Neumann's principle based eigenvector approach for deriving non-vanishing tensor elements for nonlinear optics

Quantifying the photocurrent fluctuation in quantum materials by shot noise

The DC photocurrent can detect the topology and geometry of quantum materials without inversion symmetry. Herein, we propose that the DC shot noise (DSN), as the fluctuation of photocurrent operator, can also be a diagnostic of quantum materials. Particularly, we develop the quantum theory for DSNs in gapped systems and identify the shift and injection DSNs by dividing the second-order photocurrent operator into off-diagonal and diagonal contributions, respectively. Remarkably, we find that the DSNs can not be forbidden by inversion symmetry, while the constraint from time-reversal symmetry depends on the polarization of light. Furthermore, we show that the DSNs also encode the geometrical information of Bloch electrons, such as the Berry curvature and the quantum metric. Finally, guided by symmetry, we apply our theory to evaluate the DSNs in monolayer GeS and bilayer MoS2 with and without inversion symmetry and find that the DSNs can be larger in centrosymmetric phase.

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy

Vibrational sum-frequency generation (VSFG), a second-order nonlinear optical signal, has traditionally been used to study molecules at interfaces as a spectroscopy technique with a spatial resolution of ~100 µm. However, the spectroscopy is not sensitive to the heterogeneity of a sample. To study mesoscopically heterogeneous samples, we, along with others, pushed the resolution limit of VSFG spectroscopy down to ~1 µm level and constructed the VSFG microscope. This imaging technique not only can resolve sample morphologies through imaging, but also record a broadband VSFG spectrum at every pixel of the images. Being a second-order nonlinear optical technique, its selection rule enables the visualization of non-centrosymmetric or chiral self-assembled structures commonly found in biology, materials science, and bioengineering, among others. In this article, the audience will be guided through an inverted transmission design that allows for imaging unfixed samples. This work also showcases that VSFG microscopy can resolve chemical-specific geometric information of individual self-assembled sheets by combining it with a neural network function solver. Lastly, the images obtained under brightfield, SHG, and VSFG configurations of various samples briefly discuss the unique information revealed by VSFG imaging.

Symmetry-based identification and enumeration of independent tensor properties in nonlinear and chiral optics

For many laser-based methods of material characterization and analysis, a tensor formulation of theory is necessary, especially in techniques that exploit nonlinear or chiral optics. The fundamental interactions that underpin such methods offer various levels of approach to theory, but the most rigorous often lead to equations of considerable complexity. To compute the values for individual material parameters frequently demands making assumptions of extreme simplicity, overly dependent on calculational method, yet still providing unsatisfactory results. A pragmatic and entirely rigorous symmetry-based approach to the irreducible tensorial structures circumvents many of these problems, securing reliable results and guiding the pathway to applications. Instead of focusing on individual tensor components, such an approach can rapidly determine the number of linearly independent quantities-and hence the number of operationally different setups necessary for full characterization. By such means, one can directly ascertain how variations of optical polarization and beam geometry can reliably capture the response of any material system. The use of an irreducible tensor method operates independently of any means that might be chosen to calculate material properties. It removes the need for common simplifying assumptions, such as the approximation of tensorial structure by a scalar representation, adoption of a two-state model, or disregarding near-resonance damping. It also obviates any dependence on a choice of simulation package or quantum-calculational software. In this paper, the principles are set down and illustrated by application to experiments of varying degrees of complexity, including interactions of growing significance in the realm of chiral nonlinear optics. Limitations of this approach are also critically assessed.