shaped metal groove supporting a strongly localized plasmon-polariton mode called channel plasmon-polariton (CPP) is of particular interest due to high degree of the CPP mode confinement, relatively low propagation and bending losses, and single mode operation achievable for the CPP [10–14]. The inverse geometry, namely, a triangular metal wedge supports a plasmon-polariton mode (wedge plasmon-polariton, WPP) that is, in a way, complementary to the CPP mode. Edge modes were first studied theoretically for metal triangular and parabolic edges [15,16], and later, triangular metal wedges were shown (both theoretically [17,18] and experimentally [17]) to support strongly localized plasmons. It was recently shown that WPPs, while showing significantly smaller modal size than CPPs, exhibit similar propagation length as CPPs [18]. At telecom wavelengths, WPP guiding properties were found to be superior to the ones offered by CPPs, where low losses for CPPs are achievable for relatively large mode sizes [19]. Moreover, the possibility of light focusing via the geometry-driven conversion of a standard SPP into a tightly confined WPP was recently proposed [18].

To our knowledge, only one experiment was performed to investigate the metal wedge configuration [17]. In the work by Pile and co-workers [17], highly localized WPP modes supported by a triangular silver wedge were studied in the visible regime, where the mode propagation length is quite short. Moreover, the structures were fabricated using the focused-ion beam (FIB) technique. In the perspective of future applications, the FIB-based approach has certain limitations due to high cost, complexity and low throughput. In addition, FIB-fabricated components are hard to interface with optical fibers to achieve efficient end-fire excitation. Thus, experimental realization of WPP components that are robust, simple to fabricate and easy to interface with outside world is of great interest for future investigations of subwavelength plasmon guiding as well as for development of functional plasmonic devices.

In this work, subwavelength WPP guiding along straight gold wedges is realized and the WPP propagation is studied both theoretically and experimentally. For fabricating triangular metal wedge waveguides a wafer-scale, parallel method based on standard UV lithography is developed. We focus on at telecom wavelengths where WPP losses are much lower[18] than in case of visible light[17]. The developed fabrication procedure provides waveguides that are compatible with fiber optics giving the possibility of easy in- and out coupling.

2. Fabrication

Large-scale fabrication of profiled metal surfaces remains a challenging task. While V-grooves and sharp wedges can easily be made in silicon using standard lithographic and etching techniques, profiling metal surfaces often requires complex fabrication techniques like FIB [13,14,17]. In this work, in order to fabricate triangular metal structures, we developed a flip-technique that allows fabrication of sharp metal wedges. Such geometry can not be achieved by standard deposition techniques since depositing a metal layer on a sharp tip (for example, in silicon) would result in smoothening of the edge. A standard fabrication sequence of lithographic and etching steps to achieve a wedge in a substrate combined with standard metal deposition can therefore only be used for making rounded-top or trapezium-shaped wedges [20].

The fabrication steps of the developed procedure are shown schematically in Fig. 1. To fabricate metal wedges, a silicon dioxide layer (~400 nm) is first grown on a silicon substrate by thermal oxidation. Prior to photoresist (AZ 5214E from MicroChemicals GmbH) spin, a layer of an adhesion promoter (hexamethyldisilazane, HMDS) is applied in a vapor priming oven. After hotplate baking, 1.5-µm-thick resist is patterned by standard UV lithography. Straight-waveguides pattern is then transferred into a SiO₂ layer via wet etch in buffered hydrofluoric acid (BHF) using developed and hard-baked resist as a mask. After silicon dioxide etch, the resist is stripped from the wafer, leaving SiO₂ mask ready for the next etching step. V-grooves in silicon are afterwards etched via standard KOH-etch process followed by oxide layer removal in BHF. After wafer cleaning, 500 nm of gold is e-beam evaporated on the silicon wafer with etched V-grooves. Using electroplating deposition, 53-µm-thick layer of nickel is then deposited on top of the gold-covered wafer. After electroplating step, the wafer is cut into pieces of different lengths containing straight embedded V-grooves. Removal of silicon substrate (KOH solution) from separate samples completes the fabrication sequence yielding straight V-wedges of gold (Fig. 2). The developed procedure provides straight wedges with the fixed apex angle of 70.5° (due to wet etch of silicon). The apex angle of the V-groove made in a substrate can be changed via oxidation process [21].

