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1 Citation: Wu, Yongle, Qu, Meijun, Liu, Yuanan and Ghassemlooy, Zabih (217) A Broadband Graphene-Based THz Coupler ith Wide-Range Tunable Poer-Dividing Ratios. Plasmonics, (5). pp ISSN Published by: Springer URL: < 9-9> This version as donloaded from Northumbria Research Link: Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University s research output. Copyright and moral rights for items on NRL are retained by the individual author(s) and/or other copyright oners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes ithout prior permission or charge, provided the authors, title and full bibliographic details are given, as ell as a hyperlink and/or URL to the original metadata page. The content must not be changed in any ay. Full items must not be sold commercially in any format or medium ithout formal permission of the copyright holder. The full policy is available online: This document may differ from the final, published version of the research and has been made available online in accordance ith publisher policies. To read and/or cite from the published version of the research, please visit the publisher s ebsite (a subscription may be required.)

2 A Broadband Graphene-Based THz Coupler ith Wide-Range Tunable Poer-Dividing Ratios Contents Yongle Wu 1,a), Meijun Qu 2,b), Yuanan Liu 1, and Z. Ghassemlooy 3 1 School of Electronic Engineering, Beijing Key Laboratory of Work Safety Intelligent Monitoring, Beijing University of Posts and Telecommunications, P. O. Box. 22, Beijing, 176, China. 2 School of Information and Communication Engineering, Beijing Key Laboratory of Netork System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing, 176, China. 3 Optical Communications Research Group, NCRLab, Faculty of Engineering and Environment, Northumbria University, Necastle upon Tyne, NE1 ST, U.K. Abstract... 1 Introduction... 2 Graphene-based THz broadband coupler design... 2 Parameters analysis of the proposed graphene-based coupler... 3 Results and discussions... 6 Conclusions... References... 9 Abstract: A ideband coupler based on the graphene ith inherent DC-block function and adjustable poer-dividing ratios is proposed. This coupler uses three sections of the to-line coupled lines, four sections of the three-line coupled lines and four graphene stubs (to U-shaped stubs and to rectangular stubs). The graphene stubs allo the coupler to on dynamic surface conductivity, hich could be tuned by altering the chemical potentials. The tunable poer-dividing ratios could be achieved by varying the chemical potentials applied to the U-shaped graphene stubs and the rectangular graphene elements, respectively. In addition, the idths of to-line coupled lines in the proposed coupler are analyzed to affect the poerdividing ratios in detail. Finally, the poer-dividing ratios of the proposed coupler have a variation range from 5. db to 9.56 db at 1.75 THz ith a flat 9 phase shift. The minimum -1 db impedance bandidth is % from 1.7 THz to 2.3 THz, thus indicating a ide-band performance. Key ords: ide-band, coupler, adjustable poer-dividing ratios, graphene. a Yongle Wu and b Meijun Qu contributed equally to this ork. a uyongle13@gmail.com. 1

3 I. Introduction The graphene technology has attracted groing attention due to its potential in nano-electronics and nano-photonics devices [1-]. One key feature is that the surface complex conductivity can be easily controlled by varying the applied chemical potential. The use of graphene also facilitates designing a range of devices and antennas ith adjustable features [5-7]. For example, the tunable features of the bandidth reconfigurable uniplanar coplanar aveguide (strip) poer divider [5], the Yagi-Uda antenna ith reconfigurable radiation patterns [6], and the tunable filter-integrated quasi-yagi antenna [7] have been achieved by using graphene. Noadays, the ide-band microave or terra Hertz (THz) couplers ith dissimilar poerdividing ratios (PDRs) have attracted groing interests. These devices can be applied in the feeding netork of microave/thz antennas, antenna arrays, mixers, and poer amplifiers, to name a fe. Hoever, there are no reports on a ide-band THz coupler ith tunable PDRs capability. This paper reports for the first time a novel broadband graphene-based THz coupler ith ide-range tunable PDRs. The proposed THz coupler is constructed by combining the basic circuit layout of the filter-integrated coupler in [] and four additional graphene stubs. The PDRs can be changed by altering the chemical potentials applied to the four graphene stubs. Five simulated cases are illustrated to validate our proposed idea. From the demonstrated results, it can be observed that the graphene-based THz coupler has a number of advantages including compact size, broadband operation, excellent adjustable PDRs, flat phase shift, and an inherent DC-blocking feature beteen the to arbitrary output ports. II. Design of Graphene-based THz broadband coupler Figs.1 (a) and (b) sho the top and side vies of the proposed graphene-based broadband THz coupler ith the geometrical parameters. It consists of three sections of to-line coupled lines, four sections of three-line coupled lines and four graphene stubs (shon as black sections). µ c represents the chemical potential applied to the graphene stubs. µ c1 and µ c2 are the chemical potentials applied to the to U-shaped elements and to rectangular stubs, respectively. It should be mentioned that the technology of hybrid graphene-metal implementation has been demonstrated experimentally in [9, 1]. The substrate is constructed based on SiO 2 ith a dielectric constant of 3. and a thickness of 1µm. The proposed coupler is simulated using the full-ave electromagnetic simulator (ANSYS HFSS tool based on finite element method). The graphene can be modeled as a 2-D surface ith complex conductivity σ in the full-ave simulator. The intra and inter conductivities defined by Kubo s formulas can be calculated by [5-7, 11, ] 2

