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npj Nanophotonics volume 1, Article number: 11 (2024 ) Cite this article adapter 5v 1a
High-power electromagnetic (EM) waves can directly modulate the parameters of nonlinear varactor diodes through the rectification and Kerr effects without relying on external sources. Based on this principle, we propose a power-modulated reconfigurable nonlinear device based on spoof surface plasmon polariton (SSPP) waveguide loaded by varactor diodes, without applying DC power supply or feed circuit. Increasing the input power level reduces the effective capacitance of the varactor diode, leading to a blueshift in the cutoff frequency of the SSPP waveguide. This feature can be employed to realize the switching on/off of the input signal depending on the signal power. On the other hand, the transmission state of a low-power signal can be controlled by inputting another independent high-power EM wave simultaneously. Increasing the power of the control wave will enable the low-power signal within a wider bandwidth switched from off to on states. Experimental results are presented to show the excellent performance of the power-modulated reconfigurable SSPP device. This method can reduce the system complexity and provide inspiration for reconfigurable all-passive multifunctional devices and systems.
Spoof surface plasmon polaritons (SSPPs) can mimic the dispersion characteristics of natural surface plasmon polaritons (SPPs) in microwave frequencies, confine the electromagnetic (EM) energy within subwavelength scales, and enable subwavelength manipulations1,2. The proposal of planar and flexible SSPP structures with almost negligible thickness3,4 offers significant advantages in the miniaturization and integration of SSPP devices and systems. Controlling the structural parameters of the SSPP waveguide allows for efficient modulations of the dispersion characteristics of the SSPP devices. The field compression characteristics of SSPPs also result in low transmission loss5 and high sensitivity6 to the surrounding environment, presenting high potential for engineering applications. In recent years, many researches on SSPPs have been conducted, and various microwave devices based on SSPPs have emerged, including frequency filters7,8,9,10,11,12, beam splitters13,14,15, resonators16,17,18,19,20, and antennas21,22,23. More importantly, introducing active elements into the SSPP structures enables active SSPP devices like the second-harmonic generators24,25,26,27 and amplifiers28,29. The active elements can also be used to modify the SSPP state parameters, realizing flexible and real-time controls and switches of various functions of reconfigurable devices30,31,32,33,34,35,36,37.
Among many active elements, diode is commonly used in the SSPP devices and systems. Diode is a classical type of nonlinear active elements with tunable parameters changed with the direct current (DC) voltage across the PN junction, making the diode-based devices highly tunable and reconfigurable. The traditional ways to control the diode are employing an external DC source29, a waveform generator35, and a digital microsystem30 that comprises of an external power supply. The diode can also be controlled directly by incident EM powers. When a high-power EM wave is input to the device, the current flowing through the diode induces a considerable voltage, which can modulate the diode parameters through the rectification and Kerr effects. References 38,39,40 detail the nonlinear properties of varactor diodes and demonstrate the tuning of dispersion characteristics of SRRs loaded with varactor diodes. Nonlinear PIN or Schottky diodes with only two state, “ON” and “OFF”, are commonly used in high-power limiter41,42 and high-intensity radiation field protection metasurfaces43,44,45,46,47,48,49 to protect electronic equipment from being affected.
On the other hand, the diode can undergo varied operational states with distinct incident powers, even when the external DC sources are absent. Thus, designing the unit structure containing diode will enable the entire device to function automatically with the incident power, resulting in self-reconfiguration. The self-reconfigurable and self-operating devices occupy more important positions with the developments of intelligent wireless communication and radar technologies. However, most of the self-adapting work requires a sensing circuit to identify the characteristics of the radio-frequency (RF) signals (such as the power level or waveform), as well as a micro-controller circuit to configure the state of the self-adapting systems50,51. In contrast, by using the concept that the nonlinear diodes can manipulate the EM waves through changing their own operating state according to the incident power, the systems can get rid of the external power sources and feed circuits, hence greatly reducing the system’s complexity.
