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Gain enhancement of terahertz patch antennas by coating epsilon-near-zero metamaterials
Superlattices and Microstructures 139 (2020) 106390
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Gain enhancement of terahertz patch antennas by coating epsilon-near-zero metamaterials Cong Cheng a, b, Yuanfu Lu b, **, Dongbo Zhang c, Fangming Ruan a, d, Guangyuan Li b, * a
College of Big Data and Information Engineering, Guizhou University, Guiyang, 550025, China Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China No. 16 Institute of No. 9 Academy of China Aerospace Technology Corporation, Xi’an, China d College of Big Data and Computer Science, Guizhou Normal University, Guiyang, 550001, China b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Terahertz Patch antenna Gain Epsilon-near-zero metamaterials
In this work, we propose a novel approach to enhance the gain of a terahertz patch antenna by coating an epsilon-near-zero (ENZ) metamaterial superstrate. The ENZ metamaterial is composed of indium antimonide (InSb) and silicon dioxide multilayers, of which the out-of-plane compo nent of the effective permittivity is close to zero. Results show that by coating the ENZ superstrate the peak gain of the antenna is increased from 5.37 dB to 7.79 dB, corresponding to 45% gain enhancement and greatly improved radiation directivity. We find that the ENZ frequency of the multilayer metamaterial equals to that of semiconductor InSb and thus it can be tuned dynami cally. We expect the concept of adding a multilayer ENZ metamaterial superstrate to enhance the antenna gain will find potential applications in other types of terahertz antennas and in antennas in other frequency regimes.
1. Introduction Terahertz (THz) wave refers to electromagnetic radiation with a frequency of 0.1–10 � 1012 Hz (corresponding to wavelength of 3 mm–30 μm). Because of its unique characteristics such as high spectral resolution [1], high spatial resolution [2], and transparency through many non-metallic, non-polar materials [3], terahertz radiation has been widely used in a diverse range of applications, such as ultra-broadband wireless communication systems [4,5] and high-resolution imaging systems [6]. In these applications, a terahertz antenna is a vital component for achieving unidirectional radiation with high gain [7]. Among various terahertz antennas, a microstrip patch antenna has been widely used since it is cost effective, light weight, and easy to design and fabrication [8]. However, microstrip patch antennas encounter a severe problem of surface waves that are sustained by the substrate between the patch and ground plane, resulting in deteriorated bandwidth, efficiency and gain [9]. In order to enhance the gain or to realize high directivity of the patch antenna, a variety of approaches have been utilized over the years. A commonly used method is to introduce a frequency-selective surface [10], Fabry-Perot cavity [11] or an electromagnetic bandgap metamaterial [9,12,13] on top of or beneath the microstrip patch antenna. Another approach to improve the radiation characteristic is to pattern patch antennas in a periodic array [14,15]. Recently, epsilon-near-zero (ENZ) metamaterials or zero/low-index metamaterials (ZIMs/LIMs) have been theoretically proposed and experimentally demonstrated for enhancing the antenna gain or directivity [16–18]. The operation principle is based on the * Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Lu), [email protected] (G. Li). https://doi.org/10.1016/j.spmi.2020.106390 Received 15 October 2019; Received in revised form 10 December 2019; Accepted 6 January 2020 Available online 11 January 2020 0749-6036/© 2020 Elsevier Ltd. All rights reserved.
Superlattices and Microstructures 139 (2020) 106390
C. Cheng et al.
Fig. 1. (a) Schematic of the proposed gain enhancement approach of coating a terahertz microstripe patch antenna with an ENZ metamaterial superstrate (not on scale). (b) The ENZ superstrate is composed of alternating InSb (in red) and SiO2 (in bule) multilayers with thicknesses tm and td , respectively. (c) The terahertz patch antenna has width W and length L.
