Asai Hidehiro

KADOWAKI Kazuo

Tachiki Masashi

Applied Physics Letters

Tsukuba Repository  (Tulips-R)

Proposal of terahertz patch antenna fed byintrinsic Josephson junctions著者 Asai Hidehiro, Tachiki Masashi, Kadowaki Kazuojournal orpublication titleApplied physics lettersvolume 101number 11page range 112602year 2012-09権利 Copyright (2012) American Institute ofPhysics. This article may be downloaded forpersonal use only. Any other use requiresprior permission of the author and theAmerican Institute of Physics.The following article appeared in Appl. Phys.Lett. 101, 112602 (2012) and may be found athttp://dx.doi.org/10.1063/1.4751846.URL http://hdl.handle.net/2241/118022doi: 10.1063/1.4751846Proposal of terahertz patch antenna fed by intrinsic Josephson junctionsHidehiro Asai, Masashi Tachiki, and Kazuo Kadowaki  Citation: Appl. Phys. Lett. 101, 112602 (2012); doi: 10.1063/1.4751846 View online: http://dx.doi.org/10.1063/1.4751846 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v101/i11 Published by the American Institute of Physics.  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Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsProposal of terahertz patch antenna fed by intrinsic Josephson junctionsHidehiro Asai,1 Masashi Tachiki,2 and Kazuo Kadowaki21Electronics and Photonics Research Institute, National Institute of Advanced Industrial Science andTechnology (AIST), Tsukuba, Ibaraki 305-8568, Japan2Faculty of Pure and Applied Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan(Received 8 July 2012; accepted 27 August 2012; published online 11 September 2012)We propose a THz patch antenna, in which THz ac current is fed by intrinsic Josephson junctions(IJJs). The radiation power of the antenna for three different feed positions is calculated using thefinite-difference time-domain method. We predict that the antenna will radiate sub-milliwattterahertz waves with high radiation efficiency of over 20%. The maximum radiation power willdepend on the position of the feed. We also show that the radiation characteristics of the antennaare described well by the equivalent inductance-capacitance-resistance circuit model. VC 2012American Institute of Physics. [http://dx.doi.org/10.1063/1.4751846]Over the past few decades, the search for sources ofterahertz electromagnetic (EM) waves has been a hot topicin engineering fields. The terahertz EM wave has a tremen-dous potential in the technological applications such asnon-destructive inspection, bio-sensing, and high-speedwireless communication. Various types of terahertz emitters,such as, quantum-cascade lasers1 and resonant-tunnelingdiodes,2 have been studied so far. However, the generationof high power EM waves in the frequency range 0:1  10THz, known as the “terahertz gap,” is still a challengingproblem.High-Tc superconductors have received much attentionas promising candidates for compact solid-state terahertzsources after Ozyuzer et al. reported the radiation of highlymonochromatic, continuous terahertz wave fromBi2Sr2CaCu2O8þd (Bi2212) single crystal.3 Cuprate high-Tcsuperconductors, such as Bi2212, form intrinsic Josephsonjunctions (IJJs), that is, natural stacks of Josephson junctionscomposed of the stacking of superconducting CuO2 layersand insulating layers.4 Thus, the ac Josephson current flowsthrough the crystal under dc voltage along the c axis, andradiation of EM waves is triggered by this ac current. In pre-vious experimental studies, intense terahertz radiation hasbeen observed for mesa-structured IJJ samples.3,5–10 Theemission characteristics of the IJJ mesa have also been inves-tigated theoretically,11–21 and these theoretical studies attri-bute the intense emission to the excitation of the transverseJosephson plasma. In the IJJ mesas, the transverse Josephsonplasma is excited strongly under dc voltages when the acJosephson frequencies coincide with the cavity