High-Speed Efficient Terahertz Modulation Based on Tunable

Subscriber access provided by Nottingham Trent University

Communication

High-speed efficient terahertz modulation based on tunable collective-individual state conversion within an active 3nm-two dimensional electron gas metasurface Yuncheng Zhao, Lan Wang, Yaxin Zhang, Shen Qiao, Shixiong Liang, Xilin Zhang, Xiaoqing Guo, Zhihong Feng, Feng Lan, Zhi Chen, Xiaobo Yang, and Ziqiang Yang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b01273 • Publication Date (Web): 09 Aug 2019 Downloaded from pubs.acs.org on August 11, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

High-speed efficient terahertz modulation based on tunable collective-individual state conversion within an active 3nm-two dimensional electron gas metasurface Yuncheng Zhao§1, Lan Wang§1, Yaxin Zhang*1, Shen Qiao1, Shixiong Liang2, Xilin Zhang1, Xiaoqing Guo1, Zhihong Feng2, Feng Lan1, Zhi Chen1, Xiaobo Yang1 and Ziqiang Yang1 1 School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China 2 National Key Laboratory of Application Specific Integrated Circuit, Hebei Semiconductor Research Institute, Shijiazhuang 050051, China

ABSTRACT Terahertz (THz) modulators are always realized by dynamically manipulating the conversion between different resonant modes within a single unit cell of an active metasurface. In this paper, to achieve real high-speed THz modulation, we present a staggered netlike two-dimensional electron gas (2DEG) nanostructure composite metasurface that has two states: a collective state with massive surface resonant characteristics and an individual state with meta-atom resonant characteristics. By controlling the electron transport of the nanoscale 2DEG with an electrical grid, collective-individual state conversion can be realized in this composite metasurface. Unlike traditional resonant mode conversion confined in meta-units, this state conversion enables the resonant modes to be flexibly distributed throughout the metasurface, leading to a frequency shift of nearly 99% in both the simulated and experimental transmission spectra. Moreover, such a mechanism can effectively suppress parasitic modes and significantly reduce the capacitance of the metasurface. Thereby, this composite metasurface can efficiently control the transmission characteristics of THz waves with high-speed modulations. As a result, 93% modulation depth is observed in the static experiment and modulated sinusoidal signals up to 3 GHz are achieved in the dynamic experiment while the -3dB bandwidth can reach up to 1GHz. This tunable collective-individual state conversion may have great application potential in wireless communication and coded imaging. Keywords: terahertz, spatial modulator, metasurface state conversion, 2DEG nanostructure

INTRODUCTION Since the turn of the century, research on metamaterials has progressed rapidly with substantial expansion of both the scope of novel functionalities and the operating frequency range enabled by different types of artificial structures 1-8. Of special interest has been the achievements made in realizing metamaterials in the terahertz gap (0.1-10

ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

THz) 9, where usable naturally occurring materials are somewhat rare, making this a challenging area to build traditional electronic or photonic devices. Meanwhile, due to the potential applications of THz technology in security checking, wireless communications, and imaging, THz application systems have attracted much interest 10-17. To utilize THz waves for data transmission in communication and imaging, effective and ultrafast manipulation of THz waves has been in high demand and has become a subject of intense research. The combination of metamaterials and semiconductor technologies has led to significant breakthroughs in dynamic THz functional devices, and great achievements have been obtained in THz spatial modulators (TSMs). In the last two decades, an intense effort has been devoted in the area of active THz metamaterials to develop ultrafast THz dynamic devices 18-40. Starting with the earliest work in 2006, H. T. Chen et al. of the Los Alamos National Laboratory combined split ring resonator (SRR) metamaterials and doped GaAs semiconductors to realize kHz amplitude modulation of THz waves 18. Then, a variety of doped semiconductor materials were used in combination with metamaterial structures to enable optical and electrical control of THz wave transmission 19-22. In 2011, D. Shrekenhamer et al. of Boston College first proposed a pseudomorphic high electron mobility transistor (HEMT) metamaterial device to achieve a 10 MHz modulation speed at 0.46 THz 23. In later developments, the speed of this kind of HEMT metamaterial THz modulator continued to increase and reached 1 GHz 24-25. In addition, a phase-transition material VO2 metasurface 26-30 and a graphene metasurface 31-40 have been applied to modulate THz waves. Although considerable progress has been achieved, the GHz modulation rate of TSMs has been difficult to surpass until now 25. Because the total capacitance and resistance of an active metasurface is too large to achieve a very-high-speed modulation 18, reducing the size of devices and the number of units in metamaterial arrays seem to be a feasible and mainstream ways to increase the modulation speed 24-25,33. Nevertheless, in general, TSMs are already micrometer- or millimeter-sized devices 1840, and simply reducing the size will affect the application of the devices in free space. For example, recent studies on TSM applications in compressive imaging showed the need for a relatively large size to accommodate the size of the spatial transmission THz beam 41-45. Therefore, in order to achieve a high modulation speed, a more efficient mechanism is urgently needed. In previous work, the traditional way to modulate THz waves has been based on resonant mode conversion in the unit cell, often referred to as the meta-atom of a metamaterial structure 21, 28, including conversion from inductor–capacitor (LC) to LC modes 19, 28, dipole to dipole modes 24, 32, LC to dipole modes 18, 22-23. This mode conversion mechanism is confined to the unit cell, so the metasurface only exhibits the resonant characteristics of the meta-atom and the interaction among meta-atoms just depends on the coupling effect 46-50. Accordingly, the resonance frequencies of the different kinds of modes within the unit cell are very close, so the frequency shift of such mode conversion is greatly limited, and the modulation depth is not very high. As we know, the parasitic nature of the external circuit of metamaterial structure seriously affect and hinder the improvement of the modulation speed 23. However, the coupling


