Counter-propagating Waves Research Articles

Properties of finite amplitude electromagnetic waves propagating in the quantum vacuum

We study two counter-propagating electromagnetic waves in the vacuum within the framework of the Heisenberg–Euler formalism in quantum electrodynamics. We show that the nonlinear field equations decouple for ordinary wave case and can be solved exactly. We solve the nonlinear field equations assuming the solution in a form of a Riemann wave. We discuss the properties of the nonlinear electromagnetic wave propagating in the quantum vacuum, such as the wave steepening, subsequent generation of high order harmonics and electromagnetic shock wave formation with electron–positron pair generation at the shock wave front.

Counter-propagating wave packets in the quantum transition state approach to reactive scattering.

The quantum transition state concept provides an intuitive and numerically efficient framework for the description of quantum state-resolved reactive scattering and thermal reaction processes. Combining multiconfigurational time-dependent Hartree wave packet dynamics calculations with a flux correlation function based analysis, rigorous full-dimensional calculations of initial state-selected and state-to-state reaction probabilities for six atom reactions are feasible. In these calculations, a set of wave packets is generated in the transition state region, propagated into the asymptotic area, and analyzed. In the present work, an alternative approach which employs counter-propagating sets of wave packets is introduced. Outgoing wave packets started in the transition state region are matched with incoming wave packets generated in the reactant (or product) asymptotic area. Studying the H + CH4 → H2 + CH3 reaction as a prototypical example, one finds that the incoming wave packets can be propagated closely up to the transition state region with minor numerical effort. Employing cross correlation functions of incoming and outgoing wavefunctions, the propagation times required for the outgoing wave packet and thus the numerical costs of the entire calculation can be reduced significantly. Detailed full-dimensional calculations studying initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction are presented to illustrate the new approach. It is found that converged results can be obtained using shorter propagation times of the outgoing wave packets and less single-particle functions.

Non-Linear Interactions With Backscattered Light: A Truly Single-Ended Brillouin Optical Time-Domain Analysis Technique

The non-linear interaction between a Rayleigh-backscattered wave and a forward-traveling optical pump pulse is explored using sources separated by approximately one Brillouin shift. It is shown that the pump pulse modulates the Rayleigh backscatter at those locations where the frequencies of the counter-propagating waves differ by a Brillouin shift. As a result, a new Brillouin optical time-domain analysis technique is demonstrated that measures the spatial distribution of the Brillouin gain spectrum from one end only of the sensing fiber. In our experiments, spectra were acquired at a rate of 40 spectra per second over a sensing range of order 1 km with a spatial resolution of 3 m. The experimental arrangement and data analysis are described and a dataset is processed to extract the real part of the Brillouin gain spectrum and determine the peak of the gain spectrum as a function of location along the fiber. We also show that the new technique detects local changes in the phase due to the Brillouin interaction. The potential and limitations of the new technique are also discussed.

Comparison of one-way and full-wave linear propagation models in inhomogeneous medium

One-way wave propagation models based on the parabolic approximation or its wide-angle extensions are often used for describing bounded acoustic beams. Such models are highly demanded when solving nonlinear problems that are computationally intensive and thus technically difficult to solve using full-wave approaches. When describing the propagation of a wave beam in a homogeneous medium, the one-way assumption is fulfilled exactly, and therefore, the inaccuracy is caused only by the limitations of the parabolic approximation. Such an error is significantly reduced within the wide-angle approach and completely disappears when using the exact propagator in the framework of the angular spectrum method. The situation is less obvious in the case of a heterogeneous environment, when a part of the wave energy is inevitably reflected becoming a counter-propagating wave and thus is not taken into account in the one-way approximation. The degree this phenomenon affects the accuracy of the one-way approach is still under discussion. In the current paper, a one-way propagator based on the pseudo-differential wide-angle equation is proposed. The propagator is tested for the homogeneous medium and for several configurations of media with regular and random inhomogeneities. The corresponding solutions are compared with those obtained using the k-Wave toolbox. Results of comparison show how the one-way propagator accuracy depends on the contrast and smoothness of the inhomogeneities. [Work supported by RSF No. 18-72-00196.]

