A general method for rotational averages

The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products. From it, we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics.

All-optical polarization and amplitude modulation of second-harmonic generation in atomically thin semiconductors

Second-harmonic generation is of paramount importance in several fields of science and technology, including frequency conversion, self-referencing of frequency combs, nonlinear spectroscopy and pulse characterization. Advanced functionalities are enabled by modulation of the harmonic generation efficiency, which can be achieved with electrical or all-optical triggers. Electrical control of the harmonic generation efficiency offers large modulation depth at the cost of low switching speed, by contrast to all-optical nonlinear devices, which provide high speed and low modulation depth. Here we demonstrate all-optical modulation of second-harmonic generation in MoS2 with a modulation depth of close to 100% and speed limited only by the fundamental pulse duration. This result arises from a combination of D3h crystal symmetry and the deep subwavelength thickness of the sample, it can therefore be extended to the whole family of transition metal dichalcogenides to provide great flexibility in the design of advanced nonlinear optical devices such as high-speed integrated frequency converters, broadband autocorrelators for ultrashort pulse characterization, and tunable nanoscale holograms.

Chiral high-harmonic generation and spectroscopy on solid surfaces using polarization-tailored strong fields

Strong-field methods in solids enable new strategies for ultrafast nonlinear spectroscopy and provide all-optical insights into the electronic properties of condensed matter in reciprocal and real space. Additionally, solid-state media offers unprecedented possibilities to control high-harmonic generation using modified targets or tailored excitation fields. Here we merge these important points and demonstrate circularly-polarized high-harmonic generation with polarization-matched excitation fields for spectroscopy of chiral electronic properties at surfaces. The sensitivity of our approach is demonstrated for structural helicity and termination-mediated ferromagnetic order at the surface of silicon-dioxide and magnesium oxide, respectively. Circularly polarized radiation emanating from a solid sample now allows to add basic symmetry properties as chirality to the arsenal of strong-field spectroscopy in solids. Together with its inherent temporal (femtosecond) resolution and non-resonant broadband spectrum, the polarization control of high harmonics from condensed matter can illuminate ultrafast and strong field dynamics of surfaces, buried layers or thin films.

High Field Single- to Few-Cycle THz Generation with Lithium Niobate

The transient terahertz (THz) pulse with high peak field has become an important tool for matter manipulation, enabling many applications such as nonlinear spectroscopy, particle acceleration, and high harmonic generation. Among the widely used THz generation techniques, optical rectification in lithium niobate (LN) has emerged as a powerful method to achieve high fields at low THz frequencies, suitable to exploring novel nonlinear phenomena in condensed matter systems. In this review, we focus on introducing single- to few-cycle THz generation in LN, including the basic principles, techniques, latest developments, and current limitations. We will first discuss the phase matching requirements of LN, which leads to Cherenkov-like radiation, and the tilted pulse front (TPF) technique. Emphasis will be put on the TPF technique, which has been shown to improve THz generation efficiency, but still has many limitations. Different geometries used to produce continuous and discrete TPF will be systematically discussed. We summarize the advantages and limitations of current techniques and future trends.