Page 2 of 20

Page 3 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

among meta-atoms could lead to parasitic mode which will bring negative effects to the modulators. To overcome the above issues, a brand new modulation mechanism is necessary to develop active THz modulators. Instead of modulating the mode conversion inside the meta-atoms, releasing the resonant mode from the meta-atom to the resonant states of the whole metasurface may provide versatile opportunities. Based on this consideration, in this paper, collective-individual state conversion is proposed within a staggered netlike 2DEG nanostructure active metasurface. Different from general metamaterial structures, the meta-atom of this active metasurface does not have an individual clear boundary but connects with other meta-atoms to act as a uniform whole. The resonant mode is no longer discretely distributed by the confinement of the meta-atom but is distributed by the tunable splitting and reorganization of different metasurface states. Therefore, by electrically controlling the electron transport of the 2DEG, metasurface state conversion can be realized. Benefitting from this new mechanism of tunable metasurface state conversion, the proposed staggered netlike metamaterial THz modulator (SMMTM) achieves an unprecedented frequency shift from 340 GHz to nearly zero, and by encoded control of the grouping of meta-atom, the resonance frequency is flexibly adjustable. Moreover, metasurface state conversion fundamentally suppresses the parasitic mode caused by the traditional mode conversion inside the meta-atom and significantly reduce the capacitance of the metasurface. As a result, 93% modulation depth is observed in the static experiment and modulated sinusoidal signals up to 3 GHz (-3dB bandwidth can reach to 1GHz) are achieved in the dynamic experiment without reducing the chip size.

RESULTS AND DISSCUSION 

Model and Structure

The schematic of the SMMTM is depicted in Figure 1b. The staggered netlike metal metamaterial structure is prepared on a GaN layer and a 160-µm SiC layer acts as a substrate. The 2DEG nanostructures working as dynamic switches are nested in the gaps of the metamaterial structure. As shown in a cross-sectional diagram (Figure 1a), 3-nm 2DEG nanostructures generated from the spontaneous polarization and piezoelectric polarization effect of the AlGaN/GaN heterostructure are nested in the gaps of the staggered netlike structure. The heterostructure consists of a 25-nm Al0.27Ga0.73N barrier layer and a 1.5-µm GaN layer. Both ends of the heterostructure connect to the metal metamaterial through ohmic contact plates to form the source and drain electrodes of the HEMTs. The gates cover the center of the heterostructures to form a Schottky contact as an electrical control grid. The 2DEG has a good electronic characteristic with a sheet carrier concentration of 9.2 × 1012 cm-2 and an electron mobility of 2170 cm/(V·s) at room temperature. Therefore, the metal staggered netlike structure, together with the Schottky gates and the 2DEG nanostructures, constitute an electrical-grid-controlled active metasurface. As shown in Figure 1c, the modulation voltage signal is loaded on the center grids while the source and drain connect with the ground, so the effective resonant characteristics of the net structure can be adjusted via


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

electrically controlling the carrier distribution of the 2DEG nanostructure to modulate the transmission of perpendicularly incident THz waves. In this composite metasurface, the gate length, gate width, and source-drain spacing of HEMTs are respectively 1.5µm, 16µm and 4µm. The wire width of metal net structure is 4µm and the period of the holes on the net is shown in Figure 1b. The fabricated structure and packaged device are shown in Figure 1d~1f. The fabrication processes are shown in Supporting Information Part I.

Figure 1. The designed and fabricated SMMTM. (a) Cross-sectional diagram of the HEMT. (b) Schematic of the array. (c) Schematic of the SMMTM. (d) Photograph of an HEMT. (e) Photograph of a portion of the fabricated SMMTM. (f) Image of the packaged SMMTM. 

Mechanism of State Conversion Between Collectivization and Atomization

The mechanism of state conversion has been confirmed by employing the commercial 3D fully electromagnetic simulation software CST Microwave Studio. In order to obtain accurate simulation results, the simulation model is completely based on the physical model and the equivalent circuit model of the GaN-HEMT. As shown in Figure 2a and 2b, a simplified equivalent circuit model is applied as the basis for simulation modeling. In this equivalent circuit, the CGS and CGD are respectively gate to source capacitance and gate to drain capacitance; the RGS and RGD are respectively gate to source resistance and gate to drain resistance; the Rcontact is ohmic contact resistance; the RS and RD are respectively channel resistances below the source and drain; the Rchannel and CSD are respectively channel resistance and capacitance below the gate.


