Transient Absorption

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In a pump-probe measurement, an initial pulse, the “pump” excites the sample. A second time delayed pulse, the “probe”, then measures the absorption of the sample. In a simple system, say an ensemble of identical two-level atoms, the pump will excite some of the atoms. Each of these excited atoms cannot absorb another photon, and therefore this will decrease the absorption of the probe pulse. In the time interval between the pump and the probe, some of the atoms can relax back to the grounds state. During this time the absorption will recover. As the delay between the pump and the probe is increased, the absorption will return to its original value and the rate at which it does will be provide information about the relaxation from the upper state to the lower state of the atoms.

For systems that are more complicated than identical two-level systems, the probe may experience other processes than just a decrease in absorption. For example, there may be an increase in absorption if there are higher excited states, or there may be changes in the shape of the absorption profile due to many-body interactions. These processes can be observed by making additional measurements on the transmitted probe pulses, with the most common being to measure its spectrum. This technique is often called “spectrally-resolved transient absorption”.

Transient absorption schematic
Schematic of simplest transient absorption spectroscopy. Probe transmission is modified by pump, and the difference between the absorption with and without the pump is measured.
Population decay of semiconductor resonance measured with transient absorption. The pump-probe signal (called the interaction signal) is plotted on a log scale

Heterodyne Detected Transient Absorption

Heterodyne detection can be used to isolate a differential transient absorption signal even when other optically degenerate beams impinge on the same detector.
High resolution spectral structure, which exists in (a) all pulsed lasers (i. e. a sharp lines spaced by the repetition frequency) and (b) white light, allows a small frequency shift of just 100 MHz to generate a distinct spectrum.

Though an industry standard, the above transient absorption scheme quickly breaks down if the pump and probe beams are spectrally overlapped and any pump light scatters onto the detector. For a collinear scheme, as is required for integration with a microscope, all of the pump light will impinge the detector and dominate the signal.

It is possible to isolate the nonlinear signal by frequency shifting the probe, and “heterodyne detecting” the field with an external local oscilaltor (LO) pulse that is also frequency shifted by a different amount. This technique was first introduced by K. L. Hall et al. for performing resonant pump-probe spectroscopy in waveguides.

The interference between the pump and probe is amplitude modulated by the difference in their frequencies. This beat note will also have sidebands at the chopper frequency, and these sidebands correspond to the pump-probe signal.

For frequency shifting to work it is essential for the frequency shifted probe to be distinguishable from the LO. Pulsed lasers with relatively high repetition rates (> 1 MHz) are one good option. Though the bandwidth of the pulsed laser is large, the spectrum is made up of a narrow near-delta functions spaced by the repetition frequency of the laser. In a stabilized laser, these are called comb teeth, and they have a linewidth corresponding to the coherence length of the laser. Utilizing this underlying “comb structure” is also possible here without stablized lasers because the probe and LO are generated from the same laser. Therefore the laser noise is common between them. In the figure at left, the interference of the two shifted spectra will be modulated by the applied frequency shift.

The random phase across the spectrum of an incoherent light source allows arbitrarily frequency shifted spectra to be distinguishable from their unshifted counterparts, shown in the bottom panel in the adjacent figure. The resolution is limited by the detection technique, which is typically determined by the scan duration of a Fourier transform spectrometer.

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