Microscopy of terahertz spoof surface plasmons propagating on planar metamaterial waveguides Open Access

Surface plasmon polaritons (SPPs) are electromagnetic waves that propagate at the interface between a metal and a dielectric material through coupling between delocalized electrons and the electromagnetic field. These surface waves have attracted significant interest since they permit subwavelength confinement and, thus, provide strong field enhancement.¹ In particular, there has been growing interest in the development of plasmonic circuit technology that offers a bridge between electronic and photonic devices for information processing and sensing,² with potential applications including super-resolution imaging,³ high-density optical data storage,⁴ and bio-sensing.⁵ SPPs are typically exploited at optical and UV frequencies, which are close to the plasma frequencies of metals.⁶ However, at lower frequencies, such as in the terahertz (THz) region of the spectrum, metals resemble perfect electric conductors (PECs), resulting in extremely poor confinement of SPPs such that the electromagnetic field propagates as a weakly confined Sommerfeld–Zenneck surface wave.⁷ Nevertheless, the ability to confine and control light at terahertz frequencies that offer unique opportunities for sensing in areas as diverse as bio-medicine,⁸ biological and chemical sensing,^9–12 and industrial inspection¹³ is highly desirable. This has led to the investigation of new ways to transfer the ability of SPPs to confine light tightly in deep subwavelength dimensions to these lower frequencies. In this respect, it has been shown that the addition of subwavelength corrugations to a metal surface produces an enhanced surface impedance, which can be exploited to support the propagation of surface-bound modes even in the limit of perfect conductivity,¹⁴ thereby mimicking the properties of SPPs.^15,16 These waves are known as spoof surface plasmon polaritons (SSPPs), and their dispersion relationship closely follows that of SPPs.

In the microwave and sub-millimeter frequency regimes, the propagation of SSPPs has been demonstrated experimentally on subwavelength-corrugated metallic structures, including helically grooved wires,¹⁷ periodic chains of domino structures,^18,19 and periodic metallic cylinders.²⁰ Furthermore, nearly zero-thickness metal strips printed on flexible, ultra-thin dielectric films have been shown to support the propagation of planar surface plasmon (PSP) modes that adapt to the curvature of the surface.²¹ This allows the design of flexible plasmonic circuits that can be bent, twisted, or folded. Recent advances in PSP circuitry on ultra-thin metal films have provided a wide range of planar waveguide devices operating in the microwave and millimeter-wave regions,²² including multi-band waveguides,^23,24 broadband converters from guided waves to PSPs,²⁵ ultra-wideband beam splitters,²⁶ frequency selective devices,²⁷ ultra-wideband and low-loss filters,^28–30 on chip sub-terahertz SSPP transmission lines in CMOS,³¹ and SSPP amplifiers.³² 

At higher frequencies around $∼1$ THz, periodically patterned planar structures supporting localized^33,34 and propagating^22,26 SSPPs have been proposed theoretically. Furthermore, the propagation and guiding of SSPPs on metallic surfaces patterned with a two-dimensional array of subwavelength apertures have been demonstrated experimentally at frequencies up to $∼1.5$ THz.³⁵ In this case, the propagation of SSPP modes along the metallic surfaces was verified by transmission measurements accomplished using THz time-domain spectroscopy, although this approach is sensitive only to the macroscopic device properties and is insufficient to reveal insights into the light–matter interactions on the microscopic scale. To this end, there has been considerable interest in the application of techniques for visualizing with subwavelength resolution the THz field supported on the surface of microscopic devices. In particular, one approach that provides a nanometer-scale spatial resolution that is independent of the incident wavelength is scattering-type scanning near-field optical microscopy (s-SNOM).³⁶ This technique has been successfully applied to the visualization of plasmonic³⁷ and photonic³⁸ modes in individual THz resonators, as well as the nano-imaging of THz SSPPs in doped semiconductors³⁹ and THz Dirac plasmon polaritons in topological insulators.^40,41

In this work, we report the design and experimental characterization of an ultra-thin metamaterial planar waveguide that supports SSPPs at THz frequencies. Finite-element method (FEM) simulations are shown to predict the excitation of SSPPs on the surface of our devices under free-space illumination by a narrowband beam at 3.45 THz. We further investigate the use of grating couplers integrated into the waveguides to enhance the excitation of SSPPs. We investigate these structures experimentally through the use of THz-s-SNOM to map directly the out-of-plane electric field associated with the propagation of SSPPs on the surface of the waveguides, with deeply subwavelength resolution. The experimental measurements under both s- and p-polarized excitation show good agreement with simulations. Our work represents the first direct observation of propagating THz-frequency SSPPs on a planar waveguide and paves the way for the future development of plasmonic integrated circuit technology operating in this technologically important frequency range.

