By directly incorporating a sub-wavelength amplifier chip into the spoof plasmonic resonator, the quality (Q) factor of the original passive resonator has been significantly increased by several orders of magnitude. The spoof plasmonic resonator is composed of a corrugated ring with a slit whose optimized offset angle φ is 45°, aiming to achieve a better Q-factor. By tuning the bias voltage applied to the amplifier chip that is placed across the slit, the Q factor has been increased from 9.8 to 21000 for the quadrupole mode when a plastic pipe filled with polar liquids is placed upon the resonator. Experiments at the microwave frequencies verify that the amplifier chip could greatly compensate the loss introduced by the polar liquids under investigation, resulting in an ultra-high-Q sensor for the detection of polar liquids.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Microwave sensors have been widely applied in the medical, chemical and bio-sensing fields, since they are noninvasive, contactless, and label-free, and they can be miniaturized and fully compatible with the lab-on-a-chip technology, providing the real time monitoring of process quality at a relatively low cost, a higher adaptability and flexibility . The sensors based on resonant devices (whether it be planar resonators, dielectric resonators, or metallic cavities) provide high accuracy, which are characterized by parameters such as their resonant frequency, peak attenuation, or quality factor (Q factor) . Ultrasensitive resonant label-free sensors could be only achieved by high-Q factor resonances that have extremely narrow linewidths. Although the metallic cavity has a very high Q factor, the technology was quite cumbersome and unfit for planar integration . Since metamaterials are artificially electromagnetic (EM) structures composed of sub-wavelength resonators with a narrow spectral feature, they are well suitable for sensing applications [4–6], due to the enhanced field interaction with the sample on the surface resulting from the increased Q factor of the metamaterials. By further confining the EM fields at the surface through surface plasmons (SPs), plasmonic metamaterials are particularly promising for sensing.
SPs are collective electron-photon oscillations tightly attached to the surface of a metal, which attracted major interests due to their novel properties of deep sub-wavelength confinement and field enhancement . SPs could be either propagating (surface plasmon polaritons, SPPs) in extended interfaces [8-9] or localized (localized surface plasmons, LSPs) in finite metal particles . The LSPs are highly sensitive to the particle geometry and local dielectric environments, which render them especially suited for chemical and biological sensors [11,12]. However, the SPs only slightly penetrate the metal and exhibit poor confinement at microwave and terahertz (THz) frequencies, since the frequencies are far below the metal’s plasma frequency. It has been shown that the structured metal surfaces (plasmonic metamaterials) can support spoof SPs modes, since the electric fields can effectively go further into the metal side at microwave and THz frequencies [13–16]. Textured closed surfaces using long metallic cylinders can support spoof LSPs with similar sub-wavelength confinement and field enhancement to LSPs . The multipolar spoof LSPs on an ultrathin planar textured metallic disk have been experimentally demonstrated at microwave frequencies, since the multipolar plasmonic modes have sharper resonances than the dipole mode, providing higher sensitivity . Kinds of novel devices based on spoof LSPs have been proposed [19–22].
Substantial losses in metamaterials have restricted the development of sensitive sensing devices, which include the radiative and non-radiative losses encountered in these systems . Several schemes have been demonstrated to compensate the losses such as by using the superconductor , by optimizing the sub-wavelength structures [25–27], and through exploiting the coupling effects between meta-atoms, such as Fano resonance, subradiant dark modes, lattice mode [28–31]. By incorporating a ground plane underneath the ultrathin planar textured metallic disk, higher-order spoof LSPs modes with increased Q factors have been demonstrated (the highest Q factor is 60 for dipole mode (n = 1) and it is nearly 180 for hexadecapole mode (n = 8) mode, n is mode number) . By introducing an efficient and ease-of-integration microstrip excitation, the Q factor of the spoof LSPs modes on the corrugated ring resonator has been increased from 4.48 (using monopole excitation) to 48.4 . It has been demonstrated that the Q factor of the dipole mode on the corrugated metal-insulator-metal ring resonator has been increased from 3.17 (using monopole excitation) to 70.4 and it’s has been increased from 54.28 to 184 for octopole mode (n = 4) . A planar THz Fano metamaterial with a Q factor of 227 has been experimentally demonstrated through the excitation of the non-radiative dark modes in the coupled asymmetry meta-atoms . However, almost all these sensors show a high Q-factor only if the samples under investigation are paper, oil, or other low loss thin films, etc, which are not highly absorptive. For chemical and biological sensing, polar liquids, like water (one kind of environment in which the life cycle occurs) or ethanol, are necessary and highly absorbing, whose inherent absorption will result in the broadening of the designed resonance and detrimental to the sensitivity . Furthermore, most previous works require that the distance between the sample under test and the sensor is as small as possible so as to optimize the effects of the electric fields, however, it is hard to guarantee this condition in practical operation .