Wave Turbulence of a Liquid Surface in an External Tangential Electric Field

A direct numerical simulation of the interaction of plane capillary waves on the surface of a liquid dielectric in an external tangential electric field taking into account viscous forces has been performed. It has been shown that the interaction of counter-propagating nonlinear waves can generate a direct energy cascade. In the quasistationary energy dissipation regime, probability density functions for angles of inclination of the boundary tend to a Gaussian distribution and the shape of the boundary becomes complex and chaotic. The spectrum of the surface perturbations in this regime is described by a power law $k^{-5/2}$. The energy spectrum has the form $k^{-3/2}$, which coincides with the Iroshnikov-Kraichnan energy spectrum and indicates that the observed wave turbulence of the liquid surface and the weak magnetohydrodynamic turbulence of interacting Alfv\'en waves have a related nature.

Observation of spontaneous decay of Alfvénic fluctuations into co- and counter-propagating magnetosonic waves in a laboratory plasma

We show experimentally that Alfvénic fluctuations can spontaneously decay into a fast and a slow magnetosonic wave in an inhomogeneous plasma. The fast wave of higher frequency propagates in the same direction, while the slow wave of lower frequency propagates in the opposite direction with the pump wave. Both of the daughter waves are characterized by strong parallel but modest perpendicular fluctuations. The measured frequencies and wavenumbers are found to satisfy the energy and momentum conservation conditions for a nonlinear three wave interaction. The evidence of energy flowing from pump fluctuations into daughter waves is also presented in this paper. The results may shed light on the origin of inward Alfvén waves observed in the solar corona and chromosphere and how shear Alfvén waves deposit its energy by driving compressional perturbations.

Single-Arm Frequency-Shifted Interferometry Using a Bidirectional Electro-Optic Modulator

Multiplexing fiber-optic sensors is an effective way to perform large-area quasi-distributed sensing. Among many sensor multiplexing and interrogation methods, frequency-shifted interferometry (FSI) emerges as a unique low-cost technique that is capable of resolving sensor locations using a continuous-wave broadband source, a bidirectional optical frequency shifter, and a slow photo detector. An acousto-optic modulator is typically used as the frequency shifter in FSI due to its high modulation efficiency and bidirectional operation. But its relatively low modulation bandwidth results in low spatial resolution, on the order of meters. To improve spatial resolution, single-arm FSI (SA-FSI) that employs an electro-optic modulator (EOM) as the frequency shifter was proposed, but the EOM's broad modulation bandwidth cannot be fully utilized because conventional EOMs cannot support bidirectional modulation at gigahertz frequencies due to the speed mismatch between the optical wave and the applied RF wave, especially when the two are counter propagating. In this paper, we modified a commercial EOM to increase the modulation efficiency of the counter-propagating optical wave and used it to interrogate 15 weak fiber Bragg gratings (FBGs) in an array, achieving a spatial resolution of ∼3 cm and a sensing range of >1 km. A signal-to-noise ratio as high as ∼18 dB was obtained with a 15-mW broadband amplified spontaneous emission source without any optical amplification. This is the first demonstration of both spatially resolved and spectrally resolved SA-FSI, and it is the first time that FBGs are interrogated with the SA-FSI technique.

Predictions for the First Parker Solar Probe Encounter

Abstract We examine Alfvén Wave Solar atmosphere Model (AWSoM) predictions of the first Parker Solar Probe (PSP) encounter. We focus on the 12 day closest approach centered on the first perihelion. AWSoM allows us to interpret the PSP data in the context of coronal heating via Alfvén wave turbulence. The coronal heating and acceleration is addressed via outward-propagating low-frequency Alfvén waves that are partially reflected by Alfvén speed gradients. The nonlinear interaction of these counter-propagating waves results in a turbulent energy cascade. To apportion the wave dissipation to the electron and anisotropic proton temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating as described by Chandran et al. We find that during the first encounter, PSP was in close proximity to the heliospheric current sheet (HCS) and in the slow wind. PSP crossed the HCS two times, at 2018 November 3 UT 01:02 and 2018 November 8 UT 19:09, with perihelion occurring on the south of side of the HCS. We predict the plasma state along the PSP trajectory, which shows a dominant proton parallel temperature causing the plasma to be firehose unstable.

