Spectral Caustics Research Articles

Saddle-point exciton signature on high-order harmonic generation in two-dimensional hexagonal nanostructures

The disclosure of basic nonlinear optical properties of graphene-like nanostructures with correlated electron-hole nonlinear dynamics over a wide range of frequencies and pump field intensities is of great importance for both graphene fundamental physics and for the expected novel applications of two-dimensional (2D) hexagonal nanostructures in extreme nonlinear optics. In the current paper, the nonlinear interaction of 2D hexagonal nanostructures with the bichromatic infrared driving field taking into account the many-body Coulomb interaction is investigated. Numerical investigation in the scope of the Bloch equations within the Houston basis that take into account $e\text{--}e$ and $e\text{--}h$ interactions in the Hartree-Fock approximation reveals significant excitonic effects in the high-harmonic generation process in 2D hexagonal nanostructures such as graphene and silicene. It is shown that, due to the correlated electron-hole nonlinear dynamics around the van Hove singularity, spectral caustics in the high-harmonic generation spectrum are induced near the saddle-point excitonic resonances.

Reconstruction of crystal band structure by spectral caustics in high-order harmonic generation

We propose a method to retrieve the band structure by measuring the caustic points of the harmonic spectrum generated by the interaction between laser and solid. The relation between the energy ${\ensuremath{\omega}}_{c}$ of the spectral caustic points and the external fields $F$ encodes the bandgap of the solid. Specifically, for a simple band structure, ${\ensuremath{\varepsilon}}_{g}(k)={\ensuremath{\varepsilon}}_{0}+{\ensuremath{\varepsilon}}_{1}[1\ensuremath{-}cos(k{a}_{0})]$, according to the semiclassical theory, we map the crystal momentum ${k}_{c}$ to the caustic point energy ${\ensuremath{\omega}}_{c}$ by $F$ since ${k}_{c}$ is independent of the parameters ${\ensuremath{\varepsilon}}_{0}$ and ${\ensuremath{\varepsilon}}_{1}$. Furthermore, for the general band structure, because its first-order form is a simple energy band, we can roughly retrieve the first-order form of the energy band and obtain the accurate band structure by iterative calculation. Using this method, we solve the deviation between the retrieved and the target bandgap near the Brillouin zone boundary. Also, we show that this method is suitable for wide-bandgap materials.

Plasma microlensing dynamic spectrum probing fine structures in the ionized interstellar medium

ABSTRACT Gravitational microlensing has become a mature technique for discovering small gravitational lenses in the Universe that are otherwise beyond our detection limits. Similarly, plasma microlensing can help us explore cosmic plasma lenses. Both pulsar scintillation and extreme scattering events of compact radio sources suggest the existence of ∼au-scale plasma lenses in the ionized interstellar medium (IISM), whose astrophysical correspondence remains a mystery. We demonstrate that plasma microlensing events by these plasma lenses recorded in the form of wide-band dynamic spectra are a powerful probe of their nature. Using the recently developed Picard–Lefschetz integrator for the Kirchhoff–Fresnel integral, we simulate such dynamic spectra for a well-motivated family of single-variable plasma lenses. We demonstrate that the size, strength, and shape of the plasma lens can be measured from the location of the cusp point and the shape of spectral caustics, respectively, with a combination of distances and the effective velocity known a priori or measured from the widths of the interference pattern. Future wide-band observations of pulsars, whose plasma microlensing events may be predictable from parabolic arc monitoring, are the most promising ground to apply our results for a deeper insight into the fine structures in the IISM.

Spectral caustics of high-order harmonics in one-dimensional periodic crystals.

We theoretically investigate the spectral caustics of high-order harmonics in solids. We analyze the one-dimensional model of high-order harmonic generation (HHG) in solids and find that apart from the caustics originating from the van Hove singularities in the energy band structure, another kind of catastrophe enhancement also emerges in solids when the different branches of electron-hole trajectories generating high-order harmonics coalesce into a single branch. We solve the time-dependent Schrödinger equation in terms of the periodic potential and demonstrate the control of this kind of singularity in HHG with the aid of two-color laser fields. The diffraction patterns of the harmonic spectrum near the caustics agree well with the interband electron-hole recombination trajectories predicted by the semiconductor semiclassical equation. This work is expected to improve our understanding of the HHG dynamics in solids and enable us to manipulate the harmonic spectrum by adjusting the driving field parameters.