Page 4 of 20

Page 5 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 2. Top view (a) and cross-sectional view of (b) the GaN-HEMT physical model. According to the physical model and the equivalent circuit, we combined the Drude model and the lumped model together to build the simulation model shown in Figure 3a and 3b. The nanoscale 2DEG plays a very important role in this device and acts as the dynamic controlling component of the modulation of THz wave. We applied the Drude model with equivalent characteristics to equal the actual characteristics of the 2DEG 23-24 (details shown in Supporting Information Part II). The 2DEG components are divided into three regions, one gated region and two ungated regions. In order to simulate the actual situation of the metasurface, the electron concentration in the gated region below the gate electrode varies with the change of loaded voltage, meanwhile the electron concentration in the ungated region stays with the initial value 4.85×1012 cm-2. In the actual case, due to the electrostatic field distribution the gate voltage affects the region around the gate line, therefore, in the simulation, the length of the 2DEG gated region has been set to 1.8µm which is slightly longer than the gate length (1.5µm). In this way, the circuit parameters RS and RD of the circuit model can be simulated equivalently by the Drude model of the ungated region. While the circuit parameters Rchannel and CSD can be simulated equivalently by the Drude model of the gated region. Meanwhile, a dielectric layer is set between the source/drain electrodes and the Drude model. The thickness of the dielectric layer is the same as the actual thickness of the AlGaN film and the resistivity of the dielectric layer is set to 412 Ω·µm based on the transmission-line-model (TLM) test method. As thus, the dielectric layer acts as the ohmic contact region and the circuit parameter Rchannel can be simulated equivalently. In addition, the lumped model in series style are set between the gate metal and the source/drain metal to simulate the effects of CGS, CGD, RGS and RGD.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3. Electromagnetic simulation of the HEMT. Top view (a) and cross-sectional view of (b) the GaN-HEMT simulation model. The electric field distributions for 2DEG without (c) and with (d) gate voltage. The superposition of electric field distributions for 2DEG and ohmic contact region without (e) and with (f) gate voltage. The electric field distributions for HEMT in cross-sectional view without (g) and with (h) gate voltage. Figure 3c and 3d show the electric field distribution of 2DEG. In the original case, the gate voltage is set to 0 (Figure 3c), while the electron concentrations of both gated region and ungated region are set to 4.85×1012 cm-2. In this case, the electric field of the incident terahertz wave induce a reciprocating current in the 2DEG. Therefore, the electric field of the 2DEG is very weak which can be found in the Figure 3c. When the bias voltage is loaded on the gate, the 2DEG of the gated region is depleted. In this case, the electron concentration is low as 0.08×1012 cm-2, a strong electric field is taken place in gated region, as shown in Figure 3d. Figure 3e and 3f show the superposition of the electric field of 2DEG and ohmic contact region. Since the conductivity of the ohmic contact region is significantly lower than that of the metal electrode and 2DEG, a significant electric field appears at the ohmic contact region. Figure 3g and 3h show the electric field distributions for HEMT in cross-sectional view.


Page 6 of 20

Page 7 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 4. The electric field distributions and surface current distributions for (a) the collective state and (b) the individual state of the SMMTM. (c) Simulated transmission spectra for different carrier concentrations. (d) Comparison of simulation results with and without lumped model. Figure. 4a and 4b shows the variation of the metasurface resonant mode under the regulation of the gated 2DEG. When the gated 2DEG is depleted, the conductive channels between the source and drain electrode disappeared. The incident THz wave induced a discrete zig-zag-shaped surface current between adjacent HEMTs in the vertical direction, which can be equivalent to an individual meta-atom as shown in Figure 4a. In this case, the ungated 2DEG region becomes the boundary of separated meta-atoms. The simulated results shown in Figure 4c illustrate that the 0.34 THz resonant frequency of the metasurface depends on the individual resonant


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

characteristics of the meta-atom, so we called it the individual state. Decreasing the loading voltage, the 2DEG is reverted, so the high-density carriers connect the source and drain electrode. In this case, the individual meta-atoms are connected with each other, thus the resonant mode of the meta-surface comes to a holistic dipole-like resonance with periodic S-shaped surface currents oscillating throughout the entire netlike structure (Figure 4b). The characteristics of such resonance are depend on the whole meta-surface, which is a typical collective resonance as shown in Figure 4c. Therefore, in such dynamic metasurface, the HEMT acts as a switch of the boundary of adjacent meta-atoms and could dominate the polymerization of adjacent meta-atoms. By adjusting the loaded voltage signal, the meta-atoms can be spatially grouped or dispersed so that the conversion between individual and collective states could be realized. From the simulation results shown in the Figure 4c, it can be found that such state conversion leads to a 94% modulation efficiency (η=(Tcollective-state−Tindividualstate)/Tindividual-state) at 0.34 THz. It should be noted that in the simulation the infinite periodic boundary condition is applied to simulate the meta-surface. So it can be found that the resonant frequency of the collective state is nearly 0. In fact, the designed size of the meta-surface is limited, so the resonant frequency is around 3 GHz. Relative to the fundamental frequency (0.34 THz), the frequency shift is up to 99% (frequency shift rate=(Tindividual state−Tcollective state)/Tindividual state). Figure 4d shows the comparison of simulation results with and without lumped model. The measured capacitance of single HEMT at 0V and -7V are taken as the Cvalue of lumped model in the collective state and individual state, respectively. The Rvalue of lumped model, that is, the resistance of gate to source/drain, can be calculated from the measured sheet resistance, gate-drain/gate-source spacing and electrode size. It can be found that the capacitive and resistance of gate to source/drain has a certain influence on the performance of the device in THz frequency range, which makes the resonance strength and Q-factor decrease slightly. In order to test the characteristics of manufactured meta-surface, the THz timedomain spectroscopy (THz-TDS) produced by Teraview company (TPS 3000) has been applied. The time domain waveforms of the transmitted THz wave with different voltage are illustrated in Figure 5a. By performing a fast fourier transformation (FFT) of the time domain waveform, the frequency-dependent amplitude t(ω) of the transmitted THz pulse through the metamaterial are obtained. The bare SiC substrate is considering as the reference which can be applied to normalize the electric field intensity as below: t(ω)= Esample(ω) / Ereference(ω) where Esample/reference(ω) is the electric field intensity obtained from the time domain data of sample (reference). As shown in Figure 5b, with the voltage varied from 0 to 7 V, the transmission of the SMMTM @ 0.352 THz increased from 0.05 to 0.72 and a modulation depth of 93% was achieved, which are both very close to the simulation results based on the carrier concentration decreasing from 4.85×1012 to 0.08×1012 cm−2. Obviously, in the


