IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, …

1 ieee TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 27, NO. 4, JUNE 20171502204 superconductive ultracompact magnetically CoupledResonator With Twin-Spiral StructureAlexander S. Averkin, Alexandre Karpov, Alexander P. Zhuravel, Lyudmila V. Filippenko, Valery P. Koshelets,S. M. Anlage, and Alexey V. UstinovAbstract We describe a practical design of an ultracompacton-chip superconductive microresonator as a potential magneticelement of metamaterial. The achieved resonator size with respectto the wavelength in our experiment is about /14 400. The res-onator consists of two superconducting Nb spirals, sandwichedface to face, with a small gap filled with dielectric. The spiralsare turning in opposite directions: one clockwise, another counter-clockwise. We study the resonator spectral response and its innermodes using numerical simulation in HFSS.

2 In experiment with alaser scanning microscope, we confirm the predictions for the res-onance frequencies of Nb superconductive resonator and its innermodes structures. Small size and the ease of manufacturing makethe two-spiral resonator an attractive solution for superconduc-tive filters, coupling circuits, and as a magnetic component of Terms Metamaterials, superconducting resonators ,microresonators, laser measurements, laser scanning INTRODUCTIONANUMBER of exciting applications of a medium with si-multaneous negative permittivity and permeability wastheoretically described by Veselago in 1968 [1]. About 30 yearslater, a practical example of a material with negative effectivepermeability was demonstrated by Pendryet al.[2]. In or-Manuscript received September 11, 2016; accepted December 22, of publication January 26, 2017; date of current version March 6, work was supported by the Government of Russian Federation throughGoszadanie Research Project Grant The work of A.

3 Kar-pov was supported by the Government of Russian Federation through grant Organisation of research work in Goszadanie. The work of A. S. Averkin wassupported by the Ministry of Education and Science of the Russian Federationin the framework of Increase Competitiveness Program of MISiS. The work ofA. P. Zhuravel was supported by the NASU under Grant program on Nanostruc-tures, Materials, and Technologies.(Corresponding author: Alexandre Karpov.)A. S. Averkin and A. Karpov are with the National University of Scienceand Technology (MISIS), Moscow 119049, Russia (e-mail: P. Zhuravel is with the B. Verkin Institute for Low Temperature Physicsand Engineering, National Academy of Sciences of Ukraine, Kharkov 61103,Ukraine (e-mail: V. Filippenko and V. P. Koshelets are with the Kotel nikov Institute ofRadio Engineering and Electronics, Moscow 125009, Russia M.))

4 Anlage is with the Center for Nanophysics and Advanced Materials,Physics Department, University of Maryland, College Park, MD 20742-4111 USA (e-mail: V. Ustinov is with the Physikalisches Institute, Karlsruhe Institute of Tech-nology, Karlsruhe 76131, Germany, with the National University of Scienceand Technology (MISIS), Moscow 119049, Russia, and also with the RussianQuantum Center, Moscow 143025, Russia (e-mail: versions of one or more of the figures in this paper are available onlineat Object Identifier to create the negative permeability , Pendryet anarray of split ring resonators (SRR). SRRs interacts mainly withthe magnetic component of the electromagnetic (EM) field andgives the possibility to create a medium with effective negative . The first demonstration of a medium with both negative and was done by Smithet al.))

5 In 2000 [3]. They called this arti-ficial media a metamaterial. The metamaterial was constructedof layers of copper SRRs and layers of wires. SRRs have strongcoupling with the magnetic component of the EM field, whilethe wires have a strong coupling with the electric component ofthe EM field, acting as electrical spiral resonator, as compared to an SRR, has equallystrong coupling to magnetic field, but much smaller size com-pared to the resonant wavelength than an SRR, because of thedense placement of turns. Earlier experiments [4], [5] were madewith planar spirals made of thick Cu films ( mm thick in[4] and mm thick in [5]) on dielectric substrates. Such athick coating is required to minimize the Ohmic losses, makingthe design intermediate between 2-D and 3-D. Another approachto reduce the size of the spiral resonator is the introduction of thestructure with two sandwiched spirals, studied recently by Chenet al.

