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Abstract
In the area of manipulating the spatial electromagnetic (EM) waves fields, the metasurfaces have become much more attractive and powerful in recent years. Here, we propose a design to realize the simultaneous control of spatial fundamental and harmonic EM waves applying nonlinear metasurfaces in microwave band. The proposed meta-atom composed of three topological layers which are transmitting antenna, nonlinear wave guiding and receiving antenna respectively. And the critical factor of generating the harmonic is the nonlinear chip which is integrated into the middle layer. The microstrip power divider and phase shifter in each meta-atom are preciously tailored to actualize the spatial control of the fundamental and harmonic transmission beams in the far field. One prototype of the nonlinear metasurfaces is fabricated and corresponding radiation patterns of fundamental and harmonic modes are observed very well in the experience that can verify the validity of our proposed method.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces [1–8], comprising two-dimensional subwavelength meta-atoms, have demonstrated the capacity to manipulate electromagnetic (EM) waves in space. Notably, due to their low profile, small size, and ease of processing, electromagnetic metasurfaces hold tremendous potential for development across numerous fields.
The EM nonlinearity, generally describe the performance of material that can achieve the conversion of high-order harmonic modes with incident of high-power wave, especially, the emergence of metasurfaces with strong abilities of controlling the transmission and reflection EM features can actualize the various manipulating for EM nonlinearities. Notably, recent studies on optical metasurfaces have revealed novel design with optical nonlinear properties [9–11]. For example, phase-mismatch-free nonlinear generation via intra-pulse four-wave mixing [12] and large nonlinear susceptibilities [13–15] have been proposed to relax the critical phase matching requirement. Additionally, electrically active nonlinear metamaterial devices have allowed for the purposeful control of second harmonic generation and optical rectification via applied voltage signals [16,17]. Furthermore, the nonlinear nature of metasurfaces has enabled numerous applications, including overcoming the thermal noise sensitivities and cooling requirements of traditional materials through nonlinear wave-mixing processes in infrared imaging [18]. Nonlinear metasurfaces for computational image has also shown promise in multi-dimensional holographic displays with spin and wavelength multiplexing [19,20], having the potential to enhance the security of optical data storage.
For the design of metasurfaces under microwave band, the meta-atom embedded with chip components can also generate the performance of electromagnetic nonlinearity under the active design method. With integrating the active devices of power amplifiers (PA), which can allow the one-way transmission are applied to achieve the spatial non-reciprocal features [21–23]. And for using the chips of PIN diodes [24–27] and varactors [28–33] in metasurfaces, the EM phase and amplitude of meta-atoms can be reconfigurable or programmable to realize the dynamic control of spatial EM wave. Furthermore, by introducing space-time modulation, the metasurface integrated varactors [34] can generate Doppler frequency shift. Also, the PIN diodes can be employed into meta-atoms without using magnetic or electric biasing [35] to actualize the non-reciprocal property by introducing the nonlinearity with incident of high-power waves under the EM analysis and simulation. Additionally, the chip of frequency multiplier has been integrated into the meta-atoms to achieve the reflective wave of Second-harmonic generation (SHG) [36].
In this paper, we propose a design of a nonlinear metasurface loaded with active chips of frequency multiplier to achieve the simultaneous control of spatial fundamental and harmonic EM waves. The nonlinear meta-atom consists of a receiving antenna, nonlinear wave guiding, and a transmitting antenna. One prototype of nonlinear metasurface has been fabricated for measurement, and split beams of fundamental and second-harmonic modes have been observed in our experiments.
2. Implements of microwave nonlinear metasurfaces
The diagram shown in Fig. 1 can be described as the design of beam splitters [37–39] that when incident EM wave impinges at the metasurface from left side, the fundamental and harmonic waves are deflected with predesigned angles at right side respectively.
Fig. 1. The schematic diagram of the proposed nonlinear metasurface to manipulate fundamental and harmonic modes simultaneously.
2.1 Design of meta-atoms
The proposed nonlinear metasurface comprises meta-atoms with the topological texture as depicted in Fig. 2(a). The periodic of meta-atom is 24 mm. The meta-atom consists of three topological layers shown in Fig. 2(b), including single-frequency receiving antenna located on the top layer, nonlinear wave guiding in the middle layer, and the dual-frequency transmitting antenna at the bottom layer. Also, the components of Wilkinson power divider, phase shifter and nonlinear chip are elaborately tailored and connected in the middle layer.