well-known Snell’s law of refraction, nin sinθin ¼ nout sinθout , when a ray of any incidence angle θin transmits from an extremely low index medium (nin � 0) to a high index medium (nout � 1), the output ray will transmit in a direction normal to the interface between the two media (θout � 0) [19,20]. Taking advantage of this principle, Zhou et al. [21] demonstrated that the directivity of the patch antenna is effectively enhanced based on a ZIM superstrate. Zhou and Cui [22] and Jiang et al. [23] respectively enhanced the directivity of a Vivaldi antenna by using anisotropic ZIM composed of the meander-line structure. Quite recently, El-Nady et al. [24] utilized ENZ metamaterials to improve the radiation characteristics of a millimeter wave Vivaldi antenna. In order to enhance both the antenna gain and bandwidth, Abdelgwad and Said [25] proposed an ENZ metamaterial composed of a periodic array of parallel metallic wires arranged in a rectangular pattern. Bayat and Khalilpour [26] designed a miniaturized patch antenna with an ENZ metamaterial superstrate. In these reports, however, ZIMs or ENZ metamaterials operating in the microwave or millimeter regime are realized by patterning metal into complicated structures, making these structures difficult to fabricate when their sizes are scaling down for operating in the terahertz regime, and inconvenient to tune dynamically. These drawbacks hinder practical applications in terahertz antennas. In this work, we propose a novel approach to enhance the gain of a terahertz patch antenna. This approach relies on coating an ENZ metamaterial superstrate, which is composed of alternating Indium antimonide (InSb) and silicon dioxide (SiO2) multilayers. Compared with the conventional ZIM or ENZ metamaterials that consist of complicated metallic structures and that are difficult to fabricate or dynamically tune, the multilayers are easy to fabricate and convenient to tune dynamically. The theory and the operation principle will be elaborated. The enhancement of the antenna gain and directivity will be numerically demonstrated by comparing the patch antennas with and without the ENZ metamaterial superstrate. The effects of the layer thicknesses, the distance between the multilayers and the patch antenna, and the layer number of the multilayers will also be discussed. 2. Theory and design Fig. 1(a) illustrates the proposed terahertz patch antenna that is coated by an ENZ metamaterial superstrate. The ENZ metamaterial is composed of multiple alternating thin films of InSb and SiO2 with thicknesses of tm and td , respectively, as shown by Fig. 1(b). Because the thicknesses of the thin InSb and SiO2 layers satisfy the criteria of effective medium theory (EMT), the effective permittivity of the multilayer InSb–SiO2 metamaterial can be calculated using the EMT [27], 0 1 εk 0 0 ε ¼ @ 0 εk 0 A : (1) 0 0 ε? Here the subscripts k and ? indicate the components that are parallel and perpendicular to the x-y plane (the plane of the thin films), respectively. These in-plane and out-of-plane effective permittivity components are given by Ref. [28].
εk ¼
tm εm þ td εd ; tm þ td
(2)
εm εd ðtm þ td Þ : tm εd þ td εm
(3)
ε? ¼
The dispersion relation for the effective anisotropic metamaterial is given by k2x þ k2y
ε?
þ
k2z
εk
(4)
¼ k20 ;
where kx , ky and kz are propagation constant components of light in the effective anisotropic metamaterial, and k0 is the propagation 2
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Fig. 2. (a) Real and (b) imaginary parts of the effective relative permittivity tensor components of the InSb–SiO2 multilayer metamaterial. Green and blue dots indicate εk ¼ 0 and ε? ¼ 0, respectively.
constant of light in vacuum. According to this dispersion relation, when ε? is extremely close to zero, k2x þ k2y is forced to be zero. In
other words, near-zero ε? means quasi-infinite phase velocity in the x and y directions and vanishing z-component of the electric displacement (i.e., Dz ) in the effective anisotropic metamaterial, which forces the z-component of the electric field (Ez ) in the free-space region to approach zero according to the boundary condition at the metamaterial–air interface [23]. Therefore, by coating a multilayer metamaterial superstrate with near-zero ε? , highly directional radiation with direction normal to the metamaterial-air interface can be achieved, as illustrated in Fig. 1(a). The frequency dependent complex permittivity of semiconductor InSb in the terahertz regime can be described by the Drude model [29],
εm ¼ εð∞Þ
ω2p ω þ iωγ 2
(5)
:
Here εð∞Þ is the high-frequency permittivity, ω is the excitation frequency, ω2p ¼ ne2 =ðm� ε0 Þ is the plasma frequency with n the free electron density, and e and m� the electron’s charge and effective mass, respectively, and γ ¼ 1=τ is the carrier momentum relaxation rate with τ the average collision time of the charge carriers. For undoped InSb at 300 K, εð∞Þ ¼ 15:68, ωp ¼ 4:6 � 1013 rad/s, and γ= ð2πÞ ¼ 0:05 THz [30]. We take the dielectric constant of SiO2 to be εd ¼ 3:8. Fig. 2 shows the effective permittivity tensor components for tm ¼ td ¼ 1 μm. We find that εk is close to zero at the frequency of 1.65 THz and ε? is close to zero at 1.85 THz. As we have clarified before, hereafter we focus on ε? ¼ 0 and f0 ¼ 1:85 THz in order to enhance the antenna gain and directivity. We should emphasize that, according to Eq. (3), ε? ¼ 0 is always valid provided that εm ¼ 0, which occurs when ω0 ¼ 2πf0 � ωp = pffiffiffiffiffiffiffiffiffiffi εð∞Þ. In other words, the frequency for achieving near-zero ε? is equal to that for near-zero εm of semiconductor InSb, and thus it is independent from the thicknesses of the InSb and SiO2 thin films and from εd of the dielectric. It is worth mentioning that, because ωp of the semiconductor InSb can be tuned by modulating the electron density, which can be realized electrically or optically, the operation frequency for achieving near-zero ε? and thus gain/directivity enhancement can be tuned dynamically. The terahertz patch antenna is then designed for operating at the ENZ frequency of the multilayer metamaterial, f0 ¼ 1:85 THz. The size of a rectangular patch antenna can be determined by Ref. [31]. W¼
L¼
�1=2 � c 2 ; 2f0 εr þ 1
c 1 pffiffiffiffiffiffi 2f0 εeff
(6) (7)
2ΔL ;
where εr is the relative permittivity of the substrate, εeff is effective dielectric constant, � � 1=2 ε þ 1 εr 1 h þ 1 þ 12 εeff ¼ r ; 2 2 W and ΔL is equivalent radiation gap length, � εeff þ 0:3 ðW=h þ 0:264Þ � ΔL ¼ 0:412h : εeff 0:258 ðW=h þ 0:8Þ
(8)
(9)
For a gallium arsenide (GaAs) substrate with a relative permittivity of εr ¼ 12:9 and loss tangent of tanδ ¼ 0:006, we take the thickness to be h ¼ 8 μm, which is approximately λ0 =20 with λ0 ¼ c=f0 the ENZ wavelength. By using Eqs. (6) and (7), the width and 3
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C. Cheng et al.