4 ( j2 ) kbt 2 je kbt c c/( B ) intra 2ln e kt 1, 2 (1) inter 2 je 2 c ( j2 ) ln, 2 c ( j2 ) (2) here e is the electron charge, ω is the angular frequency, k B is the Boltzmann constant, ħ is the reduced Plank constant, T is the temperature in Kelvin, τ is the electron relaxation time, and Г=1/(2τ) is the electron scattering rate. T = 3 K and τ = 1 ps is assumed [13], and only the intra-band contribution is considered in this paper. Z 5 Z l 5 Y Port 1 s 1 a l 1 s 2 s b 1 1 a X Port 2 c1 Port 3 l 3 c 2 l 3 c2 2 l 2 s : Graphene c1 Port Y The hybrid graphene-metal implementation SiO 2 s 3 (a) Ground (b) FIG. 1. Configuration of the proposed graphene-based broadband THz coupler ith geometrical parameters: (a) top vie, and (b) side vie. III. Parameters analysis of the proposed graphene-based coupler According to the results in [], the idths of to-line coupled lines are strongly related to the PDRs of this kind of coupler. In order to adjust the PDRs, four graphene stubs including to U-shaped stubs and to rectangular stubs are introduced in the interior of to-line coupled lines in the previous coupler. Thus, the dynamic PDRs can be achieved by varying the chemical potentials (i.e., µ c1 and µ c2) applied to four inserted graphene stubs. The general geometrical parameters for the folloing analysis are listed in TABLE I. 3

5 TABLE I. The geometrical dimensions of the proposed grapheme-based THz broadband coupler Parameters Values (µm) Parameters Values (µm) l l l l 23.2 l a.5 b.55 s s2.25 s3.2 s 1.75 Although four graphene stubs are inserted in this proposed tunable coupler, the idths of to-line coupled lines ( 1 and 2) have strong influence on the final PDRs, similar ith the previous microave coupler in []. As shon in Fig. 2, the PDR [- db(s 31] decreases hen the line idth 1 increases. This phenomenon exists in all four cases ith different chemical potential µ c1. Obviously, the matching and isolation performance is also affected by both the line idth 1 and the chemical potential µ c1. Fig. 3 shos the performance variation ith different values of the line idth 2 and the chemical potential µ c2. Different from the phenomenon in Fig. 2, the PDR [- db(s 31] increases ith the increasing of the line idth 2. This increasing feature can be observed in all four cases ith different chemical potential µ c2. Another important difference beteen Fig.2 and Fig. 3 is that the PDR [- db(s 31] in Fig.2 is more flatter than the one in Fig.3. Therefore, tuning the line idth 1 is preferred in designing or optimizing the desired PDR for this proposed tunable coupler. μ c1 = ev 1.51 THz 2.11 THz μ c1 = ev 1.51 THz 2.11 THz =1.μm-S 11 1 =1.μm-S 1 1 =1.5μm-S 11 1 =1.5μm-S 1 1 =2.μm-S 11 1 =2.μm-S 1 1 =2.5μm-S 11 1 =2.5μm-S (a) μ c1 =.1 ev 1. THz 1.6 THz =1.μm-S 11 1 =1.μm-S =1.5μm-S 11 1 =1.5μm-S 1 1 =2.μm-S 11 1 =2.μm-S 1 1 =2.5μm-S 11 1 =2.5μm-S (c) Poer-Dividing Ratios (db) Poer-Dividing Ratios (db) =1.μm 1 =1.5μm =2.μm 1 =2.5μm (b) μ c1 =.1 ev 1. THz 1.6 THz =1.μm - 1 =1.5μm =2.μm 1 =2.5μm (d)

