Theory of femtosecond strong field ion excitation and subsequent lasing in N₂⁺

Delayed cavity-free forward lasing at the wavelengths of 391 and 428 nm was observed in recent experiments in air or pure nitrogen pumped with an intense femtosecond laser pulse at wavelength of 800 nm. The mechanism responsible for the lasing is highly controversial. In this article we propose a model explaining the delayed lasing, which contains two parts: (i) ionization of neutral nitrogen molecules and subsequent excitation of nitrogen ions in a strong pump laser pulse, and (ii) coherent emission of excited ions due to the presence of long-lived polarizations maintained by a weak laser post-pulse and coupling simultaneously ground state X2Σg+ to states A2Π u and B2 Σu+ of singly ionized nitrogen molecules N2+. Two regimes of signal amplification are identified: a signal of a few picosecond duration at low gas pressures and a short (sub-picosecond) signal at high gas pressures. The theoretical model compares favorably with results obtained by different experimental groups.