  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.
