Interferometric Refractive Index Sensing with Terahertz Spoof Surface Plasmons
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Near field interference of spoof surface plasmons propagating on two opposing faces of a thin metal sheet waveguide perforated by a periodic array of tapered holes has been investigated by time-domain terahertz spectroscopy. Closely spaced, chirped spectral interference fringes are observed in the output near the field as a result of the different nonlinear dispersion of the two surface modes. Results illustrating the potential of such a structure for interferometric refractive index sensing of nanolitres of analytes are presented.
KeywordsMetamaterials Sensing Terahertz Refractive index Interferometry
The terahertz (THz) frequency spectrum is conventionally taken to be between about 0.1 and 10 THz and lies between microwaves which are the domain of electronics and the mid infrared, which is the domain of optics. Interest in this band is partly motivated by applications arising from the wealth of electronic and vibrational material excitations at THz frequencies and the quest for higher bandwidth signal processing and new imaging and sensing capabilities . Examples include the dielectric characterisation of materials , dynamics of optically excited materials , medical diagnostics , pharmaceutical quality control , communications , security screening  and chemical and biochemical sensing . Spectroscopic sensing applications frequently require the testing of small volumes of material. Waveguides or dielectric surfaces overlaid with metal films patterned with arrays of holes or resonators can be used to increase the sensitivity by confining the probing radiation to a sub-wavelength length scale in one or more dimensions. Various waveguide concepts that can be applied to sensing at THz frequencies have been explored , including planar stripline resonators , parallel plate waveguides  and tightly bound surface waves on structured metal surfaces [12, 13].
Structured metal or metal-dielectric surfaces, often called metamaterial surfaces, can support tightly confined surface waves at terahertz frequencies with a dispersion relationship that mimics that of surface plasmon-polaritons in the visible but with a much lower effective plasma frequency that is determined by surface geometry rather than material choice . The dispersion of these ‘spoof’ surface plasmon-polaritons (which we refer to as SSPPs hereafter) determines their spatial extent perpendicular to the surface. At terahertz frequencies, metals behave like near perfect electrical conductors and unstructured metal-dielectric interfaces cannot support tightly bound surface waves. Amongst the simplest metamaterial surfaces are flat metal films decorated with periodic arrays of blind or clear holes or grooves [12, 13, 14, 15, 16]. Here, the effective surface plasmon frequency is equal to the lowest cutoff frequency of the hole or groove cavity. In such structures, wavelength-scale out of plane confinement of surface waves is possible over roughly an octave of frequency . By analogy with integrated optoelectronic architectures at optical frequencies, planar-like guiding structures at THz frequencies have advantages, in terms of possible integration with active components, for signal processing and sensing.
In this paper, we describe experiments and numerical simulations of an interferometric metamaterial sensor. It is based on SSPP propagation on opposing sides of an optically thick metal film pierced by a hexagonal close-packed array of tapered circular apertures with different effective diameters on the two faces. SSPPs on the two metamaterial surfaces are coupled via evanescent fields in the holes, analogous to the optical frequency surface plasmons on either side of metal films of a few tens of namometre in thickness  but here, the coupling is relatively weak. The dispersion of symmetric and anti-symmetric THz SSPPs on an optically thin, 7-μm thick, metal mesh in the simpler case that the two surfaces are equivalent has been studied previously by Ulrich and Tacke .
2 Materials and Methods
Figure 1 b shows the experimental configuration used to study THz guiding along the x-direction (defined in Fig. 1a) in a 4 cm × 4 cm square of mesh cut with edges parallel to x and y and stretched flat over two metal bars leaving the top and bottom surfaces clear over a 3 cm width. Hyper-hemi-cylindrical silicon coupling lenses were placed 100 μm from each end of the mesh. These end-fire coupling lenses relay the THz beam to fibre coupled photoconductive transmitters and receivers forming a time-domain spectroscopy system in which the receiver current varies with pump-probe delay in a similar manner to the transient THz electric field. A similar arrangement has been described previously  but the present setup is modified a) by attaching the output-coupling lens to a motorised z-axis translation stage and b) by covering its flat input face with a 300-nm thick gold film which is continuous except for a 150-μm wide central sampling aperture oriented along the y-axis. i.e. parallel to the mesh surface. This aperture in the detection system allowed crude ‘near field’ probing of the waveguide output field. A pair of steel razor blades was placed in the middle of the mesh with gaps of approximately 300 μm between the blade edges and the top and bottom surfaces to minimise contributions to the signal from unguided radiation. The collimated THz beam incident on the input coupling lens had a 10-mm diameter (full width at half maximum amplitude) and the experiments were conducted in a dry air atmosphere.
To confirm the asymmetry between guiding on the top and bottom surfaces, a flat metal plate was attached to each of the surfaces in turn and the guided wave spectrum was measured. From the spectral phase data, the dispersion of SSPPs on the two surfaces for this blind hole case is obtained and shown in Fig. 1c. The top surface has larger effective diameter aperture and lower asymptotic cutoff frequency, so that over the frequency range investigated, the dispersion curve bends away from the light line more than for the bottom surface.
3 Results on Bare Mesh
It is notable that the effective Q-factors of the dips in Fig. 3a and b are as high as 50 and similar in magnitude to those reported for Fano resonances in transmission measurements on asymmetric split ring resonator arrays [23, 24] which have been suggested as potential platforms for refractive index sensing. In the asymmetric split ring case, high Q-factors are associated with low radiative damping. In the mesh case, high Q-factors are instead obtained by exploiting the narrow frequency interval between interference minima resulting from the shortened wavelength of tightly bound surface waves near cut-off.
4 Refractive Index Sensing Using a Dielectric Filled Mesh
5 Future Potential
The smallest volume of resist studied was about 400 nl. The planar waveguide geometry can in principle be improved to allow the study of smaller volumes by laterally confining the guided radiation for example by adiabatically tapering the width of the mesh along x so as to create a narrow waist where analytes can be deposited. Tests were carried out to establish whether such a structure would adequately support confined surface waves by laser-cutting a sample consisting of two 30o tapers bridged by a 4-mm long single row of holes in a bow-tie geometry. The far field–transmitted spectrum shows very little change in amplitude compared with the untapered case, which suggests that surface waves can be confined to a wavelength length scale in two dimensions with little radiative loss in this type of structure. A more versatile interferometer exploiting nonlinear SSPP dispersion on a single surface could be realised using deep silicon etching and conformal metal deposition techniques. A simple example is a pair of laterally graded blind hole or groove array guides  with different cutoff frequencies coupled to a source and detector using a pair of similarly constructed, tapered Y splitters. Such a device could feasibly be integrated with a microfluidic analyte deliver system. The application we envisage is the detection of small changes in the refractive index of a chemically or biologically active film in response to the addition of specific analytes that change the optical properties without significantly changing the thickness.
In conclusion, we have demonstrated a terahertz interferometric sensing concept using a particularly simple metal mesh waveguide that exploits the nonlinear dispersion of spoof surface plasmon-polaritons. The sensitivity of the interferometer has the potential to be further improved using microfabrication techniques so as to allow detection of small changes in the refractive index of a chemically or biologically active film in response to the addition of small quantities of analytes.
We thank the UK Engineering and Physical Science Research Council for part funding under grant EP/J007595/1. Y. Pan and S. N. M. Hashim thank the University of Bath and the Government of Malaysia respectively for financial support of studentships.
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