Pump-Probe Spectroscopy

Pump-probe and transient absorption with sequential A → B → ground-state kinetics: ΔA kinetic traces and spectra in mOD from the pump fluence and ε, with bleach, stimulated emission and excited-state absorption bands and the pump-probe cross-correlation.

Model: Textbook approximation

Pump and sample

Pump Wavelength (nm)Pump Fluence (µJ/cm²)ε at Pump (L mol⁻¹ cm⁻¹)Sample Absorbance at PumpGround-State Absorbance at Bleach Peak

Kinetics A → B → ground state

τ₁, A → B (ps)τ₂, B → ground state (ps)Cross-Correlation FWHM (fs)Max Delay (ps)

Bands (Gaussian; strength = peak ε relative to the ground-state peak)

Ground-State Band Centre (nm)Ground-State Band FWHM (nm)SE Centre (nm)SE FWHM (nm)SE StrengthESA of A Centre (nm)ESA of A FWHM (nm)ESA of A StrengthESA of B Centre (nm)ESA of B FWHM (nm)ESA of B Strength

Probe

Kinetic-Trace Wavelength (nm)Spectrum From (nm)Spectrum To (nm)Spectrum Delays (ps, comma-separated, up to 8)

Mean Excited Fraction f̄

0.556 %

σ = 3.824e-17 cm², 2.014e+14 photons/cm², front face 0.770 %

Largest |ΔA| at 500.0 nm

-2.75 mOD

at 0.102 ps; ΔT/T = 0.636 %

B Population Maximum

1.279 ps

ln(k₁/k₂)/(k₁ − k₂) without IRF; n_B = 0.7743

Photon Energies

3.100 eV pump

probe 2.480 eV

Sequential populations after the pump: n_A = e^(−t/τ₁), n_B = τ₂/(τ₂ − τ₁) · (e^(−t/τ₂) − e^(−t/τ₁)); the ground state stays depleted by n_A + n_B until B decays.

ΔA(λ, t) = f̄ · A_GS · [−(n_A + n_B) g_GS(λ) + n_A (r_ESA g_ESA(λ) − r_SE g_SE(λ)) + n_B r_B g_B(λ)]: bleach and stimulated emission are negative, excited-state absorption positive.

Excited fraction (linear regime, averaged over depth): f̄ = σJ (1 − 10^(−A_p))/(A_p ln 10), σ = ln 10 · ε/N_A, J = Fλ/(hc). Each exponential is convolved with the Gaussian pump-probe cross-correlation in closed form.

A band with strength 0 drops out. ΔT/T = 10^(−ΔA) − 1. Coherent artefacts at time zero, anisotropy (magic-angle probing assumed) and pump saturation are not modelled.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

First-order sequential kinetics with Gaussian bands you choose and a Gaussian cross-correlation (closed form); excited fraction in the linear regime. No coherent artefact, anisotropy (magic angle assumed) or pump saturation.

van Stokkum I. H. M., Larsen D. S., van Grondelle R. (2004). Global and target analysis of time-resolved spectra. Biochim. Biophys. Acta 1657, 82–104. doi:10.1016/j.bbabio.2004.04.011
Berera R., van Grondelle R., Kennis J. T. M. (2009). Ultrafast transient absorption spectroscopy: principles and application to photosynthetic systems. Photosynth. Res. 101, 105–118. doi:10.1007/s11120-009-9454-y

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