Fig. 2. (a) The exploded view of the proposed meta-atom integrated with receiving antenna, nonlinear wave guiding and transmitting antenna. And (b) the diagram of the topological flow of the nonlinear meta-atom.
For the design details of meta-atom, the receiving antenna composed of bow-tie antenna and square patch antenna are separated by an air gap of 1 mm to improve the working bandwidth of fundamental mode. In order to transmit fundamental and second-order harmonic EM waves simultaneously, the transmitting antenna must operate at dual frequencies (fundamental and multiplier frequencies). The bow-tie antenna is located on the F4B 220 substrate, which has a dielectric constant of 2.2 and a dielectric loss tangent of 0.003. The receiving and transmitting antennas are both placed on the F4B 265 substrate, which has a dielectric constant of 2.65 and a dielectric loss tangent of 0.003. The material of adhesive coating is selected as Rogers 4450F, with a dielectric constant of 3.52 and a dielectric loss tangent of 0.009.
From the Fig. 2(b), we can know that the incident spatial energy captured by receiving antenna can be converted into two guiding waves under fundamental and second harmonic frequencies separately with predesign phase shifters in the middle layer. Afterwards, the spatial EM waves under the dual frequencies can be emitted by transmitting antenna. For achieving the beam deflections in the far field, the phase distributions of whole metasurface can be calculated by synthesizing method. Thus, the phase requirement of each meta-atom should be followed as
In our design, we predesign the deflection angles of 30-degree and 0-degree under fundamental and second harmonic frequencies respectively. Based on the periodical size of the meta-atom, we can use five discrete meta-atoms with phase difference of 72 degrees to realize the gradient distribution for satisfying the requirements of the beam deflection under two frequencies based on the Eq. (1). Accordingly, the phase shifters of five different values under fundamental frequency and the ones of equal values under second harmonic frequency are designed by tailoring the microstrip lines shown in Fig. 3(a). The corresponding uniform sizes of proposed five meta-atoms are listed in Table 1 and also the dimensions of the five different microstrip lines for achieving five different phase shifts are listed in Table 2.
Fig. 3. (a) the design details of the power divider, phase shifter and nonlinear part of the proposed meta-atom; (b) the top view of the dual frequency transmitting antenna realized by two patches with corresponding sizes.
Table 1. Dimensions of the power divider and dual-frequency patch antenna
Table 2. Dimensions of five phase shifters based on microstrip line
The transmitting antenna depicted in Fig. 3(b) utilizes outer and inner patches of varying sizes to achieve radiation with the same polarization at dual frequencies. The outer patch is linked to the phase shifter of fundamental modes by Via_1, while the inner patch is appropriately connected to the phase shifter of second harmonic frequencies via Via_2.
2.2 Full wave electromagnetic simulation results
The whole meta-atom is conducted under the full-wave simulations using the commercial electromagnetic software ANSYS HFSS 2019. The simulation setup of meta-atom is carried out with periodic boundary conditions and Floquet Port excitation. The Floquet Port 1 and 2 with the vertical polarizations are set at the top and bottom places with distance of several unit sizes away from the meta-atom. Based on our predesigned EM functionalities, we can directly simulate and acquire the transmission amplitudes and phases of five individual meta-atoms from Port 1 to Port 2 for further beam synthesizing in the far field under the fundamental frequency. Due to the introducing of power divider for distributing the energies equally under fundamental and second harmonic frequencies, the theoretical energy attenuation of 3 dB is expected. The corresponding simulation results of transmission amplitudes and phases of proposed five meta-atoms are shown in Fig. 4(a) and (b) respectively, and we can observe that the transmission phase difference of approximate 72 degrees can be achieved with less than 3 dB variation of transmission amplitude under the 5 GHz. Accordingly, the spatial beam deflection under synthesizing method can be ensured based on the obtained simulations results of the five meta-atoms.