Attosecond spectral singularities in solid-state high-harmonic generation

Strong-field-driven electric currents in condensed-matter systems are opening new frontiers in petahertz electronics. In this regime, new challenges are arising as the roles of band structure and coherent electron–hole dynamics have yet to be resolved. Here, by using high-harmonic generation spectroscopy, we reveal the underlying attosecond dynamics that dictates the temporal evolution of carriers in multi-band solid-state systems. We demonstrate that when the electron–hole relative velocity approaches zero, enhanced constructive interference leads to the appearance of spectral caustics in the high-harmonic generation spectrum. We introduce the role of the dynamical joint density of states and identify its mapping into the spectrum, which exhibits singularities at the spectral caustics. By studying these singularities, we probe the structure of multiple unpopulated high conduction bands. High-harmonic waves are generated from a MgO crystal under experimental conditions where the simple semi-classical analysis fails. High-harmonic generation spectroscopy directly probes the strong-field attosecond dynamics over multiple bands.

Direct Observations of Traveling Ionospheric Disturbances as Focusers of Solar Radiation: Spectral Caustics

Abstract The solar radiation focusing effect is related to the specific phenomenon of propagation of the Sun-emitted HF and VHF waves through terrestrial ionosphere. This natural effect is observed with ground-based radio instruments running within the 10–200 MHz range as distinctive patterns—the spectral caustics (SCs)—on the solar dynamic spectra. It has been suggested that SCs are associated with medium-scale traveling ionospheric disturbances (MSTIDs). In this paper, we present the first direct observations of SCs induced by MSTIDs, using solar dynamic spectra with SCs obtained by different European radio telescopes on 2014 January 8 and simultaneous two-dimensional detrended total electron content (dTEC) maps over Europe. Spatial examination of dTEC maps as well as precise timing analysis of the maps and the dynamic spectra have been performed. First, we found several pairs of one-to-one (TID-SC) correspondences. The study provides strong observational evidence supporting the suggestion that MSTIDs are the cause of SCs.

Simulation of Focusing Effect of Traveling Ionospheric Disturbances on Meter‐Decameter Solar Dynamic Spectra

AbstractFor the first time we present simulation results of the focusing effect of the ionospheric plasma density irregularities, namely, medium‐scale traveling ionospheric disturbances (MSTIDs), on solar radio emission by applying a ray tracing method to the Earth's ionosphere with MSTIDs. With this technique we investigate the focusing effect that manifests itself in the form of peculiar spectral disturbances in intensity with specific morphology, so‐called Spectral Caustics (SCs), occasionally appearing in dynamic spectra of different solar radio instruments operating in the meter‐decameter wavelength range. We show that the simulated spectral shapes of SCs are in good agreement with the ones detected in real solar radio spectrograms. In particular, SCs that are classified as inverted V‐like, V‐like, X‐like, and fiber‐like types have been reproduced. It is also found that the seasonal dependence in the occurrence of SCs, which has been discovered recently, can be understood through a strong relation between the focusing frequency—the most important characteristic point in most SC patterns—and the elevation angle of the Sun. We find that under typical parameters of MSTIDs with spatial and temporal periods set to be 300 km and 40 min, respectively, the focusing frequency decreases with the growth of the elevation angle. Physical interpretations of the results and implications on the analysis of solar radio data with SCs are discussed.

Traveling ionospheric disturbances as huge natural lenses: Solar radio emission focusing effect