Electromagnetic shocks in the quantum vacuum

The interaction of two counter-propagating electromagnetic waves in a vacuum is analyzed within the framework of the Heisenberg-Euler formalism in quantum electrodynamics. The nonlinear electromagnetic wave in the quantum vacuum is characterized by wave steepening, subsequent generation of high order harmonics and electromagnetic shock wave formation with electron{positron pair generation at the shock wave front.

Linear and nonlinear stability of a quasigeostrophic mixing layer subject to a uniform background shear

The aim of this work is to shed light by revisiting - through the kernel-wave (KW) perspective - the breakdown of a quasi-geostrophic (QG) mixing layer (or vortex strip/filament) in atmosphere under the influence of a background shear. The QG mixing layer is modelled with a family of quasi-Rayleigh velocity profiles in which the potential vorticity (PV) is constant in patches. In the KW perspective a counter-propagating Rossby wave (CRW) is created at each PV edge, i.e. the edge where a PV jump is located. The important parameters of our study are (i) the vorticity of the uniform shear m and (ii) the Rossby deformation radius Ld, which indicates how far the pressure perturbations can vertically propagate. While an adverse shear (m < 0) stabilizes the system, a favorable shear (m > 0) strengthens the instability. This is due to how the background shear affects the two uncoupled CRWs by shifting the optimal phase difference towards large (small) wavenumber when m < 0 (m > 0). As the QG environment is introduced a general weakening of the instability is noticed, particularly for m > 0...

Асимметричная генерация в сверхизлучающем лазере с симметричным низкодобротным резонатором

On the basis of numerical solution to the Maxwell-Bloch equations within an one-dimensional two-level model of a superradiant laser with a symmetric cavity where a photon lifetime is less than an incoherent relaxation time of the optical dipole oscillations of active centers, we find that a spontaneous asymmetric generation of the counter-propagating waves is possible under a continuous homogeneous pumping of an active medium. We show that such a phenomenon of a symmetry breaking of the spatial profiles of the counter-propagating waves of an electromagnetic field as well as the polarization and population inversion of an active medium in the considered case of a weak inhomogeneous broadening of an operating transition is caused by an asymmetric half-wavelength nonlinear grating of the population inversion of the transition’s energy levels which is produced by these waves.

Особенности одновременной генерации низко- и высокодобротных мод в гетеролазерах на квантовых точках с большим временем некогерентной релаксации оптических дипольных колебаний

We investigate the features of multimode steady-state generation of the superradiant heterolasers which have an active medium formed by the quantum dots with long incoherent relaxation time and a cavity of a combined Fabry-Perot type with a distributed feedback of the counter-propagating waves. We show that a quantum-coherent dynamics of the optical dipole oscillations and a population inversion of the working levels in an ensemble of the quantum dots with a strong inhomogeneous broadening of a spectral line may lead to a simultaneous lasing of modes with a various degree of phasing and/or correlation and with qualitatively different dynamical behavior, including quasi-stationary, metastable, self-modulated, pulsed-periodic, quasi-chaotic ones.

Features of mode selection in a combined Fabry-Perot cavity with distributed feedback of counter-propagating waves

An analysis is made of the possibility of isolating relatively high-Q modes or groups of such modes in low-Q combined Fabry-Perot cavities with distributed feedback of counter-propagating waves in order to ensure resonant interaction of the electromagnetic field with the polarization oscillations of an amplifying or absorbing medium filling the cavity. We considered two-level active media with homogeneous or inhomogeneous broadening of a spectral line, which can be both smaller or larger than the photon bandgap of a cavity. Particular attention is paid to the change in the well-known spectrum of polariton modes which takes place due to the transition from an absorbing to an amplifying medium under conditions that allow the realization of spontaneous or laser generation of the so-called superradiant modes.

