2 Mechanism of Population Inversion in N 2
+
25
-100
0
100
-1
0
1
Laser field
-100
0
100
-1
0
1
Laser field
-100
0
100
-1
0
1
Laser field
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Population on excited state
k=0.01
k=10
k=100
k=100
k=10
(a)
(b)
k=0.01
Fig. 2.2 a The final population in the excited state plotted as a function of the coupling strength
parameter a. The initial conditions are 100% population in the ground level at t = −∞. b The laser
electric fields g k (τ ) cos(τ ) for k = 0.01, k = 10, and k = 100
the laser pulse and revealed the important role of the A
2
u state in reducing the
inversion threshold between the X
2
g
+ state and the B
2
u
+ state depending on the
alignment angle of the N-N axis with respect to the laser polarization direction.
While the vibrational inversion has been widely investigated, it was also suggested
that the rotational degrees of freedom can play a certain role in achieving the lasing
at 391 nm on the basis of the rotational coherence identified by the pump-probe measurements [24]. The coherent couplings between the rotational levels of the B
2
u
+
state and those of the X
2
g
+ state were identified by time-resolved spectroscopy
[25] and were theoretically interpreted [26]. It has also been suggested that the rotational excitation is one of the possible mechanisms in achieving population inversion
between the B
2
u
+ state and the X
2
g
+ state [27, 28]. It was shown that the population inversion can be achieved between rotational levels in the B
2
u
+ state and
those in theX
2
g
+ state when the wavelengths of the excitation laser were 800 nm
[27, 34] and 1500 nm [28] by spectroscopic measurements.
The simulation of rotational excitation in a rigid rotor model for molecular alignment and orientation has been established [35–38]. However, as for N 2
+ , no theoretical simulation of time-dependent population transitions between the rovibronic
states has been published. Therefore, by adopting the theoretical model developed
+
25
-100
0
100
-1
0
1
Laser field
-100
0
100
-1
0
1
Laser field
-100
0
100
-1
0
1
Laser field
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Population on excited state
k=0.01
k=10
k=100
k=100
k=10
(a)
(b)
k=0.01
Fig. 2.2 a The final population in the excited state plotted as a function of the coupling strength
parameter a. The initial conditions are 100% population in the ground level at t = −∞. b The laser
electric fields g k (τ ) cos(τ ) for k = 0.01, k = 10, and k = 100
the laser pulse and revealed the important role of the A
2
u state in reducing the
inversion threshold between the X
2
g
+ state and the B
2
u
+ state depending on the
alignment angle of the N-N axis with respect to the laser polarization direction.
While the vibrational inversion has been widely investigated, it was also suggested
that the rotational degrees of freedom can play a certain role in achieving the lasing
at 391 nm on the basis of the rotational coherence identified by the pump-probe measurements [24]. The coherent couplings between the rotational levels of the B
2
u
+
state and those of the X
2
g
+ state were identified by time-resolved spectroscopy
[25] and were theoretically interpreted [26]. It has also been suggested that the rotational excitation is one of the possible mechanisms in achieving population inversion
between the B
2
u
+ state and the X
2
g
+ state [27, 28]. It was shown that the population inversion can be achieved between rotational levels in the B
2
u
+ state and
those in theX
2
g
+ state when the wavelengths of the excitation laser were 800 nm
[27, 34] and 1500 nm [28] by spectroscopic measurements.
The simulation of rotational excitation in a rigid rotor model for molecular alignment and orientation has been established [35–38]. However, as for N 2
+ , no theoretical simulation of time-dependent population transitions between the rovibronic
states has been published. Therefore, by adopting the theoretical model developed