6 μ c1 =.3 ev 1.6 THz 1.92 THz =1.μm-S 11 1 =1.μm-S =1.5μm-S 11 1 =1.5μm-S 1 1 =2.μm-S 11 1 =2.μm-S 1 1 =2.5μm-S 11 1 =2.5μm-S (e) μ c1 =.5 ev 1.5 THz 1. THz Poer-Dividing Ratios (db) μ c1 =.3 ev 1.6 THz 1.92 THz =1.μm - 1 =1.5μm =2.μm 1 =2.5μm (f) μ c1 =.5 ev 1.5 THz 1. THz =1.μm-S 11 1 =1.μm-S 1 1 =1.5μm-S 11 1 =1.5μm-S 1 1 =2.μm-S 11 1 =2.μm-S 1 1 =2.5μm-S 11 1 =2.5μm-S Poer-Dividing Ratios (db) =1.μm 1 =1.5μm =2.μm 1 =2.5μm (g) (h) FIG. 2. The curves of matching, isolation, and poer-dividing ratios (PDRs) hen μc2 is set to ev, 2 is 3.7 um, and μc1= ev (a, b), μc1=.1 ev (c, d), μc1=.3 ev (e, f), and μc1=.5 ev (g, h), respectively. Other parameters are given in TABLE I. μ c2 = ev μ c2 = ev 1.7 THz 2. THz 1.7 THz 2. THz =2.7μm-S 11 2 =2.7μm-S 1 2 =3.2μm-S 11 2 =3.2μm-S 1 2 =3.7μm-S 11 2 =3.7μm-S 1 2 =.2μm-S 11 2 =.2μm-S (a) μ c2 =.1 ev 1.63 THz 2.22 THz =2.7μm-S 11 2 =2.7μm-S =3.2μm-S 11 2 =3.2μm-S 1 2 =3.7μm-S 11 2 =3.7μm-S 1 2 =.2μm-S 11 2 =.2μm-S (c) Poer-Dividing Ratios (db) Poer-Dividing Ratios (db) 2 =2.7μm 2 =3.2μm 2 =3.7μm 2 =.2μm μ c2 =.1 ev 2 16 (b) 1.63 THz 2.22 THz 2 =2.7μm 2 =3.2μm 2 =3.7μm 2 =.2μm (d) 5

7 μ c2 =.3 ev 1.61 THz 2.65 THz 2 =2.7μm-S 11 b 2 =2.7μm-S 1 2 =3.2μm-S 11 b 2 =3.2μm-S 1 2 =3.7μm-S 11 b 2 =3.7μm-S 1 2 =.2μm-S 11 b 2 =.2μm-S μ c2 =.5 ev 1.6 THz (e) 2.66 THz 2 =2.7μm-S 11 2 =2.7μm-S 1 2 =3.2μm-S 11 2 =3.2μm-S 1 2 =3.7μm-S 11 2 =3.7μm-S 1 2 =.2μm-S 11 2 =.2μm-S Poer-Dividing Ratios (db) Poer-Dividing Ratios (db) 16 μ c2 =.3 ev 1.61 THz 2 =2.7μm 2 =3.2μm 2 =3.7μm 2.65 THz 2 =.2μm μ c2 =.5 ev 1.6 THz (f) 2 =2.7μm 2 =3.2μm 2 =3.7μm 2.66 THz 2 =.2μm (g) (h) FIG. 3. The curves of matching, isolation, and poer-dividing ratios (PDRs) hen μc1 is set to ev, 1 is 1 um, and μc2= ev (a, b), μc2=.1 ev (c, d), μc2=.3 ev (e, f), and μc2=.5 ev (g, h), respectively. Other parameters are given in TABLE I. IV. Results and discussions The final THz couplers ith five different PDRs are designed to verify the proposed idea (Case 1: µ c1 =.3 ev, µ c2 = ev; Case 2: µ c1 = ev, µ c2 = ev; Case 3: µ c1 =.1 ev, µ c2 =.2 ev; Case : µ c1 =.1 ev, µ c2 =.1 ev; and Case 5: µ c1 = ev, µ c2 =.2 ev). TABLE I lists the final parameters values. Fig. depicts the simulated results for operating characteristics of the proposed THz coupler for a range of PDRs. Fig. (a) illustrates the excellent matching and high isolation of the proposed coupler ith the minimum -1 db impedance bandidth from 1.7 THz to 2.3 THz ( %). Fig. (b) depicts the transmission and coupling characteristics shoing five different coupling coefficients, hich are obtained over the acceptable range of 1.7 THz to 2.3 THz. The phase difference profile shoing a flat 9 phase shift and ith the largest deviation of almost ±3. can be observed from the Fig. (c). Finally, Figs. (d) and 5 illustrate the PDRs for the Cases 1. Fig. 5 accurately displays the PDRs in terms of the quantitative values at 1.65 THz, 1.75 THz and 1.5 THz. The predicted PDRs for the Cases 1 are about 5., 6.6,,.6, 9.56 db, respectively at 1.75 THz. It can be observed in Fig. 5 that the tendencies of these three curves are the same, and the values of PDRs are quite close in all the five cases, indicating a ide-band tunable PDRs function. 6

