22
Y. Zhang et al.
which pollutants in the atmosphere can be effectively detected. In the past few years,
it has been reported that by propagating an IR pump pulse in air, UV emission will be
generated from filamentation in air [3, 4]. Among the coherent emissions generated
from the laser induced filamentation in air, the forward and backward emission at
391 nm achieved by near-IR femtosecond laser pulses is reported to be the emission
between the vibrational ground states of the electronically excited B
2
u
+ state and
electronic ground X
2
g
+ state of N 2
+ [5–9], which requires the higher probability
of N 2
+ to be prepared in B
2
u
+ than in X
2
g
+ , leading to the population inversion.
For further application, especially in enhancing the emission signal, we need to
understand the mechanism of the population inversion in N 2
+
.
2.1.1 Superradiant Emission Mechanism
Through the measurement and analysis of the temporal profiles of the coherent emission, the signatures of the superradiance was reported in [10]. Since then, the superradiance, where a group of excited molecules interact with light collectively and
coherently, has been suggested as a possible mechanism of air-lasing [10–13]. Meanwhile, it has been demonstrated that seed-triggered superradiance can be enhanced by
population inversion achieved in N 2
+ [12], and a mechanism of stimulated-emissioninduced seed amplification was suggested in [6, 14, 15].
2.1.2 Excitation Mechanism
While the emission process is still controversial, the excitation process from electronically ground X
2
g
+ state to the electronically excited B
2
u
+ state of N 2
+ becomes
clearer. The field-induced inelastic recollision process was suggested as the excitation mechanism [11, 16], but later, the recollision process was reported to be not
related to the air-lasing phenomenon [17, 18]. In [6, 8, 9, 15, 19–21], the strongfield ionization induced efficient optical coupling among the three electronic states,
X
2
g
+ , A
2
u , and B
2
u
+ states of N 2
+ shown in Fig. 2.1 as well as the important
role of the electronic A
2
u state in depleting population in X
2
g
+ were proposed.
In [22, 23], it was demonstrated that the alignment angle between the molecular
axis of N 2
+ and the polarization direction of the laser pulse affects the population
transfer. Besides the vibrational population inversion, the rotational coherence in
the 391 nm air-lasing was observed by pump-probe measurements [24], the coherent
coupling between rotational states of X
2
g
+ and those of B
2
u
+ in the strong laser
field was shown by time-resolved spectroscopy [25], and interpreted theoretically
[26], and the rotational excitation was suggested as a possible mechanism of population inversion [27–29]. It was also reported based on spectroscopic measurements
that population inversion can be achieved between specific rotational states in the
Y. Zhang et al.
which pollutants in the atmosphere can be effectively detected. In the past few years,
it has been reported that by propagating an IR pump pulse in air, UV emission will be
generated from filamentation in air [3, 4]. Among the coherent emissions generated
from the laser induced filamentation in air, the forward and backward emission at
391 nm achieved by near-IR femtosecond laser pulses is reported to be the emission
between the vibrational ground states of the electronically excited B
2
u
+ state and
electronic ground X
2
g
+ state of N 2
+ [5–9], which requires the higher probability
of N 2
+ to be prepared in B
2
u
+ than in X
2
g
+ , leading to the population inversion.
For further application, especially in enhancing the emission signal, we need to
understand the mechanism of the population inversion in N 2
+
.
2.1.1 Superradiant Emission Mechanism
Through the measurement and analysis of the temporal profiles of the coherent emission, the signatures of the superradiance was reported in [10]. Since then, the superradiance, where a group of excited molecules interact with light collectively and
coherently, has been suggested as a possible mechanism of air-lasing [10–13]. Meanwhile, it has been demonstrated that seed-triggered superradiance can be enhanced by
population inversion achieved in N 2
+ [12], and a mechanism of stimulated-emissioninduced seed amplification was suggested in [6, 14, 15].
2.1.2 Excitation Mechanism
While the emission process is still controversial, the excitation process from electronically ground X
2
g
+ state to the electronically excited B
2
u
+ state of N 2
+ becomes
clearer. The field-induced inelastic recollision process was suggested as the excitation mechanism [11, 16], but later, the recollision process was reported to be not
related to the air-lasing phenomenon [17, 18]. In [6, 8, 9, 15, 19–21], the strongfield ionization induced efficient optical coupling among the three electronic states,
X
2
g
+ , A
2
u , and B
2
u
+ states of N 2
+ shown in Fig. 2.1 as well as the important
role of the electronic A
2
u state in depleting population in X
2
g
+ were proposed.
In [22, 23], it was demonstrated that the alignment angle between the molecular
axis of N 2
+ and the polarization direction of the laser pulse affects the population
transfer. Besides the vibrational population inversion, the rotational coherence in
the 391 nm air-lasing was observed by pump-probe measurements [24], the coherent
coupling between rotational states of X
2
g
+ and those of B
2
u
+ in the strong laser
field was shown by time-resolved spectroscopy [25], and interpreted theoretically
[26], and the rotational excitation was suggested as a possible mechanism of population inversion [27–29]. It was also reported based on spectroscopic measurements
that population inversion can be achieved between specific rotational states in the