1. Introduction

Surface plasmons can be viewed as quasi 2D EM excitations, propagating along a dielectric-metal interface and having the field components decaying exponentially with small skin depth into both neighboring media [1–4]. The transverse mode size supported by a plasmonic waveguide is mainly determined by the skin depth in the dielectrics [2], which can be calculated as ${\delta }_d=\frac{\lambda }{2\pi }\frac{\sqrt{-\left({\epsilon }_m+{\epsilon }_d\right)}}{{\epsilon }_d}$, where λ is the wavelength in vacuum, ε_d and ε_m are relative permittivity of the dielectrics and the metal (metal is treated as a dielectrics with complex-value permittivity), respectively. Near the plasma frequency (in the ultraviolet regime for most metals), ε_m is comparable to ε_d, resulting in a small transverse mode size. Recent breakthroughs have produced a wide range of nanoplasmonic devices that generate, guide and detect light [5–12]. However, far below plasma frequency, ε_m is approximately a pure imaginary number with large magnitude, resulting in a very large transverse mode size (~10² λ and ~10³ λ in the THz and microwave regimes, respectively). This limits some important applications of surface plasmons, especially in the THz regime, where deep subwavelength optical devices will be a critical technique for the integration of THz, photonic, and electronic circuits on the same chip using the CMOS compatible technology.

Nevertheless, this issue can be addressed by plasmonic metamaterials, where the dispersion of surface plasmons and spatial confinement of waves can be engineered by designed surface textures. This approach can date back to Goubau [13], and Mills and Maradudin [14], who discovered that a surface texture on metal, such as arrays of holes or grooves, can result in highly bounded surface waves. In 2004 and 2005, researchers established their similarity with surface plasmons and referred them to as “designer surface plasmons” or “spoof surface plasmons” [15–17]. The existence of designer surface plasmons has recently been verified both in the microwave and THz regimes [18–20]. More recently, significant progress has been made on designer surface plasmonic (DSP) devices using various types of surface textures [21–25]. However, most of effort has been focused on numerical investigations and the importance of designer surface plasmons is far from being demonstrated. Herein, we demonstrate the remarkable advantages of using the designer surface plasmons for deep subwavelength waveguiding and focusing.

2. Design and fabrication

The main structures involved in our work are simply metal gratings, specifically aluminum slabs patterned with an array of rectangular grooves. The metal gratings as DSP waveguides were investigated more recently [16,24]. Assume the width, length and depth of each groove are w, a and h, and the period of the array is d. Pendry’s pioneering work shows that a simple metal grating can work well as a DSP waveguide [15].

If only the fundamental TM-like mode (magnetic field H is parallel to the groove orientation) is considered, the dispersion of EM waves propagating in the DSP waveguide can be described as [6]

We fabricated the 3D DSP waveguide on an aluminum slab. For easy fabrication of the structures, we chose the following parameters for the DSP waveguide: h = 19.05 mm, a = 6.35 mm, d = 12.7 mm, and w = 6.35 mm. Figure 1 plots the dispersion diagram of the supported modes. When the working frequency varies from 1.4 GHz to 3.3 GHz, the effective index of the corresponding guided modes increases, and then jumps to the second band starting at 8.39 GHz, which is not shown in the figure. Compared with the dispersion relation of the 2D DSP modes (infinite width), the finite width of the 3D DSP waveguide imposes a lower-side cutoff frequency when the dispersion curve is located inside the light cone.

 

Fig. 1 The dispersion diagram of DSP waveguides. The second band is not shown in the figure. The parameters of the waveguides are d = 12.7 mm, a = 6.35mm, and h = 19.05mm. The width of the 2D DSP waveguide is assumed to be infinite; the width of the 3D DSP waveguide is w = 6.35 mm. The circles indicate the measured dispersion relation for the 3D DSP waveguide.

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3. Experimental results and analysis

