1. Introduction

Surface Plasmon Polaritons (SPPs) are electromagnetic excitations propagating along the interface between a conductor and a dielectric medium. The associated electromagnetic field is strongly confined to the interface with an amplitude decaying exponentially within both media [1]. The strong confinement of these surface waves leads to an enhancement of the electromagnetic field at the interface, resulting in an extraordinary sensitivity of SPPs to surface conditions. Natural SPPs occurring at optical frequencies within metals have attracted a great deal of attention and have been widely used in chemo- and bio-sensors [2–4]. This is due to the fact that the enhanced field at the surface can amplify certain optical effects, such as Raman scattering, fluorescence and harmonic generation. It is desirable to extend these highly localized waveguided modes and surface-enhanced effects to the terahertz and microwave regimes. However, natural SPPs are poorly confined in these bands for good conductors. Fortunately, it has been demonstrated that metals at low frequencies can be induced to support surface modes by drilling an array of subwavelength holes or grooves in the surface [5, 6]. These modes share similar features to traditional SPPs supported by noble metal films at optical frequencies and have been named spoof SPPs. The ability to engineer a surface plasmon at microwave and terahertz frequencies where none were reported before opens opportunities to control and direct radiation at surfaces over a wide spectral range. A lot of work has been dedicated to this issue. For example, through introducing periodic subwavelength corrugations on the edges of differential microstrip lines, the crosstalk between differential pair and the adjacent microstrip lines can be greatly reduced due to the strong confinement of electromagnetic wave in the corrugation [7, 8]. Besides, it has been demonstrated that corrugated structures which support spoof SPPs can be used to control the reflection of terahertz radiation [9], enhance lasing [10], and improve the performance of antenna [11] and sensor [12–15], etc. Among these the sensing application of spoof SPPs is an interesting topic, but to date most of the current efforts have been devoted to index sensing, which relies on the detection of spectral shifts caused by changes in environment refractive index. Recently, it was demonstrated that the absorption spectrum of a small amount of chemicals can be measured based on propagating surface plasmon modes [16, 17]. To achieve such a wide band detection the surface plasmon modes should have two features, i.e. confining to the surface of plasmonic materials and existing in an extended frequency band, within which the molecular vibrational modes appear.

It is well known that a parallel plate waveguide can support TM transmission mode over a wide frequency range, and the conversion from transmission mode to surface mode can be realized through a metallic structure with gradient corrugations [18–21] acting like a tapering [22]. Combining these two structures we design in this paper a corrugated parallel plate waveguide (CPPW) with gradient grooves, which has a wide pass band where surface wave exists persistently. We show that the transmission coefficient of the CPPW is directly mapping the absorption spectrum of the deposited molecular layers, giving rise to broadband molecular sensing capabilities. Last but not least, the frequency range of the pass band can be tuned by adjusting the geometry of the grooves, providing a flexible way to utilize the surface-enhanced effects in the terahertz regime.

2. Models and theory

We consider a corrugated parallel plate waveguide with infinite extent, of which the cross section is shown in Fig. 1. The structure consists of two parallel metallic plate overlaid with subwavelength grooves of height h, period d and width a ($a<d\ll \lambda$). The upper and lower groove arrays are separated by an air gap of width $g$. The metal is supposed to be highly conductive at the frequency band of interest and can be treated as a perfect electric conductor (PEC). Since each groove is a parallel plate waveguide bounded by PEC on one side and by air on the other side, it can be viewed as a cavity in the vertical direction and the resonance condition can be written as ${\omega }_m=2\pi mc/4h$. Here, $c$ is the speed of light in vacuum and $m$ is an odd positive integer. Due to the deeply-subwavelength nature of the corrugation, the only supported mode is the fundamental transverse magnetic (TM) mode for which only the z-component of the magnetic field and the x-component of the electric field are non-zero.

 

Fig. 1 Simulation model (a) The corrugated parallel plate waveguide. (b) The corrugated parallel plate waveguide with gradient groove.

