We performed the spectral measurements of a niobium based Josephson junction array in order to estimate the linewidth of Josephson emission. The array is formed by 9996 serially connected Nb/NbSi/Nb Josephson junctions occupying the area of 5 × 7 mm 2 on a silicon substrate and divided into 7 distinct subarrays. The array was immersed in a liquid helium dewar from where the emission was brought to open space via an oversize waveguide. Firstly, the measurements on a Fourier-transform spectrometer were carried out in a wide frequency range 139–343 GHz at almost all self-induced steps of current-voltage curve. As in our previous work, the observed linewidth of Josephson emission corresponded to the resolution of the spectrometer. Then, we carried out more precise and sensitive measurements using the 211–275 GHz heterodyne receiver based on a Nb/AlO x /Nb mixer with a spectral resolution better than 0.1 MHz. Dependencies of the linewidth on the step number and on the number of connected subarrays are studied. The peaks corresponding to the 2nd harmonic of the Josephson generation are also observed in the spectra. The linewidth of the main harmonic down to 1.5 MHz was observed in these measurements.

We analyze experimentally and theoretically mutual phase locking and electromagnetic interaction between two linear arrays with a large number of Josephson junctions. Arrays with different separation, either on the same chip or on two separate substrates are studied. We observe a large coherent gain, up to a factor of three, of emitted power from two simultaneously biased arrays, compared to the sum of powers from two individually biased arrays. The phenomenon is attributed to the phase locking of junctions in different arrays via a common electromagnetic field. Remarkably, the gain can exceed the factor of two expected for a simple constructive interference of two oscillators. The larger gain is explained by an additional consequence of mutual interaction between two large arrays. Mutual phase locking of large arrays does not only result in constructive interference outside the arrays, but also improved synchronization of junctions inside each array. Our conclusion is supported by numerical modelling.

The dynamics of large superwavelength open systems which are free-standing multi-wire lines with a large number of Josephson junctions, DC bias batteries and other lumped elements is analyzed using direct numerical simulation. Such systems represent the simplest version of the active Josephson antennas proposed in our earlier studies and show promise as terahertz and subterahertz radiation sources. We have studied dependences of the radiation characteristics on the antenna geometry, number of junctions, DC bias current and the lumped elements position and parameters. Detailed simulation results reveal a multitude of phase transitions between the dynamical states, which differ in the number of Josephson junctions synchronized by the excited waves of current and, hence, in the radiation power emitted into open space also as in radiation patterns. It is shown that, in the absence of noise, the Josephson antennas can emit completely coherent radiation.

The paper presents the experimental and theoretical studies of diffraction effects in intense acoustic beams diffracted by a narrow circular aperture in a screen. The characteristic acoustic pressure achieved in the experiment at the emitter aperture is 1 MPa. The operating frequency of the emitter is 2 MHz. Acoustic signals in the experiments were detected in the frequency range up to 100 MHz. Special attention in the experiments was paid to the case of passage of a nonlinear wave beam through a aperture with a diameter significantly smaller than the characteristic beam width. Theoretical studies in the paper are based on numerical simulation using the Khokhlov–Zabolotskaya–Kuznetsov equation. It is shown that the propagation of intense acoustic beams diffracted by a narrow circular aperture in the screen is accompanied by degeneration of a sawtooth wave into a sequence of short pulses. The high-frequency components of the spectrum predominate in the wave that passed through the aperture owing to spatial filtering, which leads to a change in the law of decay of the harmonics in the spectrum. The dependence of the law of decay of the harmonics in the spectrum of a sawtooth wave passing through a aperture in the screen on the ratio of the aperture diameter and characteristic width of an incident intense acoustic beam is investigated.

We performed spectral measurements of two low-temperature discrete Josephson junction (JJ) arrays on a Fourier-transform spectrometer. The arrays contain up to 9000 niobium based junctions located in the area 5 × 5 mm and composed of different designs. The spectrum of each array demonstrates a narrow peak in the frequency range near 140 GHz with the line width 160-170 MHz corresponding to the resolution limit of the spectrometer. It implies the coherent subterahertz radiation from niobium JJ arrays that is necessary for most applications where the JJ array based on similar technology would be implemented. The radiation coherence follows from numerical simulation of Josephson antennas with the self-made algorithm combining the Finite-Difference Time Domain Method with the Resistively and Capacitively Shunted Junction (RCSJ) model. Exploring the spectrum of Beverage-like Josephson antenna simulated by this algorithm we revealed the pure monochromatic emission of all junctions.

