Introduction

Artificial metallic structures, such as periodic holes and grooves have been reported to mimic surface plasmon polaritons (SPPs) at millimeter wave and terahertz frequencies where metals are regarded as perfect electric conductors1. As the low-frequency counterparts of optical SPPs, these structures imitate the same features of strong field confinement and non-diffraction limit, and typically are referred to as “spoof” SPPs2,3,4. Differing from natural SPPs, the dispersion characteristics of spoof SPPs can be designed by changing the geometric dimensions. On account of the abilities to conquer the diffraction limit and enhance the localized electric field, spoof SPPs have inspired many potential applications in sub-wavelength resolution imaging5,6, sub-wavelength circuits7, photolithography8, sensing9,10, etc.

Recently, split-ring resonators (SRRs) and complementary SRRs have been investigated to achieve a rejection function of spoof SPPs, such as ultra-wideband and multi-frequency band-stop filters11,12,13,14. To actively modulate the rejection, varactor diodes and Schottky diodes have been integrated with SRR structures, achieving frequency modulation and amplitude modulation, respectively15,16,17,18,19,20,21. These devices have been potentially applied to electrically program spoof SPPs for multifunctional applications. The approached of varactor diode were reported below 15 GHz, which may not be suitable for monolithic fabrication and millimeter wave frequencies due to the soldering integration15,16,17,18,19. Based on soldered varactor diodes, multi-frequency frequency modulation of spoof SPPs has been demonstrated below 10 GHz19. However, multi-frequency amplitude modulation (AM) of spoof SPPs has not been reported so far to the best of the authors’ knowledge.

In this work, we report multi-frequency multi-bit programmable AM of spoof SPPs based on interdigital SRRs and In-Ga-Zn-O (IGZO) Schottky diodes. In the proposed device, interdigital capacitor substitutes for parallel plate capacitor to get larger AM spectral range without sacrificing the AM depth. The SRR-based device has two modes: the fundamental one is SRR resonance, and the second-order one is spoof SPP mode. To dynamically modulate the amplitude, IGZO Schottky diodes are designed in the SRR gaps to gradually short the gap with applied bias, and thus achieve reconfiguration. To verify our design, a dual-frequency AM device was simulated, fabricated, and characterized. By using two separate bias, the transmission of spoof SPPs can be programmably tuned from −12.5 to −6.2 dB at 34.7 GHz and from −26 to −8.5 dB at 50 GHz independently, showing significant AM at millimeter wave frequencies.

Passive spoof SPP filter with interdigital SRRs

Typically, SRRs in spoof SPP band-reject devices use parallel gaps20,21, as illustrated in Fig. 1a. For multi-frequency modulation, the gap capacitance needs to be swept by changing gap dimensions, e.g., length. Take the SRRs in our previous paper as an example21, whose gap width and length are Wgap = 3 μm, and L1 = 135 μm, respectively. Extending Lout changes the spoof SPP cut-off frequency so that increasing Lin is a better choice. However, as Lin increases, parasitic coupling gets stronger and the Q-factor of SRR resonance decreases significantly. To clarify the impact, 3-D models are built in Ansys High Frequency Structural Simulator (HFSS), and their S-parameters are calculated by using Driven Mode solver. As shown in Fig. 1b, the Q-factor reduces from 171 to 0 as the frequency decreases. When Lin = 166 μm, the capacitive structure contacts the SRR loop, which eliminates the SRR resonance, as the black curve shown in Fig. 1b. In this respect, interdigital capacitors are designed to broaden the operation bandwidth, see Fig. 1c. The SRR has interdigital fingers in the split gap, whose dimensions are Wgap2 = 3 μm, L2 = 135 μm, Lf = 3 μm, and finger number is N = 5. The resonant responses of the spoof SPP waveguide with different interdigital SRRs are illustrated in Fig. 1d. It can be seen that increasing finger length Lf is an effective way to acquire lower resonant frequencies without sacrificing Q-factor. In addition, introducing more fingers can further reduce the resonant frequency. When N = 8 and Lf = 15 μm, the Q-factor is 1470 at 44 GHz; when N = 8, Lf = 29 μm, the Q-factor is 110 at 37.4 GHz. Note that the Q-factor is similar to the one without interdigital SRRs at 50 GHz.

Figure 1
figure 1

(a) Conventional SRR with parallel gap (L1 = 135 μm, Wgap = 3 μm). (b) Resonant response of conventional SRR based spoof SPP device (as the inset depicted). (c) Interdigital SRR (L2 = 135 μm, Wgap2 = 3 μm, Lf = 3 μm, N = 5) and zoom-in view of the interdigital gap. (d) Resonant response of interdigital SRR based spoof SPP device (as the inset depicted).