Fig. 3. (a) Simulated reflection coefficient S11 and (b) gain of the antenna with (“w/t”) and without (“w/o”) the multilayer superstrate as functions of frequency.
Fig. 4. (a) Phi ¼ 0o (x z plane) and (b) Phi¼ 90o (y z plane) radiation patterns of the patch antenna with and without the ENZ metamaterial superstrate at 1.85 THz. (c) and (d) are the corresponding 3D radiation patterns.
the length of radiation patch are designed to be W ¼ 30:78 μm and L ¼ 17:5 μm, respectively. pffiffiffiffiffiffiffiffiffiffiffiffi A port with standard resistance of 50 Ω is placed at the coordinate of ðL =ð2 ξre ðLÞ Þ; 0Þ ¼ ð3:2 μm; 0Þ in order to efficiently excite the terahertz patch antenna, where ξre ðLÞ ¼
εr þ 1 2
þ
� 1
εr 2
1 þ 12
h L
�
1=2
(10)
:
3. Results and discussion All the simulations in this work were performed with finite-difference-time-domain (FDTD) method based on MEEP codes. Unless otherwise specified, the thicknesses of InSb and SiO2 layers are taken to be tm ¼ td ¼ 1 μm, and the distance between the bottom 4
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Fig. 5. The near-field electric field distributions of the patch antenna (a) without (“w/o”) and (b) with (“w/t”) the multilayer ENZ superstrate.
Fig. 6. (a) Simulated reflection coefficient S11 of the patch antenna without (w/o) and with (w/t) the multilayer metamaterial. 1 : 1, 1 : 2, and 2 : 1 indicate that the thicknesses of InSb and SiO2 films are (1 μm, 1 μm), (1 μm, 2 μm), and (2 μm, 1 μm), respectively. (b) The corresponding Phi ¼ 90o (x z plane) and (c) Phi ¼ 0o (y z plane) radiation patterns at 1.85 THz. (d) Zoom-in view of the dashed box in (c).
surface of the multilayer metamaterial superstrate and the patch antenna is set to be D ¼ 10 μm. The effects of these parameters will be discussed later. The calculated reflection coefficients S11 for the terahertz patch antennas without (denoted as “w/o”) and with (“w/t”) the multilayer metamaterial are shown in Fig. 3(a). The black curve shows that the input-matching bandwidth, determined by S11 < 10 dB, for the terahertz patch antenna without the multilayer metamaterial is 0.1 THz (ranging from 1.8 THz to 1.9 THz). After coating the multilayer superstrate, the red curve shows that the antenna bandwidth decreases to 0.04 THz (ranging from 1.84 THz to 1.88 THz), whereas the input return loss dramatically decreases. Correspondingly, the gain is significantly enhanced after coating the patch antenna with the multilayer superstrate, as shown in Fig. 3(b). At the ENZ frequency of f0 ¼ 1:85 THz, the antenna gain is improved from 5.37 dB to 7.79 dB thanks to the introduction of the ENZ metamaterial superstrate. In other words, 45% gain enhancement is achieved. We emphasize that the 45% gain enhancement of terahertz patch antenna obtained with the proposed ENZ metamaterial super strate is much larger than previous approaches. For example, Nejati et al. [32] showed a gain increase of 32% by using frequency 5
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Fig. 7. (a)(c) Simulated reflection coefficients S11 and (b)(d) peak gains of the patch antenna at 1.85 THz. (a) and (b) are for different distances D between the patch and the multilayer metamaterial. (c) and (d) are for different numbers of multilayers, where “0L” indicates that there is no superstrate and “4L” indicates that there are 2 pairs of InSb and SiO2 films.