Fortunately, by introducing a gain medium [33–37], the improved performance of the metamaterials can be achieved. The efficient use of optical gain has been shown to compensate the substantial losses and to allow for loss-free operation, amplification and nanoscopic lasing [33–35]. Through employing regenerative feedback resonance (RFR) technique, the Q factor of the passive meander-shaped resonator has been greatly increased . By loading a low-noise amplifier (LNA) chip in the spoof SPPs waveguide composed of two antisymmetrical corrugated metallic strips, amplification of spoof SPPs at microwave frequencies (from 6 to 20GHz) with high gain (around 20dB) has been demonstrated . In this paper, by directly incorporating a sub-wavelength amplifier chip into the spoof plasmonic resonator, the Q factor of the passive resonator has been significantly increased by several orders of magnitude. The spoof plasmonic resonator is composed of a corrugated ring with a slit and the optimized offset angle φ of the slit is set to 45°, whose measured Q factor is 200 for the dipolar mode. However, the Q factor is decreased to 10.87 when a plastic pipe filled with water is place upon the resonator. By tuning the bias voltage applied to the amplifier chip which is placed across the slit, the Q factor has been increased from 10.87 to 19,472 for dipolar mode and it is increased from 9.8 to 21,000 for the quadrupole mode (n = 2). Hence, multiple spoof LSPs resonance modes can be amplified by adjusting the bias voltages, which is good for self-calibration. Experiments at the microwave frequencies verify that the introduced gain from the amplifier chip could greatly compensate the loss introduced by the plastic pipe filled with polar liquids, providing an ultra-high-Q sensor for polar liquids sensing.
2. Passive spoof plasmonic resonator
For brief description of the motivation and the concept of incorporating the gain at microwave frequencies, the corrugated ring structure excited by microstrip line proposed in  is used as the spoof plasmonic resonator. To incorporate the amplifier chip, a slit has been cut in the corrugated ring and the solder pads are also necessary. Figure 1(a) depicts the schematic configuration of the spoof plasmonic resonator with a slit. The three dimensional (3D) structure view of the resonator has been illustrated in Fig. 1(b). For the top textured ring, the radius r is 14 mm and the central strip width g is 1 mm. The groove height h is set to 5 mm. The length ls and width ws of the microstrip line (black dotted line) are 13 mm and 1.1 mm, respectively. The metal thickness t1 and the dielectric substrate (Rogers RO4350) thickness t2 are 0.018 mm and 1.016 mm, respectively. Based on temporal coupled-mode theory , the reflection coefficients R of single port passive resonator can be calculated by Eq. (1):Fig. 1(c). It can be observed that, far from the resonant frequency ω0, the spoof LSPs mode is not excited and the incident EM waves on the microstrip line are completely reflected. At resonance, if there is no internal loss in the resonator (1/τ0 = 0), the incident EM waves are completely coupled into the spoof LSPs mode and no reflected waves exist. However, if there is internal loss (for example, 1/τ0 = 1/τe = 0.0001), the linewidth of the spoof LSPs mode resonance is broadened and the Q factor is significantly decreased. Hence, to increase the Q factor, it is necessary to optimize the resonator. It has been found that the intensity of the resonant modes can be enhanced by adjusting the offset angle φ of the slit shown in Fig. 1(a). Hence, to increase the Q factor of the resonator in Fig. 1(a), the offset angle φ is optimized by use of the transient solver of the commercial software computer simulation technology (CST) microwave studio, which is based on FIT method. The simulated results are plotted in Fig. 1(d), where it can be seen that the linewidth of the resonance is firstly increased and then decreased when φ is increased. The final optimized φ is 45° and its Q factor is 107, while it is 40 and 77 when φ is 9° or 81°, where the Q factor is calculated by Q = f0/f3dB, where f0 is the resonant frequency and f3dB is the 3dB bandwidth.
We have fabricated the samples of the spoof plamonic resonators. Figure 2(a) illustrates the corrugated metal ring with a gap at φ = 45° and the inset of the Fig. 2(b) displays the sample with φ = 0°. The used vector network analyzer (VNA) is Agilent E5071C. The measured reflection coefficients of these two structures are compared in Fig. 2(b). It can be seen that the measurement results agree well with the simulation results. The Q factors of the resonator with φ = 45° is 200, and it is 90 for the resonator with φ = 0°. It shows that the structure with φ = 45° has a higher Q factor and the resonance linewidth is narrower. When the offset angle φ of the slit changes, it is expected that the impedance matching between the microstrip line and the passive spoof plasmonic resonator changes. To verify it, we have measured input impedances of the passive spoof plasmonic resonators with a slit at φ = 0° and φ = 45°, which are illustrated in Fig. 2(c). It can be seen that at the resonance frequency of 0.511GHz (the vertical dashed line), the input impedances are 49 + j*9.4 and 50.3-j*21.8 for the structure with a slit at φ = 45° and φ = 0°, respectively. Due to the better impedance matching, the Q factor is higher for the structure with φ = 45°.
