Focal-plane field when lighting double-ring phase elements

The focal-plane field amplitude is calculated when lighting double-ring phase elements by flat and Gaussian beams. Emerging conditions in the minimum or maximum centers, including flat-top maxima, are given. For the field amplitude, we obtain equations that define the radius of the first zero-intensity ring based on the deduced expressions. The root values are listed for several parameters of optical elements and incident beams due to the lack of analytical solutions. Numerical simulation results are given for flat incident beams; they are fully consistent with the theoretical calculations.This work was financially supported by the Russian Foundation for Basic Research (grant No. 16-07-00825)

Progressive motion of an ac-driven kink in an annular damped system

A novel dynamical effect is presented: systematic drift of a topological soliton in ac-driven weakly damped systems with periodic boundary conditions. The effect is demonstrated in detail for a long annular Josephson junction. Unlike earlier considered cases of the ac-driven motion of fluxons (kinks), in the present case the long junction is_spatially uniform_. Numerical simulations reveal that progressive motion of the fluxon commences if the amplitude of the ac drive exceeds a threshold value. The direction of the motion is randomly selected by initial conditions, and a strong hysteresis is observed. An analytical approach to the problem is based on consideration of the interaction between plasma waves emitted by the fluxon under the action of the ac drive and the fluxon itself, after the waves complete round trip in the annular junction. The analysis predicts instability of the zero-average-velocity state of the fluxon interacting with its own radiation tails, provided that the drive's amplitude exceeds an explicitly found threshold. The predicted threshold amplitude strongly depends on the phase shift gained by the wave after the round trip. A very similar dependence is found in the simulations, testifying to the relevance of the analytical consideration.Comment: revtex text file and five eps figure files. Physical Review E, in pres

Microwave-induced flow of vortices in long Josephson junctions

We report experimental and numerical study of microwave-induced flow of vortices in long Josephson junctions at zero dc magnetic field. Our intriguing observation is that applying an ac-bias of a small frequency $f \ll f_p$ and sufficiently large amplitude changes the current-voltage characteristics ($I$-$V$ curve) of the junction in a way similar to the effect of dc magnetic field, well known as the flux-flow behavior. The characteristic voltage $V$ of this low voltage branch increases with the power $P$ of microwave radiation as $V_{s}\propto P^{\alpha}$ with the index $\alpha \simeq 0.5$. Experiments using a low-temperature laser scanning microscope unambiguously indicate the motion of Josephson vortices driven by microwaves. Numerical simulations agree with the experimental data and show strongly {\it irregular} vortex motion. We explain our results by exploiting an analogy between the microwave-induced vortex flow in long Josephson junctions and incoherent multi-photon absorption in small Josephson junctions in the presence of large thermal fluctuations. In the case of long Josephson junctions the spatially-temporal chaos in the vortex motion mimics the thermal fluctuations. In accordance with this analogy, a control of the intensity of chaos in a long junction by changing its damping constant leads to a pronounced change in the shape of the $I$-$V$ curve. Our results provide a possible explanation to previously measured but not yet understood microwave-driven properties of intrinsic Josephson junctions in high-temperature superconductors.Comment: 8 pages, 13 figure

Origin of Multikinks in Dispersive Nonlinear Systems

We develop {\em the first analytical theory of multikinks} for strongly {\em dispersive nonlinear systems}, considering the examples of the weakly discrete sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise parabolic potential. We reveal that there are no $2\pi$-kinks for this model, but there exist {\em discrete sets} of $2\pi N$-kinks for all N>1. We also show their bifurcation structure in driven damped systems.Comment: 4 pages 5 figures. To appear in Phys Rev

Erratum: A one-dimensional tunable magnetic metamaterial (Optics Express)

We have detected an error in our data retrieval script which prepares the measured transmission data for the conversion to magnetic permeability. Correcting this error requires modification of Fig. 4(b) and Fig. 5 in the original publication. All methods, calculations and the conclusion in the published paper are still correct

Efficient and robust analysis of complex scattering data under noise in microwave resonators

Superconducting microwave resonators are reliable circuits widely used for detection and as test devices for material research. A reliable determination of their external and internal quality factors is crucial for many modern applications, which either require fast measurements or operate in the single photon regime with small signal to noise ratios. Here, we use the circle fit technique with diameter correction and provide a step by step guide for implementing an algorithm for robust fitting and calibration of complex resonator scattering data in the presence of noise. The speedup and robustness of the analysis are achieved by employing an algebraic rather than an iterative fit technique for the resonance circle

Bunching of fluxons by the Cherenkov radiation in Josephson multilayers

A single magnetic fluxon moving at a high velocity in a Josephson multilayer (e.g., high-temperature superconductor such as BSCCO) can emit electromagnetic waves (Cherenkov radiation), which leads to formation of novel stable dynamic states consisting of several bunched fluxons. We find such bunched states in numerical simulation in the simplest cases of two and three coupled junctions. At a given driving current, several different bunched states are stable and move at velocities that are higher than corresponding single-fluxon velocity. These and some of the more complex higher-order bunched states and transitions between them are investigated in detail.Comment: 6 pages + 6 Figures, to be published in Phys. Rev. B on July 1, 200

Incoherent microwave-induced resistive states of small Josephson junctions

We report an experimental and theoretical study of low-voltage resistive states that are observed in small tunnel Josephson junctions under microwave radiation. The studied features emerge from Shapiro steps on the current-voltage characteristics and appear when both thermal fluctuations and high frequency dissipation are strong. In the absence of microwave radiation Josephson junctions display under these conditions a phase diffusion supercurrent branch characterized by a finite small resistance and hysteretic switching to high voltage range. As the microwave radiation is applied, we experimentally observe three different types of resistive states in the currentvoltage characteristics. First, the phase diffusion branch steadily evolves and its maximum reached voltage Vm increases with the microwave power. Another interesting observed feature is a zero-crossing resistive state characterized by a negative resistance. Finally, we find that a low-voltage resistive state can split in numerous hysteretic fine branches resembling incoherent Shapiro-like steps. The appearance of a particular resistive state depends on an interrelation between the Josephson energy EJ, energy of thermal fluctuations kBT, and the frequency of microwave radiation ω. Our theoretical analysis based on an incoherent multi-photon absorption of a junction biased in the Josephson phase diffusion regime, is in a good accord with experimental observations

Observation of stochastic resonance in percolative Josephson media

Measurements of the electrical response of granular Sn-Ge thin films below the superconducting transition temperature are reported. Addition of an external noise to the magnetic field applied to the sample is found to increase the sample voltage response to a small externally applied ac signal. The gain coefficient for this signal as well as the signal-to-noise ratio displays clear maxima at particular noise levels. We interpret these observations as a stochastic resonance in the percolative Josephson media that occurs close to the percolation threshold

Maximum velocity of a fluxon in a stack of coupled Josephson junctions

Dynamics of a fluxon in a stack of inductively coupled long Josephson junctions is studied analytically and numerically. We demonstrate that the fluxon has a maximum velocity, which does not necessarily coincide with any of the characteristic Josephson plasma wave velocities. The maximum fluxon velocity is found by means of numerical simulations of the quasi-infinite system. Using the variational approximation, we propose a simple analytical formula for the dependence of the fluxon's maximum velocity on the coupling constant and on the distribution of critical currents in different layers. This analysis yields rather precise results in the limit of small dissipation. The simulations also show that nonzero dissipation additionally stabilizes the fluxon.Comment: 8 pages, 5 figures, 1 table. submitted to Phys. Lett. A. Suggestions and criticism are welcom