Spectral intensity and phase changes of short laser pulses by two-photon absorption

Abstract

We calculated third order non-linear polarization to estimate the two-photon absorption of non-interacting two-level molecules in the transmission-type degenerate pump-probe geometry. The spectral intensity and the phase changes of the laser pulses when passing through a thin dielectric slab composed of the molecules were considered. We also investigated the effect of the decay rate of the molecules and the chirp of the pulses on their spectral intensity and phase changes.Since the slab is thin, we can approximate / ≈ ∆ /∆ and / ≈ ∆ /∆ .Here, ∆ (∆ ) corresponds to change of the signal intensity (phase) before the pump pulse. ∆ can be considered as the thin slab thickness . A conventional pump-probe experiments uses the self-heterodyne detection method, which measures the difference between the probe field and the reference field (or local oscillator). We are interested in obtaining the difference or change of the signals (i.e. ∆ and ∆ ). Therefore, we ignore the z-dependence of the polarization and collect the third order terms:By considering pulse -band widths much smaller than the pulse -center frequency, the intensity change ∆ and phase change (∆ ) are proportional to:∆ ( , ) ∝ [ ( ) ( , )/ * ( )]. (9)Here, the third order polarization ( ) ( , ) is depending on , the frequency of transmitted light through the material and , the time delay between pump and probe pulses. We can estimate ∆ ( , ) and ∆ ( , ) by using the Eqs. (2), (8), and (9) if the laser pulse field is known. RESULTS AND DISCUSSIONWe simulated the TPA signal of a thin dielectric slab in the conventional laser pulse pump-probe experiment. For the simulation, we used a Gaussian-shape electric field for both the pump and probe fields of which the spectrum has the following functional form:( ) = − ( − ) − ( ) . (10)