Next, we will show that although the resonant intensity has been enhanced by improving the impedance matching between the feeding waveguide and the resonator, the introduction of polar liquids (including the container used to store the liquids) would reduce the Q factor again due to the high loss of the liquids. In Fig. 3(a), a plastic tube filled with distilled (DI) water is placed upon the spoof plasmonic resonator. The outer and inner radii of the tube are 2 mm and 1.5 mm, respectively. Its relative dielectric constant is set to 3 and the loss tangent is 0.2 in the simulation. The relative dielectric constant and loss tangent of DI water are set to 78.4 and 0.2, respectively. The simulated results are given in Fig. 3(b). It can be seen that not only does the resonant frequency of the spoof LSPs resonance mode shift after loading the high loss sample, but also its Q factor decreases from 107 to 10.6. Fortunately, the loss can be compensated by incorporating the gain medium. Theoretically, the effect of the gain can be included in Eq. (1) by replacing 1/τ0 with 1/τ0 −1/τg . The modified equation is the following Eq. (2)Fig. 3(c), the reflection coefficients are calculated and plotted for different 1/τg. Comparing with the case when 1/τ0 = 1/τe = 0.0001 (the solid black curve), we observe that the linewidth of the spoof LSPs mode resonance becomes narrower and the Q factor is significantly increased if there is 1/τg = 1/τ0. It means that no reflected waves exist at the time. Furthermore, we can see that the Q factor is improved when the loss is under-compensated (1/τg = 0.7/τ0), while it is decreased when the loss is over-compensated (1/τg = 1.3/τ0), which will also be verified by the following experiments.
3. Gain-assisted spoof plasmonic resonator for the sensing of polar liquids
The fabricated sample of the gain-assisted spoof plasmonic resonator is depicted in Fig. 4(a). The zoomed in area of the gain medium is illustrated in Fig. 4(b), where the LNA chip is MGA-53543 from Agilent Technologies with a typical gain of 15.4 dB from 0.05 GHz~6 GHz and the lumped components of the bias circuit are chosen as L1 = 3.3 nH, L2 = 47 nH, C1 = 2.2 pF, C2 = 8.2 pF, C3 = 150 pF, C4 = 100 pF, and R = 2.2 Ω on the basis of datasheet. In simulation, the unbiased amplifier chip is replaced with a 500 nH inductor . The other lumped components are inserted in the structure. According to the datasheet of the LNA, the high pass configuration consisting of the 3.3 nH inductor and the 2.2 pF capacitor is used for the input match, which provides not only the impedance transfer, but also provides excellent stability by diminishing low frequency gain. The results of the simulated and measured reflection coefficients are shown in Fig. 4(c). We can observe that there are four resonant modes below 2.5 GHz. The simulated resonant modes are marked as m1~m4, whose resonant frequencies are 0.7 GHz, 1.16 GHz, 1.60 GHz, and 2.09 GHz, respectively. The measured resonant modes are marked as M1~M4, whose resonant frequencies are 0.7 GHz, 1.15 GHz, 1.58 GHz, and 2.08 GHz, respectively. The measured results agree well with the simulated results. However, the measured Q factors of these resonant modes are lower due to the additional loss caused by the welding. Figure 4(d) illustrates the 2D Ez-field distributions on the plane located 2 mm above the spoof plasmonic resonator for the resonant modes m1~m4 and M1~M4. The measuring probe is fixed 2 mm above the sample. The sample is moved through two computer-controlled translation stages so that the VNA measures the Ez-field values at different locations, and the scanned area is 50 mm and 50 mm with a resolution of 1 mm. We can see that these modes are corresponding to n = 1, 1.5, 2, and 2.5, respectively. Similar to , both the integer modes and half integer order modes are supported in the spoof plasmonic resonator after loading the bias circuits, since the inductance of L1 in Fig. 4(b) can be regarded as a short-circuiting component at microwave frequencies (below 2.5 GHz).
