Simultaneous measurement of Raman and nonlinear optical tensors

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.

💡 Research Summary

This paper presents a comprehensive platform that simultaneously records Raman scattering and second‑harmonic generation (SHG) from the same focal spot, and introduces a novel method for extracting the full second‑order nonlinear optical tensor (χ^(2)) using a Bessel‑Gaussian (BG) ultrafast beam. The authors first describe the motivation: Raman spectroscopy provides detailed vibrational information, phase‑transition signatures, temperature and stress mapping, while SHG is uniquely sensitive to crystal symmetry and orientation, especially in non‑centrosymmetric materials. Combining the two techniques enables a richer, complementary picture of a material’s structural and electronic properties, and polarization‑resolved measurements allow the full Raman and χ^(2) tensors to be reconstructed.

The experimental setup integrates a commercial confocal Raman microscope (Horiba LabRAM HR) with a custom SHG subsystem. The Raman arm uses multiple continuous‑wave lasers (405–647 nm) with fine power control (1 µW–40 mW) and a motorized polarization state generator (quarter‑ and half‑wave plates) to produce arbitrary linear, left‑ or right‑circular states. Detection is performed with a liquid‑nitrogen‑cooled Si CCD. The SHG arm employs an 800 nm, 100 fs Ti:Sapphire oscillator whose beam is transformed into a BG profile by two axicons, yielding a donut‑shaped focus of ≈1 µm (FWHM) through a 63× high‑NA objective. The SHG signal at 400 nm is collected in epi‑geometry on a separate cooled CCD after three band‑pass filters block the pump. A specially designed non‑polarizing dichroic beam splitter, incorporating compensating rotated optics, merges the CW Raman and pulsed SHG beams while preserving their polarization states.

Traditional rotational anisotropy SHG (RA‑SHG) requires mechanical rotation of the sample to vary the incidence angle, limiting spatial resolution and increasing measurement time. The authors introduce Microscopic Rotational Anisotropy SHG (MRA‑SHG), which exploits intrinsic spatial and temporal imperfections of tightly focused beams. With a BG beam, photons arriving from opposite sides of the optical axis can either overlap in time and space at the focal plane (synchronous condition) or arrive with a relative delay (asynchronous condition). In the Fourier plane of the detection optics, the synchronous component appears as a bright central spot (normal incidence, α≈0°), while the asynchronous component forms a ring corresponding to a fixed oblique incidence angle (α≠0°). Thus a single image simultaneously contains SHG data for two distinct incidence geometries without any mechanical adjustment, reducing the effective acquisition time to the CCD exposure time.

To retrieve χ^(2) from these rich 2‑D Fourier patterns, the authors develop a ray‑tracing model that treats the beam as a grid of “polarized beamlets” characterized by 3‑D position, wave‑front curvature (q‑parameter), and Jones‑vector electric field. Propagation through each optical element is handled via the P‑matrix formalism, allowing accurate tracking of polarization changes, phase fronts, and amplitude. The effective field at the sample (E_ω,eff) generates a nonlinear field (E_NLO) according to χ^(2). Emitted beamlets are then propagated to the detector, where they are summed to form simulated Fourier images. Because the parameter space (tensor elements, crystal orientation, symmetry constraints) is high‑dimensional, a GPU‑accelerated evolutionary algorithm performs global optimization, fitting multiple polarization configurations (P/P, P/S, S/P, S/S) and data taken at different sample rotations simultaneously. This approach yields robust, high‑precision estimates of the independent χ^(2) components.

Experimental validation is performed on potassium dihydrogen phosphate (KDP, KH₂PO₄), a well‑characterized non‑centrosymmetric crystal (point group 4mm). Raman spectra obtained under the same conditions confirm the expected vibrational modes and demonstrate the system’s ability to use Raman as an in‑situ thermometer via Stokes/anti‑Stokes ratios. SHG Fourier images display the predicted central peak and surrounding ring; fitting with the ray‑tracing model reproduces the known χ^(2) tensor elements of KDP within experimental uncertainty. Compared with conventional Gaussian‑beam RA‑SHG, the BG‑based MRA‑SHG improves spatial resolution by roughly a factor of two and shortens measurement time to the detector integration period.

In summary, the paper delivers four major advances: (1) a fully integrated Raman‑SHG microscope with complete polarization control; (2) a non‑polarizing dichroic beam splitter that minimizes polarization distortion for both CW and ultrafast beams; (3) the exploitation of BG beam spatial‑temporal structure to acquire normal‑ and oblique‑incidence SHG simultaneously without mechanical motion; and (4) a comprehensive data‑analysis pipeline combining ray‑tracing, Fourier‑plane imaging, and GPU‑accelerated evolutionary fitting to extract the full second‑order nonlinear tensor. This methodology opens new avenues for rapid, high‑resolution, tensor‑level characterization of complex materials across physics, chemistry, biology, and nanotechnology.