Page 8 of 20

Page 9 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

conversion mechanism of the metasurface state, the resonance frequency is not limited by the structure and arrangement of the unit cell, so the frequency tuning range can be significantly improved. Meanwhile, the enlargement of the resonance frequency spacing (for SMMTM, △ f=fatomization-state−fcollectivization-state) increases the maximum transmission (Tc in Figure 4c and 5b) in the modulation band (Ti of approximately 0.352 THz), which in turn increases the modulation depth.

Figure 5. (a) The original time domain data tested by THz-TDS. (b) Frequencydependent transmission of THz-TDS at different voltages. Additionally, by encoded control of the electrical grid array, the individual metaatom can be orderly grouped to achieve discrete adjustment of the resonance frequency. As the schematic diagrams in Figure 6 show, the code ‘1’ indicates that a DC bias is applied to the corresponding gate, and the code ‘0’ means no signal feed. Corresponding to the case the gate lines of each row are fed, Figure 4a shows the resonant mode coded as 111111… When the code sequence changes to 101010… (Figure 6a), each adjacent basic meta-atoms converge to form a dimeric meta-atom. Correspondingly, as shown in Figure 6d, the dimeric meta-atom displays a 0.16-THz redshift from the basic metaatom resonance frequency. Analogously, under the code sequence 100100…/ 10001000… (Figure 6b/6c), trimeric/ tetrameric meta-atoms appear and the resonance frequency redshifts to 0.11 and 0.08 THz, respectively. By extending this approach, we can create larger meta-atoms, and meanwhile the resonance frequency would gradually redshift to nearly zero. Compared with a modulation of mode conversion in the unit structure, this digital modulation of the individual state of the metasurface can achieve a large and dynamically discretely adjustable frequency shift. By drawing on existing methods, the above digital modulation process can be realized by an external FPGA (Field Programmable Gate Array) control module. Each gate line could be fed by an independent electrode which is electrically connected to the external FPGA through bonding wires 51-52.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6. The electric field and surface current distributions of the (a) dimeric/ (b) trimeric/ (c) tetrameric meta-atom. (d) Simulated transmission for different meta-atom grouping. 

Suppression of Parasitic Modes and Modulation Speed Test

Notably, the state conversion mechanism of the metasurface can also effectively suppress the parasitic mode caused by the traditional mode conversion mechanism within the unit cell structure of the metasurface. Such traditional metasurfaces are usually constructed by a periodic arrangement of discrete meta-unit structures that are simply connected to each other by electrical feeder wires. As mentioned above, the resonant modes excited by an electromagnetic wave are confined to the unit structures 18-50. In this case, interference between adjacent units is very strong, so distinct parasitic modes emerge. To better analyze the generation of this parasitic mode, another 2DEG active metamaterial THz modulator (MMTM) with a limited 1-GHz modulation speed 24, which was proposed by our group earlier, is used as a representative traditional metamaterial structure for comparison with the SMMTM. The unit cell of the MMTM has a dumbbell-like structure as shown in Figure 7b. Moreover, this structure, which consists of a 1D linear meta-atom arrangement, is


Page 10 of 20

Page 11 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

developed from the traditional 2D metasurface arrangement shown in 18-40, so it improves the modulation speed significantly more than most previous work 53. Nonetheless, since the surface current is confined in the unit structure, a large amount of induced charges accumulate at the ends of the dumbbell-like meta-atom structure, which results in the appearance of a parasitic mode with a large parasitic capacitance or inductance as shown in Figure 7b. The SMMTM leads to a fresh breakthrough by preventing the occurrence of parasitic modes. Different from traditional metamaterials, the metasurface of the SMMTM on the whole acts like a large intertwined net. A traditional unit structure does not exist in the SMMTM. In the collective state, induced charges do not accumulate anywhere in the netlike metasurface for continuous and intense surface currents. Therefore, as shown in Figure 7a, the electric field of the net is very weak, and the intensity hardly fluctuates with the oscillating current. In the individual state, continuous current is cut off by the depleted 2DEG channel; thus, electric charges accumulate on the metallic plates in the gaps. As a consequence, an intense fluctuation of the electric field only appears in the 2DEG nanostructures during the charge-discharge process (Figure 7a). By comparing the surface currents and electric field distributions of the SMMTM and MMTM, we can conclude that the conversion mechanism of the metasurface state can efficaciously inhibit the parasitic modes that always result from mode conversion inside a unit structure.

