# Visualization of two-dimensional transition dipole moment texture in momentum space using high-harmonic generation spectroscopy Source: [Visualization of two-dimensional transition dipole moment texture in momentum space using high-harmonic generation spectroscopy]() Collection index: [llms.txt]() Data updated: 2025-10-25T02:07:19.980Z Authors: K. Uchida, V. Pareek, K. Nagai, K. M. Dani, K. Tanaka Published: 2020-06-16T18:00:00.000Z ## Abstract Highly nonlinear optical phenomena can provide access to properties of electronic systems which are otherwise difficult to access through conventional linear optical spectroscopies. In particular, high harmonic generation (HHG) in crystalline solids is strikingly different from that in atomic gases, and it enables us to access electronic properties such as the band structure, Berry curvature, and valence electron density. Here, we show that polarization-resolved HHG measurements can be used to probe the transition dipole moment (TDM) texture in momentum space in two dimensional semiconductors. TDM is directly related to the internal structure of the electronic system and governs the optical properties. We study HHG in black phosphorus, which offers a simple two-band system, with bandgap resonant excitation. We observed a unique crystal-orientation dependence of the HHG yields and polarizations and succeeded in reconstructing the TDM texture related to the inter-atomic bonding structure. Our results demonstrate the potential of high harmonic spectroscopy for probing electronic wavefunctions in crystalline solids. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()