 

Fig. 1. Schematic of the fabrication steps: (1) a silicon wafer is covered with a layer of silicon oxide and photoresist, (2) resist is exposed and developed, and the pattern is transferred into the oxide, (3) V-grooves are etches in silicon, (4) gold is deposited after oxide removal, (5) nickel is deposited, (6) silicon substrate is dissolved leaving gold 70.5°-wedges.

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Fig. 2. Scanning electron microscope image of (a) 8.5-µm-wide, 6-µm-high gold wedge waveguides together with (b,c) close-ups of the fabricated wedges (b - wavy edge at the lower end is due to charging effects). Marks and facet defects are due to rough sawing of the metal.

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3. Experiment

The experimental setup employed for the sample characterization is essentially the same as in our previous experiments with CPPs and photonic crystal waveguides [13,22]. It consists of a collection scanning near-field optical microscope (SNOM) with an uncoated fiber tip used as a probe and an arrangement for illuminating metal wedge waveguides with tunable (1425–1500 nm) TM/TE-polarized (the electric field is perpendicular/parallel to the sample surface plane) radiation by positioning a tapered-lensed polarization maintaining single-mode fiber [13]. The adjustment of the in-coupling fiber (with respect to the Λ-wedge position) was accomplished when monitoring the light propagation along the surface with the help of a far-field microscopic arrangement. The idea was to judge upon the WPP excitation and propagation by observing its scattering out of the surface plane by wedge imperfections. We found that for both polarizations of incident light the track of radiation propagating along a wedge waveguide was clearly distinguishable for distances of up to 300 µm from the in-coupling wedge facet in the whole range of laser tunability. Far-field experiments included also adjusting the in-coupling fiber position to maximize the coupling efficiency. After these adjustments the whole fiber-sample arrangement was moved under the SNOM head. The intensity distribution near the surface of the wedge was mapped with a sharp SNOM tip that was scanned along the sample at a constant distance of a few nanometers. The distance was maintained by shear-force feedback, and the radiation collected by the fiber was detected with a femtowatt InGaAs photo receiver.

Typical SNOM images recorded at different wavelengths for TM polarization of the incident light are shown in Figs. 3(b), 3(c) along with the corresponding topographical image (Fig. 3 (a)). The near-field optical images (obtained at λ≅1440 and 1500 nm) demonstrate efficient and well-confined WPP guiding. Pronounced intensity variations observed along the propagation direction (Figs. 3(b), 3(c)) can be most probably attributed to the interference between the WPP modes and scattered field components (including stray light), similar to that observed previously in our experiments with CPPs [13]. One can easily recognize the Λ-wedge waveguide on the topographical image (Fig. 3(a)). It is also seen that the wedge image is quite irregular showing a zigzag pattern with sudden lateral displacements, which were caused by shear-force scanning instability due to a rather large wedge height (~5 µm). The near-field optical images obtained simultaneously with the topographical ones display similar zigzag patterns replicating lateral displacements of the fiber tip (Figs. 3(b), 3(c)). Despite the aforementioned signal variations and perturbations in topographical and near-field optical images, one could determine the average full-width-at-half-maximum (FWHM) of the WPP mode and its propagation length from 32-µm-long SNOM images (Fig. 3(d)). In the wavelength range 1425–1500 nm the FWHM was practically constant (1.32±0.1 µm) whereas the WPP propagation length was found to vary between ~100 and 120 µm, depending on both the coupling arrangement and the wavelength used. We attribute these variations to poor reproducibility of the fiber coupling where the adjustment is done using far-field observations. In this case the detected signal is strongly influenced by the scattered (by the wedge imperfections) radiation. Note that the wedge tip seen from the topographical image (Figs. 3(a), 3(d)) appears rather blunt, most probably due to the convolution between the fiber probe shape and the wedge tip profile. The sharpness of the latter can more reliably be evaluated from SEM images (Fig. 2) as been on the sub-100-nm scale.