Here, we propose and demonstrate experimentally a power-modulated reconfigurable SSPP device using varactor diodes as the nonlinear elements, which does not require any external DC source and feeding circuit. The effective capacitance of the varactor diodes can be engineered by simply varying the input power level, thus allowing the dispersion property of the SSPP waveguide to be switched adaptively. This feature results in a power-selective device which lets the high-power signal pass while stopping the low-power signal, without employing any DC power supply and feed circuit, as shown in Fig. 1a. Besides, the attenuated low-power signal in this device can be switched on by adding an independent high-power pump wave, as shown in Fig. 1b, where the transmission states of the signal wave can be adjusted by judiciously varying the power level of the pump wave. The proposed all-passive SSPP structure retains the reconfigurability and flexibility of the traditional active SSPP structure, but gets rid of various forms of external sources. This simple device may find important potential applications in self-adaptive and modulation systems.
a The function of a power-selective filter, in which the high-power signals can pass through and low-power signals are reflected. b Controlling the transmission states of the low-power signal by changing the power of an independent high-power incident wave.
The model of the varactor diodes we used is MAVR-011020-1411, whose electrical specifications are shown in Table 1. Assume that the electrostatic capacitance of the diode takes the form of,
where \({C}_{0}\) , \({V}_{f}\) , and \(M\) are positive constants determined by the parameters of the varactor diode. When an intermediate power signal is input, AC current \(i=\mathop{\sum }\limits_{n=1}^{\infty }{\mathrm{Re}}({I}_{n}{\mathrm{e}}^{-in\omega t})\) running through the diode induces a voltage \(V=\mathop{\sum }\limits_{n=0}^{\infty }{\mathrm{Re}}({V}_{n}{\mathrm{e}}^{-in\omega t})\) , where ω is the radian frequency of the signal. For intermediate incident power, only the first harmonic term dominates,
where \({V}_{0}\) and \({V}_{1}\) represent the static bias voltage and the AC voltage respectively, \({\phi }_{1}\) represents the complex angle of \({V}_{1}\) . Now, we expand Eq. (1) into Taylor series around \({V}_{0}\) ,
The charge accumulation is given by,
The corresponding current can then be deduced,
Equation (5) indicates that, at the fundamental frequency,
Here, the second and third terms in the bracket result from the optical rectification and Kerr effect, respectively. Equation (6) indicates that the effective AC capacitance of the diode is,
Equation (1) indicates that, when \({V}_{0} < 0\) , \(C^{\prime} ({V}_{0})\, > \,0\) and \(C^{\prime\prime} ({V}_{0})\, > \,0\) . Hence, \({C}_{{\rm{eff}}}\) decreases with \(|{V}_{0}|\) and increases with \(|{V}_{1}|\) . Since \(|C^{\prime\prime} ({V}_{0})|\) is small, \({C}_{{\rm{eff}}}\) is more affected by \(|{V}_{0}|\) . |V0| and |V1| both increase with the input power level. As a result, \({C}_{{\rm{eff}}}\) decreases with the input power level.