Fig. 4. The simulated results of the scattering parameters of meta-atoms only including the passive structures without integrating the active chip. In this simulation, the input (RFin) and output (RFout) of the frequency multiplier of chip are indicated by Port 3 and 4. The Floquet Port 1 is defined as the incident port of the spatial wave, whereas the Floquet Port 2 represents the output port of the spatial wave. The simulated results of (a) transmission amplitudes and (b) transmission phases of proposed five meta-atoms under the fundamental frequency bands. Moreover, the simulated results of (c) transmission amplitude from Floquet Port 1 to Port 3 and return loss of proposed meta-atoms under the fundamental frequency bands. (d) The simulated transmission amplitude from Port 4 to Floquet Port 2 under the second-harmonic frequency band.
The Port 3 and Port 4 shown in Fig. 3(a) were setup as the lumped port to mimic the radio frequency (RF) input and output of the frequency multiplier. Due to the lack of the spice model or SNP files (including the scattering parameters) of the frequency multiplier chip, the field-circuit co-simulation method [22,23,33] can’t be applied. And the performance of nonlinear transmission can’t be simulated directly in ANSYS HFSS. However, we can simulate the transmission parameters from Port 1 to Port 3 and from Port 4 to Port 2 to achieve the good impedance matching work of passive components including patch antennas, microstrip lines and connection metal vias (Via_1 and Via_2) to obtain the high efficiency of the total transmission features. Also, the bias network of the chip is elaborately design for the supply of DC (direct current) power. The corresponding simulation results of S31 and S11 are shown in Fig. 4(c), also the result of S24 is presented in Fig. 4(d). Thus, all the outside parts of the frequency multiplier chip are verified in our simulations. Once the fundamental guiding wave incident into the frequency multiplier from the Port 3, it will be converted into the guiding wave under the second harmonic frequency outputting from the Port 4. And due to the predesigned functionality under the second harmonic frequency, the uniform phase shifters are required to achieve the 0-degree deflection in the far field.
3. Experimental validation
To provide further validation for the proposed design methodology, a prototype the nonlinear metasurface composed of 8 × 8 meta-atoms presented in Fig. 5 is fabricated under Printed Circuit Board (PCB) technology. The metal parts in our design are applied by copper, which is coated with tin to prevent oxidation. And the pins of DC bias (Vgg and Vdd) and the details of DC feeding network are shown in Fig. 5(a) and (b) respectively. In details, there 8 bias lines connected to the Vgg pins with -1.7 V DC supply and another 8 bias lines connected to the Vdd pins with 5 V DC supply both under the method of column control. Also, all the ground lines are connected to one pin. In addition, to isolate the signals of radio frequency (RF) and DC, all the bias lines have been equipped with the RF choke of 1 nH inductors. All of bias lines required to drive the frequency multiplier on each meta-atom is facilitated by DuPont lines inserted on the series of pins. The 100-ohm resistor is welded on the Wilkinson power divider. The air holes around the fabricated prototype are filled with nylon screws for fasten the whole metasurface.
Fig. 5. The prototype of fabricated nonlinear metasurface with integrating the frequency multiplier chips. (a) Photograph of the fabricated prototype (bottom view) composed of 8 × 8 meta-atoms with the total size of 288 × 288 mm2 including bias networks of Vgg and Vdd. (b) The top view of the fabricated active components of the receiving patch antenna, phase shifter and nonlinear active chip (ADI HMC561LP3). In the feed network of the chip, C1 represents the capacitor of 100 pF with 0402 package, C2 represents the capacitor of 1 nF with 0603 package and C3 represents the tantalum capacitor of 2.2 uF.
Fig. 6. The experimental setup for acquiring the two-dimensional radiation patterns of the azimuth plane in the microwave anechoic chamber.
Afterwards, the microwave experiment is conducted for measuring the radiation patterns of the fundamental and the second harmonic frequencies in the far field, and the experimental setup is shown in Fig. 6. Due to the measurement of nonlinear frequency, the combination of signal source and spectrum analyzer are preferred. In detail, one horn antenna closed to the metausrface is chosen as the excitation source connected with Analog Signal Generator (ASG, Agilent E8257D) and one horn antenna located at the opposite side in the far filed is selected as the receiving terminal connected with Series Spectrum Analyzer (SSA, Agilent E4447A). The RIGOL DP831A, a DC voltage source equipped with double channel control is utilized to supply voltages for the active chips of frequency multiplier. For acquiring the radiation pattern in the far field, the two-dimensional rotating platform where places the metasurface under testing is applied, and the receiving data is sampled in real-time with synchronous rotation of metasurface in azimuth plane.