 

Fig. 3. Pseudo-color (a) topographical and (b, c) near-field optical images taken with the Λ-wedge illuminated with TM-polarized light at λ≅(b) 1440, and (c) 1500 nm (the WPP propagates rightwards). The image size: 32×10 µm². (d) Cross sections of the topographical (stars) and near-field optical (filled and open circles) images of Fig. 3(a) and 3(c) averaged along 10 lines along the propagation direction or perpendicular to it. The exponential dependence fitted by the least-square method to the signal dependence along the propagation direction is also shown.

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The experiment was repeated for the TE-polarized incident light by rotating the polarization maintaining in-coupling fiber by 90°. For this polarization and the in-coupling fiber positioned symmetrically against the wedge, the WPP excitation is forbidden by symmetry. The typical topographical and corresponding near-field optical images recorded in this configuration at 1500 nm are shown in Fig. 4. In this case the intensity distribution is very broad and exhibits indeed a local minimum at the wedge top, showing instead two maxima on both sides of the wedge. These maxima are related to SPP modes that propagate along two broad (~6 µm) wedge sides and, being polarized perpendicular to the wedge sides, can be efficiently excited by TE-polarized light. These modes are somewhat similar to the SPP modes of metal stripes whose lateral confinement is rather poor [23].

 

Fig. 4. Pseudo-color (a) topographical and (b) near-field optical images taken with the Λ-wedge illuminated with TE-polarized light at λ≅(b) 1500 nm (the SPP propagates upwards). The image size: 18×32 µm². (c) Cross sections of the topographical (stars) and near-field optical (filled circles) images of Fig. 4(a) and 4(b) averaged along 10 lines along the propagation direction or perpendicular to it.

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4. Theory

The corresponding structure used for our modeling is a gold 70°-wedge surrounded by vacuum that is infinitely long in the propagation direction and rounded with the radius of curvature r. The gold dielectric constant is represented by a Drude-Lorentz type dielectric function. The size of the considered structures is sufficiently large so as to use bulk dielectric functions and neglect additional damping due to electron scattering at the metal surface. The simulations were carried out using a rigorous electrodynamics computational framework, viz. the multiple multipole and finite difference time domain methods [18]. We calculated the complex WPP propagation constant and field distribution as a function of the curvature radius of the wedge tip for the telecom wavelength of 1500 nm, allowing us to determine the mode size and propagation length (Fig. 5). Here the mode size is defined as the transverse separation between the locations where the time-averaged electric field of the WPP mode has fallen to one tenth of its maximum value. The factor 1/10 in this definition is somehow arbitrary but it is sufficient for our mode characterization purposes and consistent with the previous calculations [18]. As expected, the mode size and propagation length are increasing with the increase of the curvature radius, so that in order to achieve deep subwavelength WPP field confinement one should realize 10-nm-sharp wedges or even sharper ones (Fig. 5).

 

Fig. 5. Transverse electric field of the WPP mode at λ=1.5 µm for the curvature radius r=(a) 10 and (b) 100 nm. (c) Mode size (circles) and propagation length (triangles) of WPP mode as a function of the radius curvature (solid lines represent spline-interpolation).

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The obtained results indicate the possibility of subwavelength WPP guiding over ~100 µm for reasonable values (10–20 nm) of curvature radius (Fig. 5) in agreement with our experimental observations. Conversely, comparing the experimental results with the simulations (cf. Figs. 3(c) and 5) indicates that the curvature radius in the fabricated structures was close to ~25 nm, a value that is consistent with the SEM images of our structures (Fig. 2). Note that while accurate determination of the curvature radius from SEM images is in principle possible, it is rather difficult to actually make high-quality cross cuts of the fabricated structures required for this procedure. Overall, our experimental results are found in good agreement with the simulations results.

5. Conclusions

We realized subwavelength plasmon-polariton guiding along straight gold wedges that were fabricated via large-scale parallel process based on standard UV lithography. The developed fabrication procedure provides waveguides that are compatible with fiber optics. The WPP propagation was studied both theoretically and experimentally, and the experimental observations are consistent with numerical simulations performed with the multiple multipole and finite difference time domain methods. Using SNOM characterization, in the wavelength range 1.43–1.52 µm the FWHM and the propagation loss of the WPP mode propagating along triangular 6-µm-high and 70.5°-angle gold wedges were found to be around 1.3 µm and 120 µm respectively. The results of this work open up the possibility of developing WPP-based waveguide components for different applications ranging from integrated optics to biosensors.