4.4.4 Analytical Functions for the Amplitude E 10L
and the Laser Frequency Amendment (ν 2 ν 0n )
Now we obtain the analytical functions for an amplitude and the frequency amendment at approximation of the laser model of nonlinearity by the five-power polynomial. The equation for the amplitude in the steady-state mode E 10L can be deduced
for the second approximation with utilization of the second derivative of the
nonlinear function:
0.6
v/v 0F
E n·
E n·
E n
K 0L = 5.4
K 0L = 43.2
N 0L ·N 0 ·S(E n ), E n
S’(E n )
K 0L ·N 0
1.00002
1.00001
1.00001
1.00001
0.4
1/8
E 2
10L
1/8
1/4
1/4
G 0 = 1
G 0 = 1
0.2
0.0
0.0
10
5
4
3
2
27.2
2.4
1
-1
2
8
6
4
2
1
2
4
6
8
10
2
4
6
8
10
0.2
0.4
0.6
a)
b)
c)
d)
3.4
0.3
1
1
3
T 1n G 00
T 1n G 00 T 1n G 00
T 1n G 00
x
y
K
0.8
1.0
0.0
0.2
0.4
0.6
K
0.8
1.0
Fig. 4.15 The functions of the amplitude square (a) and the oscillation frequency amendment (b)
of the laser versus K 0L ¼ K forT 1n G 00 ¼ 0.125, 0.25, 1 for K 0L N 0 S E n
ð Þ ¼ K 0L N 0
E10n
1þT1nG00ÁE
2
10n
.
Functions of the product N Á E n in the laser versus the amplitude E n (c) and (d) for different pumping
4.4 Abbreviated DE for the Laser in Quasi-Stationary Mode
167