Extracting Complex Refractive Index Dynamics via Transfer Matrix Analysis in Dual-Channel (Transmission/Reflection) Pump–Probe Spectroscopy

Conventional pump–probe spectroscopy often relies solely on either transmission (Δ T / T 0 ) or reflection (Δ R / R 0 ) measurements and frequently attributes the transient optical response to changes in the extinction coefficient ( k ) while neglecting the concomitant variations in the real part of the refractive index ( n ). This simplification could sometimes introduce significant uncertainty or irrationality in explaining ultrafast dynamics. Here, we introduce a generalized methodology that integrates transmission/reflection dual-channel (DC) detection with optical transfer matrix (OTM) analysis, enabling complete and independent extraction of both Δ n ( t ) and Δ k ( t ) dynamics. We validate this DC-OTM approach through systematic studies of gallium arsenide (GaAs) and silicon (Si). In the direct-bandgap GaAs, the traditional analysis holds primarily in the quasi-equilibrium regime but exhibits significant deviations during the initial nonequilibrium stage. More strikingly, in the indirect-bandgap Si, we observe a carrier-density-driven sign reversal in Δ k at an 820 nm probe wavelength, a phenomenon invisible to single-channel methods, which we attribute to the competition between band-filling and free-carrier absorption. Furthermore, we demonstrate the existence of scenarios where the pump–probe response is dominated by the changes in the real part of the refractive index (Δ n ). Our work not only challenges the conventional interpretation framework but also establishes a robust strategy for uncovering complex photophysical processes, particularly in regimes where Δ n and Δ k are both significant or competing mechanisms coexist.