Universal symmetry-breaking dynamics for the Kerr interaction of counterpropagating light in dielectric ring resonators

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry breaking mechanism in electrodynamics occurs between counter-propagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counter-propagating light in bi-directionally pumped microresonators finds application in the realisation of optical non-reciprocity (for optical diodes), studies of PT-symmetric systems, and the generation of counter-propagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr-interaction of counter-propagating light in a dielectric ring resonator. In particular, we study discontinuous behaviour in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realise, for example, highly sensitive near-field or rotation sensors. We then generalise to a time-dependent model, which predicts new types of dynamical behaviour, including oscillatory regimes that could enable Kerr-nonlinearity-driven all-optical oscillators. The physics of our model can be applied to other systems featuring Kerr-type interaction between two distinct modes, such as for light of opposite circular polarisation in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations.

Flying focus and its application to plasma-based laser amplifiers

Combining a chirped laser pulse with a chromatic lens yields a flying focus—a laser focus that moves dynamically in time. This provides control over the propagation of the peak laser intensity within an extended focal region that can be many times larger than the system’s Rayleigh length. Any velocity is achievable, including backward relative to the laser propagation direction. Previous simulation results have shown that a laser beam with a flying focus can create a counter-propagating ionization wave and subsequently pump a frequency-downshifted laser via the stimulated Raman scattering instability. Compared to a conventional Raman amplification scheme, several advantages were highlighted, including improved temperature control, plasma uniformity, and precursor growth mitigation. Here, we extend those results to demonstrate additional benefits: (1) the flying focus makes it possible for an unseeded Raman amplifier to produce a short, high-intensity beam; and (2) the flying focus minimizes collisional absorption of the pump, facilitating amplifier operation at higher plasma densities. Preliminary experiments have laid the groundwork for a high-performance plasma-based laser amplifier. The focal spot dynamics were initially confirmed at low intensity. It was subsequently demonstrated that ionization waves of arbitrary velocity can be produced at higher intensity. Here, we show a counter-propagating ionization front moving at approximately the speed of light—the optimal result for a Raman amplifier.

Reflection and transmission spectra of dynamic optical fiber gratings

Due to elasto-optical effect, dielectric index of silica is a function of stress. Therefore, two beams of counter-propagating sonic wave inside optical fibers may induce periodical refractive index change along fiber axis. This sonic wave-stimulated periodical index change acts like time dependent fiber gratings. In this article, we deduced the relationship between dielectric index and strain, as well as the time and space distribution of dynamic fiber gratings. Reflection and transmission models of dynamic fiber gratings were built based on coupled mode theory, with or without the consideration of attenuation of sonic wave. Furthermore, we discussed the characters of reflection and transmission spectra in detail. Resonant wavelength shift was found mathematically for the first time, to our best knowledge. The influence of fiber length between two sonic sources were also discussed. From the results, it is possible to use DFBG as a generator of laser pulse series, or a periodical optical shutter.

Two- and Three-dimensional Nonlinear Instabilities of Whistler Waves

Abstract Recently, two-dimensional (2D) nonlinear instabilities of whistler waves from resonant wave–wave interaction have gained much attention in numerical simulations as well as observations in space plasmas. In this paper, both 2D and three-dimensional (3D) nonlinear instabilities of whistler waves are investigated using electron magnetohydrodynamics (EMHD). It is found that decay instabilities can excite waves with a broadband wavenumber spectrum, including highly oblique propagating whistler waves. Whistler waves with λ e k = 1 would excite counter-propagating whistler waves, and the wave with can produce both co- and counter-propagating whistler waves, where λ e is the electron inertial length and k is the wavenumber. Moreover, it is shown that 3D instabilities have similar nonlinear growth rate distributions as in 2D decay for the azimuthal wavelength much larger than λ e . These results suggest that nonlinear wave–wave interaction can play an important role in the scattering of whistler waves in the solar wind and the Earth’s magnetosphere, and are also helpful for understanding nonlinear wave–wave interaction in the formation and development of EMHD turbulence.

