Ye Jianpeng Direct and indirect band gaps play a crucial role in nonlinear absorption in semiconductors. Direct band gap semiconductors allow electrons to directly emit or absorb photons without changing their momentum, while indirect band gap semiconductors require electron interaction with phonons to conserve momentum.
If you'd like to read more about this topic, here are some articles you might find interesting:
Intensity Dependent Nonlinear Absorption in Direct and Indirect Band Gap Crystals under Nano and Picosecond Z-Scan
Linear and Nonlinear Intersubband Optical Properties of Direct Band Gap GeSn Quantum Dots