Time-resolved nonlinear microspectroscopy with Gaussian beams: Spatial coherence dynamics in quantum materials

We present a theoretical framework for time-resolved nonlinear microspectroscopy using structured light to probe spatial coherence transfer in condensed-matter systems. Unlike traditional photon echo (PE) spectroscopy, our method employs Laguerre-Gaussian (LG) modes to encode and track quantum coherence migration spatially. By expanding the diffusion propagator in LG modes, we reveal radial mode mixing and conservation of orbital angular momentum during coherence migration. Analytical formulas for heterodyne-detected PE signals and two-dimensional spectra show distinct signatures of spatial coherence transfer in decay and line shapes. This technique allows differentiation between coherent and incoherent transfer, enabling measurement of exciton coherence diffusion constants in materials such as organic semiconductors, perovskites, and two-dimensional materials and provides new insights into coherence dynamics for quantum materials and energy transport applications.