Population inversion in the rotational levels of the superradiant N2 + pumped by femtosecond laser pulses

Controlling the Polarization of Nitrogen Ion Lasing

Air lasing provides a promising technique to remotely produce coherent radiation in the atmosphere and has attracted continuous attention. However, the polarization properties of N2+ lasing with seeding have not been understood since it was discovered 10 years ago, in which the polarization behaviors appear disordered and confusing. Here, we performed an experimental and theoretical investigation of the polarization properties of N2+ lasing and successfully revealed its underlying physical mechanism. We found that the optical gain is anisotropic, owing to the permanent alignment of N2+ induced by the preferential ionization of the pump light. As a result, the polarization of the N2+ lasing tends to align with that of the pump light after amplification, which becomes more pronounced as the amplification factor increases. Based on the permanent alignment of N2+, we built a theoretical model that analytically interpreted and numerically reproduced the experimental observations, which points out the key factors for controlling the polarization of N2+ lasing.

Optical amplification from high vibrational states of ionized nitrogen molecules generated by 800-nm femtosecond laser pulses

We experimentally investigated the interaction between nitrogen molecules and intense femtosecond laser pulses. When irradiated by an 800-nm pump laser and a delayed 355-nm seed laser, the spectral lines around 353.3 nm and 353.8 nm are observed to be greatly amplified, no matter whether the pump laser is circularly or linearly polarized. The two spectral lines correspond to the transition of N₂⁺ (B, ν' = 5 → X, ν = 4) and N₂⁺ (B, ν' = 4 → X, ν = 3), respectively. In comparison with the spectral lines related with ground vibrational states of nitrogen molecular ion, the observed amplification exhibits different polarization dependence of the pump laser. This distinctive change can be explained by the population variation of high vibrational states caused by the pump laser with different polarizations.

Ramsey interferometry through coherent A2Πu-X2Σg+-B2Σu+ coupling and population transfer in N2+ air laser

Motivated by the hot debate on the mechanism of laser-like emission at 391 nm from N₂ gas irradiated by a strong 800 nm pump laser and a weak 400 nm seed laser, we theoretically study the temporal profile, optical gain, and modulation of the 391 nm signal from N2+. Our calculation sheds light on the long standing controversy on whether population inversion is indispensable for optical gain and show the Ramsey fringes of the emission intensity at 391 nm formed by additionally injecting another 800 nm pump or 400 nm seed, which provides strong evidence for the coherence driven modulation of transition dipole moment and population transfer between the A²Π_u(ν=2)-X²Σg+ states and the B²Σu+(ν=0)-X²Σg+ states. Our results show that the 391 nm optical gain is susceptible to the population inversion within N2+ states manipulated by the Ramsey technique and thus clearly reveal their symbiosis. This study reveals not only the physical picture of producing N2+ population inversion but also versatile control of the N2+ air laser.

Optimization of N2+ lasing by waveform-controlled polarization-skewed pulses

Optical ionization of N₂ and subsequent population redistribution among the ground and excited states of N2+ in an intense laser field are commonly accepted to be fundamentally responsible for the generation of N2+ lasing. By finely controlling this two-step process, the optimization of N2+ lasing is possibly achieved. Here, we design a waveform-controlled polarization-skewed (PS) pumping pulse, in which the leading and falling edges are orthogonally polarized, and their relative field strength and phase can be well controlled. We demonstrate that precise manipulation of the N2+ lasing at 391 nm and 428 nm emissions can be achieved by modulating both the relative phase and amplitudes of the two orthogonally polarized components of the pumping PS pulse. We find that the optimization of N2+ lasing depends not only on the competitive balance between the ionization and post-ionization coupling that varies in different pumping energies but also on the phase with the maximum intensity appearing at the phase of nπ. Orders of magnitude enhancement in the N2+ lasing intensity is observed as the phase changes from (n+1/2)π to nπ. The PS pulse with a controllable spatiotemporal waveform provides us a robust and straightforward tool to efficiently enhance the N2+ lasing emission.