resonantfrequencies that are determined by the mesa geometries. Atpresent, IJJ-based terahertz emitters are able to cover thefrequency range of 0:3  1 THz with the radiation power ofapproximately 10 lW.In the IJJ mesas, large Joule dissipation occurs under dcvoltages. In a typical IJJ mesa studied by Minami et al.,5 forexample, Joule dissipation of over 10 mW occurs when themesa emits terahertz EM waves. This large dissipationimplies that the radiation efficiency is extremely low, and isof order 0.1%. An improvement of the radiation efficiency isa crucial task for the practical application of the IJJ-basedterahertz emitter.In this letter, we propose an IJJ-based terahertz emitterthat overcomes the problem of low radiation efficiency. Weperform a numerical simulation of THz radiation from proto-type emitters and predict intense emission of sub-THz EMwaves with radiation efficiency that reaches 23%.In Fig. 1(a), we show a schematic view of the terahertzpatch antenna. A square metal patch is placed on a dielectricsubstrate, and the patch and the ground plane are electricallyconnected by a rectangular solid of IJJs. The dc external cur-rent injected into the metal patch flows through the IJJs tothe ground plane. The IJJ layers stack along the z axis, andthus the ac Josephson current flows between the patch andthe ground plane when the IJJs are in resistive states. There-fore, the IJJs act as the “feed line” of the antenna.The dimensions of the antenna in the x-y plane are givenin Fig. 1(b). We set the thickness of the antenna to 4 lm andthe relative dielectric constant of the dielectric substrate tos ¼ 2:25.Of particular note is that the dimensions of the IJJ sam-ple in our antenna are substantially small compared to thoseof the terahertz IJJ emitters reported in the previous studies.The dissipation in the IJJs is greatly suppressed in thisantenna because of this. In previous studies, the terahertzemission was achieved by the excitation of transverseJosephson plasma waves in mesa-structured IJJs. The dimen-sions of these mesas are in the range 50  500 lm, and arecomparable to the wavelength of the Josephson plasmawave. In contrast, in our antenna, the IJJs are used as the“feed” of the terahertz patch antenna, and thus the dimen-sions of the IJJs can be much smaller than the wavelength ofthe plasma wave.We use the finite-difference time-domain (FDTD)method to investigate the time evolution of the electromag-netic field around the patch antenna and the radiation power.In this calculation, we assume that the dielectric substrateand the ground plane have infinite size in the x-y plane.Moreover, we treat the metal patch and the ground plane asperfect electric conductors. In the regions outside the IJJs,we solve the three-dimensional Maxwell’s equations. Insidethe IJJs, we solve the dynamical equation of the phase differ-ence and the electric field for each layer which are describedas follows:0003-6951/2012/101(11)/112602/4/$30.00 VC 2012 American Institute of Physics101, 112602-1APPLIED PHYSICS LETTERS 101, 112602 (2012)Downloaded 06 Dec 2012 to 130.158.56.101. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsh2eDddtPl ¼ aEz;l1  aEz;lþ1 þ ð1þ 2aÞEz;l; (1)c0ddtEz;l ¼ IOS þ IextSab jc sinPl  rcEz;l: (2)Here, Ez;l and Pl are the z component of the electric fieldand the phase difference between the lth and l  1th layers,a is the capacitive coupling parameter between IJJ layers,22c is the dielectric constant of IJJs along the c axis, Iext is theexternal dc current, rc is the conductivity for the quasi parti-cle current, Sab is the area of the IJJ plane parallel to the a- bplane, and jc ¼ /0=ð2pl0k2cDÞ is the critical current densityof the IJJs. D is the thickness of the insulating layer, kc is thepenetration depth along the c axis, and /0 is the flux quan-tum. The external oscillating current IOS which is induced bythe external field is given by IOS ¼ÐCHOSdl, where