selective surface (FSS) and photonic band gap (PBG) structures, Kushwaha et al. [33] showed a gain increase of 20% by employing a PBG crystal substrate, and Azizi et al. [34] showed a 25% improvement in the gain of a patch antenna by replacing copper with graphene. Fig. 4(a) and (b) show the Phi ¼ 0o (x z plane) and Phi ¼ 90o (y z plane) radiation patterns for the patch antenna without and with the multilayer metamaterial at f0 ¼ 1:85 THz. Results show that the directivity of the antenna is greatly improved. More spe cifically, the main beam width in the y z plane of the antenna with the ENZ superstrate is compressed sharply, whereas that in the x z plan is compressed slightly. This means that the ENZ superstrate plays a reforming role in the y z plane. The 3D radiation patterns in Fig. 4(c)(d) further show that the directivity of the patch antenna has been greatly enhanced due to the ENZ superstrate. In order to understand the gain enhancement and the directivity improvement, we plot the near-field electric field distributions for the patch antenna without and with the ENZ superstrate in Fig. 5(a) and (b), respectively. Results show that the patch antenna without the ENZ superstrate generates spherical-like waves, resulting in small gain and low directivity, whereas by coating the patch antenna with the anisotropic ENZ superstrate, the near-field electric fields become plane-like waves, leading to enhanced gain and improved directivity. Although previously we have clarified that the frequency for achieving near-zero ε? is independent from the thicknesses of the InSb and SiO2 thin films, we find that these thicknesses have a large impact on the reflection coefficient, but have a small influence on the antenna radiation patterns, as shown by Fig. 6. Fig. 6(a) shows that the best performance with a wide 10 dB impedance bandwith and meanwhile a large gain is achieved when tm ¼ td ¼ 1 μm. Fig. 6(b)–(d) shows that both tm ¼ td ¼ 1 μm and (tm ¼ 2 μm; td ¼ 1 μm) result in the best Phi ¼ 90o and Phi ¼ 0o radiation patterns, and the corresponding peak gains are both approximate to 7.80 dB. We now investigate the effects of the distance D between the patch and the multilayer metamaterial, and of the layer number of the multilayers. As D increases from 10 μm to 30 μm, Fig. 7(a) shows that the dip of S11 shifts to lower frequency, whereas the peak gain slightly decreases from 7.65 dB to 7.04 dB, as shown by Fig. 7(b). This is because as the ENZ metamaterial superstrate gets closer to the patch antenna, more upward radiations from the antenna can be re-directed into the normal direction in the air, resulting in a larger gain. As we have shown previously, the patch antenna without the metamaterial superstrate (denoted as “0L”), as a reference, has a wide bandwidth of 0.1 THz and a relatively small gain of 5.37 dB. Fig. 7(c) and (d) show that, by adding 2 pairs of InSb–SiO2 multilayers (denoted as “4L”), the bandwidth is reduced to 0.04 THz and the gain increases dramatically to 6.84 dB. As the layer number increases, the bandwidth varies slightly; whereas the antenna gain first increases, then saturates at 7.80 dB for “12L”, and gradually decreases as the layer number further increases. This is because as the pair number of InSb–SiO2 multilayers increases, the equivalence of ENZ bulk material is more accurate, resulting in higher antenna gain. On the other hand, however, more multilayers lead to longer propagation 6
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length and thus larger insertion loss although weak. Therefore, the antenna gain first increases dramatically, then saturates, and finally decreasing because the loss becomes more important. 4. Conclusion In conclusion, we have proposed a novel approach to enhance the gain of a terahertz patch antenna based on ENZ metamaterial superstrate, which is composed of InSb–SiO2 multilayers. By deriving the dispersion relation for the effective anisotropic metamaterial, we have theoretically shown that, near-zero ε? can lead to highly directional radiation with direction normal to the multilayers-air interface, and that the frequency for achieving near-zero ε? is determined only by that for near-zero εm of semiconductor InSb and thus it can be dynamically tuned through modulating the electron density. Simulation results have shown that, by coating the multilayer metamaterial and at the frequency of 1.85 THz when ε? ¼ 0, the patch antenna gain is enhanced by 45%, from 5.37 dB to 7.80 dB. Correspondingly, radiation patterns, especially that in the y z plane, show greatly improved directivity. We have found that the thicknesses of the InSb and SiO2 layers are important for achieving the best reflection coefficient. We have also shown that as the distance between the path antenna and the metamaterial superstrate increases, the peak gain decreases slightly, suggesting that this parameter makes little difference on the antenna gain. As the layer number of the InSb–SiO2 multilayers increases, the antenna gain first increases dramatically due to more accurate equivalence of effective ENZ material, then saturates and gradually decreases because the loss becomes more important. Since the multilayer ENZ metamaterial is easy to fabricate and is convenient to tune dynamically, we expect that the proposed gain enhancement approach will find attractive applications in various terahertz antennas, as well as in antennas in other frequency regimes. CRediT authorship contribution statement Cong Cheng: Methodology, Investigation, Data curation, Writing - original draft. Yuanfu Lu: Validation, Resources, Project administration. Dongbo Zhang: Visualization, Software. Fangming Ruan: Methodology, Supervision. Guangyuan Li: Conceptual ization, Methodology, Software, Writing - review & editing, Supervision, Funding acquisition. Acknowledgement The work was supported by the Shenzhen Research Foundation (Grant Nos. JCYJ20180507182444250, JCYJ20160608153308846, JCYJ20170413152328742), the Youth Innovation Promotion Association of the Chinese Academy of Sciences (No. 2016320), Guizhou Province Project of Innovation Talents Teams of Electrostatic and Electromagnetic Protection (No. [2016]5653), and Academician Liu Shanghe Fund of Electrostatic Protection Research (Grant No. BOIMTLSHJD20161004). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.spmi.2020.106390.
