Simultaneous measurement of Raman and nonlinear optical tensors

TL;DR

The paper presents a unified polarization-resolved platform for simultaneous Raman and SHG microscopy, exploiting a Bessel-Gaussian focal field to access complete Raman and second-order nonlinear optical tensors. A BG-driven MRA-SHG method paired with a polarization-resolved ray-tracing model and GPU-accelerated optimization enables rapid, quantitative extraction of $\chi^{(2)}$ and Raman tensors from micro-scale samples. Validation on KDP and LiNbO3 demonstrates accurate tensor recovery and consistent crystal orientation fitting, with Kleinman symmetry supported under near-IR excitation. The approach offers a robust pathway to characterize nonlinear optical properties in nano-objects and 2D materials, potentially enabling global tensor fitting from polarization maps of randomly oriented dielectrics.

Abstract

Raman spectroscopy and Second Harmonic Generation (SHG) are complementary, non-destructive techniques that provide rich and distinct insights into the structural and electronic properties of materials. Raman spectroscopy offers detailed information on vibrational modes, phase transitions, temperature, and local stress, while SHG is highly sensitive to symmetry and orientation, particularly in non-centrosymmetric structures. In this work, in addition to combining both techniques, we propose a novel approach to determine the nonlinear optical tensor, leveraging the spatial and ultra-fast temporal offset of a Bessel-Gaussian laser beam at the microscope's focal point.

Figures (5)

• Figure 1: overview of the experimental setup for simultaneous Raman and SHG measurements with a close-up on the lasers coupling region. A detailed Scheme is provided in Figure SM-1
• Figure 2: a) Polarization state at the focal point of BG beam excitation (in red) under a) synchronous and b) asynchronous conditions. c) Azimuthal dependence of the polarization state for the excitation BG beam polarized at an angle $\phi$ relative to the sample x-axis. d-e) Corresponding patterns and polarization configurations for the (SHG) signal. The central part corresponds to the synchronous state probing normal incidence configuration XX, XY (S and P states are equivalent), while the ring is associated with the fixed incidence asynchronous polarization configuration. f) Definition of the different sectors and angles used for data analysis.
• Figure 3: a) SHG image collected at Fourier plane on LiNbO3 for an incoming polarisation $\phi_n=69^o$ in parallel mode. b) fit of the Fourier image. c-d) Procedure to display the set of raw and fitted Fourier maps into a single $\phi$ / $\theta$ polar map . c) Scheme of the analyzed ring identifying angle $\phi_n$ as the angle of the incoming polarization relative to $x$ axis and $\theta_m$ the angle between the incoming polarization and the $m^{th}$ sector. d) resulting polar map after integration of all sectors relative to the two angles. e) Integrated values of the central intensity as a function of $\phi$.
• Figure 4: a) Raman and b) global SHG temperature dependence of a KDP crystal. dashed line corresponds to the temperature of the structural transition.
• Figure 5: Full set of polarization resolved SHG (b-g) and Raman (h,i) data with the corresponding fit using the unified model described in the text. Each column corresponds to KDP (1,2) or LiNbO3 (3,4) crystals with specific orientation. a) Optical images of the crystals with crystallographic axis (a red, b green, c blue). b and e, experimental SHG intensity maps in parallel and crossed configurations respectively extracted from the "ring" part of images in Fourier plane. c and f, corresponding fits. d and g, polarization resolved SHG intensities in parallel and crossed configurations respectively, extracted from the "central" part of the images in Fourier plane. h and i, polarization resolved Raman scattering intensities measured in parallel and crossed configurations respectively. (h,i;1,2), A$_1$ Raman mode of KDP at 915 cm$^{-1}$ and (h,i;3,4), E Raman mode of LiNbO3 at 580 cm$^{-1}$ for corresponding orientation of the crystals. Legends and axes of all polar plots match those in d1.