Two-Temperature Model — Ultrafast Laser Heating

After femtosecond laser excitation, electrons heat to thousands of Kelvin while the lattice stays cold. The TTM describes how electron-phonon coupling drives equilibration over picoseconds.

Laser Pulse

Material (metal)

Controls

T_electrons300 K
T_lattice300 K
ΔT_e0 K
Time (ps)0.00
Eq. reached?No
Two-Temperature Model (TTM)
C_e dT_e/dt = S(t) − G(T_e − T_l)
C_l dT_l/dt = G(T_e − T_l)

Electrons absorb photons in ~10 fs, reaching ~10,000 K. Electron-phonon coupling G transfers energy to lattice over 1–10 ps. Used to model laser ablation, ultrafast demagnetization, nonthermal melting.