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Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Gain enhancement of terahertz patch antennas by coating epsilon-near-zero metamaterials Cong Cheng a, b, Yuanfu Lu b, **, Dongbo Zhang c, Fangming Ruan a, d, Guangyuan Li b, * a
College of Big Data and Information Engineering, Guizhou University, Guiyang, 550025, China Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China No. 16 Institute of No. 9 Academy of China Aerospace Technology Corporation, Xi’an, China d College of Big Data and Computer Science, Guizhou Normal University, Guiyang, 550001, China b c
A R T I C L E I N F O
A B S T R A C T
Keywords: Terahertz Patch antenna Gain Epsilon-near-zero metamaterials
In this work, we propose a novel approach to enhance the gain of a terahertz patch antenna by coating an epsilon-near-zero (ENZ) metamaterial superstrate. The ENZ metamaterial is composed of indium antimonide (InSb) and silicon dioxide multilayers, of which the out-of-plane compo nent of the effective permittivity is close to zero. Results show that by coating the ENZ superstrate the peak gain of the antenna is increased from 5.37 dB to 7.79 dB, corresponding to 45% gain enhancement and greatly improved radiation directivity. We find that the ENZ frequency of the multilayer metamaterial equals to that of semiconductor InSb and thus it can be tuned dynami cally. We expect the concept of adding a multilayer ENZ metamaterial superstrate to enhance the antenna gain will find potential applications in other types of terahertz antennas and in antennas in other frequency regimes.
1. Introduction Terahertz (THz) wave refers to electromagnetic radiation with a frequency of 0.1–10 � 1012 Hz (corresponding to wavelength of 3 mm–30 μm). Because of its unique characteristics such as high spectral resolution [1], high spatial resolution [2], and transparency through many non-metallic, non-polar materials [3], terahertz radiation has been widely used in a diverse range of applications, such as ultra-broadband wireless communication systems [4,5] and high-resolution imaging systems [6]. In these applications, a terahertz antenna is a vital component for achieving unidirectional radiation with high gain [7]. Among various terahertz antennas, a microstrip patch antenna has been widely used since it is cost effective, light weight, and easy to design and fabrication [8]. However, microstrip patch antennas encounter a severe problem of surface waves that are sustained by the substrate between the patch and ground plane, resulting in deteriorated bandwidth, efficiency and gain [9]. In order to enhance the gain or to realize high directivity of the patch antenna, a variety of approaches have been utilized over the years. A commonly used method is to introduce a frequency-selective surface [10], Fabry-Perot cavity [11] or an electromagnetic bandgap metamaterial [9,12,13] on top of or beneath the microstrip patch antenna. Another approach to improve the radiation characteristic is to pattern patch antennas in a periodic array [14,15]. Recently, epsilon-near-zero (ENZ) metamaterials or zero/low-index metamaterials (ZIMs/LIMs) have been theoretically proposed and experimentally demonstrated for enhancing the antenna gain or directivity [16–18]. The operation principle is based on the * Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Lu), [email protected] (G. Li). https://doi.org/10.1016/j.spmi.2020.106390 Received 15 October 2019; Received in revised form 10 December 2019; Accepted 6 January 2020 Available online 11 January 2020 0749-6036/© 2020 Elsevier Ltd. All rights reserved.
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Fig. 1. (a) Schematic of the proposed gain enhancement approach of coating a terahertz microstripe patch antenna with an ENZ metamaterial superstrate (not on scale). (b) The ENZ superstrate is composed of alternating InSb (in red) and SiO2 (in bule) multilayers with thicknesses tm and td , respectively. (c) The terahertz patch antenna has width W and length L.
