A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

The electronic properties of graphene can give rise to a range of nonlinear optical responses. One of the most desirable nonlinear optical processes is high-harmonic generation (HHG) originating from coherent electron motion induced by an intense light field. Here, we report on the observation of up to ninth-order harmonics in graphene excited by mid-infrared laser pulses at room temperature. The HHG in graphene is enhanced by an elliptically polarized laser excitation, and the resultant harmonic radiation has a particular polarization. The observed ellipticity dependence is reproduced by a fully quantum mechanical treatment of HHG in solids. The zero-gap nature causes the unique properties of HHG in graphene, and our findings open up the possibility of investigating strong-field and ultrafast dynamics and nonlinear behavior of massless Dirac fermions.

http://science.sciencemag.org/content/sci/356/6339/736.full.pdf

High-harmonic generation in graphene enhanced by elliptically polarized light excitation

2D layered materials (2DLMs) are a subject of intense research for a wide variety of applications (e.g., electronics, photonics, and optoelectronics) due to their unique physical properties. Most recently, increasing research efforts on 2DLMs are projected toward the nonlinear optical properties of 2DLMs, which are not only fascinating from the fundamental science point of view but also intriguing for various potential applications. Here, the current state of the art in the field of nonlinear optics based on 2DLMs and their hybrid structures (e.g., mixed-dimensional heterostructures, plasmonic structures, and silicon/fiber integrated structures) is reviewed. Several potential perspectives and possible future research directions of these promising nanomaterials for nonlinear optics are also presented.

/pdf/nonlinear-optics-with-2d-layered-materials-2vqqmfom9u.pdf

Nonlinear Optics with 2D Layered Materials.

High-harmonic generation in atomic gases has been studied for decades, and has formed the basis of attosecond science. Observation of high-order harmonics from bulk crystals was, however, reported much more recently, in 2010. This Review surveys the subsequent efforts aimed at understanding the microscopic mechanism of solid-state harmonics in terms of what it can tell us about the electronic structure of the source materials, how it can be used to probe driven ultrafast dynamics and its prospects for novel, compact short-wavelength light sources. Although most of this work has focused on bulk materials as the source, recent experiments have investigated high-harmonic generation from engineered structures, which could form flexible platforms for attosecond photonics. This Review surveys recent efforts at understanding and characterizing generation of high harmonics from solid-state materials.

High-harmonic generation from solids

In the future, sources of intense terahertz radiation will open up an era of extreme terahertz science featuring nonlinear light–matter interactions and applications in spectroscopy and imaging.

Extreme terahertz science

Observations of high-harmonic generation from a single layer of a transition metal dichalcogenide opens the door to studying strong-field and attosecond phenomena in two-dimensional materials. High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales1,2,3,4,5,6. The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands7,8,9,10,11,12,13,14. Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process15,16, including different symmetries17,18,19, access to individual valleys20,21 and enhanced many-body interactions22,23,24,25. Here we demonstrate non-perturbative HHG from a monolayer MoS2 crystal, with even and odd harmonics extending to the 13th order. The even orders are predominantly polarized perpendicular to the pump and are compatible with the anomalous transverse intraband current arising from the material’s Berry curvature, while the weak parallel component suggests the importance of interband transitions. The odd harmonics exhibit a significant enhancement in efficiency per layer compared to the bulk, which is attributed to correlation effects. The combination of strong many-body Coulomb interactions and widely tunable electronic properties in two-dimensional materials offers a new platform for attosecond physics.

High-harmonic generation from an atomically thin semiconductor

High-harmonic generation in a solid turns out to be sensitive to the interatomic bonding — a very useful feature that could enable the all-optical imaging of the interatomic potential. The microscopic valence electron density determines the optical, electronic, structural and thermal properties of materials. However, current techniques for measuring this electron charge density are limited: for example, scanning tunnelling microscopy is confined to investigations at the surface, and electron diffraction requires very thin samples to avoid multiple scattering1. Therefore, an optical method is desirable for measuring the valence charge density of bulk materials. Since the discovery of high-harmonic generation (HHG) in solids2, there has been growing interest in using HHG to probe the electronic structure of solids3,4,5,6,7,8,9,10,11. Here, using single-crystal MgO, we demonstrate that high-harmonic generation in solids is sensitive to interatomic bonding. We find that harmonic efficiency is enhanced (diminished) for semi-classical electron trajectories that connect (avoid) neighbouring atomic sites in the crystal. These results indicate the possibility of using materials’ own electrons for retrieving the interatomic potential and thus the valence electron density, and perhaps even wavefunctions, in an all-optical setting.

Anisotropic high-harmonic generation in bulk crystals

We investigate high-power terahertz (THz) generation in two-color laser filamentation using terawatt (TW) lasers including a 0.5?TW, 1?kHz system, as well as 2 and 30?TW systems both operating at 10?Hz. With these lasers, we study the macroscopic effect in filamentation that governs THz output energy yields and radiation profiles in the far field. We also characterize the radiation spectra at a broad range of frequencies covering radio?micro-waves to infrared frequencies. In particular, our 1?kHz THz source can provide high-energy (>1??J), high average power (>1?mW), intense (>1?MV?cm?1) and broadband (0.01?60?THz) THz radiation via two-color filamentation in air. Based on our scaling law, an ?30?TW laser can produce >0.1?mJ of THz radiation with multi-gigawatt peak power in ?1.5?m long filamentation.

/pdf/intense-terahertz-generation-in-two-color-laser-4uim0uy3ol.pdf

Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems

We observe off-axis phase-matched terahertz generation in long air-plasma filaments produced by femtosecond two-color laser focusing. Here, phase matching naturally occurs due to off-axis constructive interference between locally generated terahertz waves, and this determines the far-field terahertz radiation profiles and yields. For a filament longer than the characteristic two-color dephasing length, it emits conical terahertz radiation in the off-axis direction, peaked at 4-7° depending on the radiation frequencies. The total terahertz yield continuously increases with the filament length, well beyond the dephasing length. The phase-matching condition observed here provides a simple method for scalable terahertz generation in elongated plasmas.

/pdf/off-axis-phase-matched-terahertz-emission-from-two-color-56k34n2f7w.pdf

Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments.

High-harmonic generation in isolated atoms and molecules has been widely utilized in extreme ultraviolet photonics and attosecond pulse metrology. Recently, high-harmonic generation has been observed in solids, which could lead to important applications such as all-optical methods to image valance charge density and reconstruct electronic band structures, as well as compact extreme ultraviolet light sources. So far these studies are confined to crystalline solids; therefore, decoupling the respective roles of long-range periodicity and high density has been challenging. Here we report the observation of high-harmonic generation from amorphous fused silica. We decouple the role of long-range periodicity by comparing harmonics generated from fused silica and crystalline quartz, which contain the same atomic constituents but differ in long-range periodicity. Our results advance current understanding of the strong-field processes leading to high-harmonic generation in solids with implications for the development of robust and compact extreme ultraviolet light sources. Although higher harmonic generation from solids has become of interest in many fields, its observation is typically limited to crystalline solids. Here, the authors demonstrate that higher harmonics can be generated from amorphous solids.

/pdf/high-harmonic-generation-in-amorphous-solids-43zqh1afb6.pdf

Yong Sing You

Papers

High-harmonic generation from an atomically thin semiconductor

Anisotropic high-harmonic generation in bulk crystals

Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems

Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments.

High-harmonic generation in amorphous solids