The DC voltage \({V}_{0}\) is generated due to the presence of nonlinear resistance of the varactor diode. The minority carrier diffusion current can be approximately calculated as,
where \({I}_{s}\) is a constant determined by the parameters of the varactor diode and \({V}_{T}\) is the thermal voltage. Express Eq. (8) into Taylor series around \({V}_{0}\) ,
The constant component of \({I}_{G}\) at the zero frequency can be found as,
where \({I}_{0}(\cdot )\) is zeroth modified Bessel function of the first kind. Since the constant component of \({I}_{G}\) must vanish, the nonzero reverse DC voltage is required, given by
The SSPP structure should have enough space and degrees of freedom to be integrated with active elements and is more sensitive to the parameters of the active elements. For this goal, we design the SSPP waveguide shown in Fig. 2a. The detailed unit cell is presented in Fig. 2b, which ensures to create fundamental and high-order SPP modes and to be connected with a varactor diode, forming the power-modulated reconfigurable SSPP device. When the incident SSPP signal power is large enough, the effective capacitance of the varactor diodes will be directly affected by the power magnitude, thus our SSPP waveguide shown in Fig. 2a does not require any external DC source, feed circuit, and sensing circuit, greatly reducing the system complexity. The detailed design of the SSPP unit is shown in Fig. 2b, with the structural parameters of h = h2 = 6 mm, h1 = 3 mm, d = 3 mm, d1 = d2 = 1 mm, s = 0.3 mm, w = 1.6 mm, and p = 4 mm. The metallic copper strip has a thickness of 0.018 mm and is printed on a Rogers RO4350B substrate with the thickness of 0.508 mm, relative permittivity of 3.66, and loss tangent of 0.0037. Each SSPP unit is loaded with a varactor diode of type MAVR-011020-1411 with an ideal capacitance variation range from 0.025 to 0.275 pF. From Eq. (1) it can be seen that the capacitance of this varactor diode varies exponentially with the bias voltage, which means that the capacitance drops very sharply at first and then flattens out as the voltage increases, so that the incident high-power signal only needs to generate a small bias voltage to cause a significant change in the capacitance of the varactor diode.
a The reconfigurable SSPP waveguide without using any external DC source, feed circuit, or sensing circuit. b The unit structure of the SSPP waveguide, in which a varactor diode is integrated. c The simulated results of dispersion curves for the reconfigurable SSPP waveguide under different diode capacitances.
Figure 2c demonstrates the simulated dispersion curves of the SSPP waveguide under different varactor capacitances, in which both fundamental SPP modes and high-order SPP modes are excited. Figure 3 presents the simulated near-field distributions of the fundamental mode at 2.6 GHz and high-order mode at 6.42 GHz. Clearly, the fundamental mode is an even mode that is similar to the conventional SSPP waveguide3,4, while the high-order mode is an odd mode with jointly opposite field distributions. Both modes are confined and transmitted along the waveguide, which can be controlled by adjusting the diode capacitance.
a The fundamental mode at 2.6 GHz. b The high-order mode at 6.42 GHz.
We note that the dispersion curves of both fundamental and high-order modes are all on the right side of the light line and far away from it, indicating that the SSPP waves are sensitive to the environment due to their strong confinement capabilities, as shown in Fig. 2. When the varactor capacitance decreases from 0.22 pF to 0.08 pF, the cutoff frequencies of both fundamental and high-order modes increase significantly. This enables to create two passbands for the fundamental and high-order modes, as shown in Fig. 2c. In the bandwidths of the passbands (two colored regions), the fundamental and high-order SPP modes will be cut off when the capacitance \(C=0.22{\rm{pF}}\) ; while they can be transmitted when the capacitance \(C=0.08{\rm{pF}}\) . This important feature makes it possible for us to establish the power-modulated reconfigurable SSPP devices and systems. In this article, we mainly discuss two functions: power-selective transmissions and manipulations of low-power SPP signals by controlling external high-power EM waves.
In order to demonstrate the reconfigurable functions of the power-modulated SSPP device, we fabricate an experimental sample based on the design procedure shown in the above subsection, as illustrated in Fig. 4. Since the signal generator can provide a larger power level than the vector network analyzer (VNA), and the spectrum analyzer (SA) comes with RF attenuation and receives a larger input power than VNA, we mainly use the signal generator and spectrum analyzer for testing in our experiments. The experimental setup to achieve the power-selected transmission is simple and does not require the connection to the DC source and its associated devices, but only needs a separate SSPP waveguide, as shown in Fig. 4. As discussed in above, a high-power EM wave can induce a considerable voltage across the varactor diodes. The higher the power level is, the larger reverse DC bias voltage and AC voltage can be induced, causing the effective capacitance of the diode to decrease. Since the SSPP teeth are independent of each other, the voltage value of each diode is not exactly the same, but the fluctuation is within a small range. The good news is that when the bias voltage is larger than 2 V, the voltage fluctuation will only cause the capacitance value of the varactor diodes to have an error of about 0.01 pF.
