Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals

The propagation of high-power femtosecond light pulses in lithium niobate crystals $\left(\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3\right)$ is investigated experimentally and theoretically in collinear pump-probe transmission experiments. It is found within a wide intensity range that a strong decrease of the pump transmission coefficient at wavelength $388\mathrm{nm}$ fully complies with the model of two-photon absorption; the corresponding nonlinear absorption coefficient is ${\beta }_p\simeq 3.5\mathrm{cm}∕\mathrm{GW}$. Furthermore, strong pump pulses induce a considerable absorption for the probe at $776\mathrm{nm}$. The dependence of the probe transmission coefficient on the time delay $\Delta t$ between probe and pump pulses is characterized by a narrow dip (at $\Delta t\simeq 0$) and a long (on the picosecond time scale) lasting plateau. The dip is due to direct two-photon transitions involving pump and probe photons; the corresponding nonlinear absorption coefficient is ${\beta }_r\simeq 0.9\mathrm{cm}∕\mathrm{GW}$. The plateau absorption is caused by the presence of pump-excited charge carriers; the effective absorption cross section at $776\mathrm{nm}$ is ${\sigma }_r\simeq 8\times {10}^{-18}{\mathrm{cm}}^2$. The above nonlinear absorption parameters are not strongly polarization sensitive. No specific manifestations of the relaxation of hot carriers are found for a pulse duration of $\simeq 0.24\mathrm{ps}$.

Figure 1

Schematic diagram of a collinear pump-probe experiment; M is a dichroic mirror, L is a long-focus $\left(500\mathrm{mm}\right)$ lens, F is a band edge filter for the pump light, D is a photodetector, DS is a probe delay stage, and R are reflectors.

Figure 2

Transmission coefficient $T_p$ versus peak pump pulse intensity $I_p^0$. The squares, triangles, and crosses correspond to samples 1, 2, and 3, respectively.

Figure 3

Transverse beam profile (normalized intensities) for different values of the product ${\beta }_p{I}_p^{0}x$. Lines 1, 2, and 3 are plotted for ${\beta }_p{I}_p^{0}x=0$ (the input shape), 10, and 100.

Figure 4

Dependence of the transmission coefficient $T_p$ on ${\beta }_p{I}_p^{0}d$. The solid line (characteristic curve) is calculated from Eq. (4). The squares, triangles, and crosses represent the experimental data on $T_p\left(I_p^{0}d\right)$, scaled by a factor of ${\beta }_p=3.5\mathrm{cm}∕\mathrm{GW}$, for samples 1, 2, and 3, respectively.

Figure 5

Normalized transmission coefficient $T_r$ for the probe pulse versus the time delay $\Delta t$ for sample 4 and four different values of the pump intensity. The stars, crosses, circles, and squares correspond to $I_p^0\simeq 43$, 68, 93, and $139\mathrm{GW}∕{\mathrm{cm}}^2$, respectively.

Figure 6

Transmission coefficient $T_r$ versus $\Delta t$ for different pump and probe polarizations; the first and second characters of each pair in the inset (e.g., $YZ$) specify the orientation of the polarization vector of the pump and probe pulses, respectively.

Figure 7

Normalized transmission coefficient $T_r$ for the probe pulse versus the time delay $\Delta t$ for sample 1 $(d=1\mathrm{mm})$ and four different values of the pump intensity. The stars, crosses, circles, and squares correspond to $I_p^0\simeq 24$, 49, 101, and $147\mathrm{GW}∕{\mathrm{cm}}^2$, respectively.

Figure 8

Dependence of the dip and plateau amplitudes on the product ${\beta }_p{I}_p^{0}d$ for sample 3 and two different pump-probe polarization states. The points are experimental data and the solid lines are theoretical fits.

Figure 9

The normalized transmission coefficient $T_r$ versus $\Delta t∕t_p$ for ${\beta }_r∕{\beta }_p=0.2$ and $q_p=1$, 2, 4, 8, and 16 (curves 1, 2, 3, 4, and 5, respectively).

Figure 10

Dependence of the dip amplitude on $q_p$; lines 1, 2, 3, and 4 are plotted for ${\beta }_r∕{\beta }_p=0.1$, 0.2, 0.3, and 0.4, respectively.

Figure 11

The normalized transmission coefficient $T_r$ versus $\Delta t∕t_p$ for $d=1\mathrm{mm}$, ${\beta }_r∕{\beta }_p=0.2$, and ${\delta }_0=5$. Curves 1, 2, 3, and 4 are plotted for $q_p=1$, 5, 10, and 20, respectively.

Figure 12

Dependence of the plateau amplitude on the pump absorption parameter $q_p$; lines 1, 2, 3, 4, and 5 are plotted for $b=0.01$, 0.03, 0.06, 0.09, and 0.12, respectively.