Pump-probe spectroscopy

Pump-probe spectroscopy measures how a material evolves after it is excited, on time scales far shorter than any photodetector can follow. A strong pump pulse excites the sample; a weak probe pulse arrives a time $\tau$ later and its transmission or reflection is recorded. Repeating the measurement for many delays, set by the extra path length in an optical delay line, traces the response as a function of time. Because the detector only integrates the probe energy, the time resolution comes from the pulses: with 100 fs pulses from a Ti:sapphire ultrafast laser, relaxation of excited carriers, recovery of a saturable absorber and coherent lattice vibrations can all be followed. The quantity measured is usually the differential transmission $\Delta T/T$, the change caused by the pump, with typical magnitudes from 10⁻³ down to 10⁻⁵ or below.

Setup

A single laser output is split into a pump and a probe, so that the two pulses are synchronized without electronic timing. The probe arm passes a retroreflector on a motorized stage; moving the stage by $d$ changes the probe path by $2d$ and the delay by

$$\Delta\tau = \frac{2d}{c}.$$

A 1 mm move adds 6.67 ps, and a 1 µm step corresponds to 6.67 fs. A 150 mm stage therefore covers about 1 ns of delay. The two beams are focused to overlap in the sample, with the probe spot made smaller than the pump spot so that it samples a nearly uniform excitation. In the simplest degenerate form both beams have the same wavelength; two-color experiments convert the pump or probe with a nonlinear crystal or an optical parametric amplifier, and transient-absorption spectrometers use a white-light continuum probe dispersed onto a detector array to record a full spectrum at each delay.

The pump-induced change is small next to the probe's own intensity noise, so the pump is modulated and the probe signal is detected synchronously with a lock-in amplifier. With a 1 kHz amplified laser the pump is chopped at 500 Hz and every pair of shots is compared. With an 80 MHz oscillator, modulating the pump in the megahertz range moves the measurement above most of the laser's technical noise, and a balanced detector removes much of the remainder.

Time resolution and excitation density

For Gaussian pulses of durations $\tau_{pu}$ and $\tau_{pr}$, the instrument response is their cross-correlation,

$$\tau_{IRF} = \sqrt{\tau_{pu}^2 + \tau_{pr}^2},$$

141 fs for two 100 fs pulses. Dispersion in the sample, lenses and cuvette windows lengthens the pulses and degrades this; the autocorrelation or a cross-correlation measured at the sample position gives the real figure.

The signal depends on how strongly the sample is excited, so the pump fluence is always reported. At 800 nm a photon carries 1.55 eV, and a fluence of 10 µJ/cm² delivers 4.0 × 10¹³ photons/cm². If all are absorbed within 1 µm, the excited carrier density is about 4.0 × 10¹⁷ cm⁻³, before correction for reflection at the surface. Many decay rates depend on this density, through Auger recombination, bimolecular recombination or saturation, so a series at several fluences is part of any careful measurement.

Applications

The method measures carrier lifetimes and relaxation in semiconductors, the recovery time of a saturable absorber used for mode-locking, gain recovery in semiconductor optical amplifiers and spectral hole burning in inhomogeneous media. Coherent phonons appear as oscillations of $\Delta T/T$ at the phonon frequency. Continuous-wave and modulated variants measure cross-phase modulation and Raman gain in fibers.

Pitfalls

• Accumulation. Pulses from an 80 MHz oscillator are 12.5 ns apart. A response that has not decayed by then builds up from pulse to pulse, and the signal at negative delay is not zero.
• Coherent artifact. Near zero delay, interference between pump and probe and cross-phase modulation in the sample or substrate produce a spike that is not a population effect.
• Pump scatter. Scattered pump light reaching the detector is also modulated and appears as an offset; a polarizer, a spectral filter or a non-collinear geometry suppresses it.
• Polarization. Molecules that are oriented by the pump rotate over time, and that reorientation mixes into a population decay. Setting the probe polarization at 54.7° to the pump (the magic angle) removes it.
• Beam pointing. A beam not parallel to the stage travel walks the probe spot as the delay changes, and the overlap drifts with delay.

Common questions

What does ΔT/T mean in a pump-probe measurement?

It is the change in probe transmission caused by the pump, divided by the transmission without the pump. For a thin sample with small changes it equals $-\Delta\alpha L$, where $\Delta\alpha$ is the pump-induced change in absorption coefficient and $L$ the thickness.

How is the time resolution of pump-probe set?

By the duration of the two pulses at the sample, through their cross-correlation; the speed of the detector and electronics does not enter.

How does pump-probe differ from time-correlated single-photon counting?

TCSPC times the arrival of emitted photons with electronics and its resolution is usually limited to a few tens of picoseconds by detector timing jitter. Pump-probe reaches femtoseconds and measures absorption or reflection changes, including from states that do not emit.

References: J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, 2nd ed. (Springer, 1999); J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic Press, 2006); S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, 1995).