38
Y. Zhang et al.
ground state of N 2 to the vibrational ground state of N 2
+ is 0.9, N 2
+ ion generated
by the intense laser pulse is assumed to be prepared 100% in the vibrational ground
level in the X
2
g
+ state (labeled as X (v = 0)) at t = 0.
As shown in Fig. 2.8a, population inversion is not achieved between X
2
g
+ and
B
2
u
+ when the field intensity is 2 × 10
14 Wcm
−2 . On the other hand, as shown in
Fig. 2.8c, when the field intensity becomes sufficiently large, the population inversion
between the rotational states of X
2
g
+ and B
2
u
+ is achieved in the wide range of
the K quantum number so that the net population inversion is achieved between
X (v = 0) and B (v = 0). At the medium field intensity 4 × 10
14 Wcm
−2 , it can
be seen in Fig. 2.8b that B (v = 0, K ) is more populated than X (v = 0, K − 1)
when K ≥ 15 and that B (v = 0, K ) is more populated than X (v = 0, K + 1) and
X (v = 0, K − 1) when K ≥ 21, showing that the lasing at the P-branch emission
is realized when K ≥ 15 and that the lasing at the R-branch emission can also be
realized when K ≥ 21, which is consistent with the experimental results reported
in [28].
2.5 Summary
Our recent theoretical approaches to exploring the mechanism of population inversion
in N 2
+
, resulting in the generation of the coherent emission at 391 nm called air-lasing,
have been reviewed. Because the ionization preferentially proceeds at the peak laser
field intensity within one optical cycle, N 2
+ created in the laser field starts interacting
with the intense laser field immediately after its birth and is excited electronically
by the laser field. This experimental situation can be simulated theoretically as the
optical excitation of N 2
+ by a sudden turn-on pulse [6].
We demonstrated by quasi-stationary Floquet theory [32] that an efficient population transfer occurs in a two-level system when it interacts with a sudden turn-on
pulse even when the carrier frequency is off-resonance with the energy separation
of the two levels. We applied this sudden turn-on model to N 2
+ interacting with
an intense near-IR laser field and confirmed that the population in the light-dressed
B
2
u
+ is adiabatically transformed to the field free B (v = 0) state when the pulsed
laser field vanishes [33]. We also confirmed on the basis of the sudden turn-on model
that the population inversion between B (v = 0) and X (v = 0) can be achieved rotationally even when the net population inversion is not achieved between B (v = 0)
and X (v = 0). Furthermore, the resonant transition between A
2
u and X
2
g
+ contributes to the decrease in the final population in the X
2
g
+ and to the modification
of the rotational distributions in the vibronic states involved in the air-lasing. The
sudden turn-on model that we have been developing in the past several years to investigate the population transfer among the rovibronic levels of N 2
+ can be applied to
the investigation of time-dependent population transfer processes of any atomic and
molecular ions that are created suddenly within an intense laser field.
Y. Zhang et al.
ground state of N 2 to the vibrational ground state of N 2
+ is 0.9, N 2
+ ion generated
by the intense laser pulse is assumed to be prepared 100% in the vibrational ground
level in the X
2
g
+ state (labeled as X (v = 0)) at t = 0.
As shown in Fig. 2.8a, population inversion is not achieved between X
2
g
+ and
B
2
u
+ when the field intensity is 2 × 10
14 Wcm
−2 . On the other hand, as shown in
Fig. 2.8c, when the field intensity becomes sufficiently large, the population inversion
between the rotational states of X
2
g
+ and B
2
u
+ is achieved in the wide range of
the K quantum number so that the net population inversion is achieved between
X (v = 0) and B (v = 0). At the medium field intensity 4 × 10
14 Wcm
−2 , it can
be seen in Fig. 2.8b that B (v = 0, K ) is more populated than X (v = 0, K − 1)
when K ≥ 15 and that B (v = 0, K ) is more populated than X (v = 0, K + 1) and
X (v = 0, K − 1) when K ≥ 21, showing that the lasing at the P-branch emission
is realized when K ≥ 15 and that the lasing at the R-branch emission can also be
realized when K ≥ 21, which is consistent with the experimental results reported
in [28].
2.5 Summary
Our recent theoretical approaches to exploring the mechanism of population inversion
in N 2
+
, resulting in the generation of the coherent emission at 391 nm called air-lasing,
have been reviewed. Because the ionization preferentially proceeds at the peak laser
field intensity within one optical cycle, N 2
+ created in the laser field starts interacting
with the intense laser field immediately after its birth and is excited electronically
by the laser field. This experimental situation can be simulated theoretically as the
optical excitation of N 2
+ by a sudden turn-on pulse [6].
We demonstrated by quasi-stationary Floquet theory [32] that an efficient population transfer occurs in a two-level system when it interacts with a sudden turn-on
pulse even when the carrier frequency is off-resonance with the energy separation
of the two levels. We applied this sudden turn-on model to N 2
+ interacting with
an intense near-IR laser field and confirmed that the population in the light-dressed
B
2
u
+ is adiabatically transformed to the field free B (v = 0) state when the pulsed
laser field vanishes [33]. We also confirmed on the basis of the sudden turn-on model
that the population inversion between B (v = 0) and X (v = 0) can be achieved rotationally even when the net population inversion is not achieved between B (v = 0)
and X (v = 0). Furthermore, the resonant transition between A
2
u and X
2
g
+ contributes to the decrease in the final population in the X
2
g
+ and to the modification
of the rotational distributions in the vibronic states involved in the air-lasing. The
sudden turn-on model that we have been developing in the past several years to investigate the population transfer among the rovibronic levels of N 2
+ can be applied to
the investigation of time-dependent population transfer processes of any atomic and
molecular ions that are created suddenly within an intense laser field.