Next, when the bias voltage is applied to the amplifier chip, the measured reflection coefficients with different bias voltages are shown in Fig. 5(a), from which we can observe that the modes M1 and M3 have been enhanced, while the modes M2 and M4 have been broadened and damped. For M1 and M3 modes, there exists optimized applied bias voltage when the Q factor is the maximum. Figures 5(b) and 5(c) plot the measured reflection coefficients of M1 and M3 for different bias voltages. It can be seen that the optimized bias voltage of M1 mode is 2.55V when the Q factor is 19,472 and it is 1.91V for M3 mode when the Q factor is 21,000. Comparing the case when the bias voltage is set to 0 V in Fig. 4(c), the Q factor of mode M1 has been increased from 10.87 to 19,472 and the Q factor of mode M3 is increased from 9.8 to 21,000. The Q factors changing with the bias voltages are depicted in Fig. 5(d) for M1 and M3 modes. For M1 mode, when the internal loss is still under-compensated (the applied bias voltage is smaller than 2.55 V), the Q factor is increased with the increasing bias voltage. Then, when the internal loss is over-compensated (the applied bias voltage is larger than 2.55 V), the Q factor is decreased with the increasing bias voltage. The measured results agree well with the theoretical analysis shown in Fig. 3(c). The same applies to the M3 mode.
To explain why the modes M1 and M3 have been enhanced while the modes M2 and M4 were broadened and damped, the complex input impedances Z11* and Z11 are measured by using VNA. The definition of Z11* and Z11 are shown in Fig. 6(a). Here no special input matching network has been designed and only the simple high pass configuration consisting of the 3.3 nH inductor and the 2.2 pF capacitor from the datasheet of the LNA is used for the input match. The real part and the imaginary part of the measured input impedances are illustrated in Figs. 6(b) and 6(c), respectively, where only the curves corresponding to 1V, 2V, 3V and 4V are shown and the vertical dashed lines correspond to the measured resonant frequencies of 0.7 GHz, 1.15 GHz, 1.58 GHz, and 2.08 GHz for the resonator loaded with the amplifier chip when the bias voltage is 0 V. From Figs. 6(b) and 6(c), it can be clearly seen that the complex input impedances of the LNA varies with the applied bias voltage. Furthermore, at the resonant frequencies of M1 and M3 (around 0.7 GHz and 1.58 GHz), complex conjugate matching is satisfied, while for the modes of M2 and M4 (around 1.15 GHz and 2.08 GHz), the condition is not satisfied. That’s why M1 and M3 resonances can be enhanced by tuning the applied bias voltages while M2 and M4 resonances were damped.
As stated earlier, when a plastic tube filled with polar liquids is placed upon the spoof plasmonic resonator, the Q factor would be significantly decreased. Now, the tube is place upon the active spoof plasmonic resonator, as shown in Fig. 7(a). Here the polar liquids under test are ethanol and DI water. Figure 7(b) shows the measured reflection coefficients of M1 mode for different materials inside the tube when the applied bias voltage is 0 V and the optimized value (1.8 V). For clearer view, Figs. 7(c) and 7(d) show the measured reflection coefficients of M3 mode for different materials when the bias voltage is 0 V and the optimized value (2.0 V), respectively. The optimized bias voltages are different from the previous cases (2.55 V and 1.91 V, respectively) when there is no tube, since the introduced internal loss changes. It can be clearly observed that when the applied bias voltage is 0V, since its Q factor is very low, the resonant frequency shift is difficult to distinguish and the exact resonant frequency may be hard to obtain when measured by a practical detecting circuit (not using the highly accurate VNA). For M1 mode, when the optimized bias voltage is applied, the resonant frequency is obviously shifted from 723.56 MHz to 721.19 MHz to 718.19 MHz when the material inside the tube is changed from air to ethanol and then to DI water. For M3 mode, when the optimized bias voltage (2V) is applied, the corresponding resonant frequency shifts from 1596.78 MHz to 1593.14 MHz to 1590.03 MHz. Furthermore, since both modes M1 and M3 work, the self-calibration can also be implemented by use of the proposed active spoof plasmonic resonator.
In this paper, we have experimentally demonstrated that the designed gain-assisted spoof plasmonic resonator can achieve an ultra-high Q factor even for polar liquids sensing. By directly incorporating a sub-wavelength amplifier chip into the spoof plasmonic resonator, the Q factor of the passive resonator has been significantly increased by several orders of magnitude. By tuning the bias voltage applied to the amplifier chip, the Q factor has been increased from 9.8 to 21000 for the quadrupole mode when a plastic pipe filled with polar liquids is placed upon the resonator, and it has been increased from 10.87 to 19,472 for dipolar mode. The proposed sensor has advantages of compactness, high resolution, as well as compatibility with lab-on-a-chip platforms.
National Natural Science Foundation of China (61307129); Science and Technology Commission Shanghai Municipality (STCSM) (18ZR1413500, SKLSFO2017-05).
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