Counter-propagating modes in a Fabry-Perot-type resonator.

The longitudinal optical modes of a Fabry-Perot resonator are investigated. We consider (1)the three- and one-dimensional spectral mode density in free space and in standing-wave resonators, (2)the infinite sum of mode profiles, resulting in the Airy distribution, (3)comparison between a two-mirror resonator and an infinite periodic lensguide, and (4)comparison between a two-mirror resonator and a ring resonator. It is consistently deduced that the two counter-propagating waves with wave vectors ±|kq| at the same resonance frequency νq and polarization constitute independent optical modes with mode indices ±|q|.

Nonlinear X-wave ultrasound imaging of acoustic biomolecules.

The basic physics of sound waves enables ultrasound to visualize biological tissues with high spatial and temporal resolution. Recently, this capability was enhanced with the development of acoustic biomolecules - proteins with physical properties enabling them to scatter sound. The expression of these unique air-filled proteins, known as gas vesicles (GVs), in cells allows ultrasound to image cellular functions such as gene expression in vivo, providing ultrasound with its analog of optical fluorescent proteins. Acoustical methods for the in vivo detection of GVs are now required to maximize the impact of this technology in biology and medicine. We previously engineered GVs exhibiting a nonlinear scattering behavior in response to acoustic pressures above 300 kPa, and showed that amplitude-modulated (AM) ultrasound pulse sequences that both excite the linear and nonlinear GV scattering regimes were highly effective at distinguishing GVs from linear scatterers like soft biological tissues. Unfortunately, the in vivo specificity of AM ultrasound imaging is systematically compromised by the nonlinearity added by the GVs to propagating waves, resulting in strong image artifacts from linear scatterers downstream of GV inclusions. To address this issue, we present an imaging paradigm, cross-amplitude modulation (xAM), which relies on cross-propagating plane-wave transmissions of finite aperture X-waves to achieve quasi artifact-free in vivo imaging of GVs. The xAM method derives from counter-propagating wave interaction theory which predicts that, in media exhibiting quadratic elastic nonlinearity like biological tissue, the nonlinear interaction of counter-propagating acoustic waves is inefficient. By transmitting cross-propagating plane-waves, we minimize cumulative nonlinear interaction effects due to collinear wave propagation, while generating a transient wave-amplitude modulation at the two plane-waves' intersection. We show in both simulations and experiments that residual xAM nonlinearity due to wave propagation decreases as the plane-wave cross-propagation angle increases. We demonstrate in tissue-mimicking phantoms that imaging artifacts distal to GV inclusions decrease as the plane-wave cross-propagation angle opens, nearing complete extinction at angles above 16.5 degrees. Finally, we demonstrate that xAM enables highly specific in vivo imaging of GVs located in the gastrointestinal tract, a target of prime interest for future cellular imaging. These results advance the physical facet of the emerging field of biomolecular ultrasound, and are also relevant to synthetic ultrasound contrast agents.

Gravity-capillary waves on the free surface of a liquid dielectric in a tangential electric field

Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The computational method is based on the time-dependent conformal transformation of the region occupied by the fluid into a half-plane. In the limit of a strong electric field, when the gravitational and capillary forces are negligibly small, there exists an exact analytical solution of the electro-hydrodynamic equations describing propagation without distortions of nonlinear surface waves along (or against) the electric field direction. In the situation where gravity and capillarity are taken into account, the results of numerical simulations indeed show that, for large external field, the waves traveling in a given direction tend to preserve their shape. In the limit of a strong electric field, the interaction of counter-propagating waves leads to the formation of regions, where the electrostatic and dynamic pressures undergo a discontinuity, and the curvature of the surface increases infinitely. The Fourier spectrum of the surface perturbations tends to the power-law distribution (k^-2). In the case of a finite electric field, the wave interaction results in a radiation of massive cascade of small-scale capillary waves that causes the chaotic behavior of the system. The investigated mechanism of interaction between oppositely-traveling waves can enhance development of the capillary turbulence of the fluid surface.