The fabricated sample of the power-modulated reconfigurable SSPP waveguide and experimental setup employed to measure the power-selected SSPP transmissions.
In the experiment, the input of a 0 dBm signal cannot induce a DC voltage \({V}_{0}\) , and the input of a 20 dBm signal can excite a reverse DC voltage of around −3 V. The AC voltage \({V}_{1}\) caused by a 0 dBm signal is also near to zero and the AC voltage caused by a 20 dBm signal can be estimated as \({V}_{1}=\sqrt{2P{Z}_{1}}=\sqrt{10}{\rm{V}}\) . Due to the limitation of the experimental condition, we cannot directly measure the capacitance value of the varactor diodes so we should estimate it by calculations and simulations. As shown in Table 1, the parameter values of the varactor diode given in the diode datasheet are range values rather than exact values, so we do the simulations to fit with the measured results to determine the value of \({C}_{0}\) , \({V}_{f}\) , and \(M\) in Eq. (1) and then calculate the effective capacitance using Eq. (7) to verify the capacitance fitted by the simulation. Figure 5a shows that the measured S21 curves for 0 dBm and 20 dBm signals agree well with the simulated S21 curves when the varactor capacitance has values of 0.22 pF and 0.08 pF, respectively. This means that the capacitance \({C}_{0}\) corresponding to 0 V voltage is 0.22 pF, within the range of 0.19~0.275 pF given in Table 1. The value range of \({V}_{f}\) and \(M\) is calculated by substituting the possible corresponding capacitances at −4V and −15 V in Table 1, and then the value range of the effective capacitance at 20 dBm can be calculated through the Eq. (7), which includes 0.08 pF and matches the simulation results. So we can obtain the most appropriate \({C}_{eff}\) at 20 dBm is 0.08 pF and \({V}_{f}=1.55{\rm{V}}\) and \(M=0.68\) .
a The simulated and measured S21 curves under low and high-power SSPP signals. b The S21 curves under different power levels of the SSPP signal measured by the vector network analyzer and spectrum analyzer, respectively.
From Fig. 5a, we can see that when the frequency of the input signal is in the range of 4.6–5.7 GHz (the fundamental SPP mode, blue-shaded region) and 6.9–7.4 GHz (the high-order SPP mode, yellow-shaded region), high-power signals can be transmitted, while low-power signals have very large transmission losses and will be filtered out, realizing the adaptive power-selective function. To further verify the accuracy of the measurements, we also use a vector network analyzer to measure the transmission coefficients of the SSPP waveguide. The VNA can conveniently measure the transmission coefficients at different power levels, but the source is unleveled at high-power output of 20 dBm. Figure 5b presents the S21 curves at different signal powers measured with both VNA and spectrum analyzer. First of all, we can see that the transmission curves corresponding to the power levels of -20dBm and 0 dBm are completely coincident, which means that signals with the power level of 0 dBm and below cannot induce the DC voltage across the varactor diodes. Then, as the power level increases, the cutoff frequencies of the S21 curves gradually blueshift. When the input power switches from 0 to 20 dBm, the operating bandwidths of fundamental mode and high-order mode are about 1.07 and 0.63 GHz, respectively. And when the input power only switches from 0 to 13 dBm, the waveguide cannot work at the high-order mode and the operating bandwidth of the fundamental mode is 0.4 GHz. Overall, the results from the vector network analyzer and the spectrum analyzer are basically the same, except that the two curves with the power level of 20 dBm have errors when the signal frequency is higher than 7.2 GHz, which is due to the fact that the output power of the VNA cannot reach 20 dBm in this case. Actually, the proposed SSPP structure can also realize the inverse design in which the signals can pass through at low input power and be reflected at high input power in narrow operating bandwidth or in wide operating bandwidth by replacing the varactor diodes with PIN diodes (detailed discussions are shown in the Supplementary Information).