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For multi-frequency AM, we employ two sets of interdigital SRRs, whose resonant frequencies are 37.4 and 52.8 GHz, respectively, as shown in Fig. 2. Their specific dimensions can be obtained from the option of Fig. 2a. The proposed device is designed on silicon substrate, consisting of CPWs for feeding, CPW-to-spoof SPP waveguide transitions for momentum matching and interdigital SRRs. The whole device has a total length of 11.13 mm (about 1.38 wavelength at 37.4 GHz), which is much smaller than the reported multi-frequency spoof SPPs11,12,13,14,19. The dispersion curves of the spoof SPP units I and II with different SRRs are shown in Fig. 2b, which is simulated by using HFSS Eigen Mode Solver. The pitch of the in-series SRRs is 0.75 mm. Each spoof SPP unit has two modes: the first is SRR resonant mode21, as the dotted solid lines shown, and the latter is spoof SPP mode, as the dotted dash lines shown. It can be clearly seen that all four dispersion curves gradually separate from the curve of light, and then asymptotically arrive at a cut-off frequency. Due to the different interdigital gaps, the two SRRs in Fig. 2a have different resonant frequencies, i.e., 37.4 and 52.8 GHz. The grey parts in Fig. 2b elucidate the rejection bands for spoof SPPs due to the SRR resonances12. At the non-resonant frequencies, these two SRRs works as the conventional metallic rectangles to guide spoof SPPs20, and share the same cut-off frequency of 62 GHz, which corresponds to the dotted dash lines in Fig. 2b. Due to the same profile dimensions and period, the dispersion curves of the two spoof SPP units overlap, which can be explained using Eq. (1) in Ref.22.

Figure 2
figure 2

(a) Schematics of the two-frequency spoof SPP device with interdigital SRRs (The yellow part is gold, and the blue part is Si), whose dimensions are Wg = 80 μm, Lm = 166 μm, W1 = 37 μm, L2 = 135 μm, Wc1 = 66 μm, Lf1 = 29 μm, Wgap2 = 3 μm, Wf1 = 6.2 μm, Pf1 = 29 μm, Wc2 = 40 μm, Lf2 = 3 μm, Wgap2 = 3 μm, Wf2 = 10.5 μm, Pf2 = 27 μm, Df = 1.5 μm. (b) Dispersion diagram of the spoof SPP units. The grey rectangles are rejection bands. The inset shows the spoof SPP and SRR modes of the two spoof SPP units. (c) E-field distributions of the spoof SPP device with in-series interdigital SRRs. (d) Surface current density distributions the two spoof SPP units.

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To further illustrate the discrepancy between spoof SPP and SRR modes, the E-field distributions of the spoof SPP device with in-series interdigital SRRs are shown in Fig. 2c. At the resonant frequencies, the SRR modes have strong E-field confinement in their split gaps, which significantly attenuates wave propagation. At the non-resonant frequencies, the spoof SPP modes have relatively uniform field distributions in the split rings. From Fig. 2d, we can clearly observe various surface current density distributions for the resonant SRR modes and non-resonant spoof SPP modes.

The simulated transmission and reflection of the passive devices are illustrated in Fig. 3a. The SRR resonant frequencies are 37.4 and 52.8 GHz, respectively, which fits dispersion curves in Fig. 2b very well. Figure 3b shows the E-field distribution of the passive device. At the resonant frequencies, e.g. 37.4 and 52.8 GHz, spoof SPPs are strongly reflected due to the SRR resonance. At the non-resonant frequencies, e.g. 46 GHz, spoof SPPs propagate to the signal output terminal with little loss.

Figure 3
figure 3

(a) Simulated S-parameters of the passive spoof SPP device. (b) E-field distribution of the device.

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Dual-frequency multi-bit amplitude modulation

The fabricated two-frequency AM device is shown in Fig. 4a, which is made with standard photolithography and vacuum evaporation technology. The dark area is 200-μm thick silicon substrate with a resistivity of 10,000 Ω·mm and a 100-nm SiO2 insulator. The pink area is a 500-nm amorphous IGZO film with an electron mobility of 10–50 cm2/Vs, which was deposited by RF sputtering at room temperature. In addition to the merits of low-temperature fabrication process, large area, high yield, and low cost, amorphous IGZO has found attractive prospects in flexible applications and large-area industrial fabrication23,24,25. The transmission line with interdigital SRRs, i.e., Schottky electrode, is composed of 10 nm Ti/300 nm Au/ 50 nm Pd. Prior to IGZO deposition, the Pd film was treated with oxygen plasma to form Schottky junction at the interface with IGZO film. The square Ohmic electrodes composed of 10 nm Ti/300 nm Au are bonded to the printed circuit board (PCB) with gold wire. Thus, the left three SRRs are controlled by the input voltage V1 and the right three SRRs are controlled by the input voltage V2.