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The dispersion relation of the CPPW satisfies $\sqrt{{\beta }^2-k_0{}^2}\tan h(\frac{g}{2}\sqrt{{\beta }^2-k_0{}^2})/k_0=a\tan (k_{0}h)/d$ and $\sqrt{{\beta }^2-k_0{}^2}\coth (g\sqrt{{\beta }^2-k_0{}^2}/2)/k_0=a\tan (k_{0}h)/d$ [23], where $k_0=\omega /\sqrt{{\epsilon }_0{\mu }_0}$ is the wave vector of vacuum and the solution beta is the propagation constant of the modes. The dispersion diagram is plotted in Fig. 2. As can be seen, a bandgap emerges due to the excitation of spoof surface plasmon polaritons. Comparing Figs. 2(a) with Fig. 2(b), it is clear that the lower limit of the bandgap is mainly dependent on the height of the groove, and with the increase of the bandgap move to the lower frequency side; the top of the bandgap shown in Fig. 2 represents the equivalent plasma frequency of the structure like that found in a plasmonic material assisted parallel plate waveguide [24]. Note that because of the planar mirror, the higher order spoof-plasmon modes are now allowed to cross into the propagating sector, intersecting the light line. Comparing Figs. 2(a) with Fig. 2(c) we can find that for a fixed groove height the width of the bandgap is inversely proportional to the width of the air gap . Figure 2(d) shows the dispersion diagram of the CPPW for different value of . It is seen that the dispersion relation is red-shifted as the height of the groove is increased. This means that the energy of the electromagnetic wave will become much more confined by increasing , since a large corresponds to an increased wave vector at constant frequency. Next, we design a wave converter which is capable of converting transmission wave to surface wave and back to transmission wave again. The schematic diagram of the converter is given in Fig. 1(b). It consists of five sections: the left most and rightmost sections are two CPPWs with $a=0.9\mu m$, $d=1.8\mu m$, $g=27\mu m$, $h=25\mu m$; the middle CPPW has a groove height of $h^{\prime }=1.65h$; the remainders are two adiabatically gradient CPPWs with $h$ increasing linearly from the leftmost to the middle, and from the middle to the rightmost.

 

Fig. 2 Dispersion diagram of the CPPW with $a=0.9\mu m$, $d=1.8\mu m$. (a) $g=27\mu m$, $h=25\mu m$;(b) $g=27\mu m$, $h=41.25\mu m$; (c) $g=12\mu m$, $h=41.25\mu m$;(d) The upper branch of the dispersion diagram for different values of $h$. From top to bottom the curves are corresponding to $h=20\mu m$, $25\mu m$, $35\mu m$, $41.25\mu m$ and $45\mu m$. The diagonal dashed red line is the light line representing the dispersion relation of electromagnetic waves in air.

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3. Results and discussion

3.1 Transmission characteristic of the CPPW waveguide

Numerical simulations based on CST STUDIO are performed to investigate the transmission properties of the CPPW. In the simulations, perfect electric conductor and perfect magnetic conductor boundaries were applied to the $x$ and $y$ surface of the structure to mimic the propagation of TM waves; the waveguide is terminated on both sides by a wave port through which the electromagnetic waves enter and exit the model. The transmission coefficients (S21) for the CPPW and the gradient CPPW are plotted in Fig. 3. It is seen that the band gap of the gradient CPPW is much wider than the CPPW due to the increase of the groove height, which is in good agreement with the theoretical predication; moreover, the lower (respectively higher) limit of the band gap is dependent on the maximum (respectively the minimum) groove height. Simulation results of electric field distribution at one frequency in the pass band (3.7-5.2THz) and the stop band (1.6-3.7THz) are shown in panels (a) (c) of Fig. 4. Electric field distribution for the CPPW is also shown in Fig. 4 for comparison. It is clear that transmission modes only exist in the pass band of the CPPW. But for the gradient CPPW, the field patterns are converted from transmission wave to surface wave by the first gradient, then from surface wave to transmission wave by the second one in the pass band, while the stop band has nearly no power transmission. As a result, the power flow becomes localized around the edges of the grooves in the middle region of the gradient CPPW in the pass band, which strongly suggests that this section will be ultra-sensitive to changes in the dielectric environment.

 

Fig. 3 Transmission coefficient of the CPPW with and without tapering. a = 0.9μm, d = 1.8μm, g = 27μm. Groove height of the gradient CPPW is set to be h = 25μm, $h^{\prime }$ = 1.65h.

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Fig. 4 (Left) electric field (Ey) and (right) the corresponding power flow distribution. (a) (b) Cross section of the gradient CPPW (in the pass band and f_r = 5THz). (c) (d) Cross section of the gradient CPPW (in the stop band at f_r = 3THz). (e) (f) Cross section of the CPPW (in the pass band at f_r = 5THz).