Figure 7. The electric field distributions for (a) the SMMTM and (b) the MMTM. (c) The C-V relation of a single HEMT. (d) The C-V relation of MMTM and SMMTM. The error bars represent the root-mean-square-deviation of the measured capacitance at


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

each voltage. The experimental results of the C-V characteristics of the SMMTM and MMTM tested by an Agilent B1500A analyzer verified the analysis and the simulation results above. All measurements were made after open- and short-calibration process and the frequency of the test signal is 5MHz. As shown in Figure 7c, as the gate voltage increases, the capacitance of single HEMT monotonically decreases from 16.5fF to 3fF. Due to no metamaterial structural interference, the single HEMT's capacitance tuning ratio (Defined as (Cmax －Cmin)/ Cmax) is as high as 81.8%. The mean of the voltagedependent capacitances with error bar (MMTM and SMMTM) obtained from multiple measurements and the corresponding fitted results are shown in Figure 7d. Although both the fitted results of SMMTM and MMTM are completely consistent with the C-V variation characteristics of single HEMT, the capacitance tuning ratio of SMMTM (63.8%) is much higher than MMTM’s (15.4%) and close to HEMT’s (81.8%). It should be noted that the C-V relation measured at MHz only, the capacitance turning ratio may be reduced at GHz range. However, large difference in capacitance tuning ratio still suggests that, compared with the mode conversion in MMTM, the metasurface state conversion in SMMTM exerts less interference on electrical performance of HEMT. Moreover, due to the significant reduction in parasitic capacitance of metasurface, the average capacitance of SMMTM is about 2.1 pF, significantly smaller than MMTM’s 6.2 pF. To ensure the validity of the above results, the same fabrication process was used for the MMTM and the SMMTM. These two chips have a same dimension of 6.8×6.8 mm2. The distribution of HEMTs array in MMTM and SMMTM is respectively 42×42 (1764) and 30×59 (1770). Thus, the number of HEMTs in both chips can be seen as the same. More importantly, the staggered netlike distribution of the meta-atoms of this 2DEG nanostructure composite metasurface leads to a very complicated circuit model of the whole structure. The HEMTs arrays are not simply parallel together but series-multiple connected with each other. So the equivalent circuit of the metasurface is just a series parallel connection model whose total capacitance is nonlinearly changed with the number of meta-atoms. As a result, in the test, it can be found that the total capacitance is quite smaller than the sum of all the individual HEMT capacitances.


Page 12 of 20

Page 13 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 8. Dynamic THz experimental results. (a)~(c) Modulated THz waves (300 MHz~2.3 GHz) detected by a detector. (d)~(f) Modulation signals (2~3 GHz) and corresponding second harmonics measured by a spectrum analyzer.

Figure 9. Normalized power of sinusoidal waveforms as a function of frequency.

Next, a dynamic experiment was performed to further test the real-time modulation speed of the SMMTM by applying a sinusoidal voltage to the gate to modulate the THz carrier wave (see Supporting Information Part III for details regarding the dynamic test system). A THz detector was used to detect the modulated signal. The dynamic test results for modulation frequency of 300 MHz~3 GHz are shown in Figure 8. If the modulation speed is slower than the timescale of the loaded voltage signal, triangular