6 [6]. The demonstrated twin-spiral magnetic metamaterialcomponent size is below /1300 [6].A further miniaturization of normal-metal spiral resonatorshas its natural limitation due to the scaling of Ohmic dissipationwith spiral width and thickness [7], [8]. In order to demon-strate a deep sub-wavelength size resonator, it appears promis-ing to utilize ultra-compact superconductive spiral superconducting spiral resonator and one-dimensional planararray of spiral resonators made of Nb film was studied by Kurteret al. [9]. This resonator has a fundamental resonance frequencyof 74 MHz, and its size is as small as this work we achieve a strong reduction of the resonatorsize, using the two superconductive Nb spirals, sandwiched faceto face with a small gap in between. The two spirals of theresonator have a strong capacitive coupling.

7 As a result, thefrequency of the fundamental mode is lowered by more than20 times with respect to a single resonator. The resonator is pro-duced by photolithography. We demonstrate that the resonatordiameter may take only a small fraction of the wavelength size,below 1 TWO-SPIRALMICRO-RESONATORDESIGNWe consider the two planar Archimedean spirals identical inshape, but turning in opposite directions (clockwise and counter-1051-8223 2017 ieee . Personal use is permitted, but republication/redistribution requires ieee for more TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 27, NO. 4, JUNE 2017 Fig. 1. (a) A sketch of the two-spiral resonator. The two planar Archimedeanspirals are superposed with a thin dielectric layer in between. Spirals are identicalin shape and turning in opposite directions: one clockwise, another counter-clockwise.)

8 Both spirals are shaped as a ring, with no central part. The spiral armsoverlaps play a role of interlayer capacitors, when the other sections of the spiralare still highly inductive, as in a free standing spiral. The additional capacitiveloading leads to the reduction of speed of propagation of the signals alongthe spirals. The spirals act as a distributed RF resonator with multiple modes,and the reduction of the phase speed in the structure gives a lower resonancefrequency. The two-spiral structure is made by photo lithography as a three layercircuit. (b) A photo of the two-spiral resonator used in our experiment. At theleft blow-up image the windings of the two spirals are matched (overlapped),forming capacitive elements, at the bottom blow-up image the windings aremismatched because the two spirals are turning in the opposite ), and superposed with a thin dielectric layer inbetween (see Fig.

9 1). The two ring-shaped Archimedean spi-rals (with no central part) are well coupled to the external RFmagnetic field and act as distributed resonant structures. At thevisible intersections of the spiral lines there are areas with over-lap of the spirals with a strong capacitive coupling along thespiral line. The two spirals have a strong RF coupling and havecommon resonant modes. The two-spiral on-chip resonator ismade as a three layer printed circuit in a single Nb processat Si substrate. The two Archimedean spirals have outer di-ameter 3 mm and with inner diameter mm, 40 turns ofNb wire 5 m wide. The spirals are separated with 300 nmSiO2layer and turning in opposite directions (one clockwise,another counter-clockwise). The resulting resonator remains adistributed structure, with multiple modes resonances, where thefirst resonance frequency is much lower than the frequency ofa single spiral resonator.

10 The RF experiments with a two-spiralsuperconductive resonator are presented in the next EXPERIMENTIn experiment we measure the inner modes resonancefrequencies and the RF current distributions for the 4 first innermodes of the resonator. The RF test setup for Nb superconduct-ing resonator is cooled in a cryostat to the temperature of K. The RF characterization of the two-spiral resonator ismade in a circuit similar to Fig. 2. There the resonator is mag-netically coupled to the two RF loop probes. The coupling of thetwo probing loops (S21) depends on the distance between themand is set relatively small, at about 60 to 80 dB. The super-conductive resonator is placed in between the magnetic 2. Experimental RF test setup as simulated numerically in HFSS. Asample of twin-spiral resonator is placed between the two RF loop probes.