Supercontinuum of a $3.9-\mu \mathrm{m}$ filament in air: Formation of a two-octave plateau and nonlinearly enhanced linear absorption

Through numerical simulations we reveal the scenario of $3.9-\mu \mathrm{m}$ filament spectrum enrichment in the atmosphere in the cases of linear and circular polarization of the incident pulse. The discrete spectrum of odd harmonics transforms into the two-octave plateau in the case of linear polarization. In contrast, in the case of circular polarization of the incident pulse, the harmonic-free flat supercontinuum appears with the plasma onset, reaching the tenth harmonic of the input radiation. We identify the energy balance specific to the filamentation near 4 $\mu \mathrm{m}$: the absorption on ${\mathrm{CO}}_2$ lines in the atmosphere is accelerated by the self-phase modulation in the Kerr nonlinearity early before the plasma channel is formed. This nonlinearly enhanced linear absorption overwhelms the plasma losses and conversion of the input pulse energy to the higher harmonics as well as the plateau.

Figure 1

(a) Absorption and refractive indices in Mathar model [26] [red (gray) lines] and our simulations (black lines); input pulse spectrum (gray area). (b) Overall parabolic dependence of refractive index in the mid- and near infrared.

Figure 2

(a) Third and fifth harmonics spectra evolution with propagation distance for a 12-mJ pulse. Each harmonic has its own linear color scale. White curves indicate conversion efficiency (i.e., the spectrum integrated over a 200–250 THz or 360–410 THz range). (b) Normalized spectra of harmonics at several distances, marked with the arrows in panel (a).

Figure 3

(a)–(f) Spatiotemporal distributions of the fundamental radiation (black contour), the third harmonic [red (light-gray) filled contour], and the fifth harmonic [blue (dark-gray) filled contour] for a 12-mJ pulse. (g) Third-harmonic spectrum at $z=14\text{m}$, where two third-harmonic subpulses are 125 fs away from each other, and the spectrum $S_{\text{twin}}\left(\omega \right)$. (h) Normalized time-dependent envelope of the first harmonic (black curve), field of the third and the fifth harmonics [red (light-gray) and blue (dark-gray) curves, respectively] on the beam axis at $z=14\text{m}$.

Figure 4

Evolution with the propagation distance $z$ of the spectra of 80-mJ (a) linearly and (b) circularly polarized pulses (logarithmic color scale). (c) The comparison between the spectra induced by the linearly [blue (dark-gray) curve] and circularly [red (light-gray) curve] polarized pulses.

Figure 5

(a) Deposition of 80-mJ pulse energy into the ${\mathrm{CO}}_2$ band at 70 THz (black solid curve), high-frequency continuum [150–750 THz, blue (dark-gray) curve], and plasma [both ionization and $J_{\text{free}}$ relaxation, orange (light-gray) curve]. Black dashed curve is absorption in the atmosphere in the linear propagation case. Green (light-gray) dotted curve (corresponds to right axis) is peak free electron density. (b)–(d) Spectral broadening over the absorption band at several distances (black lines) and absorption index [red (gray) curve, right axis].