Figure 4
figure 4

(a) Fabricated tunable two-frequency spoof SPP device and equivalent circuit models for the two spoof SPP units. (b) IGZO resistance within the SRR gap as a function of voltage at 34.7 GHz and 50 GHz, respectively. The inset shows the resistance–voltage curves of the Schottky diodes with various IGZO thickness. (c) System set-up with Agilent PNA N5247 and SMU B2902A. The inset shows the device under test. (d) Measured S-parameters of the fabricated device.

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To better show the mechanism, the equivalent circuit model of the two spoof SPP units with an IGZO Schottky diode is shown in Fig. 4a. The SRR can be regarded as RLC circuit26. Ls is the inductance of the coincidence region of SRR and transmission line, R1 and R2 are the resistances of the ring, LS1 and LS2 are inductances of the ring and Cg1 and Cg2 are the capacitances of the interdigital capacitors. Rg1 and Rg2 are variable attenuation due to the substrate free carries absorption within the SRR gap20. The parameters of circuit components in Fig. 4a were calculated using the methods reported in Ref.26, as listed in Table 1. The resistance–voltage curves of Schottky diodes with various IGZO thickness is illustrated as the inset picture in Fig. 4b. The channel length and width are 3 and 40 μm, respectively. Note that the channel resistance reduces as the film thickness enlarges. When the DC bias is zero, the phenomenon of the IGZO film depletion in the gap is equivalent to a large resistance, so that a strong rejection is induced with SRR resonance. When the bias increases, the free carriers with increasing density gradually short out the capacitor, thus the attenuation reduces. The corresponding relation between resistance and bias is illustrated in Fig. 4b. Rg1 is 16,800 Ω, 2780 Ω, and 1470 Ω at 34.7 GHz with V1 = 0, 10, 20 V, respectively, and Rg2 is 50,500 Ω, 4960 Ω, and 2300 Ω at 50 GHz with V2 = 0, 20, 40 V, respectively, which corresponds to the multi-bit modulation in Fig. 5.

Table 1 Equivalent circuit component value of the proposed SRR at the operational frequencies.
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Figure 5
figure 5

Dual-frequency multi-bit AM of spoof SPPs with individual bias. The inset shows the transmission values under various bias at 34.7 and 50 GHz.

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Agilent programmable network analyzer (PNA) N5247 and dual channel source measure unit (SMU) B2902A was employed to characterize the proposed device, and the system set-up is illustrated in Fig. 4(c). The measured S-parameter of the fabricated spoof SPPs at zero forward bias are illustrated in Fig. 4(d), showing a good agreement with the simulated data. It can be seen that the proposed device has two stop band at 34.7 GHz and 50 GHz, respectively. And its propagation attenuation is less than 5.5 dB out of the stop band. Compared with simulated results, the central frequencies of both resonant responses have a red shift of about 2.7 GHz due to the dielectric constant of a-IGZO23.

The transmission modulation of the fabricated device with different bias are illustrated in Fig. 5, showing large AM depth at different frequencies and good spectral stability. When V1 is on and V2 is off, the transmission at 34.7 GHz can be continuously tuned from −12.5 to −6.3 dB with increasing input voltage V1, as shown in the top right figure. When V1 is off and V2 is on, the transmission at 50 GHz can be tuned from −26 to −8.6 dB with a forward bias up to 40 V, as shown in the bottom left figure. When V1 and V2 are open at the same time, the two-frequency device achieves significant AM of from −12.5 to −6.2 dB at 34.7 GHz and from −26 to −8.5 dB at 50 GHz independently, as shown in the bottom right figure. It should be noted that the resonant deeps show little spectral shift within a large range of the applied bias. Additionally, 3-bit AM has been demonstrated at 34.7 and 50 GHz independently and simultaneously, as illustrated in Fig. 5. The spoof SPP transmission is −12.5 dB, −9 dB, and −6.2 dB at 34.7 GHz with V1 = 0, 10, 20 V, respectively, and is −26 dB, −13 dB, and −8.5 dB at 50 GHz with V2 = 0, 20, 40 V, respectively. With more different SRRs and more independent bias, multi-frequency AM of spoof SPPs can be achieved with multi-bit modulation from 34.7 to 50 GHz, which enables a novel approach for programmable AM within a large bandwidth.

Conclusion

We proposed a programmable approach for multi-frequency multi-bit AM of spoof SPPs with interdigital SRRs by using IGZO Schottky diodes. Interdigital SRRs are proposed to obtain large operation bandwidth of from 37.4 to 52.8 GHz with minimized parasitic coupling and high Q-factor. Schottky diode fabricated in the SRR gap reconfigures the SRRs to metallic loops, which enables significant AM of from −12.5 to −6.2 dB at 34.7 GHz and from −26 to −8.5 dB at 50 GHz, respectively. Based on the interdigital SRRs and IGZO Schottky diodes, a dual-frequency device with cascaded SRRs was designed and fabricated, achieving 3-bit AM at 34.7 and 50 GHz with programmable bias. The proposed method provides a novel insight into multi-frequency multi-bit programmable modulation of spoof SPPs at microwave and THz regime.