Temporal solitons in air

Analysis of the group-velocity dispersion (GVD) of atmospheric air with a model that includes the entire manifold of infrared transitions in air reveals a remarkably broad and continuous anomalous-GVD region in the high-frequency wing of the carbon dioxide rovibrational band from approximately 3.5 to 4.2 μm where atmospheric air is still highly transparent and where high-peak-power sources of ultrashort midinfrared pulses are available. Within this range, anomalous dispersion acting jointly with optical nonlinearity of atmospheric air is shown to give rise to a unique three-dimensional dynamics with well-resolved soliton features in the time domain, enabling a highly efficient whole-beam soliton self-compression of such pulses to few-cycle pulse widths.

Figure 1

(a) The refractive index of atmospheric air calculated with the full model including the entire manifold of hitran-database infrared transitions (blue solid line) and the polynomial-fit model (magenta dashed line). (b) Blowup of the refractive index of atmospheric air within the 2.6–4.2-μm wavelength range calculated with the full model including the entire manifold of hitran-database infrared transitions (blue solid line) and the polynomial-fit model (magenta dashed line). (c) Absorption spectrum of atmospheric air $\kappa \left(\lambda \right)$ calculated with the full model including the entire manifold of hitran-database infrared transitions. (d) Group-velocity dispersion ${\beta }_2$ of atmospheric air within the 2.6–4.2-μm wavelength range calculated with the full model including the entire manifold of hitran-database infrared transitions (blue solid line) and the polynomial-fit model (magenta dashed line). The 3.0–3.3-μm anomalous-GVD artifact is contoured by a dashed circle. Full-model calculations are performed for atmospheric air at a temperature of $17.5{}^{\circ }\mathrm{C}$, humidity of $10\%$, pressure of 101 325 Pa, and $\mathrm{C}{\mathrm{O}}_2$ content of 370 ppm; $n_0\approx 1.000269919$ is the refractive index of air at $\lambda =3.9\mu \mathrm{m}$.

Figure 2

Nonlinear dynamics midinfrared pulses with ${\lambda }_0=3.9\mu \mathrm{m}, {\tau }_0=250\mathrm{fs}, W_0=25\mathrm{mJ}$, and $d_0=14\mathrm{mm}$ in air in (a)–(d) ($3+1$)-D and (e)–(h) ($1+1$)-D simulations (a)–(f) with and (g) and (h) without dispersion and absorption: (a) beam dynamics with the beam radius $r_b$ calculated in the full model of beam dynamics (solid line) and with self-focusing disabled (dashed line), (b) temporal evolution of the field intensity integrated over the entire beam, (c) and (d) temporal (c) and spectral (d) evolution of the field intensity on the beam axis, and (e)–(h) temporal (e) and (g) and spectral (f) and (h) evolution in 1D dynamics (e) and (f) with and (g) and (h) without dispersion and absorption.

Figure 3

Soliton self-compression of midinfrared pulses with ${\lambda }_0=3.9\mu \mathrm{m}, {\tau }_0=250\mathrm{fs}, W_0=25\mathrm{mJ}$, and $d_0=4.2\mathrm{mm}$ in air: (a) beam dynamics, (b) spectral evolution, (c) the spectrum at the point of maximum pulse compression $z=42\mathrm{m}$ with the absorption spectrum of air shown by gray shading, (d) temporal evolution of the field intensity on the beam axis, (e) temporal evolution of the field intensity integrated over the entire beam, and (f) temporal envelope of the midinfrared pulse on the beam axis (dashed line) and integrated over the entire beam (solid line) at the point of maximum pulse compression, $z=42\mathrm{m}$ versus the input pulse (dashed-dotted) line.