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

waveforms caused by the slow modulator response time will be displayed on the oscilloscope. It is clear that this phenomenon does not occur in this device from 300 MHz to 2.3 GHz (Figure 8a−8c), and all of the detected signals are standard sinusoidal waveforms. However, due to the bandwidth and sampling rate of our oscilloscope, signal frequencies above 2.3 GHz cannot be displayed according to the manufacturer. Therefore, a spectrum analyzer was applied to measure higher-frequency modulated signals. Signals at 2.0, 2.5, 3.0 GHz and the corresponding second harmonics are shown in Figure 8d~8f. The spectrum analyzer provides more intuitive results of the modulation ability, due to the nonlinear characteristics of the 2DEG of the AlGaN/GaN heterostructure, and the modulated second harmonics can also be observed. Moreover, the power of the second harmonic modulation signal is 50 dB less than that of the original modulation signal, which shows good modulation performance and is beneficial for application in a communication system. Figure 9 shows the normalized power of sinusoidal waveforms received by detector as a function of frequency. All datas are normalized with the power of 1MHz signal as the reference. It can be found that the measured -3dB bandwidth of the device is 1GHz. Besides, -5dB and -10dB bandwidth is 1.3 GHz and 1.7 GHz, respectively. Therefore, according to the above experimental results, this TSM can load up to 3 GHz of data on a THz carrier wave, which is much faster than the modulation rate of existing TSMs. Considering that the SMMTM contains thousands of HEMTs, impedance matching between the modulator and other electronic equipment in the dynamic test system is a tedious engineering problem. Especially within a large bandwidth, from MHz to GHz, the problem of impedance mismatch will be prominent. Due to the impedance mismatch between modulator and modulation signal feeding circuit, as shown in Figure 8, with the increase of frequency, the loss of the modulation signal became larger and larger when it is loaded into the grid, which caused a decrease in amplitude of the received modulated signal. This problem will be resolved in subsequent technological work. Nevertheless, the excellent modulation performance of this modulator has been proved by experiments, verifying that the advantages of the state conversion mechanism lead to a significant increase in modulation rate. CONCLUSIONS In this paper, we propose a very-high-speed THz modulation mechanism based on tunable collective-individual state conversion with a staggered netlike active 2DEG metasurface. By controlling the electron transport of the 2DEG with an electrical grid, collective-individual state conversion can be manipulated efficiently, leading to a frequency shift of 99% and modulation frequency up to 3 GHz with the -3dB bandwidth of 1GHz. In addition, the modulation depth can be up to 93% in static test. These parameters verify that the state conversion remarkably improves the performance of a traditional THz modulator based on a mode conversion mechanism within a meta-unit. Moreover, the mechanism described here can be combined with the concept of coding metamaterials to achieve wide-band frequency tunability. Therefore, this metasurface state conversion modulator has great application potential in wireless communication and coded imaging.


Page 14 of 20

Page 15 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

AUTHOR CONTRIBUTIONS §Yuncheng

Zhao and Lan Wang are co-first authors.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] Notes The authors declare no conflict of interest. ACKNOWLEDGMENTS This work is supported by the The National Key Research and Development Program of China under Contract No. 2018YFB1801503，National Natural Science Foundation of China under Contract Nos. 61741121, 91438118 and 61501094. Supporting information available Detailed descriptions of the MMTM fabrication processes, Drude model and dynamic experiment system setup. The Supporting Information is available free of charge on the ACS Publications website. REFERENCES (1) Smith, D. R.; Pendry, J. B.; Wiltshire, M. C. K. Metamaterials and negative refractive index. Science 2004, 305, 788–792. (2) Pendry, J. B.; Holden, A. J.; Robbins, D. J.; Stewart, W. J. Magnetism from conductors and enhanced nonwirear phenomena. IEEE Trans. Microw. Theory Tech. 1999, 47, 2075–2084. (3) Smith, D. R.; Padilla, W. J.; View, D. C.; Nemat-Nasser, S. C.; Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 2000, 84, 4184–4187. (4) Fang, N.; Lee, H.; Sun, C.; Zhang, X. Sub-diffraction-limited optical imaging with a silver superlens. Science 2005, 308, 534–537. (5) Pendry, J. B.; Schurig, D.; Smith, D. R. Controlling electromagnetic fields. Science 2006, 312, 1780–1782. (6) Tsakmakidis, K. L.; Boardman, A. D.; Hess, O. ‘Trapped rainbow’ storage of light in metamaterials. Nature 2007, 450, 397–401. (7) Leonhardt, U. Optical conformal mapping. Science 2006, 312, 1777–1780. (8) Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 2000, 85, 3966–3969. (9) Padilla, W. J.; Aronsson, M. T.; Highstrete, C.; Mark, L.; Taylor A. J.; Averitt, R. D. Electrically resonant terahertz metamaterials: theoretical and experimental investigations. Phys. Rev. B 2007, 75, 041102. (10)Siegel, P. H. Terahertz Technology. IEEE Trans Microwave Theory Tech. 2002,