We also measured the near-field distributions for the fundamental and high-order modes at the high and low input powers to visualize the power-selective transmission functions of the SSPP waveguide more intuitively, as illustrated in Fig. 6. Comprehensively analyzing Figs. 5a and 6, we observe that, for the SSPP signals with frequencies of 2.6 GHz and 6.42 GHz, they can always be transmitted regardless of their power levels, as shown in Fig. 6a. We also note that their transmission fundamental and high-order mode patterns are in good agreements with the near-field simulation results presented in Fig. 3. However, when the frequencies are slightly above the cutoff frequencies of the fundamental mode and high-order mode in the transmission curve at low power level, for example, at 5.21 GHz and 7.16 GHz, which are in the bandwidths shown in Fig. 5a, we observe that only the high-power SSPP signals can be transmitted, while the energy of the low-power SSPP signals tends to stop at the first SSPP unit. This clearly verifies the power-selective function of the reconfigurable SSPP waveguide.
a At the non-operating frequencies. b At the operating frequencies.
Since inputting a high-power EM wave can directly tune the capacitances of the varactor diodes and change the transmission states, we can use this high-power EM wave as a control signal to regulate the SSPP transmission states, thus manipulating the on-off transmissions of low-power SSPP signals. The working mechanism is illustrated in Fig. 7, in which a coupler is introduced to provide a high-power control signal which can propagate along the waveguide to excite the bias voltage across the varactor diodes of every SSPP unit and broaden the passband of the waveguide. When only a low-power signal is transmitted, the varactor diodes work at 0 V, and S21 curve is the same as the black curves in Fig. 5. Thus, the SSPP signals with the frequencies between the cutoff frequencies of the black and red curves cannot be transmitted. However, if the SSPP waveguide is fed with a high-power EM wave, the varactor diodes will work at higher voltages. Thus these low-power SSPP signals that could not be transmitted before will propagate as the cutoff frequencies of the fundamental mode and high-order mode are increased. Similarly, we do not require the DC source and feed circuit to control the reconfigurable functions.
Diagram of experimental setup employed to measure the low-power signal transmission controlled by high-power wave.
We demonstrate the function to use a high-power wave as a switch to selectively pass through a low-power signal by comparing the low-power signal transmission curves with and without inputting the high-power control signal. The black dot lines in Fig. 8 represent the S21 curves when only a low-power signal is input, while the colored dot lines represent the simultaneous input of the low-power signal and a high-power wave, which are clearly separated. Figure 8 clearly illustrates that the transmission coefficients of a single low-power signal are consistently below -10dB in the frequency range shown, and the additional input of a high-power wave can enable the low-power signals in a certain frequency band to propagate, in which the bandwidth depends on the power level of the high-power signal. For the fundamental mode, a 12 dBm high-power wave can provide 0.35 GHz operating bandwidth (red-shaded region). As the power level of the high-power wave increases to 15, 18, and 22 dBm, the operating bandwidth will continue to expand to 0.65, 0.8, and 1 GHz. The high-order mode signals require a higher start-up power level: the 15 dBm high-power wave can only provide 0.1 GHz operating bandwidth (see the blue-shaded region). The operating bandwidth can also be manipulated by increasing the power level of the high-power wave, which will increase to 0.25, 0.4, and 0.7 GHz as the power level increases to 18, 20, and 23 dBm.
a For the fundamental-mode band. b For the high-order-mode band.
