Coupling of ${\mathrm{N}}_2^{+}$ rotational states in an air laser from tunnel-ionized nitrogen molecules

We report on experimental and theoretical investigations of dynamic evolution of individual $R$-branch laser lines from tunnel-ionized nitrogen molecules based on a pump-probe scheme. Our observation shows that the intensities of the $R$-branch laser lines exhibit rapid oscillations which can be decomposed into periodic oscillations at different frequencies. The oscillations can be attributed to the coupling between the rotational quantum states mediated either by the probe pulses or by the $P$-branch laser emission from the molecular ions.

Figure 1

Schematic diagram of the experimental setup. BS: beam splitter; GT: Glan-Taylor prism; DM: dichroic mirror with high reflectivity at ∼400 nm and high transmission at ∼800 nm; HWP: broadband half wave plate at ∼800 nm; filter: neutral density filter.

Figure 2

(a) A typical forward lasing spectrum based on the pump-probe configuration. The inset is a close-up view of the $R$-branch transition, and the numbers label the rotational levels of molecular ions on the excited state. (b) The lasing intensities of each individual rotational state $J$ of the $R$ branch as a function of time delay between the pump and probe pulses. (c) The Fourier transforms of the corresponding curves in (b).

Figure 3

(a) The forward lasing spectrum of $R$-branch transitions at a pump energy of 2.4 mJ. (b) The Fourier transforms of time-dependent lasing intensities of $R$-branch transitions.

Figure 4

The mechanisms of the modulations in the populations (a) in the rotational level $J$ of the excited state $B^2{\Sigma }_u^{+}$ and (b) in the rotational level $J-1$ of the ground state $X^2{\Sigma }_g^{+}.$

Figure 5

(a) The formation of a bandhead centered at $J$ = 13 of $P$-branch transitions of $N_2^{+}$ $[B^2{\Sigma }_u^{+}(\upsilon =0)\to X^2{\Sigma }_g^{+}(\upsilon =0)\text{]}$. (b) Schematic illustrations of the resonant Raman coupling processes of $|J\rangle \leftrightarrow |J+2\rangle$ and $|26-J\rangle \leftrightarrow |28-J\rangle$. The $P$-branch photon of the same photon energy involved in both the processes is indicated with the arrows.