Our waveguide structure supporting SSPPs at THz frequencies is based on a plasmonic metamaterial consisting of an ultra-thin metallic comb structure supported by a rigid substrate, as depicted in Fig. 1 (inset). This design is adapted from Ref. 21, where experimental results were reported at microwave frequencies (f = 10 GHz). To support SSPPs at the target frequency $>3$ THz, our structure is designed with a period d = 7.5 μm, which is treated as the unit length, and a duty-cycle a/d = 0.733, total width w = 8 μm, stub length h = 6 μm, and film thickness t = 100 nm. The metallization used to form the plasmonic waveguide is gold, and it is supported on a float-zone silicon substrate of thickness 500 μm with a dielectric constant ɛ_r = 11.65 at frequency f = 3.45 THz, as determined experimentally from THz time-domain spectroscopy measurements (see the supplementary material, Fig. S1). The dispersion relation for the fundamental mode of the TM-polarized waves supported by the structure was calculated using the eigenmode solver in ANSYS HFSS, in which a unit cell of the waveguide was considered with periodic boundaries in the x-direction and PEC boundaries in the y-direction. As shown in Fig. 1, the dispersion relation deviates significantly from the light line, indicating that the waveguide supports the propagation of confined modes. The SSPP wavelength is related to the SSPP wave-vector according to the relation λ_SP = 2π/k_x, which yields a value of λ_SP = 18.5 μm at the target frequency of 3.45 THz.

In the case of free-space excitation of SSPPs on the waveguide, the momentum mismatch between the incident beam and the subwavelength SSPPs should be considered. Simulations have confirmed this momentum mismatch can be addressed by exploiting diffraction of the free-space beam at the edge of our waveguide structure, whereby components of the diffracted light whose wave-vector coincides with the SSPP wave-vector can couple to surface polaritons (see the supplementary material, Figs. S3 and S4). Nevertheless, to improve the coupling of an obliquely incident beam to SSPPs further, we have employed an integrated grating structure as shown in Fig. 3(a). The coupling efficiency of light to SSPPs on the waveguide depends primarily on the grating period, α, but also on the grating duty-cycle, β, the width w_s of the grating apertures, and the total length of the grating structure, L_g. Through variation of these parameters in FEM simulations, we have determined, for the illumination geometry corresponding to our experimental system, an optimum grating period of α = 23 μm in the case when β = 50%, w_s = 25 μm, and L_g ≈ λ₀ = 87 μm (see the supplementary material, Figs. S5 and S6).

In order to confirm the excitation of SSPPs on our structures and to investigate their properties experimentally, we have employed THz-s-SNOM to map the spatial distribution of the out-of-plane field on the surface of the waveguides. The s-SNOM system employs a 3.45-THz quantum cascade laser (QCL) as both an excitation source and a coherent receiver by exploiting the laser self-mixing effect, as described elsewhere.³⁷ The QCL was cooled using a continuous-flow liquid–He cryostat and maintained at a heat sink temperature of 20 ± 0.01 K. A current source was used to drive the laser with a dc of 420 mA, and emission from the QCL was focused on the $∼20$ nm apex of a vertically aligned near-field microscope probe positioned in the near-field of the sample surface at an incident angle of $∼54$° to the surface normal. Radiation scattered to the far-field by the probe was coupled back to the QCL along the same optical path as the incident beam and reinjected into the laser cavity. To isolate the signal component arising from the near-field interaction between the probe and the sample, the microscope probe was operated in tapping mode, and the QCL terminal voltage was amplified using an ac-coupled low-noise voltage amplifier and then demodulated at the harmonics of the probe tip’s tapping frequency (Ω ∼ 80 kHz) using a lock-in amplifier. The tapping amplitude was A_tip ≈ 200 nm, and the time constant used was τ_s = 50 ms. Under these experimental conditions, the feedback parameter has been measured to be C ∼ 0.1, and the noise equivalent power of the self-mixing detection scheme is estimated to be $∼3$ pW.