To experimentally explore its performance, we built a microwave near-field measurement setup based on a vector network analyzer [27–29], where the propagation of EM waves in a waveguide can be measured by the raster scan of a 1-mm microwave monopole to detect the evanescent tails. One monopole was fed as the source and another was used as the detector. The movement of the detector in x and y directions was controlled by a motion controller. In order to show the mode profiles rather than in x-y plane, a manual stage (along z-axis moving range: 25 mm, minimum resolution: 0.025 mm) was used in the experiments to control the movement of the detector in z direction. The precise control of the motion of the detector and the small size of the detector ensured that the experimental results were reliable [30]. To get accurate results, the maximum pixel size was set to be 0.5 mm by 0.5 mm in the measurements related to the calculations of mode sizes along different directions. Both the amplitude and phase of each measurement point were recorded by the E8362A PNA vector network analyzer. After a raster-scan of the detector at different locations over the structure, we observed good guided modes at frequencies between 1.5 GHz and 3.5 GHz, which respectively coincide with the lower and upper cutoffs of the numerical results as shown in Fig. 1. Furthermore, according to the phase distribution along the waveguide, we can calculate the propagation constants at different frequencies. As shown in Fig. 1, the measured dispersion curve is in good agreement with the simulated one. Figure 2 shows the intensity of the mode profile in different directions at f = 2.25 GHz. Figure 2(a) is the fabricated 3D DSP waveguide. As shown in Figs. 2(b)-2(d), the guided mode is tightly “nailed” on the metal rods of the grating and slightly diverges between the rods. The slightly beating of the intensity shown in Fig. 2(d) is due to the back reflection. The maximum of the mode size can be mapped in the middle plane of two neighboring rods. The mode size slightly varies with different frequencies and minimizes at 5.5mm-by-4.5mm (or 0.04λ-by-0.03λ) by intensity full width at half maximum (FWHM) at 2.25 GHz, as shown in Fig. 2(e). Over the metal rod, the mode size is 7.00mm-by-1.00mm as shown in Fig. 2(c). And the mode size measured along the side wall of the rod shown in Fig. 2(f) is 15.00mm-by-1.30mm. Therefore, the overall mode size relies on the dimensions of rods and can go into the deep subwavelngth scale.

 

Fig. 2 (a) The fabricated 3D DSP waveguide. The measured mode profile (shown in intensity) in different directions: (b) Side (over rods, in x-z plane), (c) Cross section over a rod (in y-z plane), (d) Top view (over rods, in x-y plane), the dashed blue squares indicate the positions of the metal rods, (e) Cross section in a groove (in y-z plane), (f) Cross section along the side wall of a rod (in y-z plane).

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Theoretically, the propagation loss is very small because the 3D DSP waveguide supports a guided mode with small effective index (n _eff = 1.2 at f = 2.25 GHz) and the small mode size supported by the waveguide is due to the interference of surface waves. The propagation attenuation mainly comes from the scattering due to fabrication imperfection. In our microwave device, the attenuation is very small and cannot be accurately measured within a short propagation distance.

To further demonstrate the function of the metal grating as a deep subwavelength DSP waveguide, we aligned two identical waveguides in parallel and formed a directional coupler as shown in Fig. 3(a) . The EM source was then fed from one of the waveguides. Figure 3(b) shows that the EM wave switches between the waveguides at f = 3.25 GHz. The distance between the two identical waveguides is 12.7 mm (from center to center).

 

Fig. 3 (a) Two DSP waveguides in parallel form a directional coupler. (b) The EM wave (shown in amplitude) propagates in the directional coupler.

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As shown in Fig. 1, the decrease of the waveguide width does not significantly affect the dispersion of the guided modes. This enables the mode-tapering in the transverse direction from a wide waveguide into deep subwavelength waveguide with high efficiency. The simulation of the taper in the terahertz regime was reported in recent work [24]. Our work in this aspect is focused on the experimental demonstration of this technique in the microwave regime. To this end, we fabricated a tapered DSP waveguide as the input of the uniform waveguide as shown Fig. 4(a) . The waveguide is tapered from 203 mm into 6.35 mm within the distance of 216 mm. In the experiment, we fed the taper with a monopole in the far end and partial EM waves are coupled to the taper. Figure 4(b) shows the measured intensity distribution on the device surface. As can be seen, when the EM waves propagate in the taper, the mode size becomes smaller and smaller with the intensity gradually increasing, and eventually EM waves are coupled into the deep subwavelength mode. This is an essentially squeezing or focusing process. Note that the tapered mode will be eventually end up as the guided mode of the 3D deep subwavelength DSP waveguide with dimensions 0.04λ-by-0.03λ.

 

Fig. 4 (a) The integration of the 3D subwavelength DSP waveguide with a tapered DSP waveguide as input. (b) Measured intensity distribution when EM waves are coupled from a 2D DSP waveguide and a 3D DSP waveguide.

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4. Conclusions

To summarize, we have experimentally investigated the metal grating as a deep subwavelength DSP waveguide, where mode cross section down to 0.04λ-by-0.03λ can be achieved in air. We also demonstrated an efficient coupler for the deep subwavelength waveguide, which provides a means to squeeze or focus EM waves into the deep subwavelength scale. It is worth noting that the modeling of the devices is based on perfect electric conductor (PEC) for metal and hence there is no difficulty to be scaled down into the THz regime, where metal can still be roughly treated as a PEC. In addition, the working wavelength is scalable with the index of the surrounding medium as opposed to air. This is evident that when we immersed the device in low loss oil with refractive index$n_d\approx 2$, the working frequency shifted to approximate half of its original value. Thus, the mode size to wavelength ratio is inversely proportional to the refractive index. In particular, the mode size can be further shrunk into 0.01λ ₀-by-0.02λ ₀ (λ ₀ is the wavelength in free space), if silicon ($n_d\approx 3.5$) is coated on a 3D DSP waveguide in the THz regime.