Final Report Summary - THZ RADIATION (Controlling terahertz radiation using layered superconductors)
Terahertz (THz) science has attracted a lot of interest in recent years due to many important applications of THz technology in physics, astronomy, chemistry, biology, and medicine, including THz imaging, spectroscopy, tomography, medical diagnosis, health monitoring, environmental control, as well as chemical and biological identification. Despite of a variety of proposed and even realized optical and semiconducting THz devices, there is still lack of a concept for well-integrated and well-controllable THz devices. In this respect, superconducting devices employing Josephson effect are considered as an opportunity for a single chip multifunctional THz devices, where an unprecedented level of controllability can be achieved by tuning the external electric and magnetic fields. Despite the number of experimental and theoretical works, detailed mechanisms of emission and propagation of THz electromagnetic waves in layered superconductors are poorly understood. Therefore, the main purpose of this research project was to get fundamental understanding of basic and advanced mechanisms that are potentially useful for controlling THz radiation in layered superconductors with the following core objectives: 1) to produce coherent emission and super-radiance by driven vortex lattice; 2) to generate THz radiation using cavity resonance with zero magnetic field; 3) to perform effective filtering of THz radiation; 4) to explore the analogy between nonlinear optics and nonlinear Josephson plasma waves; and 5) to propose superconducting THz meta-materials. To achieve these objectives, the fellow has conducted extensive scientific research, which is summarized below (see the attached document for more detailed scientific report):
1. The dynamical stabilization of a square Josephson vortex (fluxon) lattice by applying both ac and dc driving currents. In Josephson systems, the inductive interlayer coupling promotes the formation of the triangular vortex lattice. However, to generate noticeable radiation, oscillations induced by the moving lattice have to be in phase in the different layers, which is realized only when the moving vortices form a rectangular lattice. Using advanced computer simulations, the fellow has shown that such “super-radiant” flux-flow state can be achieved by adding a small time-periodic ac component to constant biasing dc current. Coherent motion of fluxons is observed for a broad frequency range of the applied drive with maximum output signal at the characteristic frequency of the system determined by the crossing of fluxons across the sample. These findings can be of practical interest for applications of Josephson coupled layered superconductors as THz radiation sources, especially in synchronizing Josephson oscillations in all junctions in order to realize significant radiation.
Stabilization of a moving square Josephson vortex lattice due to interaction with spatial periodic modulations. The formation of the “super-radiant” flux-flow state can occur due to competition between vortex-vortex repulsion favouring a triangular vortex lattice and periodic potential stabilizing a square vortex lattice. The fellow has considered artificial stacks of superconducting–normal–superconducting (SNS) Josephson junctions in the presence of a square/rectangular array of pinning centres (holes). Computer simulations revealed that in the absence of the pinning, the rectangular lattice of moving fluxons is observed only at larger currents, whereas at small current values fluxons in different junctions move out of phase forming a periodic triangular lattice. The stability range of this super-radiant state becomes considerably larger in the presence of ordered pinning. Detailed studies have been conducted to understand the effect of density and strength of the pinning centres on the stability of the rectangular fluxon lattice. Predicted synchronized motion of fluxons in the presence of ordered pinning can be detected experimentally using the rf response of the system, where enhancement of the Shapiro-like steps is expected due to the synchronization. This research is potentially useful for design powerful superconducting THz generators.
Effect of magnetic pinning centres on the dynamics of fluxons is very different than the effect of non-magnetic pinning centres. To reveal the effect of such magnetic inclusions, the fellow has considered artificial stacks of SNS Josephson junctions under external dc and ac current in the presence of ordered out-of-plane magnetic dots. It was found that at larger dc current biasing, the triangular arrangement of moving fluxons transits to a rectangular lattice. Such a “super-radiant” flux-flow state is found to be stable in a wide region of applied dc current and reproduces commensurability features in the current-voltage characteristics of the system. Extra features appear on the response of the system to the applied current for larger magnetization of the dots due to the formation of vortex-antivortex pairs under the magnetic dots. However, such vortex-antivortex pairs results in the significant disorder in the dynamics of the fluxons and, consequently, their synchronization becomes difficult. Synchronized motion of the fluxons becomes more pronounced by adding a small ac component to the biasing dc current for a broad frequency range of the applied ac drive. The conclusion of this study was that it is more difficult to control the dynamics of the fluxons in Josephson systems using magnetic pinning centres as compared to the case of non-magnetic pinning. However, the chaotic dynamic of Josephson vortices is potentially useful for THz emitters with broad spectrum.
