Experimental study of the third-order nonlinearity of atomic and molecular gases using 10-μm laser pulses

We present measurements of the third-order optical nonlinearity of Kr, Xe, ${\mathrm{N}}_2, {\mathrm{O}}_2$, and air at a wavelength near 10 µm by using four-wave mixing of $\sim 15-\mathrm{GW}/\mathrm{c}{\mathrm{m}}^2$, 200-ps (full width at half maximum) $\mathrm{C}{\mathrm{O}}_2$ laser pulses. Measurements in molecular gases resulted in an asymmetric four-wave mixing spectrum indicating that the nonlinear response is strongly affected by the delayed, rotational contribution to the effective nonlinear refractive index. Within the uncertainty of our measurements, we have found that the long-wavelength nonlinear refractive indices of these gases are consistent with measurements performed in the near IR.

Figure 1

(a) A dual-wavelength laser pulse is transformed into a family of sidebands by FWM in a nonlinear medium. (b) Experimental setup for nonlinear refractive index measurements of gases. The inset shows a representative temporal pulse profile used for nonlinear refractive index measurements. OAP stands for off-axis parabolic mirror and HCT stands for HgCdTe detector.

Figure 2

The evolution of the major and minor diameters of the elliptical beam used for nonlinear refractive index measurements in gases. The insets of the figure show example images of the beam as measured with a pyroelectric camera.

Figure 3

Energy of the first anti-Stokes sideband as a function of pressure in laboratory air. The dashed and solid lines were produced using 200 and 130 MW, respectively.

Figure 4

Energy in the first Stokes sideband plotted as a function of the energy of the 10.6-µm pump times the energy in the 10.3-µm pump squared for 380 Torr of dry air. Note that $W_{\lambda }$ is the energy of the laser pulse.

Figure 5

Energy in the first Stokes sideband plotted as a function of the energy of the 10.6-µm pump squared times the energy in the 10.3-µm pump for 380 Torr of xenon gas. Note that $W_{\lambda }$ is the energy of the laser pulse.

Figure 6

Energy in the first Stokes sideband plotted as a function of the energy of the 10.6-µm pump times the energy in the 10.3-µm pump squared for (a) 380 Torr of ${\mathrm{N}}_2$ gas and (b) 250 Torr of ${\mathrm{O}}_2$ gas. Note that $W_{\lambda }$ is the energy of the laser pulse.

Figure 7

A typical FWM spectrum obtained in 380 Torr of laboratory air.

Figure 8

(a) The resonant third-order polarizability of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ in the range of 400–1200 GHz and (b) a closeup of the vicinity of the 882-GHz beat frequency used for nonlinear refractive index measurements.