For the analysis convenience, reminding that we consider the quasi-harmonic
oscillations in nonconservative oscillating system, we introduced the normalized
OTF K E ( p) ¼ K E0 ( p)/p and K P ( p) ¼ p Á K P0 ( p). Then, the DE system is written in
the compact form as:
E n ¼ K E p
ð Þ Á P n
P n ¼ K P p
ð Þ Á N Â E n
pN ¼ α N0 À
N
T 1
À N Â Re E n Á P
Ã
n
Â
Ã
8
> > <
> > :
,
ð4:22Þ
Figure 4.3 shows plots of modules and arguments of OTF of QWLD K P , K E ,
K P Á K E for the values of the optical resonator Q-factor Q OF ¼ 100 and the Q-factor of
the spectral line of the active medium Q 02 ¼ 10. The detuning of the natural
frequencies (ν 0n À ν 12 )/ν 12 ¼ 0.1 is presented for clearness. In the real QWLDs,
the tuning is less than 0.001.
Plots of OTF modules and arguments of the laser at Q-factors of the optical
resonators Q OF ¼ 100 and the spectral line of the active medium Q 02 ¼ 10 demonstrate the narrow spectral line of the module of the total OTF, which in this example
is defined by the high-Q optical resonator.
K P , K E , K P ·K E
K P ·K E
K E
K P
arg
arg
arg
500
400
300
200
100
3
2
1
-1
0.5
1.0
1.5
2.0
-2
-3
v 12
v 12
v 12
v 0n
v 0n
v 12
0.5
a)
b)
1.0
1.5
2.0
K P ·K E
K P
K E
Fig. 4.3 Modules and
arguments of OTF of
QWLD K P , K E ,K P Á K E at Qfactor values of the optical
resonator Q OF ¼ 100 and the
Q-factor of the spectral line
of the active medium
Q 02 ¼ 10. The detuning of
natural frequencies
(ν 0n À ν 12 )/ν 12 ¼ 0.1 is
given for clearness
4.2 Constitutive Equations of a Laser
145