Self-channeling of high-power laser pulses through strong atmospheric turbulence

We present an unusual example of truly long-range propagation of high-power laser pulses through strong atmospheric turbulence. A form of nonlinear self-channeling is achieved when the laser power is close to the self-focusing power of air and the transverse dimensions of the pulse are smaller than the coherence diameter of turbulence. In this mode, nonlinear self-focusing counteracts diffraction, and turbulence-induced spreading is greatly reduced. Furthermore, the laser intensity is below the ionization threshold so that multiphoton absorption and plasma defocusing are avoided. Simulations show that the pulse can propagate many Rayleigh lengths (several kilometers) while maintaining a high intensity. In the presence of aerosols, or other extinction mechanisms that deplete laser energy, the pulse can be chirped to maintain the channeling.

Figure 1

Simulation results showing fractional power, $P_{W_0}/P$ contained within a radius $W_0$ (the initial beam radius) as a function of propagation distance $z$ (in units of the Rayleigh length, $Z_R$) for various powers $P$ (in units of the nonlinear power $P_{NL}$). The initial beam is collimated and has a Gaussian intensity profile.

Figure 2

Simulation results showing isosurfaces of 0.5 times the normalized beam intensity as a function of transverse position and scaled propagation distance for a representative ensemble of turbulence realizations. The initial beam is collimated with a Gaussian intensity profile and $P=0.945P_{NL}$.

Figure 3

Ensemble-averaged fractional power, $P_{W0}/P$, as a function of propagation distance, $z$ (in units of the Rayleigh length, $Z_R$), for ${\sigma }_R^2=3,P=0.945P_{NL}$, and (1) $W_0/{\ell }_0=0.1$, (2) $W_0/{\ell }_0=1$, and (3) $W_0/{\ell }_0=10$. Curves representing the case of no turbulence (solid red curve) and diffraction in vacuum (dotted black curve) are shown for comparison.

Figure 4

Ensemble-averaged probability density vs spot size, $W$ (in units of the initial spot size, $W_0$), after propagating a distance 15 $Z_R$ with ${\sigma }_R^2=3$ and $P=0.945P_{NL}$ for cases (1) $W_0/{\ell }_0=0.1$ and (3) $W_0/{\ell }_0=10$ corresponding to Fig. 3. Insets show ensemble-averaged normalized intensity contours for each case. Beam wander has been subtracted to illustrate short-time profiles.

Figure 5

Ensemble-averaged coherence radius ${\rho }_0$ (yellow dots), spot size $W=\sqrt{2}{W}_{rms}$ (dashed red curve), and full width half maximum (FWHM, dotted gray curve) vs propagation distance, $z$ (in units of the Rayleigh length, $Z_R$), for ${\sigma }_R^2=3$, and $P=0.945P_{NL}$, with (a) $W_0/{\ell }_0=0.1$ and (b) $W_0/{\ell }_0=10$. Theoretical low-power plane wave coherence radii for $W_0/{\ell }_0=0.1$ (black curve) and $W_0/{\ell }_0=10$ (blue curve) are also plotted for comparison.

Figure 6

Ensemble-averaged rms centroid displacement (wander) vs propagation distance, $z$ (in unit of the Rayleigh length, $Z_R$), in the regimes $W_0/{\ell }_0\ll 1$ (yellow dashed curve) and $W_0/{\ell }_0\gg 1$ (blue dashed curve). The solid black curve denotes the theoretical wander of a low-power ($P\ll P_{NL}$), collimated Gaussian beam in the regime $W_0/{\ell }_0\gg 1,\mathrm{\Lambda }\ll 1$.

Figure 7

Simulation result showing laser intensity contours vs radial coordinate, $r$ (in units of the initial spot size, $W_0$), and axial coordinate, $t-z/v_g$ (in units of initial pulse duration, $T_0$), for (a) $z=0$, (b) $z=10Z_R$, and (c) $z=13Z_R$. Simulations use a negatively chirped Gaussian pulse with scaled input parameters $L_T/Z_R=13.2,P/P_{NL}=0.8,\alpha Z_R=0.053,n_2{I}_0=4.8\times {10}^{-10}$, and $Z_R/Z_T=2\times {10}^{-3}$

Figure 8

Panel (a): rms pulse duration, $T_{rms}$, in units of initial pulse duration, $T_0$, (red dashed curve) and peak power $P/P_{NL}$ (blue curve) vs propagation distance, $z$ (in units of the Rayleigh length, $Z_R$). Panel (b): radial FWHM (gray curve), beam radius $W=\sqrt{2}{W}_{rms}$ (dashed red curve), fractional power within radius $W_0$ (dashed blue curve), and fraction power for vacuum propagation (dotted black curve) vs propagation distance $z$. Simulations use a negatively chirped Gaussian pulse with the same input parameters as in Fig. 7, and with ${\sigma }_R^2=1.5,W_0/{\ell }_0=1,{\rho }_0/W_0=1.9$ at $z=15Z_R$.

Figure 9

Measured intensity of laser pulse from Astrella laser (dots) vs transverse position. A Gaussian best-fit (black curve) and two-Gaussian fit (red curve) are shown for comparison.

Figure 10

Ensemble-averaged fractional power contained within the initial beam radius $W_0$ as a function of propagation distance, $z$ (in units of the Rayleigh length, $Z_R$), for (a) $P=1.06P_{NL}$ and (b) $P=1.03P_{NL}$. The Rytov variance ${\sigma }_R^2=3$ at $z=15Z_R$. Curves represent $W_0/{\ell }_0=0.1$ (yellow dashes), (2) $W_0/{\ell }_0=1$ (green dashes), and $W_0/{\ell }_0=10$ (shorter dashes). Curves representing the case of no turbulence (solid red curve) and diffraction in vacuum (dotted black curve) are shown for comparison.