2. The effect of initial and boundary conditions on the dynamics of Josephson vortices. The research started with considering the effect of a nonrectangular cross section of an artificial stack of SNS Josephson junctions on the dynamics of fluxons under time-periodic ac and constant dc biasing currents. It was found that very small deviations of the sidewalls of the system from its vertical position strongly affect the collective behaviour of the junctions, resulting in a transition from coherent motion of fluxons to less ordered dynamics of fluxons. No phase synchronization is observed for larger asymmetry in the distribution of junction cross sections, where the dynamic state is characterized by a chaotic motion of fluxons. The fellow also searched for the other kinds of boundary conditions, which can be used to generate tuneable electromagnetic radiation from Josephson junction systems. Using advanced three-dimensional simulations, he showed that an Abrikosov vortex, trapped inside a cavity perpendicular to an artificial Josephson junction, can serve as a very efficient source for generation of Josephson vortex-antivortex pairs in the presence of the applied electric current. In such a case, the nucleation rate of the pairs can be tuned in a broad range by an out-of-plane ac magnetic field in a broad range of frequencies. Reported tuneability of the Josephson oscillations can be useful for developing high-frequency emission devices which frequency and power can be tuneable in a very wide range.
The contribution of both in-plane and out-of-plane currents to the hot spot formation due to nonuniformity of current flow. Non-uniform current distribution has a pronounced effect on the physical processes taking place in Josephson junction system. Such current flow can be created by, e.g. nonuniform boundaries, non-magnetic and magnetic inclusions, or short junctions connecting the superconducting layers (i.e. pillars). The fellow has shown that such nonuniform distribution of the current can result in very interesting phenomena, which have not been reported so far in Josephson systems. For example, he found a new kind of vortex matter in superconductors - the Josephson vortex loops - formed and stabilized in planar junctions or layered superconductors as a result of nontrivial cutting and recombination of Josephson vortices. Engineering latter barriers opens broad perspectives on loop manipulation and control of other possible knotted/linked/entangled vortex topologies in nanostructured superconductors. In the context of Josephson devices proposed to date, the high-frequency excitations of the Josephson loops can be utilized in future design of powerful emitters, tunable filters and waveguides of high-frequency electromagnetic radiation, thereby pushing forward the much needed Terahertz technology.
3. Scattering of THz waves on moving (or oscillating) lattices of Josephson vortices. The fellow has found that the Abrikosov vortices have significant effect of the dynamics of the fluxons, consequently on the properties of electromagnetic radiation due to the moving fluxons. For example, the analysis revealed controllability of the frequency of Josephson oscillations with over 80% by changing just the magnetic field, whereas the maximum 40% tunability has been achieved to date (by changing bias current and bath temperature). These findings can have important implications for the design of tunable high-frequency electromagnetic radiation sources.
4. To explore the analogy between nonlinear optics and nonlinear Josephson plasma waves. Using the computer simulations the fellow has shown that an Abrikosov vortex, trapped inside a cavity perpendicular to an artificial Josephson junction, can serve as an efficient source for generation of Josephson vortex-antivortex pairs. Such essentially nonlinear parametrically amplified vortex-antivortex nucleation can be considered as a macroscopic analog of the dynamic Casimir effect in optical systems, where fluxon pairs mimic the photons and the ac magnetic field plays the role of the oscillating mirrors. The emerging vortex pairs in our system can be detected by the pronounced features in the measured voltage characteristics, or through the emitted electromagnetic radiation, and exhibit resonant dynamics with respect to the frequency of the applied magnetic field.
