PHYSICAL REVIEW B 104, 224308 (2021) Broadband coherent anti-Stokes Raman scattering for crystalline materials Franz Hempel, 1 , * , † Sven Reitzig , 1 , * , ‡ Michael Rüsing , 1 and Lukas M. Eng 1, 2 1 Institut für Angewandte Physik, Technische Universität Dresden, 01062 Dresden, Germany 2 ct.qmat: Dresden-Würzburg Cluster of Excellence–EXC 2147, TU Dresden, 01062 Dresden, Germany (Received 5 October 2021; accepted 9 December 2021; published 30 December 2021) Broadband coherent anti-Stokes Raman scattering (B-CARS) has emerged in recent years as a promising chemosensitive high-speed imaging technique. B-CARS allows for the detection of vibrational sample properties in analogy to spontaneous Raman spectroscopy, but also makes electronic sample environments accessible due to its resonant excitation mechanism. Nevertheless, this technique has only gained interest in the biomedical field so far, whereas CARS investigations on solid-state materials are rare and concentrate on layered, two-dimensional materials such as graphene and hexagonal boron nitride . In this work, we discuss the specific properties of this technique when applied to single-crystalline samples, with respect to signal generation, phase matching, and selection rules in the model systems lithium niobate and lithium tantalate. Via polarized B-CARS measurements and subsequent phase retrieval, we validate the predicted selection rules, unequivocally assign the phonons of the A 1 (TO), E(TO) and A 1 (LO) branches to the detected CARS peaks, and address differences in spontaneous Raman spectroscopy concerning peak frequencies and scattering efficiencies. We thus establish this technique for future investigations of solid-state materials, specifically in the field of ferroelectric single crystals. DOI: 10.1103/PhysRevB.104.224308 I. MOTIVATION Microscopical spectroscopy techniques are of fundamen- tal importance for scientific fields ranging from biology to crystallography and material sciences due to their cost ef- ficiency, ease of use, and versatile detection options with spatial resolutions down to the diffraction limit. One of these techniques, coherent anti-Stokes Raman scattering (CARS), has seen increased use for chemosensitive imaging in re- cent years. CARS is a coherent four-wave mixing (4WM) Raman-scattering technique that resonantly enhances anti- Stokes scattering processes. The third-order nonlinear CARS process is described by a χ (3) tensor. Owing to its coherent nature and spectral sensitivity, it enables chemically and struc- turally sensitive investigations with high signal intensities. Due to these features, CARS has gained attention primarily for imaging of biological structures [1–3]. In the field of solid- state materials, however, CARS has only been used for the analysis of low-dimensional materials like carbon nanotubes (CNTs) [4,5], graphene [6–8], and hexagonal boron nitride (hBN) [9]. So far, no investigations of bulk single crystals have been reported, to the best of our knowledge. Compared with typical biological samples or two- dimensional (2D) materials, CARS investigations within solid, single-crystalline materials come with additional chal- lenges. For example, inorganic crystals usually exhibit much higher absolute refractive indexes n, as well as a larger dispersion than the aqueous media of biological * These authors contributed equally to this paper. † franz.hempel@tu-dresden.de ‡ sven.reitzig@tu-dresden.de tissue [e.g., n SiC (1064 nm) = 2.59, n GaAs (1064 nm) = 3.45, whereas n H 2 O (1064 nm) = 1.32). This significantly impacts the phase matching between interacting waves and causes a stronger distortion of the incident laser beams and of the respective focal point. Furthermore, in anisotropic crystals, birefringence might additionally disturb the focal overlap of the lasers, hence causing additional complexity in phase matching. Moreover, in bulk crystals the nonlinear material usually fills the complete focus area, while biological cell structures are usually only several hundred nanometers to a micron in thickness. Thus, phase matching considerations become much more relevant to bulk crystals [10]. Solid-state samples also may show large electronic backgrounds that might additionally disturb the resonant vibrational CARS sig- nal. Finally, the vibrational motions detected in crystals are not molecular vibrations without directional orientation but phonons that possess an inherent momentum q. While for idealized crystals it may be assumed that only phonons with zero momentum (q = 0) are detected, defects in real crystals cause the detection of phonons with q = 0. These defects in crystal structures thus provide an additional complexity in the analysis of CARS data. In contrast with these challenges, the CARS technique exhibits distinct advantages in comparison to the established technique of spontaneous Raman scattering (SR). Similar to SR, the CARS process is sensitive to vibrational motions. However, the χ (3) tensors that determine the CARS effi- ciency obey different selection rules, providing advantages for certain scenarios [11], and enable a higher sensitivity to geometry changes in the scattering process when compared with SR [12]. Furthermore, whereas SR shows a comparably low scattering efficiency and thus requires long acquisition times in regard to hyperspectral imaging, the nonlinear nature of CARS allows a much faster spectral acquisition, especially 2469-9950/2021/104(22)/224308(11) 224308-1 ©2021 American Physical Society