In the measurement, the fundamental wave can be excited by transmitting horn antenna and the Signal Generator. Afterwards, the corresponding frequency spectrum of the fundamental and second harmonic modes can be captured simultaneously by receiving horn antenna and Spectrum Analyzer located in the far field. And the measurement results of the radiation patterns due to our predesigned requirement are shown in Fig. 7 and Fig. 8 based on incident fundamental frequencies of 4.9 GHz and 5.0 GHz respectively. For the results shown in Fig. 7, the beam deflection of approximate 30 degree and 0 degree can be realized under the incident fundamental frequency of 4.9 GHz. And for the results shown in Fig. 8, the beam deflection of 27 degree is achieved under the incident fundamental frequency of 5.0 GHz. The levels of side-lobe are both more than 10 dB compared with the main lobe due to the measurement results shown in Fig. 7 and Fig. 8. Also, the deviate of the working frequency has been observed compared with our predesign, and the reasons can be attributed to the metasurface with finite size, sample fabrication, chip welding and experimental environment. The scattering parameter of return loss is also measured that the corresponding result is shown in Fig. 9 where we can find that the good performance of matching work (return loss is below -10 dB) for proposed metasurface is accomplished from 4.88 GHz to 5.09 GHz with the bandwidth ratio of 4.2%.
Fig. 7. The radiation patterns of the fundamental and second harmonic waves under the incident frequency of 4.9 GHz. (a) the radiation pattern of fundamental frequency which is 4.9 GHz; (b) the second harmonic frequency which is 9.8 GHz.
Fig. 8. The radiation patterns of the fundamental and second harmonic waves under the incident frequency of 5.0 GHz. (a) the radiation pattern of fundamental frequency which is 5.0 GHz; (b) the second harmonic frequency which is 10.0 GHz.
The total EM performance shown in Fig. 7 and Fig. 8 can be described as the nonlinear beam splitter. In addition, the level difference of main lobes between fundamental and second harmonic waves of the nonlinear splitter can be manipulated by adjusting the incident power due to the ability of gain performance in the frequency multiplier chip. As shown in Fig. 10, the received power of second-harmonic exhibits nonlinear dependence on the input power from ASG. And also, the power allocation of the fundamental and the second harmonic waves in space can be realized by adjusting power ratio of the Wilkinson power divider. By synthetically considering of the two methods to distribute the power of the main lobes under two frequencies, the level difference between the fundamental and the second harmonic waves will be designed in a wide range which can include the result of equal level. Further, if the power allocation of the Wilkinson power dividers and the phase shifters in each meta-atom can be reconfigurable or programmable [39,40], the power levels and the deflected angles of beams under the fundamental and the second harmonic frequencies can have much more flexibilities to be controlled independently
Fig. 10. The received power ratio between the second harmonic (SH) and the fundamental frequencies (FF) at series of intensities and frequencies of the incident fundamental waves.
4. Conclusions
In this paper, we propose the design for the manipulation of fundamental and second-harmonic waves simultaneously by using the nonlinear metasurface which meta-atoms are composed of receiving antennas, nonlinear wave guiding and transmitting antennas. And the reason of generating the nonlinear performance can be attributed to the introducing of active chip which is frequency multiplier. With tailoring the phase shifters of meta-atom based on the synthesizing method in the far field, the good performance of radiation patterns which have the main radiate directions of 30 degree under the fundamental frequency and 0 degree under the second harmonic frequency can be observed by measuring the fabricated prototype of metasurface. The metasurface which have the nonlinear beam splitter like performance can have the potential applications in intelligent systems [41,42] and advanced communication systems based on multiplexing method.
Funding
General Technical Research Project (20201116-0155-001-001); Defense Industrial Technology Development Program, Foundation Strengthening Program Technology Field Fund (2020-JCJQ-JJ-266); National Natural Science Foundation of China (62271146).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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