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3.2 Sensing characteristics of the gradient CPPW

In order to access the performance of the gradient CPPW as a molecular sensor, we now consider the effect of an analyte on the transmission coefficient. Suppose two liquid layers with a thickness of t = 0.4µm are deposited on the upper and lower side of the gradient CPPW, in the middle region of the device where surface wave appears in the pass band, as indicated by the dashed line in Fig. 4(a). We choose here toluene molecules as an example, for which the transmission spectrum is obtained from the National Institute of Standards and Technology (NIST) [25]. From Beer-Lambert's relation $T=\exp (-\alpha x)$, where $x$ is the path length of light within the solution, the absorption coefficient $\alpha$ can be extracted. The refractive index of the layer which is adopted in the simulations can then be calculated through the Kramers - Kronig's relation [16]. We will focus on the infrared spectrum of the molecule which acts as an unique fingerprint allowing clear and unambiguous identification and therefore adjust the geometry of the waveguide to a = 0.2322μm, g = 7μm, d = 0.58μm, h = 4.5μm, $h^{\prime }$ = 6.75μm in order to operate in the corresponding frequency range. Due to limits in computation in resolving the fine corrugation while assigning a finite conductivity to the metal, we still consider here the case of PEC walls. Although some slight spectral blueshift is to be expected with a realistic conductivity, it is quite known that a PEC model does not differ in effects nor features compared to a real metal in the frequency range treated here [23]. The transmission coefficient of the gradient CPPW after the deposition of toluene is shown in Fig. 5. As can be seen, two thin layers of analyte deposited on the surface of the waveguide can produce more than 5 dB drop in transmission . Moreover, the variation of the signal directly maps the strong characteristic features of the molecule infrared absorption spectrum shown in the inset of Fig. 5. This allows for a clear identification of the molecule easily recognizable through its main vibrational modes. Therefore it leads to a powerful sensing technique in which complex mixtures can be analysed, retrieving unambiguously each chemical species and their respective concentration [16]. Besides, we perform the same simulation with a 0.4µm layer of toluene deposited at the center of the waveguide between the upper and the lower corrugation. The result is indicated by the dashed line in Fig. 5 for comparison. We can see that the transmission coefficient for this case is featureless, which further demonstrated that the drops on the curve are due to the enhanced light-matter interactions between the spoof surface plasmons and the toluene.

 

Fig. 5 Transmission coefficient of the gradient CPPW for toluene deposited on the upper and lower surface. The inset shows the absorption spectrum of toluene [25].

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Since the characteristic absorption peaks of molecules can be located within different frequency bands it is important to be able to tailor our broadband sensing device for particular applications. To demonstrate the designing flexibility of the gradient CPPW for the detection of different chemicals, we tune the pass band to the frequency range of 24-36THz, in which the absorption spectrum of ethanol molecules shows up. In this case the geometry parameters of the structure are set to be $a=0.23\mu m$, $g=5\mu m$, $h=3.71\mu m$, $h^{\prime }=1.5h$, $d=0.58\mu m$. Futhermore, the thickness of the molecule layers is varied from 0.4µm to 0.04µm to highlight the effect of the quantity or concentration on the sensitivity of the device. As before, a transmission spectrum which directly maps the fingerprint of the molecule is obtained, as shown in Fig. 6. This means the working frequency of the gradient CPPW can be flexibly tailored by tuning the height of the groove and provides an effective way of designing broadband sensors for molecular identification. Note that the attenuation of transmission coefficient increases exponentially with the molecule thickness, as expected from Beer-Lambert's relation. When the thickness of the layer is greater than 0.1µm a drop in intensity greater than 3dB should be observed.

 

Fig. 6 Transmission coefficient of the gradient CPPW for ethanol deposited on the upper and lower surface for different thicknesses of the ethanol layer ranging from 0.4 to 0.04µm from bottom to top. The inset shows the absorption spectrum of ethanol [25].

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4. Conclusion

In this work, we have shown that the conversion between transmission mode and surface mode can be realized based on a CPPW with gradient grooves, which has band gap and band-pass characteristics. The broadband localization capability of the surface wave in the band-pass region allows for broadband molecular sensing. The chemical identification is made easy and very sensitive, consisting in a simple transmission measurement with a strongly enhanced signal which reproduces the absorption features of the deposited molecules. Furthermore, we demonstrated that the band pass region can be adjusted to a great extent through a tuning of the groove height, giving access to other frequency bands and hence a large range of chemicals. The proposed gradient CPPW provides therefore an effective way to design sensors in the terahertz and infrared regimes where most molecules have characteristic absorption spectrum.