well-known Snell’s law of refraction, nin sinθin ¼ nout sinθout , when a ray of any incidence angle θin transmits from an extremely low index medium (nin � 0) to a high index medium (nout � 1), the output ray will transmit in a direction normal to the interface between the two media (θout � 0) [19,20]. Taking advantage of this principle, Zhou et al. [21] demonstrated that the directivity of the patch antenna is effectively enhanced based on a ZIM superstrate. Zhou and Cui [22] and Jiang et al. [23] respectively enhanced the directivity of a Vivaldi antenna by using anisotropic ZIM composed of the meander-line structure. Quite recently, El-Nady et al. [24] utilized ENZ metamaterials to improve the radiation characteristics of a millimeter wave Vivaldi antenna. In order to enhance both the antenna gain and bandwidth, Abdelgwad and Said [25] proposed an ENZ metamaterial composed of a periodic array of parallel metallic wires arranged in a rectangular pattern. Bayat and Khalilpour [26] designed a miniaturized patch antenna with an ENZ metamaterial superstrate. In these reports, however, ZIMs or ENZ metamaterials operating in the microwave or millimeter regime are realized by patterning metal into complicated structures, making these structures difficult to fabricate when their sizes are scaling down for operating in the terahertz regime, and inconvenient to tune dynamically. These drawbacks hinder practical applications in terahertz antennas. In this work, we propose a novel approach to enhance the gain of a terahertz patch antenna. This approach relies on coating an ENZ metamaterial superstrate, which is composed of alternating Indium antimonide (InSb) and silicon dioxide (SiO2) multilayers. Compared with the conventional ZIM or ENZ metamaterials that consist of complicated metallic structures and that are difficult to fabricate or dynamically tune, the multilayers are easy to fabricate and convenient to tune dynamically. The theory and the operation principle will be elaborated. The enhancement of the antenna gain and directivity will be numerically demonstrated by comparing the patch antennas with and without the ENZ metamaterial superstrate. The effects of the layer thicknesses, the distance between the multilayers and the patch antenna, and the layer number of the multilayers will also be discussed. 2. Theory and design Fig. 1(a) illustrates the proposed terahertz patch antenna that is coated by an ENZ metamaterial superstrate. The ENZ metamaterial is composed of multiple alternating thin films of InSb and SiO2 with thicknesses of tm and td , respectively, as shown by Fig. 1(b). Because the thicknesses of the thin InSb and SiO2 layers satisfy the criteria of effective medium theory (EMT), the effective permittivity of the multilayer InSb–SiO2 metamaterial can be calculated using the EMT [27], 0 1 εk 0 0 ε ¼ @ 0 εk 0 A : (1) 0 0 ε? Here the subscripts k and ? indicate the components that are parallel and perpendicular to the x-y plane (the plane of the thin films), respectively. These in-plane and out-of-plane effective permittivity components are given by Ref. [28].
εk ¼
tm εm þ td εd ; tm þ td
(2)
εm εd ðtm þ td Þ : tm εd þ td εm
(3)
ε? ¼
The dispersion relation for the effective anisotropic metamaterial is given by k2x þ k2y
ε?
þ
k2z
εk
(4)
¼ k20 ;
where kx , ky and kz are propagation constant components of light in the effective anisotropic metamaterial, and k0 is the propagation 2
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Fig. 2. (a) Real and (b) imaginary parts of the effective relative permittivity tensor components of the InSb–SiO2 multilayer metamaterial. Green and blue dots indicate εk ¼ 0 and ε? ¼ 0, respectively.
constant of light in vacuum. According to this dispersion relation, when ε? is extremely close to zero, k2x þ k2y is forced to be zero. In
other words, near-zero ε? means quasi-infinite phase velocity in the x and y directions and vanishing z-component of the electric displacement (i.e., Dz ) in the effective anisotropic metamaterial, which forces the z-component of the electric field (Ez ) in the free-space region to approach zero according to the boundary condition at the metamaterial–air interface [23]. Therefore, by coating a multilayer metamaterial superstrate with near-zero ε? , highly directional radiation with direction normal to the metamaterial-air interface can be achieved, as illustrated in Fig. 1(a). The frequency dependent complex permittivity of semiconductor InSb in the terahertz regime can be described by the Drude model [29],
εm ¼ εð∞Þ
ω2p ω þ iωγ 2
(5)
:
Here εð∞Þ is the high-frequency permittivity, ω is the excitation frequency, ω2p ¼ ne2 =ðm� ε0 Þ is the plasma frequency with n the free electron density, and e and m� the electron’s charge and effective mass, respectively, and γ ¼ 1=τ is the carrier momentum relaxation rate with τ the average collision time of the charge carriers. For undoped InSb at 300 K, εð∞Þ ¼ 15:68, ωp ¼ 4:6 � 1013 rad/s, and γ= ð2πÞ ¼ 0:05 THz [30]. We take the dielectric constant of SiO2 to be εd ¼ 3:8. Fig. 2 shows the effective permittivity tensor components for tm ¼ td ¼ 1 μm. We find that εk is close to zero at the frequency of 1.65 THz and ε? is close to zero at 1.85 THz. As we have clarified before, hereafter we focus on ε? ¼ 0 and f0 ¼ 1:85 THz in order to enhance the antenna gain and directivity. We should emphasize that, according to Eq. (3), ε? ¼ 0 is always valid provided that εm ¼ 0, which occurs when ω0 ¼ 2πf0 � ωp = pffiffiffiffiffiffiffiffiffiffi εð∞Þ. In other words, the frequency for achieving near-zero ε? is equal to that for near-zero εm of semiconductor InSb, and thus it is independent from the thicknesses of the InSb and SiO2 thin films and from εd of the dielectric. It is worth mentioning that, because ωp of the semiconductor InSb can be tuned by modulating the electron density, which can be realized electrically or optically, the operation frequency for achieving near-zero ε? and thus gain/directivity enhancement can be tuned dynamically. The terahertz patch antenna is then designed for operating at the ENZ frequency of the multilayer metamaterial, f0 ¼ 1:85 THz. The size of a rectangular patch antenna can be determined by Ref. [31]. W¼
L¼
�1=2 � c 2 ; 2f0 εr þ 1
c 1 pffiffiffiffiffiffi 2f0 εeff
(6) (7)
2ΔL ;
where εr is the relative permittivity of the substrate, εeff is effective dielectric constant, � � 1=2 ε þ 1 εr 1 h þ 1 þ 12 εeff ¼ r ; 2 2 W and ΔL is equivalent radiation gap length, � εeff þ 0:3 ðW=h þ 0:264Þ � ΔL ¼ 0:412h : εeff 0:258 ðW=h þ 0:8Þ
(8)
(9)
For a gallium arsenide (GaAs) substrate with a relative permittivity of εr ¼ 12:9 and loss tangent of tanδ ¼ 0:006, we take the thickness to be h ¼ 8 μm, which is approximately λ0 =20 with λ0 ¼ c=f0 the ENZ wavelength. By using Eqs. (6) and (7), the width and 3
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Fig. 3. (a) Simulated reflection coefficient S11 and (b) gain of the antenna with (“w/t”) and without (“w/o”) the multilayer superstrate as functions of frequency.