5. THz meta-materials in layered superconductors. One of the main objectives of the current project proposal was to propose new superconducting meta-materials, which could give possibility of controlling the propagation of THz radiation in superconducting systems. Our preliminary simulation results show that once created in Josephson junctions, superconducting vortex loops interact very differently with the propagating THz radiation. There is a possibility of creating superconducting meta-materials from the Josephson junctions with ordered arrays of vortex loops, which can allow tuning nonlinear electromagnetic transparency of Josephson junction stacks and designing nonlinear THz filters. The fellow has shown that the Josephson vortex loops can be formed and stabilized in planar junctions or layered superconductors as a result of nontrivial cutting and recombination of Josephson vortices around the barriers for their motion. Engineering latter barriers opens broad perspectives on loop manipulation and control of other possible knotted/linked/entangled vortex topologies in nanostructured superconductors. Currently we are working on a theory to describe the propagation of THz radiation in superconducting meta-materials consisting of Josephson vortex loops.
PS: the extended final report and submitted (but not yet published) articles are in the attached file.
1. The dynamical stabilization of a square Josephson vortex (fluxon) lattice by applying both ac and dc driving currents. In Josephson systems, the inductive interlayer coupling promotes the formation of the triangular vortex lattice. However, to generate noticeable radiation, oscillations induced by the moving lattice have to be in phase in the different layers, which is realized only when the moving vortices form a rectangular lattice. Using advanced computer simulations, the fellow has shown that such “super-radiant” flux-flow state can be achieved by adding a small time-periodic ac component to constant biasing dc current. Coherent motion of fluxons is observed for a broad frequency range of the applied drive with maximum output signal at the characteristic frequency of the system determined by the crossing of fluxons across the sample. These findings can be of practical interest for applications of Josephson coupled layered superconductors as THz radiation sources, especially in synchronizing Josephson oscillations in all junctions in order to realize significant radiation.
Stabilization of a moving square Josephson vortex lattice due to interaction with spatial periodic modulations. The formation of the “super-radiant” flux-flow state can occur due to competition between vortex-vortex repulsion favouring a triangular vortex lattice and periodic potential stabilizing a square vortex lattice. The fellow has considered artificial stacks of superconducting–normal–superconducting (SNS) Josephson junctions in the presence of a square/rectangular array of pinning centres (holes). Computer simulations revealed that in the absence of the pinning, the rectangular lattice of moving fluxons is observed only at larger currents, whereas at small current values fluxons in different junctions move out of phase forming a periodic triangular lattice. The stability range of this super-radiant state becomes considerably larger in the presence of ordered pinning. Detailed studies have been conducted to understand the effect of density and strength of the pinning centres on the stability of the rectangular fluxon lattice. Predicted synchronized motion of fluxons in the presence of ordered pinning can be detected experimentally using the rf response of the system, where enhancement of the Shapiro-like steps is expected due to the synchronization. This research is potentially useful for design powerful superconducting THz generators.
Effect of magnetic pinning centres on the dynamics of fluxons is very different than the effect of non-magnetic pinning centres. To reveal the effect of such magnetic inclusions, the fellow has considered artificial stacks of SNS Josephson junctions under external dc and ac current in the presence of ordered out-of-plane magnetic dots. It was found that at larger dc current biasing, the triangular arrangement of moving fluxons transits to a rectangular lattice. Such a “super-radiant” flux-flow state is found to be stable in a wide region of applied dc current and reproduces commensurability features in the current-voltage characteristics of the system. Extra features appear on the response of the system to the applied current for larger magnetization of the dots due to the formation of vortex-antivortex pairs under the magnetic dots. However, such vortex-antivortex pairs results in the significant disorder in the dynamics of the fluxons and, consequently, their synchronization becomes difficult. Synchronized motion of the fluxons becomes more pronounced by adding a small ac component to the biasing dc current for a broad frequency range of the applied ac drive. The conclusion of this study was that it is more difficult to control the dynamics of the fluxons in Josephson systems using magnetic pinning centres as compared to the case of non-magnetic pinning. However, the chaotic dynamic of Josephson vortices is potentially useful for THz emitters with broad spectrum.