In this work, we propose a power-modulated reconfigurable SSPP waveguide which can realize power-selective transmission and spectrum-tunable transmission-state selection for low-power signals controlled by a high-power wave. This work obviates the need for designing feed or sensing circuits on the waveguide or connecting external sources such as DC power supply, which significantly simplifies the design and usage and facilitates easy integration into wireless communication systems. The input power level influences the effective capacitance of the varactor diodes, so the transmission coefficient curve of the SSPP waveguide varies with the power level of the input signal to realize adaptive power-selective transmission. In addition, the extra input of a high-power wave at different power levels can also make the low-power signals in different frequency bands change from a state that cannot be transmitted to a state that can be transmitted. The significant tunability range in our experiments is due to two factors: the signal rectification caused by the DC voltage generated by the AC diffusion current, and the Kerr effect caused by the AC voltage, so it is larger than the tunability range resulting from the Kerr effect alone. Our proposed device may be used in the integration of radar detection and secure communications, where communication only occurs when strong radar signals from friendly targets are detected and not when weak unknown communication signals from enemy targets are detected.
The dispersion and transmission coefficient curves of the SSPP waveguide were obtained using the eigenmode solver and time-domain solver of Commercial Software, CST Microwave Studio. We simulated the varactor diode using a lumped element of type RLC serial, in which the inductance of the lumped element was set as 0H. Since the eigenmode solver only supports a lossless environment, the resistance was also set as 0Ω in the simulation of the dispersion curves, and only the capacitance parameter was swept. The time-domain solver can support lossy environments, so both capacitance and resistance values were assigned in simulations.
The nonlinear SSPP waveguide consists of three layers: a 0.018 mm-thick copper SSPP layer, a 0.508 mm-thick Rogers RO4350B substrate layer, and a 0.018 mm-thick copper ground layer. The fabrication error of structures is within \(\pm\) 0.03 mm.
Two signal generators, Agilent E8257D-520, and E8257D-540, were used to provide the signals. When we measured the power-selective SPP-mode transmissions, the signal output from the signal generator passed directly through the coaxial line into the nonlinear SSPP waveguide. When we used a high-power wave to control the transmission of a low-power SSPP signal, the two waves were coupled by a coupler (Midwest Microwave, CPL-5231-16-001-79) and input together to the SSPP waveguide. The output waves were monitored by a signal analyzer (Agilent N9040B). In addition, we used a vector network analyzer (Ceyear 3672B) to directly measure the S21 curves at different power levels as a reference.
No datasets were generated or analysed during the current study.
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This work was supported by the National Natural Science Foundation of China (62271139, U21A20459 J.Z. and 62288101 T.J.C.), the National Key Research and Development Program of China (2022YFA1404903 J.Z.), the Jiangsu Province Frontier Leading Technology Basic Research Project (BK20212002 T.J.C.), the 111 Project (111-2-05 T.J.C.), and the Postgraduate Research & Practice. Innovation Program of Jiangsu Province (3304002304D W.Y.C.). Y.L. is sponsored in part by Distinguished Professor Fund of Jiangsu Province (Grant No. 1004-YQR24010).
State Key Laboratory of Millimeter Waves and Institute of Electromagnetic Space, Southeast University, Nanjing, China
Wen Yi Cui, Jingjing Zhang & Tie Jun Cui
State Key Laboratory of Terahertz and Millimeter Waves, City University of Hong Kong, Hong Kong SAR, China
National Key Laboratory of Microwave Photonics, Nanjing University of Aeronautics and Astronautics, Nanjing, China
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T.J.C., J.Z. and Y.L. suggested the designs and planned and supervised the work. Y.L. performed theoretical analysis. W.Y.C. conceived the idea and carried out the numerical simulations. W.Y.C. and X.G. carried out the experiments. W.Y.C., J.Z., Y.L. and T.J.C. wrote the manuscript.
Correspondence to Jingjing Zhang, Yu Luo or Tie Jun Cui.
The authors declare no competing interests.
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Cui, W.Y., Gao, X., Zhang, J. et al. Power-modulated reconfigurable nonlinear plasmonic devices without DC power supply and feed circuit. npj Nanophoton. 1, 11 (2024). https://doi.org/10.1038/s44310-024-00012-x
DOI: https://doi.org/10.1038/s44310-024-00012-x
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