C is theclosed loop around the surface of the IJJs, HOS is the oscillat-ing part of magnetic field. Since the electrodes are wellconductive, the electric field in the electrode region Ez;0 andEz;N is negligibly small compared with that in the IJJsEz;1  Ez;N1. Hence, we take Ez;0 ¼ Ez;N ¼ 0. In this letter,we take r ¼ 5 S=m; kc ¼ 100 lm, a ¼ 0:1, D¼ 12 A˚ and thethickness of the superconducting layer s¼ 3 A˚. Since the heightof the IJJs is 4 lm in our model, the number of IJJ layers N is2667. These values are comparable to those of Bi2212 samples.In the above equations, we assume that the Pl and the currentdistribution are uniform in the ab plane because the sizes of theIJJs in the a-b plane are much smaller than the penetrationdepth kc. We consider three different positions of the IJJsLfeed ¼ 20; 44, and 68 lm (Lfeed is shown in Fig. 1), and calcu-late the radiation power for each of these positions.Figures 2(a) and 2(b) show the current and the radiationpower as functions of voltage per IJJ layer (i.e., the totalvoltage divided by N) for the three feed positions. In thiscalculation, we decrease the external current from 0.48 toFIG. 1. A schematic view of the terahertzpatch antenna proposed in this letter. Thefigure on the right shows the projection viewof the patch antenna on the x-y plane.FIG. 2. (a) The current-versus-voltage(I-V) curves and, (b) the radiation power-versus-voltage (P-V) curves forLfeed ¼ 20; 44; 68lm.112602-2 Asai, Tachiki, and Kadowaki Appl. Phys. Lett. 101, 112602 (2012)Downloaded 06 Dec 2012 to 130.158.56.101. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions0.26 mA in the resistive state, and then increase the currentfrom 0.26 mA to 0.48 mA.In the current versus voltage (I-V) curve, a voltage stepappears at 1.31mV for all feed positions (see Fig. 2(a)). Theradiation powers sharply increase around these steps, asshown in the power versus voltage (P-V) curve (see Fig.2(b)). The width of the steps and the radiation powersbecome larger as Lfeed is increased, and the maximum radia-tion power of 0.37 mW is obtained when Lfeed ¼ 68 lm andV¼ 1.31mV. Since the input power corresponding to thisradiation is estimated to be 1.61 mW from the I-V curve, theradiation efficiency is 23%.Figure 3 shows the amplitude of the displacement cur-rent in the IJJs as a function of the voltage for L¼ 68 lm.The displacement current in the IJJs is strongly enhanced at1.31mV. In Fig. 3(b), we show the Fourier transform of theEM wave emitted from the antenna at V¼ 1.31mV forLfeed ¼ 68 lm. The peak frequency 0.63 THz is exactly equalto the ac Josephson frequency fJ ¼ 2 eV=h. Moreover, higherharmonics (1.26 THz) appear due to the nonlinearity of theac Josephson effect.The inset in Fig. 3(b) shows a snapshot of the oscillatingpart of Ez at V¼ 1.31mV, and this corresponds to the stand-ing wave mode. The appearance here of the standing wavemode is due to the fact that the ac Josephson frequency0.63 THz is equal to the resonance frequency fc of the funda-mental cavity mode, where fc is given by fc ¼ c0=ð2wﬃﬃps),c0 is the light velocity in free space, and w is the width of themetal patch.In this case, the field oscillation in the IJJs is amplifiedby receiving a strong feedback from the EM standing wave.Consequently, the radiation power of the patch antennaincreases drastically. In this manner, the strong radiationpeaks appear due to the commensuration between the acJosephson frequency of the IJJs and the cavity resonance fre-quency of the antenna structure. Hence, the resonance volt-age and the radiation frequency are uniquely determined bythe geometry of the antenna. The strength of the couplingbetween the field oscillation inside the IJJs and the EMstanding wave in the antenna depends on the position of theIJJ feed. As shown in Figs. 2(a) and 2(b), this couplingbecome stronger when the IJJ feed is located near the edgeregion of the