2. The effect of initial and boundary conditions on the dynamics of Josephson vortices. The research started with considering the effect of a nonrectangular cross section of an artificial stack of SNS Josephson junctions on the dynamics of fluxons under time-periodic ac and constant dc biasing currents. It was found that very small deviations of the sidewalls of the system from its vertical position strongly affect the collective behaviour of the junctions, resulting in a transition from coherent motion of fluxons to less ordered dynamics of fluxons. No phase synchronization is observed for larger asymmetry in the distribution of junction cross sections, where the dynamic state is characterized by a chaotic motion of fluxons. The fellow also searched for the other kinds of boundary conditions, which can be used to generate tuneable electromagnetic radiation from Josephson junction systems. Using advanced three-dimensional simulations, he showed that an Abrikosov vortex, trapped inside a cavity perpendicular to an artificial Josephson junction, can serve as a very efficient source for generation of Josephson vortex-antivortex pairs in the presence of the applied electric current. In such a case, the nucleation rate of the pairs can be tuned in a broad range by an out-of-plane ac magnetic field in a broad range of frequencies. Reported tuneability of the Josephson oscillations can be useful for developing high-frequency emission devices which frequency and power can be tuneable in a very wide range.
The contribution of both in-plane and out-of-plane currents to the hot spot formation due to nonuniformity of current flow. Non-uniform current distribution has a pronounced effect on the physical processes taking place in Josephson junction system. Such current flow can be created by, e.g. nonuniform boundaries, non-magnetic and magnetic inclusions, or short junctions connecting the superconducting layers (i.e. pillars). The fellow has shown that such nonuniform distribution of the current can result in very interesting phenomena, which have not been reported so far in Josephson systems. For example, he found a new kind of vortex matter in superconductors - the Josephson vortex loops - formed and stabilized in planar junctions or layered superconductors as a result of nontrivial cutting and recombination of Josephson vortices. Engineering latter barriers opens broad perspectives on loop manipulation and control of other possible knotted/linked/entangled vortex topologies in nanostructured superconductors. In the context of Josephson devices proposed to date, the high-frequency excitations of the Josephson loops can be utilized in future design of powerful emitters, tunable filters and waveguides of high-frequency electromagnetic radiation, thereby pushing forward the much needed Terahertz technology.
3. Scattering of THz waves on moving (or oscillating) lattices of Josephson vortices. The fellow has found that the Abrikosov vortices have significant effect of the dynamics of the fluxons, consequently on the properties of electromagnetic radiation due to the moving fluxons. For example, the analysis revealed controllability of the frequency of Josephson oscillations with over 80% by changing just the magnetic field, whereas the maximum 40% tunability has been achieved to date (by changing bias current and bath temperature). These findings can have important implications for the design of tunable high-frequency electromagnetic radiation sources.
4. To explore the analogy between nonlinear optics and nonlinear Josephson plasma waves. Using the computer simulations the fellow has shown that an Abrikosov vortex, trapped inside a cavity perpendicular to an artificial Josephson junction, can serve as an efficient source for generation of Josephson vortex-antivortex pairs. Such essentially nonlinear parametrically amplified vortex-antivortex nucleation can be considered as a macroscopic analog of the dynamic Casimir effect in optical systems, where fluxon pairs mimic the photons and the ac magnetic field plays the role of the oscillating mirrors. The emerging vortex pairs in our system can be detected by the pronounced features in the measured voltage characteristics, or through the emitted electromagnetic radiation, and exhibit resonant dynamics with respect to the frequency of the applied magnetic field.
5. THz meta-materials in layered superconductors. One of the main objectives of the current project proposal was to propose new superconducting meta-materials, which could give possibility of controlling the propagation of THz radiation in superconducting systems. Our preliminary simulation results show that once created in Josephson junctions, superconducting vortex loops interact very differently with the propagating THz radiation. There is a possibility of creating superconducting meta-materials from the Josephson junctions with ordered arrays of vortex loops, which can allow tuning nonlinear electromagnetic transparency of Josephson junction stacks and designing nonlinear THz filters. The fellow has shown that the Josephson vortex loops can be formed and stabilized in planar junctions or layered superconductors as a result of nontrivial cutting and recombination of Josephson vortices around the barriers for their motion. Engineering latter barriers opens broad perspectives on loop manipulation and control of other possible knotted/linked/entangled vortex topologies in nanostructured superconductors. Currently we are working on a theory to describe the propagation of THz radiation in superconducting meta-materials consisting of Josephson vortex loops.
PS: the extended final report and submitted (but not yet published) articles are in the attached file.