Layered superconductors as nonlinear waveguides for terahertz waves (original) (raw)
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Analogues of nonlinear optics using terahertz Josephson plasma waves in layered superconductors
2006
E lectromagnetic waves in layered superconductors are known as Josephson plasma waves (JPWs). An important property of JPWs is the gap in their energy spectrum: JPWs can propagate if the frequency ω is above the Josephson plasma frequency ω J (refs 1,2), which being in the terahertz (THz) range, is important for applications 3 . This feature is fuelling a growing interest in studies of JPWs (see, for example, refs 4-7). However, nonlinear (NL) JPWs have not yet been studied. It is a challenge to understand nonlinearities around the plasma frequency, where the interplay between the unusual spectrum and the nonlinearity of the JPWs is most pronounced. Here, we predict the propagation of NL JPWs with frequencies below ω J , which is unusual for plasma-like excitations. In analogy to NL optics, these waves exhibit numerous remarkable features, including the slowing down of light (when the group velocity ∂ω/∂ k ≈ 0), self-focusing effects and the pumping of weaker waves by stronger ones. The nonlinearity for ω > ω J can potentially be used for transforming continuous THz radiation into amplified pulses.
Nonlinear Josephson plasma waves in slabs of layered superconductors
For layered superconductors, we study the specific nonlinear Josephson plasma waves (NJPWs) propagating along thin superconducting slabs and damping away from them. Two cases are considered, when the superconductor is surrounded by either vacuum or metals. The magnetic field of the NJPW is distributed symmetrically with respect to the middle of the sample and can change its sign inside the slab. The impedance ratio of the tangential electric and magnetic field amplitudes for NJPWs can be of the order of unity. For the case of a superconductor surrounded by the vacuum, this results in a non-monotonic dispersion relation, x(k), strongly sensitive to the NJPW amplitudes. Therefore, the ''stopping light" phenomenon can be observed at frequencies where dx(k)/dk = 0. Resonance excitations of the NJPWs should produce anomalies in the amplitude dependence of the reflectivity and transmissivity of the incident THz waves, which could be useful for THz devices. Animations illustrating the results presented here, are available online at dml.riken.go.jp/nonlinear.
The recent growing interest in terahertz (THz) and sub-THz science and technology is due to its many important applications 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. We review the problem of linear and nonlinear THz and sub-THz Josephson plasma waves in layered superconductors and their excitations produced by moving Josephson vortices. We start by discussing the coupled sine-Gordon equations for the gauge-invariant phase difference of the order parameter in the junctions, taking into account the effect of breaking the charge neutrality, and deriving the spectrum of Josephson plasma waves. We also review surface and waveguide Josephson plasma waves. The spectrum of these waves is presented, and their excitation is discussed. We review the propagation of weakly nonlinear Josephson plasma waves below the plasma frequency, ω J , which is very unusual for plasma-like excitations. In close analogy to nonlinear optics, these waves exhibit numerous remarkable features, including a self-focusing effect and the pumping of weaker waves by a stronger one. In addition, an unusual stop-light phenomenon, when ∂ω/∂k ≈ 0, caused by both nonlinearity and dissipation, can be observed in the Josephson plasma waves. At frequencies above ω J , the current-phase nonlinearity can be used for transforming continuous sub-THz radiation into short, strongly amplified, pulses. We also present quantum effects in layered superconductors, specifically, the problem of quantum tunneling of fluxons through stacks of Josephson junctions. Moreover, the nonlocal sine-Gordon equation for Josephson vortices is reviewed. We discuss the Cherenkov and transition radiations of the Josephson plasma waves produced by moving Josephson vortices, either in a single Josephson junction or in layered superconductors. Furthermore, the expression for the Cherenkov cone of the excited Josephson plasma waves is derived. We also discuss the problem of coherent radiation (superradiance) of the THz waves by exciting uniform Josephson oscillations. The effects reviewed here could be potentially useful for sub-THz and THz emitters, filters and detectors. Rep. Prog. Phys. 73 (2010) 026501 S Savel'ev et al
Nonlinear electrodynamics in layered superconductors
Physical Review B, 2008
We analyze theoretically the effect of a weak nonlinearity on the propagation of Josephson plasma waves in layered superconductors. The nonlinearity originates from the Josephson relation between the current density across superconducting layers and gauge-invariant phase difference of the order parameter. We show that strong nonlinear effects can be observed for electromagnetic waves with frequency slightly above or slightly below the plasma frequency. We study the nonlinear plasma resonance accompanied by the hysteretic dependence of the wave amplitude on the frequency. This hysteresis transforms the continuous terahertz radiation into a series of short electromagnetic high-amplitude pulses. We also consider the propagation of a nonlinear terahertz beam localized in the direction across the superconducting layers. This phenomenon is an analog of the self-focusing effect in nonlinear optics. The nonlinear phenomena in layered superconductors considered here can be potentially useful for the design of a new generation of terahertz devices.
