Models of the delayed nonlinear Raman response in diatomic gases

We examine the delayed response of a diatomic gas to a polarizing laser field with the goal of obtaining computationally efficient methods for use with laser pulse propagation simulations. We demonstrate that for broadband pulses, heavy molecules such as ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$, and typical atmospheric temperatures, the initial delayed response requires only classical physics. The linear kinetic Green's function is derived from the Boltzmann equation and shown to be in excellent agreement with full density-matrix calculations. A straightforward perturbation approach for the fully nonlinear, kinetic impulse response is also presented. With the kinetic theory a reduced fluid model of the diatomic gas’ orientation is derived. Transport coefficients are introduced to model the kinetic phase mixing of the delayed response. In addition to computational rapidity, the fluid model provides intuition through the use of familiar macroscopic quantities. Both the kinetic and the fluid descriptions predict a nonlinear steady-state alignment after passage of the laser pulse, which in the fluid model is interpreted as an anisotropic temperature of the diatomic fluid with respect to motion about the polarization axis.

Figure 1

Coordinate system for molecular alignment. The vertical axis represents the polarization axis of the polarizing laser pulse.

Figure 2

Comparison of the classical theory in red (dashed) with a full quantum-mechanical density-matrix calculation in black (solid). In (a) nitrogen is considered while in (b) oxygen is considered.

Figure 3

Comparison of the classical theory in red (dashed) with a full quantum-mechanical density-matrix calculation in black (solid) for nitrogen at $T=20\hspace{0.5em}\mathrm{K}$ and $T=100\hspace{0.5em}\mathrm{K}$.

Figure 4

Comparison of the classical theory in red (dashed) with a full quantum-mechanical density-matrix calculation in black (solid) for hydrogen at $T=294\hspace{0.5em}\mathrm{K}$.

Figure 5

Comparison of the fully nonlinear quantum theory in black (solid) and the first- and second-order classical theory in red (dashed) for nitrogen at $T=294\hspace{0.5em}\mathrm{K}$. The fist-order classical theory is plotted for reference in gray (thin line). The inset shows a zoomed-in region detailing the constant offset in the molecular alignment.

Figure 6

Comparison of the fully nonlinear quantum theory in black (solid) and the two-moment fluid response with viscosity in green (dashed) for nitrogen at $T=294\hspace{0.5em}\mathrm{K}$.

Figure 7

Comparison of the fully nonlinear quantum theory in black (solid) and the three-moment fluid response in green (dashed) for nitrogen at $T=294\hspace{0.5em}\mathrm{K}$.