Giant Enhancement of Air Lasing by Complete Population Inversion in N_{2}^{+}

A fine manipulation of population transfer among molecular quantum levels is a key technology for control of molecular processes. When a light field intensity is increased to the TW-PW cm^{-2} level, it becomes possible to transfer a population to specific excited levels through nonlinear light-molecule interaction, but it has been a challenge to control the extent of the population transfer. We deplete the population in the X^{2}Σ_{g}^{+}(v=0) state of N_{2}^{+} almost completely by focusing a dual-color (800 nm and 1.6  μm) intense femtosecond laser pulse in a nitrogen gas, and make the intensity of N_{2}^{+} lasing at 391 nm enhanced by 5-6 orders of magnitude. By solving a time-dependent Schrödinger equation describing the population transfer among the three lowest electronic states of N_{2}^{+}, we reveal that the X^{2}Σ_{g}^{+}(v=0) population is depleted by the vibrational Raman excitation followed by the electronic excitation A^{2}Π_{u}(v=2,3,4)←X^{2}Σ_{g}^{+}(v=1)←X^{2}Σ_{g}^{+}(v=0), resulting in the excessive population inversion between the B^{2}Σ_{u}^{+}(v=0) and X^{2}Σ_{g}^{+}(v=0) states. Our results offer a promising route to efficient population transfer among vibrational and electronic levels of molecules by a precisely designed intense laser field.

Rotational, Vibrational, and Electronic Modulations in N_{2}^{+} Lasing at 391 nm: Evidence of Coherent B^{2}Σ_{u}^{+}-X^{2}Σ_{g}^{+}-A^{2}Π_{u} Coupling

We investigate lasing of a N_{2} gas induced by intense few-cycle near-IR laser pulses. By the pump-probe measurements, we reveal that the intensity of the B^{2}Σ_{u}^{+}-X^{2}Σ_{g}^{+} lasing emission of N_{2}^{+} oscillates at high (0.3-0.5 PHz), medium (50-75 THz), and low (∼3  THz) frequencies, corresponding to the energy separations between the rovibrational levels of the A^{2}Π_{u} and X^{2}Σ_{g}^{+} states. By solving the time-dependent Schrödinger equation, we reproduce the oscillations in the three different frequency ranges and show that the coherent population transfer among the three electronic states of N_{2}^{+} creates the population inversion between the B^{2}Σ_{u}^{+} and X^{2}Σ_{g}^{+} states, resulting in the lasing at 391 nm.

Enhanced Coherent Emission from Ionized Nitrogen Molecules by Femtosecond Laser Pulses

The forward emission spectra were experimentally measured for ionized nitrogen molecules by an 800 nm pump laser and a delayed seed laser. It was found that emission lines around both 428 and 391 nm are greatly enhanced upon use of a 391 or 428 nm seed laser. The emission lines around 391 and 428 nm can be assigned to the rotational transitions of N₂⁺ [B²Σ_u⁺(v' = 0) → X²Σ_g⁺(v = 0)] and N₂⁺ [B²Σ_u⁺(v' = 0) → X²Σ_g⁺(v = 1)], respectively. They originate from seed-induced superfluorescence and resonant stimulated Raman scattering. The genetic algorithm was utilized to simulate the experimental observations and determine the relative population of B²Σ_u⁺(v' = 0), X²Σ_g⁺(v = 1), and X²Σ_g⁺(v = 0). The result verifies that vibrational population inversion is achieved between B²Σ_u⁺(v' = 0) and X²Σ_g⁺(v = 0) by the 800 nm pump laser. Our finding provides new insights into controlling the coherent emission of ionized nitrogen molecules, which has promising application in filamentation-based remote atmospheric sensing.

Subfemtosecond-resolved modulation of superfluorescence from ionized nitrogen molecules by 800-nm femtosecond laser pulses

Superfluorescence emission around 391 nm is generated when nitrogen molecules are irradiated by a strong 800-nm pump laser and a delayed seed laser. The emission corresponds to the transition between N2+(B²Σu+,ν^″=0) and N2+(X²Σg+,ν=0). When another weak 800-nm probe laser is injected and scanned after the pump laser, the superfluorescence intensity is observed to exhibit periodical modulation. The period is determined to be ~2.63 fs, corresponding to the transition frequency between N2+(A²Π_u,ν^'=2) and N2+(X²Σg+,ν=0). Based on theoretical derivation, these observations can be attributed to the laser-induced population transfer and polarization variation between the relevant electronic states of ionized nitrogen molecules.

Testing the Role of Recollision in N_{2}^{+} Air Lasing

It has been known for many years that during filamentation of femtosecond light pulses in air, gain is observed on the B to X transition in N_{2}^{+}. While the gain mechanism remains unclear, it has been proposed that recollision, a process that is fundamental to much of strong field science, is critical for establishing gain. We probe this hypothesis by directly comparing the influence of the ellipticity of the pump light on gain in air filaments. Then, we decouple filamentation from gain by measuring the gain in a thin gas jet that we also use for high harmonic generation. The latter allows us to compare the dependence of the gain on the ellipticity of the pump with the dependence of the high harmonic signal on the ellipticity of the fundamental. We find that gain and harmonic generation have very different behavior in both filaments and in the jet. In fact, in a jet we even measure gain with circular polarization. Thus, we establish that recollision does not play a significant role in creating the inversion.