Physical Review B, 2018
We study theoretically the optic transmission through a slab of layered superconductor separated from two dielectric leads by spatial gaps. Based on the transfer matrix formalism along with the Josephson plasma electrodynamic approach, we derive analytic expressions for the transmittance and identify the conditions for the perfect transmission. The special interest of the study is focused on the resonant transmission, which occurs when the wave does not propagate in the spatial gaps. Far from the resonance, the transmittance is exponentially small due to the total internal reflection from the lead-gap interface. However, the excitation of electromagnetic modes localized on the layered superconductor gives rise to a remarkable resonant enhancement of the transmission. Moreover, this phenomenon is significantly modified for the layered superconductors in comparison with usual dielectrics or conductors. The dispersion curves for the modes localized on the layered superconductor are proved to be nonmonotonic, thus resulting in the specific dependence of the transmittance T on the incidence angle θ. In particular, we predict the onset of two resonant peaks in the T (θ) dependence and their subsequent merge into the broadened single peak with increasing of the wave frequency. Our analytical results are demonstrated by numerical data.
New Journal of Physics, 2013
We predict the enhanced transmissivity of modulated slabs of layered superconductors for terahertz radiation due to the diffraction of the incident wave and the resonance excitation of the eigenmodes. The electromagnetic field is transferred from the irradiated side of a slab of layered superconductor to the other one by excited waveguide modes (WGMs) which do not decay deep into the slab, contrary to metals, where the enhanced light transmission is caused by the excitation of the evanescent surface waves. We show that a series of resonance peaks (with T ∼ 1) can be observed in the dependence of the transmittance T on the varying incidence angle θ, when the dispersion curve of the diffracted wave crosses successive dispersion curves for the WGMs.
Surface and waveguide Josephson plasma waves in slabs of layered superconductors
Physical Review B, 2011
We discuss the propagation of symmetric and antisymmetric Josephson plasma waves in a slab of layered superconductor clad between two identical dielectrics. We predict two branches of surface waves in the terahertz frequency range, one above and another below the Josephson plasma frequency. Apart from this, there exists a discrete set of waveguide modes with electromagnetic fields oscillating across the slab thickness and decaying exponentially away from the slab. We consider the excitation of the predicted waves by means of the attenuatedtotal-reflection method. It is shown that for a specific set of the parameters of the structure, the excitation of the waveguide modes is accompanied by the total suppression of specular reflection.
Physical Review Letters, 2012
We predict a complete TM↔TE transformation of the polarization of terahertz electromagnetic waves reflected from a strongly anisotropic boundary of a layered superconductor. We consider the case when the wave is incident on the superconductor from a dielectric prism separated from the sample by a thin vacuum gap. The physical origin of the predicted phenomenon is similar to the Wood anomalies known in optics, and is related to the resonance excitation of the oblique surface waves. We also discuss the dispersion relation for these waves, propagating along the boundary of the superconductor at some angle with respect to the anisotropy axis, as well as their excitation by the attenuated-total-reflection method.
Excitation of surface Josephson plasma waves in layered superconductors
Physical Review B, 2007
This is a theoretical study of the resonant suppression of the specular reflection of terahertz waves in layered superconductors due to the excitation of surface Josephson plasma waves ͑SJPWs͒. Here, we consider in detail the specific case of SJPW excitations by evanescent electromagnetic waves via the attenuated total reflection of incident waves in a dielectric prism. We also derive the dispersion relation for surface waves propagating along the vacuum-superconductor interface parallel to the ab plane. We show that, due to the SJPW excitation, the reflectivity of the incident wave depends resonantly on both its frequency and incident angle. We find the optimal conditions for the best matching of the incident wave and SJPWs, as well as for the total suppression of the specular reflection.
Physical Review B, 2021
We show that layered superconductors, due to their peculiar nonlinear response to a weak dc magnetic field, behave as tunable hyperbolic media within a wide terahertz range. Thereby, various attractive phenomena intrinsic in hyperbolic materials can be controlled by dc magnetic field. In particular, in this work a resonant transparency of a layered superconductor induced by the excitation of localized waves with nonmonotonic dispersion, is studied. We reveal the dc magnetic field is able to adjust the electromagnetic properties of a layered superconductor in order to observe specific twin peaks in the transmittance-vs-angle dependence. In addition, solving the problem by the transfer-matrix method, we succeed in deriving the matrix responsible for the effect of dc magnetic field. It is notable that this specific matrix depends neither on the size of the layered superconductor, nor on the parameters of surroundings.