Figures 3(e) and 3(f) show the values of $Re(sze−iϕz)$ obtained in this way following spatial averaging over 192 pixels within each stub of the waveguide and subtraction of the constant offset described above. Since the waveguide length L = 208 μm is greater than the expected propagation length of SSPPs in this structure, we assume negligible interaction between SSPPs launched from opposite ends and, therefore, analyze SSPPs on each half of the waveguide independently. Figures 3(e) and 3(f) show the resulting fits of the data to Eq. (1), from which the estimates k_x = 4180 ± 360 cm⁻¹ and L_p = 51 ± 30 μm are obtained. The large relative uncertainties in these values arise from the low sampling resolution along the x-direction. Notably, this fitted value of the wave-vector is greater than that obtained from the eigenmode simulations (k_x = 3400 cm⁻¹), which itself is congruous with values obtained from FEM simulations under plane wave illumination (see the supplementary material). One possible explanation for this is the influence of the probe tip in the near-field of the sample, which is not accounted for in our simulations. Indeed, it is well known that the process of measurement in s-SNOM can result in the modification of photonic modes supported by nanophotonic systems,^43,44 owing to the near-field interaction between the tip and the sample. In addition, the charge distribution induced directly on the surface of the waveguide by the obliquely incident THz field may cause departures from the simple model for the out-of-plane field described by Eq. (1). Another possible explanation for the observed discrepancy is that there are slight differences between the dimensions of the experimental samples and the ideal designs used in the simulations, which can occur owing to edge-roughness/blurring in the optical lithography process used. Nevertheless, we note reasonable agreement between the values of L_p obtained experimentally and from simulations. Finally, from the data in Fig. 3, we can compare the amplitude of SSPPs launched from the grating structure [shown in Fig. 3(e)] with those launched from the unmodified end of the waveguide [shown in Fig. 3(f)]. We find the former, for which the fitted value E₀ = 5.1 ± 3.2 a.u. is obtained, to be slightly larger than the latter, for which the value E₀ = 3.1 ± 1.7 a.u. is obtained from the fitting procedure. The ratio of these values, γ ≈ 1.6, indicates our integrated grating structure is effective at improving the coupling of the obliquely incident beam to SSPPs on the waveguide, in agreement with predictions from simulation, which yield γ ≈ 1.5. However, we note that the large uncertainties in these experimental values, which arise from the reduced sampling resolution along the x-direction, make an accurate quantitative comparison difficult.

When the incident beam is p-polarized as above, z-components of the radiation field will interact strongly with the vertically aligned s-SNOM tip. Due to the strong confinement effect at the tip apex, a non-negligible component of the photon momentum is thereby generated at the SSPP wave-vector, which can launch SSPPs in the near-field of the tip.⁴⁵ In order to circumvent this possibility, we also investigate the direct excitation of SSPPs on our waveguide structures using an s-polarized incident beam, as shown in Fig. 4(a). To this end, we have employed a quartz zero-order half-wave plate (HWP), positioned in the beam path between the QCL and the near-field probe, to control the incident polarization state in our system. As shown elsewhere,³⁷ the p-polarized field scattered from the tip may still generate a small but measurable SM voltage signal owing to a small but non-negligible component of circularly polarized light in the QCL radiation field. Figure 4(b) shows the spatial distribution of this signal obtained by THz-s-SNOM from a waveguide incorporating a grating structure of period α = 23 μm. The corresponding values of $Re(sze−iϕz)$ obtained from the signal spatially averaged within each stub of the waveguide, following subtraction of the dipole interaction term in Eq. (2), are shown in Figs. 4(c) and 4(d). As before, SSPPs are seen to be launched from each end of the waveguide, which is characterized by an oscillatory out-of-plane field that decays as the SSPPs propagate along the waveguide axis. To quantify the amplitudes of the SSPPs launched from each end of the waveguide, we again fit the experimental values to Eq. (1), using the previously determined parameters k_x = 4180 cm⁻¹ and L_p = 51 μm. These fits, shown in Figs. 4(c) and 4(d), yield the values E₀ = 0.4 ± 0.3 a.u. for the end of the waveguide incorporating the grating and E₀ = 0.3 ± 0.1 a.u. for the unmodified waveguide. From the ratio of these values, γ ≈ 1.3, which also agrees with the value γ ≈ 1.5 obtained from simulations, it can again be concluded that the grating structure is effective at improving the coupling of the s-polarized beam to SSPPs on the waveguide. It should also be noted that these values being considerably smaller than those obtained under p-polarized excitation do not indicate a weaker out-of-plane field associated with SSPPs under s-polarized excitation; rather, this is due to much weaker mixing between the orthogonal polarization states of the incident and scattered fields in this case.

