Contrast-enhanced phase-resolved second harmonic generation microscopy.

The characterization of inverted structures (crystallographic, ferroelectric, or magnetic domains) is crucial in the development and application of novel multi-state devices. However, determining these inverted structures needs a sensitive probe capable of revealing their phase correlation. Here a contrast-enhanced phase-resolved second harmonic generation (SHG) microscopy is presented, which utilizes a phase-tunable Soleil-Babinet compensator and the interference between the SHG fields from the inverted structures and a homogeneous reference. By this means, such inverted structures are correlated through the π-phase difference of SHG, and the phase difference is ultimately converted into the intensity contrast. As a demonstration, we have applied this microscopy in two scenarios to determine the inverted crystallographic domains in two-dimensional van der Waals material MoS2. Our method is particularly suitable for applying in vacuum and cryogenic environments while providing optical diffraction-limited resolution and arbitrarily adjustable contrast. Without loss of generality, this contrast-enhanced phase-resolved SHG microscopy can also be used to resolve other non-centrosymmetric inverted structures, e.g. ferroelectric, magnetic, or multiferroic phases.

Nonlinear optical signatures of topological Dirac fermion.

Dirac fermion in topological materials exhibits intriguing nonlinear optical responses. However, their direct correlation with the linearly dispersed band remains elusive experimentally. Here, we take topological semimetal ZrSiS as a paradigm, unveiling three unique nonlinear optical signatures of Dirac fermion. These signatures include strong quadrupolar response, quantum interference effect, and exponential divergent four-wave mixing (FWM), all of which are described by the prominent third-order nonlinear optical susceptibility. Resonantly enhanced by linear bands, quadrupolar second harmonic generation in centrosymmetric bulk overwhelms the electric-dipole contribution at the surface with inherent inversion symmetry breaking. Furthermore, owing to the interference between multiple resonant transition pathways within linear bands, difference-frequency FWM is several orders of magnitude stronger than sum-frequency FWM and third harmonic generation. The difference-frequency FWM further displays an inverse-square divergence toward degenerate excitation, whose scaling law perfectly matches with the long-sought behavior of Dirac fermion. These signatures lay the solid foundation toward the practical applications of topological materials in nonlinear optoelectronics and photonics.