Unconventional rf photoresponse from a superconducting spiral resonator

Superconducting thin film resonators employing strip geometries show great promise in rf/microwave applications due to their low loss and compact nature. However, their functionality is limited by nonlinear effects at elevated rf/microwave powers. Here, we show that by using a planar spiral geometry carrying parallel currents in adjacent turns, this limitation can be minimized. We investigate the rf current distributions in spiral resonators implemented with Nb thin films via laser scanning microscopy. The rf current density profile along the width of the individual turns of the resonators reveals an unconventional trend: maximum current in the middle of the structure and decaying toward its edges. This unusual behavior is associated with the circular nature of the geometry and the cancellation of magnetic field between the turns, which is favorable for handling high powers since it allows the linear characteristics to persist at high rf current densities.

Figure 1

Schematic sketch of a coplanar wave guide (a) and a spiral resonator (b). The rf currents flow as shown with the red arrows when the resonators are excited.

Figure 2

Simplified schematic representation of the LSM setup used for 2D visualization of microwave photoresponse of the tested resonator structure. Drawing is not to scale.

Figure 3

(a) 2D LSM image showing current distributions in a Nb spiral with an outer diameter of 6 mm and 40 turns, at the fundamental resonant mode of 74 MHz, $T_B=4.5$ K, $P_{\mathrm{rf}}=14.8$ dBm. (b) 2D LSM reflectivity image showing the individual turns within an area on the spiral marked with a green box in (a). (c) The power-dependent ${\mathrm{PR}}_R$ along the cross section of the spiral shown with $\mathit{S}$ line; maximum at the center, minimum at the edges. The dots are the estimated $J_{\mathrm{rf}}^2$ profile for a simple standing wave current pattern at each $P_{\mathrm{rf}}$.

Figure 4

(a) 3D LSM image showing the power dependence of ${\mathrm{PR}}_{\mathrm{IL}}$ over the $S$-line scan shown in Fig. 3a. (b) Experimental LSM PR vs $P_{\mathrm{rf}}$ on a linear scale, taken at three neighboring strips (strip B is located at the center of the $S$-line scan between strip A and strip C). Both data are obtained at a temperature well below $T_c$, 4.5 K.

Figure 5

2D LSM (a) ${\mathrm{PR}}_{\mathrm{IL}}$ and (b) reflectivity images taken from $40\times 40\mu {\text{m}}^2$ area on the Nb spiral resonator at a laser power of about 1 $\mu \text{W}$. (c) 2D LSM ${\mathrm{PR}}_{\mathrm{IL}}$ image at 10 $\mu \text{W}$. Inset shows rf power dependence of LSM ${\mathrm{PR}}_{\mathrm{IL}}$ on the same area, showing the $J_{\mathrm{rf}}$ profiles at low and high rf stimulus. The $x$-line cut is at the same location in the figure and inset. (d) LSM PR coming from two neighboring Nb turns at two different laser powers; 1 $\mu \text{W}$ and 10 $\mu \text{W}$. The data are taken at $P_{\mathrm{rf}}=7$ dBm.

Figure 6

Power dependence of dissipative LSM ${\mathrm{PR}}_{\mathrm{IL}}$ profiles showing the broadening of the critical state along the same 40 $\mu$m line $x$ scan through the width of two Nb turns at a laser power of about 1 $\mu \text{W}$.

Figure 7

Large-scale $7\times 7{\text{mm}}^2$ LSM PR images showing rf current induced dissipation in a Nb spiral at 4.5 K, 10 dBm and at (a) the second harmonic (219 MHz), (b) the third harmonic (355 MHz), and (c) the forth harmonic (498 MHz). The area marked A in (b) indicates the position of a detailed 2D image (d) that shows the same rf dissipation in a $125\times 125\mu {\text{m}}^2$ region localized at the center of the $3\lambda /2$ standing wave pattern. (e) LSM PR profile along a 125-$\mu$m $x$ scan corresponding to the bottom line-scan in (d).