8 Phase Differences (Degree) THz 2.3 THz Case 1: S 11 Case 1: S 1 Case 2: S 11 Case 2: S 1 Case 3: S 11 Case 3: S 1 Case : S 11 Case : S 1 Case 5: S 11 Case 5: S (a) 1.7 THz 2.3 THz Angle(S 21 )-Angle(S 31 ) 92.2 o 6.2 o Case 1 Case 2 7 Case 3 Case Case Poer-Dividing Ratios (db) Transmission & Coupling (db) THz 2.3 THz Case 1: S 21 Case 1: S 31 Case 2: S 21 Case 2: S 31 Case 3: S 21 Case 3: S 31 Case : S 21 Case : S 31 Case 5: S 21 Case 5: S THz (b) 2.3 THz Case 1 2 Case 2 Case 3 Case Case (c) (d) FIG.. The simulated results for the proposed THz coupler for: (a) matching and isolation, (b) transmission and coupling, (c) phase differences, and (d) tunable poer-dividing ratios. Poer-Dividing Ratios (db) THz 1.75 THz 1.5 THz Cases [1] FIG. 5. The values of poer-dividing ratios at 1.65 THz, 1.75 THz, and 1.5 THz in the proposed tunable coupler. 7

9 Port 2:Pass through Path 1 λ/ Port 1:Input Path Path 2 Port 3:Coupling Path 3 Port :Isolation λ/ E Field [V/m] 2.5^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 3 FIG. 6. The E field distributions in the proposed graphene-based tunable coupler ith 5.-dB PDR at 1.75 THz. In order to explain the coupling mechanism of this proposed graphene-based tunable coupler, the electric E field distributions are presented in Fig. 6. It can be obtained from Fig. 6 that the electromagnetic energy from Port 1 is mainly transmitted to Port 2 hile other smaller part of the electromagnetic energy is coupled to Port 3. Note that there is not any electromagnetic energy outputting from Port. The electrical lengths of Path 1, Path 2, Path 3, and Path are about 9 at 1.75 THz. Therefore, the phase difference beteen Port 2 and Port 3 is almost 9, and the corresponding electric E field distributions in Fig.6 can verify this phase-difference performance. V. Conclusions A broadband coupled-line THz coupler based on the graphene ith ide-range tunable poer-dividing ratios and a DCblocking feature has been presented. The poer-dividing ratio of the proposed THz coupler can readily be changed by altering the chemical potentials applied to the four graphene stubs (to U-shaped stubs and to rectangular stubs) ithout deteriorating the matching, isolation and phase-difference performances. In addition, the idths of to-line coupled lines in the graphene-based coupler are analyzed to affect the poer-dividing ratios in detail. The simulated results sho that this proposed coupler can achieve higher tunable poer-dividing ratios from 5. db to 9.56 db at 1.75 THz ith a flat 9 phase shift. The minimum -1 db impedance bandidth is % from 1.7 THz to 2.3 THz, thus achieving the broadband operation. Acknoledgments This ork as supported by National Basic Research Program of China (973 Program) (No. 21CB3399), and National Natural Science Foundations of China (No , No.61671, and No ).

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