Miniaturized Superconducting Metamaterials for Radio Frequencies 1,A͒ 1,2 1 2 Cihan Kurter, John Abrahams, and Steven M

APPLIED PHYSICS LETTERS 96,1͑2010͒

1 Miniaturized superconducting metamaterials for radio frequencies 1,a͒ 1,2 1 2 Cihan Kurter, John Abrahams, and Steven M. Anlage 3 1Department of Physics, Center for Nanophysics and Advanced Materials, University of Maryland, 4 College Park, Maryland 20742-4111, USA 5 2Department of Electrical and Computer Engineering, University of Maryland, College Park, 6 Maryland 20742-3285, USA

7 ͑Received 3 April 2010; accepted 2 June 2010; published online xx xx xxxx͒

8 We have developed a low-loss, ultrasmall radio frequency ͑rf͒ metamaterial operating at ϳ76 MHz. 9 This miniaturized medium is made up of planar spiral elements with diameter as small as ϳ␭/658 10 ͑␭ is the free space wavelength͒, fashioned from Nb thin ﬁlms on quartz substrates. The 11 transmission data are examined below and above the superconducting transition temperature of Nb 12 for both, a single spiral and a one dimensional array. The validity of the design is tested through 13 numerical simulations and good agreement is found. We discuss how superconductors enable such 14 a compact design in the rf with high loaded-quality factor ͑in excess of 5000͒, which is in fact 15 impossible to realize with ordinary metals. © 2010 American Institute of Physics. 16 ͓doi:10.1063/1.3456524͔ 17

18 The wavelength of visible light is orders of magnitude line was found to resonate at frequencies as low as 125 MHz. 56 19 larger than the size of the atoms in most dielectric media. However significant and maximum losses were observed at 57 17 20 Therefore, light is not sensitive to the details of the atomic- the resonance of the effective permeability. Magnetically 58 21 scale electromagnetic fields but to coarse-grained properties coupled elements were also realized to not only modify the 59 22 of the structure. Since metamaterials mimic natural materi- propagation of transverse electromagnetic waves but also to 60 18,19 23 als, artificial electromagnetic structures must have elements generate magnetoinductive waves. This sort of radiation 61 9,20 21,22 24 whose dimensions are much smaller than the free space was examined both in planar and bulk geometries to 62 25 wavelength ͑␭͒ at which the metamaterial operates. Up to gain insight about its dispersion and propagation character- 63 26 now, research has focused on metamaterials functioning at istics. 64 27 gigahertz or higher frequencies, since the electrical size of Our design has two key advantages over previous work 65 28 the inclusion of such a medium can be kept reasonably making the element size especially compact: a truly planar 66 1–5 29 small. Many metamaterials are based on split ring resona- spiral geometry and superconducting thin films. The spiral 67 30 tors ͑SRRs͒ and their variations to create subwavelength design utilizes the LC analogy just like SRRs. If a single 68 31 magnetically active features. The SRR geometry is typically spiral element is unwound, the length of the entire winding 69 32 composed of two concentric rings, each with a capacitive would be ϳ0.6 m which is comparable to the wavelength. 70 33 split, and can be understood in terms of the inductor- Keeping the strip width small ͑10 ␮m͒ enables many turns 71 34 capacitor ͑LC͒ analogy. However this design calls for com- in a spiral with a small outer diameter, which increases the 72 35 paratively large dimensions for radio frequency ͑rf͒ metama- total inductance as well as capacitance thus decreasing the 73 36 terials, since the wavelength is on the order of meters. fundamental resonance frequency, f0. Moreover, due to the 74 37 Although there are few studies available on rf metama- superconductivity, there is a significant contribution of ki- 75 ͑ ͒ 23 38 terials, they have great potential in applications such as magnetic inductance Lk to the total inductance. Lk is a mea- 76 39 netic resonance imaging ͑MRI͒ devices for noninvasive and sure of kinetic energy of charge carriers in a current carrying 77 6,7 40 high resolution medical imaging. They may also improve material and is intimately related to the superfluid density 78 41 rf antenna efficiency and directivity as well as reduce their dependence on temperature in superconductors. Lk could also 79 8 9 42 size. Microwave delay lines, magnetoinductive lenses for be modified through application of large rf magnetic fields or 80 10 11 24 43 near field imaging, rf filters, and compact resonators may dc magnetic field, as long as the sample remains in the 81 44 also be enabled by rf metamaterials. Meissner state. This kind of inductance is negligibly small in 82 45 The first practical demonstration of those metamaterials normal metals at any temperature and frequency in the rf 83 6,12,13 46 was implemented by Wiltshire et al. using a Swiss roll band. 84 14 ͑ ͒ 47 geometry as suggested earlier by Pendry. An array of the The geometrical inductance Lg of a spiral with N 85 48 rolls made of Cu/Kapton layers wounded around a dielectric turns, outer diameter of Do and inner diameter of Di can 86 25 ͑␮ 2 ͒/ ͓ ͑ / ͒ 2͔ 49 mandrel was used in an MRI machine for guiding rf flux be approximated as: Lg = 0N Davg 2 ln 2.46 a +0.2a 87 50 caused by magnetic resonance to the receiver coil in the where D =͑D −D ͒/2 and a=͑D −D ͒/͑D +D ͒. The dis- 88 6,15 avg o i o i o i 51 system. Though the design had some disadvantages, such tributed capacitance of planar spirals is given in Ref. 26 as 89 52 as being lossy, three-dimensional, and nonuniform, it was C͑pF͒=0.035D ͑mm͒+0.06. As seen here, both L and C 90 16 o g 53 well-suited for such applications. A planar version of the ͑ ͒ increase with Do thus reducing the resonant frequency , 91 54 Swiss roll geometry fabricated with a thick copper film on a however there is also a need to minimize the size of each 92 55 dielectric substrate and excited by a microstrip transmission Ӷ ͑ element. For temperatures T Tc Tc is the superconducting 93 transition temperature͒, the resonance frequency can be esti- 94 a͒ /͑ ␲ͱ ͒ Electronic mail: [email protected]. mated by ignoring Lk as f =1 2 LgC . However at tem- 95