Fig. 4. (a) Phi ¼ 0o (x z plane) and (b) Phi¼ 90o (y z plane) radiation patterns of the patch antenna with and without the ENZ metamaterial superstrate at 1.85 THz. (c) and (d) are the corresponding 3D radiation patterns.
the length of radiation patch are designed to be W ¼ 30:78 μm and L ¼ 17:5 μm, respectively. pffiffiffiffiffiffiffiffiffiffiffiffi A port with standard resistance of 50 Ω is placed at the coordinate of ðL =ð2 ξre ðLÞ Þ; 0Þ ¼ ð3:2 μm; 0Þ in order to efficiently excite the terahertz patch antenna, where ξre ðLÞ ¼
εr þ 1 2
þ
� 1
εr 2
1 þ 12
h L
�
1=2
(10)
:
3. Results and discussion All the simulations in this work were performed with finite-difference-time-domain (FDTD) method based on MEEP codes. Unless otherwise specified, the thicknesses of InSb and SiO2 layers are taken to be tm ¼ td ¼ 1 μm, and the distance between the bottom 4
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Fig. 5. The near-field electric field distributions of the patch antenna (a) without (“w/o”) and (b) with (“w/t”) the multilayer ENZ superstrate.
Fig. 6. (a) Simulated reflection coefficient S11 of the patch antenna without (w/o) and with (w/t) the multilayer metamaterial. 1 : 1, 1 : 2, and 2 : 1 indicate that the thicknesses of InSb and SiO2 films are (1 μm, 1 μm), (1 μm, 2 μm), and (2 μm, 1 μm), respectively. (b) The corresponding Phi ¼ 90o (x z plane) and (c) Phi ¼ 0o (y z plane) radiation patterns at 1.85 THz. (d) Zoom-in view of the dashed box in (c).
surface of the multilayer metamaterial superstrate and the patch antenna is set to be D ¼ 10 μm. The effects of these parameters will be discussed later. The calculated reflection coefficients S11 for the terahertz patch antennas without (denoted as “w/o”) and with (“w/t”) the multilayer metamaterial are shown in Fig. 3(a). The black curve shows that the input-matching bandwidth, determined by S11 < 10 dB, for the terahertz patch antenna without the multilayer metamaterial is 0.1 THz (ranging from 1.8 THz to 1.9 THz). After coating the multilayer superstrate, the red curve shows that the antenna bandwidth decreases to 0.04 THz (ranging from 1.84 THz to 1.88 THz), whereas the input return loss dramatically decreases. Correspondingly, the gain is significantly enhanced after coating the patch antenna with the multilayer superstrate, as shown in Fig. 3(b). At the ENZ frequency of f0 ¼ 1:85 THz, the antenna gain is improved from 5.37 dB to 7.79 dB thanks to the introduction of the ENZ metamaterial superstrate. In other words, 45% gain enhancement is achieved. We emphasize that the 45% gain enhancement of terahertz patch antenna obtained with the proposed ENZ metamaterial super strate is much larger than previous approaches. For example, Nejati et al. [32] showed a gain increase of 32% by using frequency 5
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Fig. 7. (a)(c) Simulated reflection coefficients S11 and (b)(d) peak gains of the patch antenna at 1.85 THz. (a) and (b) are for different distances D between the patch and the multilayer metamaterial. (c) and (d) are for different numbers of multilayers, where “0L” indicates that there is no superstrate and “4L” indicates that there are 2 pairs of InSb and SiO2 films.
