E 10n ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4α 01 =3β 03
p
Á 1 À 1= α 01 K L
j j
ð
Þ
½
Š
1=2 ,
ð4:71Þ
where |K L | is the module of the operator transfer function which takes into consideration the Q-factors of the optical resonator and the spectral line of the laser active
medium.
Figure 4.23a shows the plots of E 10n (ν/ν 0F ) for different values of
K 00 N 0 ¼ K 00 N 00 ¼ 0.001–0.1 for Q-factors of the spectral line of emission
Q 02 ¼ 100 and of the optical resonator Q 0F ¼ 20, and Fig. 4.23b shows the plots
of E 10n (ν/ν 0F ) at the Q-factor Q 02 ¼ 100 and N 00 K 00 ¼ 0.1 for different values
1/Q 0F ¼ 0.7 – 0.001.
As the initial symbolic equations of the laser model, we take equations of fourth
order taking into account the inertial property T 1n , considered earlier:
p
4
00 þ
1
Q 0F
þ
1
Q 02
p
3
00 þ 2 þ
1
Q 0F
1
Q 02
p
2
00 þ
1
Q 0F
þ
1
Q 02
p 00 þ 1
!
E n
¼ p
2
00
K 00 N 0 E n
1 þ T 1n G 00 E n
ð Þ
2
:
ð4:72Þ
2.0
1.5
1.0
0.5
2.0
1.5
0.1
0.3
0.7
0.95
1.05
1.00
1.10
1.0
0.5
0.95
optical frequency
a)
b)
v
v 0n
optical frequency
v
v 0n
1.00 1.05
0.01
I/Q 2 = 0.01
I/Q OF = 0.05
I/Q OF = 0.05; 0.01;0.001
I/Q 2 = 0.01
K 00 N 00 = 0.01
0.005
0.001
0.1
K 00 N 00 =
E n0
E n0
1.10
Fig. 4.23 The resonance
characteristics of QWLD at
different values of the Qfactor of the optical
resonator. Plots of the first
harmonic amplitude
E n0 ¼ E 10n (ν/ν 0F ) (a) for
Q 0F ¼ 20, Q 02 ¼ 100 for
different values of
N 00 K 00 ¼ N 0 K 00 ; (b) for
N 00 K 00 ¼ 0.01, Q 02 ¼ 100
for different values of 1/Q 0F
182
4 Semiclassical Theory and Laser Differential Equations for Optoelectronic. . .