= Time-resolved spectroscopy
<Time-resolved spectroscopy> measures how a spectroscopic response changes after a defined excitation or other reference event. Instead of only a time-integrated <spectrum>, it records a response such as $S(\nu,t)$ as a function of <frequency> and delay. A changing spectral feature can distinguish population loss, changing molecular environment and motion of a resonance; a single integrated intensity need not separate them.
In <pump-probe spectroscopy>, a pump pulse prepares the sample and a delayed probe interrogates it. A movable mirror in a double-pass optical path provides a precise delay change:
$$
\Delta t=\frac{2\Delta L}{c}.
$$
For an original displacement of 15 micrometres, the delay changes by about 100 femtoseconds. A spectrally resolved detector records the response while delay is scanned. The time resolution is set by pulse overlap, jitter and the detection scheme, rather than by mirror step size alone. <Ahmed H. Zewail>'s lecture explains how such optical timing enabled <femtochemistry>.<Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers by Ahmed H. Zewail>[Pump–Probe Femtoscopy; discussion of temporal resolution]{ref}
An original decay example assumes an isolated feature with background already removed and response
$$
S(t)=A e^{-t/\tau}\quad(t\geq0).
$$
If its intensity at 3 picoseconds is $1/e$ of its intensity at 1 picosecond, then $e^{-2\,\mathrm{ps}/\tau}=1/e$ and $\tau=2\,\mathrm{ps}$. This inference assumes the same feature is measured at both delays and that the instrument response is sufficiently short. A shifting line observed through a narrow spectral window can change intensity without following that simple population law.
Finite resolution instead produces a convolution. For a time-invariant <instrument response function> $R$ at a selected spectral channel,
$$
S_{\rm measured}(t)=\int R(t-u)S_{\rm true}(u)\,du.
$$
For ideal Gaussian pump and probe intensity envelopes, their <cross-correlation> width is the square root of the sum of their squared widths. Chosen full widths of 80 and 100 femtoseconds therefore give about 128 femtoseconds before other contributions. This original calculation describes pulse-overlap resolution, not an arbitrary material lifetime.
A motivating historical example is Zewail's discussion of the NaI/NaBr experiments reported in 1988. Delay-dependent signals probe evolving molecular motion and final fragments, supplying information absent from a static spectrum. His lecture presents the NaI dynamics in Figure 15.<Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers by Ahmed H. Zewail>[The NaI Discovery, Figure 15]{ref}
A practical experiment compares pumped and unpumped records, checks delay zero and <wavelength calibration>, and varies excitation strength to test whether the response remains in the intended regime. Negative-delay data, backgrounds and the measured <instrument response function> help distinguish sample dynamics from timing and detection artifacts.
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