selective surface (FSS) and photonic band gap (PBG) structures, Kushwaha et al. [33] showed a gain increase of 20% by employing a PBG crystal substrate, and Azizi et al. [34] showed a 25% improvement in the gain of a patch antenna by replacing copper with graphene. Fig. 4(a) and (b) show the Phi ¼ 0o (x z plane) and Phi ¼ 90o (y z plane) radiation patterns for the patch antenna without and with the multilayer metamaterial at f0 ¼ 1:85 THz. Results show that the directivity of the antenna is greatly improved. More spe cifically, the main beam width in the y z plane of the antenna with the ENZ superstrate is compressed sharply, whereas that in the x z plan is compressed slightly. This means that the ENZ superstrate plays a reforming role in the y z plane. The 3D radiation patterns in Fig. 4(c)(d) further show that the directivity of the patch antenna has been greatly enhanced due to the ENZ superstrate. In order to understand the gain enhancement and the directivity improvement, we plot the near-field electric field distributions for the patch antenna without and with the ENZ superstrate in Fig. 5(a) and (b), respectively. Results show that the patch antenna without the ENZ superstrate generates spherical-like waves, resulting in small gain and low directivity, whereas by coating the patch antenna with the anisotropic ENZ superstrate, the near-field electric fields become plane-like waves, leading to enhanced gain and improved directivity. Although previously we have clarified that the frequency for achieving near-zero ε? is independent from the thicknesses of the InSb and SiO2 thin films, we find that these thicknesses have a large impact on the reflection coefficient, but have a small influence on the antenna radiation patterns, as shown by Fig. 6. Fig. 6(a) shows that the best performance with a wide 10 dB impedance bandwith and meanwhile a large gain is achieved when tm ¼ td ¼ 1 μm. Fig. 6(b)–(d) shows that both tm ¼ td ¼ 1 μm and (tm ¼ 2 μm; td ¼ 1 μm) result in the best Phi ¼ 90o and Phi ¼ 0o radiation patterns, and the corresponding peak gains are both approximate to 7.80 dB. We now investigate the effects of the distance D between the patch and the multilayer metamaterial, and of the layer number of the multilayers. As D increases from 10 μm to 30 μm, Fig. 7(a) shows that the dip of S11 shifts to lower frequency, whereas the peak gain slightly decreases from 7.65 dB to 7.04 dB, as shown by Fig. 7(b). This is because as the ENZ metamaterial superstrate gets closer to the patch antenna, more upward radiations from the antenna can be re-directed into the normal direction in the air, resulting in a larger gain. As we have shown previously, the patch antenna without the metamaterial superstrate (denoted as “0L”), as a reference, has a wide bandwidth of 0.1 THz and a relatively small gain of 5.37 dB. Fig. 7(c) and (d) show that, by adding 2 pairs of InSb–SiO2 multilayers (denoted as “4L”), the bandwidth is reduced to 0.04 THz and the gain increases dramatically to 6.84 dB. As the layer number increases, the bandwidth varies slightly; whereas the antenna gain first increases, then saturates at 7.80 dB for “12L”, and gradually decreases as the layer number further increases. This is because as the pair number of InSb–SiO2 multilayers increases, the equivalence of ENZ bulk material is more accurate, resulting in higher antenna gain. On the other hand, however, more multilayers lead to longer propagation 6
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length and thus larger insertion loss although weak. Therefore, the antenna gain first increases dramatically, then saturates, and finally decreasing because the loss becomes more important. 4. Conclusion In conclusion, we have proposed a novel approach to enhance the gain of a terahertz patch antenna based on ENZ metamaterial superstrate, which is composed of InSb–SiO2 multilayers. By deriving the dispersion relation for the effective anisotropic metamaterial, we have theoretically shown that, near-zero ε? can lead to highly directional radiation with direction normal to the multilayers-air interface, and that the frequency for achieving near-zero ε? is determined only by that for near-zero εm of semiconductor InSb and thus it can be dynamically tuned through modulating the electron density. Simulation results have shown that, by coating the multilayer metamaterial and at the frequency of 1.85 THz when ε? ¼ 0, the patch antenna gain is enhanced by 45%, from 5.37 dB to 7.80 dB. Correspondingly, radiation patterns, especially that in the y z plane, show greatly improved directivity. We have found that the thicknesses of the InSb and SiO2 layers are important for achieving the best reflection coefficient. We have also shown that as the distance between the path antenna and the metamaterial superstrate increases, the peak gain decreases slightly, suggesting that this parameter makes little difference on the antenna gain. As the layer number of the InSb–SiO2 multilayers increases, the antenna gain first increases dramatically due to more accurate equivalence of effective ENZ material, then saturates and gradually decreases because the loss becomes more important. Since the multilayer ENZ metamaterial is easy to fabricate and is convenient to tune dynamically, we expect that the proposed gain enhancement approach will find attractive applications in various terahertz antennas, as well as in antennas in other frequency regimes. CRediT authorship contribution statement Cong Cheng: Methodology, Investigation, Data curation, Writing - original draft. Yuanfu Lu: Validation, Resources, Project administration. Dongbo Zhang: Visualization, Software. Fangming Ruan: Methodology, Supervision. Guangyuan Li: Conceptual ization, Methodology, Software, Writing - review & editing, Supervision, Funding acquisition. Acknowledgement The work was supported by the Shenzhen Research Foundation (Grant Nos. JCYJ20180507182444250, JCYJ20160608153308846, JCYJ20170413152328742), the Youth Innovation Promotion Association of the Chinese Academy of Sciences (No. 2016320), Guizhou Province Project of Innovation Talents Teams of Electrostatic and Electromagnetic Protection (No. [2016]5653), and Academician Liu Shanghe Fund of Electrostatic Protection Research (Grant No. BOIMTLSHJD20161004). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.spmi.2020.106390.
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