AbstractWe present an in‐depth study into spectral perturbations appearing in solar dynamic spectra and being manifestations of the focusing effect of low‐frequency solar emission by the Earth's ionosphere. Such perturbations are considered to be the result of radio waves focusing by medium scale traveling ionospheric disturbances (MSTIDs). Using the Nançay Decametric Array (NDA) data set, we have conducted a statistical analysis of the spectral structures in solar dynamic spectra within 10–80 MHz. We have detected the spectral structures in the NDA spectral data for 129 observation days from 1999 to 2015. On spectrograms they appear as intensity variations different from well‐known solar radio bursts. The sharp edges with enhanced intensity are distinctive characteristics of the structures for most events. Due to this spectral feature, they are termed as Spectral Caustics (SCs). We have classified the SCs observed by the NDA as several types, based on their spectral morphology, namely: inverted V like, V like, X like, fiber like, and fringe like. We have found that the rate of occurrence of SCs in dynamic spectra depends on the phase of the solar cycle. About 81% of all days with detected SCs fall on active phases of solar cycles 23 and 24 (48% and 33%, respectively). We have also established the seasonal dependence in occurrence of the SCs. It was found that about 95% of days with SCs belong to autumn‐winter months, whereas only near 5% of days with SCs belong to spring‐summer months. This is well correlated with the reported dependence in MSTID occurrence rate.

Probe of Multielectron Dynamics in Xenon by Caustics in High-Order Harmonic Generation.

We investigated the giant resonance in xenon by high-order harmonic generation spectroscopy driven by a two-color field. The addition of a nonperturbative second harmonic component parallel to the driving field breaks the symmetry between neighboring subcycles resulting in the appearance of spectral caustics at two distinct cutoff energies. By controlling the phase delay between the two color components it is possible to tailor the harmonic emission in order to amplify and isolate the spectral feature of interest. In this Letter we demonstrate how this control scheme can be used to investigate the role of electron correlations that give birth to the giant resonance in xenon. The collective excitations of the giant dipole resonance in xenon combined with the spectral manipulation associated with the two-color driving field allow us to see features that are normally not accessible and to obtain a good agreement between the experimental results and the theoretical predictions.

Spectral caustics in laser assisted Breit–Wheeler process

Electron-positron pair production by the Breit-Wheeler process embedded in a strong laser pulse is analyzed. The transverse momentum spectrum displays prominent peaks which are interpreted as caustics, the positions of which are accessible by the stationary phases. Examples are given for the superposition of an XFEL beam with an optical high-intensity laser beam. Such a configuration is available, e.g., at LCLS at present and at European XFEL in near future. It requires a counter propagating probe photon beam with high energy which can be generated by synchronized inverse Compton backscattering.

Caustic structures in x-ray Compton scattering off electrons driven by a short intense laser pulse

We study the Compton scattering of x-rays off electrons that are driven by a relativistically intense short optical laser pulse. The frequency spectrum of the laser-assisted Compton radiation shows a broad plateau in the vicinity of the laser-free Compton line due to a nonlinear mixing between x-ray and laser photons. Special emphasis is placed on how the shape of the short assisting laser pulse affects the spectrum of the scattered x-rays. In particular, we observe sharp peak structures in the plateau region, whose number and locations are highly sensitive to the laser pulse shape. These structures are interpreted as spectral caustics by using a semiclassical analysis of the laser-assisted QED matrix element, relating the caustic peak locations to the laser-driven electron motion.

Spectral Caustics in Attosecond Science

A unique type of singularity common in wave phenomena, known as caus- tics, links processes observed in many different branches of physics (1). We investigate the role of caustics in attosecond science and in particular the physical process behind high harmonic generation. By exploiting singularities of the three-step model that de- scribes HHG, we can manipulate and enhance specific features in the emitted harmonic spectrum. This new level of control holds promises in both scientific and technological aspects of attosecond science, and provides a deeper insight into the basic mechanism underlying the high harmonic generation process.

Spectral caustics in attosecond science

Many intriguing phenomena in nature—from phase transitions to black holes—occur at singularities. A unique type of singularity common in wave phenomena, known as caustics1,2, links processes observed in many different branches of physics3,4. Here, we investigate the role of caustics in attosecond science and in particular the physical process behind high harmonic generation5. We experimentally demonstrate spectral focusing in high harmonic generation, showing a robust intensity enhancement of an order of magnitude over a spectral width of several harmonics. This new level of control holds promises in both scientific and technological aspects of attosecond science6,7. Moreover, our study provides a deeper insight into the basic mechanism underlying the high harmonic generation process, revealing its quantum nature8 and universal properties. By applying catastrophe theory to high-harmonic generation, researchers identify caustics relating to regions of spectral focusing and greatly enhanced field intensity.