Nonlinear rovibrational polarization response of water vapor to ultrashort long-wave infrared pulses

We study the rovibrational polarization response of water vapor using a fully correlated optical Bloch equation approach employing data from the HITRAN database. For a $10\text{−}\mu \mathrm{m}$ long-wave infrared pulse the resulting linear response is negative, with a negative nonlinear response at intermediate intensities and a positive value at higher intensities. For a model atmosphere comprised of the electronic response of argon combined with the rovibrational response of water vapor this leads to a weakened positive nonlinear response at intermediate intensities. Propagation simulations using a simplified noncorrelated approach show the resultant reduction in the peak filament intensity sustained during filamentation due to the presence of the water vapor.

Figure 1

(a) Energy spectrum of the rovibrational states and (b) coupling of dipole-allowed transitions in (2). In (a) the energy is shown versus the (highest) rotational quantum number, the energy being on the right-hand vertical axis, and for various vibrational states indicated along the left-hand vertical axis. In (b) the solid line identifies a particular transition, for which the polarization is to be computed, and the dashed lines symbolize coupled transitions.

Figure 2

Linear absorption spectrum of water vapor according to the HITRAN database, the LWIR photon energy being indicated by the vertical arrow, with the horizontal line showing the spectral width of a $50\text{−}\mathrm{fs}$ pulse.

Figure 3

Linear polarization responses of the rovibrational transitions of water for (a) $200\text{−}\mathrm{fs}$ and (b) $50\text{−}\mathrm{fs}$ LWIR pulses. The dashed green line shows the shape of the applied electric field for each case.

Figure 4

Polarization responses of the rovibrational transitions of water for $200\text{−}\mathrm{fs}$ LWIR pulses with peak intensities of ${10}^{16}$ (black line) and ${10}^{17}\mathrm{W}/{\mathrm{m}}^2$ (blue line) normalized to the electrical field. The green dashed line shows the shape of the applied electric field.

Figure 5

(a) Real and (b) imaginary parts of the effective susceptibility ${\chi }_{\mathrm{eff}}\left(\omega \right)$ at the carrier frequency as a function of peak intensity for $50\text{−}\mathrm{fs}$ (circles), $100\text{−}\mathrm{fs}$ (squares), and $200\text{−}\mathrm{fs}$ (triangles) LWIR pulses.

Figure 6

Absorption due to the rovibrational transitions for the initial thermal distribution (blue line) and after excitation with a $50\text{−}\mathrm{fs}$ pulse of peak intensity $7\times {10}^{16}\mathrm{W}/{\mathrm{m}}^2$ (black line). The vertical arrow indicates the carrier frequency of the LWIR pulse and the spectral regions marked by thick green horizontal lines exhibit gain following the excitation.

Figure 7

Real part of the effective nonlinear susceptibility at the carrier frequency as a function of peak intensity for $50\text{−}\mathrm{fs}$ (black solid line), $100\text{−}\mathrm{fs}$ (green long-dashed line), and $200\text{−}\mathrm{fs}$ (dotted blue line) LWIR pulses in a model atmosphere composed of $99\%$ argon and $1\%$ water. The black short-dashed line indicates the effect of the electronic Kerr effect alone.

Figure 8

Maximum intensity over the transverse plane versus propagation distance for 100-fs LWIR pulses of peak powers 1.6 TW (black lines) and 3.2 TW (blue lines). The dashed lines are for argon gas alone and the solid lines are with $1\%$ water vapor. In both cases the nuclear response of the water content reduces the self-focusing leading to lower peak intensities compared to the case of pure argon cases.