Phase-locking of oscillators leads to superradiant amplification of the emission power. This is particularly important for development of THz sources, which suffer from low emission efficacy. In this work we study large Josephson junction arrays containing several thousands of Nb-based junctions. Using low-temperature scanning laser microscopy we observe that at certain bias conditions two-dimensional standing-wave patterns are formed, manifesting global synchronization of the arrays. Analysis of standing waves indicates that they are formed by surface plasmon type electromagnetic waves propagating at the electrode/substrate interface. Thus we demonstrate that surface waves provide an effective mechanism for long-range coupling and phase-locking of large junction arrays.

In laboratory conditions, the vertical structure of short mode pulses was studied near the critical thicknesses of hydroacoustic waveguides of constant and variable depth with different bottom models.

The dynamics of large, significantly exceeding the wavelength open systems such as free-standing multi-wire lines with a large number of built-in Josephson junctions is analyzed using direct numerical simulation. Such systems represent the simplest version of the Josephson active antennas proposed in our earlier studies and show promise as generators of terahertz and subterahertz radiation. Detailed simulation results reveal a multitude of phase transitions between the dynamical states, which differ in the number of Josephson junctions synchronized by the excited current waves and, hence, in the intensity of radiation emitted into open space and radiation patterns.

В лабораторных условиях проведено исследование вертикальной структуры коротких модовых импульсов вблизи критических толщин гидроакустических волноводов постоянной и переменной глубины с различными моделями дна.

The temperature dependence of the linear electrodynamic response of thin-film superconductor (MoN)–normal metal (Al) hybrid structures with a high conductivity ratio in the normal state has been theoretically and experimentally investigated. Low-frequency measurements of the coefficient of mutual induction of two coils with a sample placed between them indicate an increase in the magnetic screening of the superconductor–normal metal (SN) structures with an increase in the Al layer thickness dAl near liquid-helium temperatures. Measurements of the frequency shift δf of a microwave dielectric resonator, brought into contact with the sample, as a function of temperature and dAl showed that (i) the character of the dependence δf(T) depends strongly on dAl and (ii) the resonance frequency shift of SN structures at temperatures close to the critical temperature Tc is not described by dependence const/(1 – T/Tc), which is typical of thin superconducting films. Numerical calculations performed within the Usadel model well describe the observed effects. Thus, these anomalies of the electrodynamic properties of SN structures can be explained by the presence of a minigap in the spectrum of quasiparticles due to the proximity effect in a normal-metal layer, which depends on dAl, and by the high conductivity of the Al layer.

Temperature dependence of linear electrodynamic response of thin-film hybrid structures superconductor (MoN) — normal metal (Al) with large ratio of normal-state conductivities was studied theoretically and experimentally. Low-frequency measurements of the mutual inductance of two coils with a sample placed between them indicated an increase in magnetic screening ability of the superconductor – normal metal (SN) hybrid structures at liquid helium temperatures as $d_Al$ increases, where $d_Al$ is the thickness of the Al layer. Measurements of the frequency shift $\delta f$ of the microwave dielectric resonator, which was in contact with the SN samples as a function of temperature and $d_Al$ demonstrated that (i) type of the $\delta f(T)$ dependence depends significantly on $d_Al$ and (ii) the shift of resonant frequency of the SN structures at temperatures close to the critical temperature Tc cannot be approximated by a functional dependence $const/(1–T/T_c)$, which is typical for thin superconducting films. Numerical calculations performed within the Usadel model describe the observed effects quite well. Thus, the mentioned anomalies of the electrodynamic properties of the SN hybrid structures can be explained by an appearance of a mini-gap in the spectrum of quasi-particle excitation caused by the proximity effect in the normal metal layer, which depends on $d_Al$ as well as by the high conductivity of the Al layer.