patch.Finally, we show that the radiation characteristics of theabove patch antenna are well described by the equivalentinductance-capacitance-resistance (LCR) circuit model.Figure 4(a) shows a schematic figure of the IJJs shunted bythe LCR circuit that corresponds to the patch antenna struc-ture. In this equivalent circuit, Q2=2Cþ ðL=2ÞðdQ2=dt2Þ isthe electromagnetic energy accumulated in the patchantenna. The radiation power of the antenna is expressed asthe enegy loss RI2 of the circuit. The parameters L, C, and RFIG. 3. (a) The displacement current as afunction of voltage. (b) The frequency spec-trum of the EM wave emitted by the antennaat 1.31mV. An inset shows a snapshot of theoscillating part of Ez at 1.31mV.FIG. 4. (a) A schematic diagram of the equivalentLCR circuit model. (b) I-V and P-V curves (solidcurves) calculated using the LCR circuit model.112602-3 Asai, Tachiki, and Kadowaki Appl. Phys. Lett. 101, 112602 (2012)Downloaded 06 Dec 2012 to 130.158.56.101. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsare the equivalent inductance, capacitance, and radiation re-sistance of the patch antenna, respectively. The time evolu-tion of the charge accumulated on the equivalent capacitor Qis given byLd2Qdt2þ R dQdtþ QC¼XNl¼1h2edPldt: (3)In this circuit model, the external oscillating currentdensity IOS in Eq. (2) is given by dQ/dt.Based on this equivalent circuit model, we numericallyevaluate the radiation power RI2 of the antenna. In Fig. 4(b),we show the I-V and P-V curves (solid curves) which areobtained by solving Eqs. (1), (2), and (3) with L¼ 0.386 nH,C¼ 0.175 fF, R¼ 17.9 X. The open circles indicate the cal-culated values in the above FDTD simulation forLfeed ¼ 68 lm. As seen in Fig. 4(b), the results obtained bythe FDTD simulation are in good agreement with those ofthe LCR circuit model. The above results imply that the radi-ation characteristics of the patch antenna fed by IJJs aredescribed well by the equivalent LCR circuit model, whereinthe sharp peaks in the the P-V curve of the antenna are attrib-uted to the LC resonance.In summary, we proposed a THz patch antenna fed byIJJs, and investigated the radiation characteristics of theantenna. We predicted that the antenna emits sub-milliwattterahertz waves with high radiation efficiency over 20%. Wealso showed that the radiation characteristics of the antennaare well described by the equivalent LCR circuit model.We wish to thank Dr. T. Kashiwagi, Dr. H. Minami, andMr. M. Tsujimoto (University of Tsukuba) for valuable dis-cussions and comments. This work was supported in part byCREST-JST (Japan Science and Technology Agency).1R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. 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Jpn. 80, 094709 (2011).9T. M. Benseman, A. E. Koshelev, K. E. Gray, W.-K. Kwok, U. Welp, K.Kadowaki, M. Tachiki, and T. Yamamoto, Phys. Rev. B 84, 064523(2011).10H. B. Wang, S. Guenon, B. Gross, J. Yuan, Z. G. Jiang, Y. Y. Zhong, M.Gruenzweig, A. Iishi, P. H. Wu, T. Hatano, D. Koelle, and R. Kleiner,Phys. Rev. Lett. 105, 057002 (2010).11S. Lin and X. Hu, Phys. Rev. Lett. 100, 247006 (2008).12X. Hu and S. Lin, Phys. Rev. B 78, 134510 (2008).13L. N. Bulaevskii and A. E. Koshelev, Phys. Rev. Lett. 99, 057002 (2007).14A. E. Koshelev and L. N. Bulaevskii, Phys. Rev. B 77, 014530 (2008).15A. E. Koshelev, Phys. Rev. B 78, 174509 (2008).16T. Koyama, H. Matsumoto, M. Machida, and K. Kadowaki, Phys. Rev. B79, 104522 (2009).17T. Koyama, H. Matsumoto, M. Machida, and Y. Ota, Supercond. Sci.Technol. 24, 085007 (2011).18R. A. Klemm and K. Kadowaki, J. Phys. Condens. Matter 22, 375701(2010).19M. Tachiki, S. Fukuya, and T. Koyama, Phys. Rev. Lett. 102, 127002(2009).20M. Tachiki, K. Ivanovic, K. 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Proposal of terahertz patch antenna fed by intrinsic Josephson junctions

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