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

50, 910-928. (11)Federici, J. F.; Schulkin, B.; Huang, F.; Gary, D.; Barat, R.; Oliveira, F.; Zimdars, D. THz imaging and sensing for security applications—explosives, weapons and drugs. Semicond. Sci. Technol. 2005, 20, S266-S280. (12)Tonouchi, M. Cutting-edge terahertz technology. Nat. Photon. 2007, 1, 97-105. (13)Zheludev, N. I.; Kivshar, Y. S. From metamaterials to metadevices. Nat. Mater. 2012, 11, 917-924. (14)Savinov, V.; Fedotov, V. A.; Anlage, S. M.; Zheludev, N. I. Modulating Sub-THz Radiation with Current in Superconducting Metamaterial. Phys. Rev. Lett. 2012, 109, 243904. (15)Watts, C. M.; Shrekenhamer, D.; Montoya, J.; Lipworth, G.; Hunt, J.; Sleasman, T.; Krishna, S.; Smith, D. R.; Padilla, W. J. Terahertz compressive imaging with metamaterial spatial light modulators. Nat. Photon. 2014, 8, 605-609. (16)Mendis, R.; Nagai, M.; Wang, Y. Q.; Karl, N.; Mittleman, D. M. Terahertz Artifcial Dielectric Lens. Sci. Rep. 2016, 6, 23023. (17)Mittleman, D. M. Frontiers in terahertz sources and plasmonics. Nat. Photon., 2013, 7, 666-669. (18)Chen, H. T.; Padilla, W. J.; Zide, J. M. O.; Gossard, A. C.; Taylor, A. J.; Averitt, R. D.; Taylor, A. J. Active terahertz metamaterial devices. Nature. 2006, 444, 597600. (19)Shen, N. H.; Massaouti, M.; Gokkavas, M.; Manceau, J. M.; Ozbay, E.; Kafesaki, M.; Koschny, T.; Tzortzakis, S.; Soukoulis, C. M. Optically Implemented Broadband Blueshift Switch in the Terahertz Regime. Phys. Rev. Lett. 2011, 106, 037403. (20)Shen, X. P.; Cui, T. J. Photoexcited broadband redshift switch and strength modulation of terahertz metamaterial absorber. J. Opt. 2012, 14, 114012. (21)Gu, J. Q.; Singh, R.; X. J. Liu,; Zhang, X. Q.; Ma, Y. F.; Zhang, S.; Maier, S. A.; Tian, Z.; Azad, A. K.; Chen, H. T.; Taylor, A. J.; Han, J. G.; Zhang, W. L. Active control of electromagnetically induced transparency analogue in terahertz metamaterials. Nat. Commun. 2012, 3, 1151. (22)Chen, H. T.; Padilla, W. J.; Cich, M. J.; Azad, A. K.; Averitt, R. D.; Taylor, A. J. A metamaterial solid-state terahertz phase modulator. Nat. Photon. 2009, 3, 148151. (23)Shrekenhamer, D.; Rout, S.; Strikwerda, A. C.; Bingham, C.; Averitt, R. D.; Sonkusale, S.; Padilla, W. J. High speed terahertz modulation from metamaterials with embedded high electron mobility transistors. Opt. Express. 2011, 19, 99689975. (24)Zhang, Y. X.; Qiao, S.; Liang, S. X.; Wu, Z. H.; Yang, Z. Q.; Feng, Z. H.; Sun, H. ; Zhou, Y. C.; Sun, L. L.; Chen, Z.; Zou, X. B.; Zhang, B.; Hu, J. H.; Li, S. Q.; Chen, Q.; Li, L.; Xu, G. Q.; Zhao, Y. C.; Liu, S. G. Gbps Terahertz External Modulator Based on a Composite Metamaterial with a Double-Channel Heterostructure. Nano. Lett. 2015, 15, 3501-3506. (25)Nouman, M. T.; Kim, H. W.; Woo, J. M.; Hwang, J. H.; Kim, D.; Jang, J. Terahertz Modulator based on Metamaterials integrated with Metal-Semiconductor-Metal