FIG. 1. ͑Color online͒͑a͒ SEM image of a single Nb ␮ spiral with Do =6 mm, N=40, w=s=10 mona quartz substrate and ͑b͒ the SEM image of right part of the spiral marked by yellow in ͑a͒ showing the windings.

96 123 peratures close to Tc, Lk should be added to Lg to get a tive force and current. The magnetic field generated through 97 precise value for the resonance frequency. the spiral due to the circulating current couples to the bottom 124 98 Fabrication of our rf metamaterials begins with deposi- loop in the same way. The inset of Fig. 2 is a simulation 125 99 tion of a 200 nm Nb thin film on a 350 ␮m thick quartz showing the magnetic flux lines in the sample-probe configu- 126 100 wafer, 3Љ in diameter, using the rf sputtering technique. Su- ration done by high frequency structure simulator ͑HFSS͒. 127 101 perconductivity of the Nb thin films is tested by resistivity The experiments have been conducted in an evacuated probe 128 ϳ 102 measurements which give a Tc of 9.24 K. Photolithogra- inside a cryogenic dewar and the temperature has been pre- 129 103 phy is applied to pattern the film surface into the shape of cisely adjusted by a Lakeshore 340 Temperature Controller. 130 ␮ 104 spirals having 40 turns of w=10 m wide wires with s The transmission data ͉S ͉ on an element of our rf 131 ␮ 21 105 =10 m spacing. The chemically reactive plasma generated metamaterial, a single spiral with D =6 mm, N=40 turns 132 / ͑ ͒ o 106 by a mixture of CF4 O2 10% O2 etches the film down to and w=s=10 ␮m, are shown in the main panel of Fig. 2 133 107 the quartz to give a final shape to the spiral resonators. The ͑ ͒ while Nb is both in the superconducting below Tc and nor- 134 108 quartz is diced into chips having single spirals or arrays. In mal state ͑above T ͒. Below T , f appears at ϳ76 MHz 135 ͑ ͒ ͑ ͒ c c 0 109 Fig. 1 a , a scanning electron microscopy SEM image of a followed by harmonics, whereas the normal state does not 136 110 representative single spiral with Do =6 mm is shown, while show any resonant features. The inset of Fig. 3 shows an 137 ͑ ͒ 111 Fig. 1 b shows the details of the same spiral. HFSS simulation of current density ͑J͒ distribution in the 138 112 For measurement of the rf properties, the quartz sub- spiral for n=1 ͑fundamental mode͒ and n=2 ͑second har- 139 113 strate with Nb spiral is sandwiched between two magnetic monic͒. The red areas indicate where the current is strong, 140 114 loops connected to an Agilent E5062A rf network analyzer. whereas green corresponds to small values of J. As seen 141 115 The magnetic loops ϳ6 mm in diameter are made by bend- from the simulations, for n=1 there is a robust current dis- 142 116 ing the stripped inner conductors and soldering them to the tribution flowing through the middle windings, which gets 143 117 outer parts of the coax cables. The rf excitation is provided to weaker around the edges of the spiral. However for n=2, 144 118 the spiral resonator by the top loop. The transmission is there are two counter-propagating current distributions and a 145 119 picked up by the bottom loop and sent to the rf network large degree of cancellation. The main panel of Fig. 3 shows 146 120 analyzer. The alternating current flowing along the top loop the calculated mutual inductance M between the resonating 147 121 creates a time varying magnetic field which couples to the 122 spiral via a mutual inductance M and induces an electromo- 0.025 J @ fundamental mode J@2nd harmonic 0

