Two-photon vibrational excitation of air by long-wave infrared laser pulses

Ultrashort long-wave infrared (LWIR) laser pulses can resonantly excite vibrations in ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ through a two-photon transition. The absorptive vibrational component of the ultrafast optical nonlinearity grows in time, starting smaller than but quickly surpassing the electronic, rotational, and vibrational refractive components. The growth of the vibrational component results in a novel mechanism of third-harmonic generation, providing an additional two-photon excitation channel, fundamental + third harmonic. The original and emergent two-photon excitations drive the resonance exactly out of phase, causing spatial decay of the absorptive vibrational nonlinearity. This nearly eliminates two-photon vibrational absorption. Here we present simulations and analytical calculations demonstrating how these processes modify the ultrafast optical nonlinearity in air. The results reveal nonlinear optical phenomena unique to the LWIR regime of ultrashort pulse propagation in the atmosphere.

Figure 1

Amplitude of the effective electronic (blue dashed curve), rotational (green dotted curve), absorptive (red solid curve), and refractive (purple dashed-dotted curve) vibrational susceptibilities as a function of pulse frame coordinate after ${15}_{}\mathrm{cm}$ of propagation. From left to right the plots show examples of below-resonant, resonant, and above-resonant excitations, respectively.

Figure 2

(a) Resonant absorptive vibrational susceptibility as a function of pulse frame coordinate and propagation distance. (b) Resonant absorptive vibrational susceptibility at $\tau =4_{}\mathrm{ps}$ (black solid curve and bottom horizontal axis) and total pulse fluence (red dashed curve and top horizontal axis) as a function of propagation distance.

Figure 3

Normalized fluence of the third harmonic as a function of propagation distance for resonant (red solid curve) and off-resonant (blue dashed curve) vibrational excitations. The values are normalized to the total fluence of the pulse.

Figure 4

Resonant absorptive vibrational susceptibility as a function of propagation distance at $\tau =4_{}\mathrm{ps}$. The solid black, red dashed, and blue dotted curves show the results from the simulation including only the ${\mathrm{N}}_2$ vibrational nonlinearity, the multiscale calculation, and the perturbation solution Eq. (10), respectively. The green dashed-dotted line displays the result of the simulations when third-harmonic generation is suppressed.

Figure 5

Pulse fluence as a function of propagation distance. The solid black and green dashed-dotted lines show the results with and without third-harmonic generation in the simulations including only the ${\mathrm{N}}_2$ vibrational nonlinearity. The resonant third-harmonic generation contributes to the near elimination of two-photon vibrational absorption.