We have numerically investigated a series array of electromagnetically coupled Josephson junctions considering the coupling delay. In the general case of a nonzero delay, we have derived equations for the slow and fast phases in the low-frequency approximation. We have studied the regimes of oscillations of a Josephson junction array for different positions of the bias point on the current–voltage characteristics (including its reverse branch). Similar analysis has been performed for systems of equations without coupling delay and for an arbitrary bias current. Several regimes of steady-state oscillations have been detected, i.e. synchronous oscillations, traveling wave regime, regime of partial switching-off of junctions, and chimera states.

We performed the numerical investigation of the one-dimensional series Josephson junction array with electromagnetic coupling and taking into account the delay. In general case of nonzero delay the equations for fast and slow phases have been obtained in the high-frequency (HF) approximation. The regimes of oscillations of the junction array have been studied at the different position on the current-voltage characteristic (IVC), including on its reverse branch. The same investigation has been performed for the systems of equations without delay of interaction and for the arbitrary bias current. Several stationary regimes of oscillations have been observed: synchronous oscillations, regime of traveling wave, regime of partial transition of junctions to the superconducting state and also chimera states.

Mutual synchronization of many Josephson junctions is required for superradiant enhancement of the emission power. However, the larger the junction array is, the more difficult is the synchronization, especially when the array size becomes much larger than the emitted wavelength. Here, we study experimentally Josephson emission from such larger-than-the-wavelength Nb/NbSi/Nb junction arrays. For one of the arrays we observe a clear superradiant enhancement of emission above a threshold number of active junctions. The arrays exhibit strong geometrical resonances, seen as steps in current-voltage characteristics. However, radiation patterns of the arrays have forward-backward asymmetry, which is inconsistent with the solely geometrical resonance (standing-wave) mechanism of synchronization. We argue that the asymmetry provides evidence for an alternative mechanism of synchronization mediated by unidirectional traveling-wave propagation along the array (such as a surface plasmon). In this case, emission occurs predominantly in the direction of propagation of the traveling wave. Our conclusions are supported by numerical modeling of Josephson traveling-wave antenna. We argue that such a nonresonant mechanism of synchronization opens a possibility for phase locking of very large arrays of oscillators.

A terahertz superconducting oscillators based on large amount of Josephson junction embedded in open system guiding traveling electromagnetic wave is theoretically considered and computer simulated. It is shown that such active Josephson antennae represent oscillator effectively radiated into open space with power scaled with the system size and number of junctions. Dynamics and directivity patterns of such Josephson antennae depending on bias current is investigated and it is shown that such oscillator with sufficiently large junction amount can be competitive with quantum cascade lasers.

We consider propagation of intense acoustic beams having a noise temporal structure at the initial aperture. The evolution of the probability distribution and the wave spectrum at a discontinuous stage of propagation is studied experimentally when the field on the radiator axis represents a sequence of discontinuities with universal behavior between them. It has been shown, both theoretically and experimentally, that in this case the field spectrum retains its shape determined by the probability distribution of the frequency of the initial wave.

The algorithms developed for reconstructing the geoacoustic parameters of the bottom layers during their coherent sounding are experimentally verified under laboratory conditions. The algorithms use the parametric models of forming the signals reflected from the layered half-space. To solve the problem, an experimental setup for measuring the parameters of the sounding acoustic pulses reflected from a set of elastic layers placed in a water tank is developed at the Acoustics Division of N. I. Lobachevsky State University of Nizhny Novgorod. The devices for forming, radiating, and receiving the acoustic pulses reflected from the layered system are developed. The structure of reverberation interference in the measuring tank is studied. The parameters of the layered-bottom model are experimentally estimated for the optimized parameters of the sounding signals.

We consider degenerate parametric interaction in intense acoustic beams. It is shown that the field at large times has universal structure which is determined only by the wave period. At the same time, the distance in which this universal waveform is formed strongly depends on the fine structure of the initial field. The main part of this work is devoted to an experimental study of degenerate interaction in the intense acoustic beams. The employed experimental tools allow one to change the phase relationships among the radiated signals and study the processes of formation of the universal signal waveform at large distances, depending on the initial conditions.