-10 0.020 H) n -20 ( 0.015 ) -30 dB ( | -40 uctance 21 d 0.010 n=1

S n=2

max n |

-50 lI H 0.005 -60 utua

data @ T~4.1 K min M -70 data @ T~127 K 0.000 -80 HFSS simulation

200 400 600 800 1000 -0.005 f (MHz) 0123456789101112 Mode Number ͑ ͒ ͉ ͉ AQ: FIG. 2. Color online Transmission S21 vs frequency for a single Nb spiral ͑ ͒ #1 with Do =6 mm measured between two rf magnetic loops at temperatures FIG. 3. Color online Calculation of mutual inductance M between a single ͑ ͒ ͑ ͒ ␮ below the solid bright red curve and well above the solid blue curve the spiral with Do =6 mm, N=40, w=s=10 m and a magnetic loop with di- Tc of Nb. The dashed dark red curve is a numerical calculation done by ameter 6 mm as a function of standing wave mode number in the spiral. The HFSS. The inset shows the sample-loop conﬁguration during transmission planes of the loop and the spiral are parallel and 3.25 mm apart. The inset measurements as well as the distribution of the magnetic ﬂux lines simulated shows HFSS simulations of distributed J in the spiral at the fundamental by HFSS. mode and second harmonic. 1-3 Kurter, Abrahams, and Anlage Appl. Phys. Lett. 96,1͑2010͒

12 183 -40 2 interaction between far neighbors as well, which may 3 5 T= 4.4 K modify the shapes of the resonance curves. 184 185 Nb spiral 4 T= 87 K We have demonstrated electrically small rf metamaterials with magnetically active elements as small as ϳ␭/658, 186 -50 yet retaining a high loaded Qϳ5000. These superconducting 187 quartz metamaterials have many advantages over their normal metal 188 substrate 7 peaks below T c counterparts, such as minimizing the Ohmic losses, compact 189

| (dB) -60 structure, and sensitive tuning of resonant features via tem- 190 21 1 |S perature and magnetic field. Moreover, the design promises 191 192 6 further reduction in resonant frequency down to 10 MHz -70 7 with a modified geometry ͑with thinner windings͒ and en- 193 hanced Lk as well as Josephson and vortex inductances. 194 No peak above T c -80 This project has been supported by the U.S. Office of 195 Naval Research through Grant No. N000140811058 and the 196 Center for Nanophysics and Advanced Materials at the Uni- 197 72 73 74 75 76 77 78 79 80 81 versity of Maryland. We would like to thank Brian Straughn, 198 f (MHz) John Hummel, and Jonathan Hood for their assistance. 199

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