Wavelength dependence of laser pulse filamentation in the close spectral vicinity of atomic resonances

TL;DR

The study addresses how laser filamentation and long plasma channels in rubidium vapor depend on the pulse wavelength near atomic resonances. It combines a SEWA-based propagation model with explicit rubidium state dynamics and wavelength-dependent ionization to capture resonant and near-resonant effects. Key findings show a strong asymmetry around the $780$ nm D2 line: sub-resonant wavelengths produce confinement and plasma boundaries similar to resonance, while wavelengths above $780$ nm exhibit weaker self-focusing and diffuse channels, governed by anomalous dispersion, excited-state transitions, and MPI rates. These insights inform the design of multi-meter plasma channels for wakefield acceleration and related applications in remote sensing and lightning protection.

Abstract

We investigate the propagation and nonlinear self-focusing of TW power laser pulses that create 10-m-scale, highly homogeneous plasma channels in rubidium vapor. Using computational solutions of the relevant propagation equations, we study the effects of the ionizing pulse central wavelength in relation to the resonance frequencies of atomic rubidium. Recent experiments show that pulse propagation and plasma channel creation is distinctly different for 780 nm laser pulses (resonant with the rubidium $D_2$ line) and 810 nm laser pulses. We study pulse propagation in a $\pm$30 nm range around the $D_2$ resonance and find that the results are distinctly different when tuning to sub-resonant wavelengths from those obtained for super-resonant wavelengths. For pulse wavelengths below the resonance the behavior is similar to the resonant case, characterized by strong self-focusing and a sharp plasma boundary. Pulse wavelengths above 780 nm on the other hand yield gradually weaker self-focusing and an increasingly diffuse plasma boundary. Our results suggest that the observed behavior can be attributed to an interplay between multiple factors: anomalous dispersion around atomic resonances, resonant transitions between excited states of Rb lying in the 740-780 nm range and wavelength-dependent multiphoton ionization rates.

Figures (8)

• Figure 1: a) Electronic levels of the rubidium atom that are included in the theoretical model. Horizontal lines labeled above mark atomic levels, lines labeled above and below mark groups of fine-structure sublevels that are not resolved on the scale of the figure. Red and black arrows mark allowed dipole transitions between the states, or groups of transitions (transitions between different fine-structure sublevels are not resolved on the figure). Red arrows labeled with wavelength values mark transitions or groups of transitions that come close to resonance with $\lambda=750-810\mathrm{~nm}$ light. Blue lines mark a 760 nm two-photon transition. Energy is measured relative to the ground state energy, horizontal dashed line marks the ionization limit.
• Figure 2: Transmitted pulse properties at $z=10$ m propagation distance as a function of input pulse energy $E_{in}$ for the different central wavelengths. a) Transmitted pulse $D4\sigma$ width. b) Transmitted energy $E_{out}$.
• Figure 3: a) Plasma channel radius $r_p$ and b) plasma channel sheath width $w_p$ at a propagation distance $z=10$ m as a function of input pulse energy $E_{in}$ for the different central wavelengths.
• Figure 4: Contour plots of the ionization probability $P_{ion}(r,z)$ showing the plasma channels created by the laser pulses in the vapor (left $y$-axis). Line plots of the plasma sheath width $w_p$ along the vapor (magenta line, right $y$-axis). $E_{in}=30$ mJ.
• Figure 5: Contour plots of the ionization probability $P_{ion}(r,z)$ showing the plasma channels created by the laser pulses in the vapor (left $y$-axis). Line plots of the plasma sheath width $w_p$ along the vapor (magenta line, right $y$-axis). $E_{in}=70$ mJ.