To conclude, we have presented the design, simulation, and experimental demonstration of an ultra-thin metamaterial planar waveguide that supports spoof surface plasmon polaritons at THz frequencies. We have also successfully mapped, with deep subwavelength resolution, the spatial distribution of the electric field associated with SSPPs propagating on such waveguides for the first time. Our results confirm the excitation of SSPPs on these structures under both p-polarized and s-polarized excitation by a free-space beam at 3.45 THz. We have also shown that grating structures integrated into the waveguide can be used to enhance the coupling of light to SSPPs on the waveguides. Our work paves the way for future development of plasmonic integrated circuit technologies and components operating in the THz frequency band, including, for example, transmission lines, beam-splitters, frequency selective devices, multiplexers, ultra-wideband, and low-loss filters. Future possible research directions include the development of conformal THz waveguides printed on flexible films that can be bent or twisted,²¹ or active devices whereby the transmission of SSPPs along the waveguide can be controlled electronically.

The supplementary material shows the dielectric constant of silicon as a function of frequency measured using THz-TDS. The S21 parameter of the waveguide structure is shown, calculated using ANSYS HFSS for a waveguide with a total length of L = 73 μm. The simulation of the waveguides under illumination by a free-space beam and the optimization of grating parameters are also shown for the cases of p-polarized and s-polarized excitations, according to the geometries shown in Fig. 3(b) and Fig. 4(a), respectively. Approach curves obtained from the n = 1–5 harmonics of the demodulated self-mixing voltage signal in THz-s-SNOM are also shown.

The authors acknowledge the support from EPSRC (UK) Program grants “HyperTerahertz” (Grant No. EP/P021859/1) and “Teracom” (Grant No. EP/W028921/1), EPSRC Grant No. EP/V004743/1, the Royal Society, and the Wolfson Foundation (Grant Nos. WM110032 and WM150029).

The authors have no conflicts to disclose.

P.D. and N.S. conceived the idea, developed the experimental setup, and performed the measurements. Waveguide structures were designed by N.S. and simulations were performed by N.S. and S.J.P. Structures were fabricated by N.S. and M.S. Measurements of the dielectric constant of silicon as a function of frequency were acquired by A.D.B. Data were analyzed by N.S. with support from P.D. and J.E.C. The QCL structure was grown by L.L. under the supervision of E.H.L. Devices were processed by P.R. under the supervision of E.H.L. and A.G.D. The manuscript was written by N.S., P.D., and J.E.C. with contributions from all the authors.

N. Sulollari: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). S. J. Park: Software (supporting); Validation (supporting); Writing – review & editing (supporting). M. Salih: Resources (supporting); Validation (supporting); Writing – review & editing (supporting). P. Rubino: Resources (supporting). A. D. Burnett: Formal analysis (supporting); Investigation (supporting); Writing – review & editing (supporting). L. Li: Resources (lead). E. H. Linfield: Funding acquisition (lead); Project administration (supporting); Resources (lead); Supervision (supporting); Writing – review & editing (supporting). A. G. Davies: Funding acquisition (lead); Project administration (supporting); Supervision (supporting); Writing – review & editing (supporting). J. E. Cunningham: Funding acquisition (lead); Project administration (lead); Software (supporting); Supervision (lead); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). P. Dean: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data utilized in the development of this article can be found at https://doi.org/10.5518/1456.