Nonlinear Fourier space imaging of 2D materials.

• Applicant: Dr. Lucas Lafeta Prates da Fonseca, Ph.D.
• Subject Area: Experimental Condensed Matter Physics ; Synthesis and Properties of Functional Materials
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 558231736

Nonlinear optical spectroscopy has become essential for probing two-dimensional (2D) materials, with techniques such as Second-Harmonic Generation (SHG) and four-wave mixing (FWM) providing crucial insights into layer number, crystal structure, orientation, defects, and electronic properties. However, conventional polarization-resolved techniques for determining crystallographic symmetry and orientation are time-consuming and require rotating the samples or adjusting polarizers and lasers. In addition, they do not provide detailed insights into signal formation and the full breadth of light-matter interactions. To address these limitations, we have recently implemented Fourier space SHG imaging using various focused laser modes to study 2D materials. This Fourier imaging technique can be directly integrated into conventional optical microscopes. We demonstrated that the Fourier images generated by SHG and two-photon excited photoluminescence are noticeably distinct, reflecting key differences in spatial coherence and polarization of the emitted fields. Using an azimuthally polarized laser mode, we can determine the crystal symmetry and orientation of materials belonging to the point group D3h in a single Fourier space image. This approach improves acquisition speed, orientational precision, and provides detailed information on the signal formation process. Building on this, we will pursue these three objectives in this project: First, we aim to develop Fourier space SHG imaging of 2D materials into a general characterization technique by exploring 2D materials with different crystal symmetries, the influence of one-dimensional defects and metamaterials formed by 2D layers. SHG, however, is restricted to noncentrosymmetric materials. Our second objective is thus to explore Fourier space images generated by third-order nonlinear effects such as FWM and Coherent Anti-Stokes Raman Scattering (CARS), both of which can also occur in centrosymmetric materials. Fourier space CARS images are exciting because they can contain orientational information on Raman active vibrational modes. The spatial resolution of conventional microscopy is diffraction limited. While tip-enhanced near-field optical techniques, in which a sharp metal tip acts as a nanoantenna, can provide nanoscale sub-diffraction resolution, efficiently suppressing detrimental background signal contributions can be very challenging. Our third objective is to disentangle the complex interplay of signal contributions in tip-enhanced nonlinear spectroscopy using Fourier space imaging and our detailed understanding of the contrast formation obtained within this project. Projected outcomes are a significantly improved understanding of the nonlinear signal formation processes in 2D materials that form the basis of powerful new characterization techniques enabling novel insights into light-matter interactions and sample properties with high spatial resolution and detection sensitivity.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Achim Hartschuh