Page 16 of 20

Page 17 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Varactors. Sci. Rep. 2016, 6, 26452. (26)Driscoll, T.; Kim, H. T.; Chae, B. G.; Kim, B. J.; Lee, Y. W.; Jokerst, N. M. S.; Smith, D. R.; Ventra, M. D.; Basov, D. N. Memory Metamaterials. Science. 2009, 325, 1518-1521. (27)Jeong, Y. G.; Bernien, H.; Kyoung, J. S.; Park, H. R.; Kim, H. S.; Choi, J. W.; Kim, B. J.; Kim, H. T.; Ahn, K. J.; Kim, D. S. Electrical control of terahertz nano antennas on VO2 thin film. Opt. Express. 2011, 19, 21211-21215. (28)Zhang, Y. X.; Qiao, S.; Sun, H.; Shi, Q. W.; Huang, W. X.; Yang, Z. Q. Photoinduced active terahertz metamaterials with nanostructured vanadium dioxide film deposited by sol-gel method. Opt. Express. 2014, 22, 11070-11078. (29)Liu, L.; Kang, L.; Mayer, T. S.; Werner, D. H. Hybrid metamaterials for electrically triggered multifunctional control. Nat. Commun. 2016, 7, 13236. (30)Zhao, Y. C.; Zhang, Y. X.; Shi, Q. W.; Liang, S. X.; Huang, W. X.; Kou, W.; Yang Z. Q. Dynamic Photoinduced Controlling of the Large Phase Shift of Terahertz Waves via Vanadium Dioxide Coupling Nanostructures. ACS Photonics 2018, 5, 3040−3050. (31)Rodriguez, B. S.; Yan, R.; Kelly, M. M.; Fang, T.; Tahy, K.; Hwang, W. S.; Jena, D.; Liu, L.; Xing, H. G. Broadband graphene terahertz modulators enabled by intraband transitions. Nat. Commun. 2012, 3, 780. (32)Lee, S. H.; Choi, M.; Kim, T. T.; Lee, S.; Liu, M.; Yin, X.; Choi, H. K.; Lee, S. S.; Choi, C. G.; Choi, S. Y.; Zhang, X.; Min, B. Switching terahertz waves with gatecontrolled active graphene metamaterials. Nat. Mater. 2012, 11, 936-941. (33)Liu, P. Q.; Luxmoore, I. J.; Mikhailov, S. A.; Savostianova, N. A.; Valmorra, F.; Faist, J.; Geoffrey, R. N. Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons. Nat. Commun. 2015, 6, 8969. (34)Rodriguez, B. S.; Yan, R.; Rafique, S.; Zhu, M.; Li, W.; Liang, X.; Gundlach, D.; Protasenko, V.; Kelly, M. M.; Jena, D.; Liu, L.; Xing, H. G. Extraordinary Control of Terahertz Beam Reflectance in Graphene Electro-absorption Modulators. Nano Lett. 2012, 12, 4518-4522. (35)Liu, M.; Yin, X.; Avila, E. U.; Geng, B.; Zentgraf, T.; Ju, L.; Wang, F.; Zhang, X. A graphene-based broadband optical modulator. Nature. 2011, 0, 1-4. (36)Meng, D.; Wang, S.; Sun, X.; Gong, R.; Chen, C. Actively bias-controlled metamaterial to mimic and modulate electromagnetically induced transparency. Appl. Phys. Lett. 2014, 104, 261902. (37)Li, Q.; Zhen, T.; Zhang, X. Q.; Singh, R.; Du, L. L.; Gu, J. Q.; Han, J. G.; Zhang, W. L. Active graphene–silicon hybrid diode for terahertz waves. Nat. Commun. 2015, 6, 7082. (38)Yan, R.; Arezoomandan, S.; Berardi, S. R.; Xing, H. G. Exceptional Terahertz Wave Modulation in Graphene Enhanced by Frequency Selective Surfaces. ACS Photonics. 2016, 3, 315−323. (39)Arezoomandan, S.; Yang, K.; Berardi S. R. Graphene-based electrically reconfigurable deep-subwavelength metamaterials for active control of THz light propagation. Appl. Phys. A 2014, 117, 423–426.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(40)Yang, K.; Liu, S. C.; Arezoomandan, S.; Nahata, A.; Berardi, S. R. Berardi Sensale-Rodriguez. Graphene-based tunable metamaterial terahertz filters. Appl. Phys. Lett. 2014, 105, 093105. (41)Chan, W. L.; Chen, H. T.; Taylor, A. J.; Brener, I.; Cich, M. J.; Mittleman, D. M. A spatial light modulator for terahertz beams. Appl. Phys. Lett. 2009, 94, 213511. (42)Shrekenhamer, D.; Montoya, J.; Krishna, S.; Padilla, W. J. Four-Color Metamaterial Absorber THz Spatial Light Modulator. Adv. Optical Mater. 2013, 1, 905–909. (43)Savo, S.; Shrekenhamer, D.; Padilla, W. J. Liquid Crystal Metamaterial Absorber Spatial Light Modulator for THz Applications. Adv. Optical Mater. 2014, 2, 275– 279. (44)Watts, C. M.; Shrekenhamer, D.; Montoya, J.; Lipworth, G.; Hunt, J.; Sleasman, T.; Krishna, S.; Smith, D. R.; Padilla, W. J. Terahertz compressive imaging with metamaterial spatial light modulators. Nat. Photo. 2014, 8, 605-609. (45)Fan, K.; Suen, J. Y.; Padilla, W. J. Graphene metamaterial spatial light modulator for infrared single pixel imaging. Opt. Express. 2017, 25, 25318. (46)Naranjo, G. A.; Peralta, X. G. Lattice Induced Modulators at THz frequencies. Opt. Lett. 2017, 42, 23. (47)Chen, C. Y.; Wu, S. C.; Yen, T. J. Experimental verification of standing wave plasmonic resonances in split-ring resonators. Appl. Phys. Lett. 2008, 93, 034110. (48)Jakovljevic´, M. M.; Isic´, G.; Vasic´, B.; Oates, T. W. H.; Hinrichs, K. ; Bergmair, I.; Hingerl, K.; Gajic, R. Spectroscopic ellipsometry of split ring resonators at infrared frequencies. Appl. Phys. Lett. 2012, 100, 161105. (49)Yin, S.; Hu, F. R.; Chen, X. Y.; Han, J. G.; Chen, T.; Xiong, X. M.; Zhang, W. T. Ruler equation for precisely tailoring the resonance frequency of terahertz U-shaped metamaterials. J. Opt. 2019, 21,025101. (50)Kim, H. K.; Lee, D.; Lim, S. Frequency-tunable metamaterial absorber using a varactor-loaded fishnet-like resonator. Applied Optics, 2016, 55(15):4113-4118. (51)Cui, T. J.; Qi, M. Q.; Wan, X.; Zhao J.; Cheng, Q. Coding metamaterials, digital metamaterials and programmable metamaterials. Light: Science & Applications. 2014, 3, e218. (52)Li, L.; Cui, T. J.; Ji, W.; Liu, S.; Ding , J.; Wan, X.; Li, Y. B.; Jiang, M. H.; Qiu, C. W.; Zhang, S. Electromagnetic reprogrammable coding-metasurface holograms. Nat. Commun. 2017, 8, 197. (53)Chen, H. T.; Taylor, A. J.; Yu, N. F. A review of metasurfaces: physics and applications. Rep. Prog. Phys. 2016, 79, 076401.


Page 18 of 20

Page 19 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Table of Contents (TOC) Graphic


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42


Page 20 of 20

High-Speed Efficient Terahertz Modulation Based on Tunable

Recommend Documents