764 CHINESE OPTICS LETTERS / Vol. 8, No. 8 / August 10, 2010
Amplified spontaneous emission and power amplification in
high-power DF laser systems
Xing Chen ( ((()
∗
, Wenguang Liu (444©©©222), and Zongfu Jiang (ñññmmm444)
College of Photon-Electron Science and Engineering, National University of Defense Technology, Changsha 410073, China
∗
E-mail: chenx04@126.com
Received December 30, 2009
Amplified spontaneous emission (ASE) always occurs in high-power DF laser systems with master
oscillator-p ower amplifier (MOPA) configuration. ASE not only reduces the energy extraction efficiency
of the laser system, but also negatively influences its heat management. The interaction between the ASE
flux and the coherent laser flux, as well as the effect of ASE on cuboid DF amplifiers, is studied using a
finite difference method and an iterative arithmetic. In addition, the influence of ASE on coherent laser
amplification is discussed in detail.
OCIS co des: 140.4480, 140.1550, 140.3280.
doi: 10.3788/COL20100808.0764.
The influence of amplified spontaneous emission (ASE)
on high-power laser systems and laser amplifiers has been
studied in a number of papers
[1−4]
. ASE is esp ecially un-
desirable in high-gain systems because it can grow to a
level at which it begins to deplete the excited popula-
tions, thereby reducing the energy extraction efficiency
of the laser system.
Hunter et al. estimated the reduction in extraction
efficiency caused by ASE in a one-dimensional steady-
state amplifier
[5]
. In the treatment, ASE was considered
as an average radiation within an average solid angle. A
more detailed treatment of a similar case was conducted
by Lowenthal et al.
[6]
, in which ASE was calculated by a
partially analytical method. Sasaki et al. calculated the
distribution of ASE in an amplifier that had a cylindri-
cal symmetry and small aspect ratio, and analyzed the
influence of ASE on extraction efficiency
[7]
.
In this letter, the interaction between the ASE flux and
the coherent laser flux, as well as the effect of ASE on
cuboid DF amplifiers, is studied using a finite difference
method and an iterative arithmetic. The influence of
ASE on coherent laser amplification is also discussed in
detail.
To calculate the influence of ASE on energy extraction
efficiency in the amplifier, the equations of ASE and the
coherence laser are given. Figure 1 is the model of ASE
calculations. ASE intensity at the “observation point” is
obtained by integrating ASE into the entire gain media.
Assuming the light is monochromatic, ASE intensity
from the emitting volume dV at P
0
is seen at the obser-
vation point P (x, y, z) as
[6,7]
dI
ASE
= hf
N
∗
(x
0
, y
0
, z
0
)df
τ
R
dV
4π |r|
2
exp
·
Z
[g (l) − α] dl
¸
, (1)
where f is the frequency of light; h is the planck constant; N
∗
(x
0
, y
0
, z
0
) is the upper-state population density; τ
R
is
the sp ontaneous lifetime of the upper state; r is the distance between the observation point and the emitting point; α is
the nonsaturable absorption coefficient; g(l) denotes the gain coefficient in the amplification with l being propagation
distance in the gain media, which depends on local light intensity. By integrating Eq. (1), the total ASE intensity at
P is
I
ASE
(x, y, z) =
ZZZ
"
hfN
∗
(x
0
, y
0
, z
0
)
τ
R
dV
4π |r|
2
exp
µ
Z
[g (l) − α] dl
¶
#
. (2)
The total light intensity is the sum of ASE intensity and coherent intensity I
f
(x, y, z):
I (x, y, z) =
ZZZ
"
hfN
∗
(x
0
, y
0
, z
0
)
τ
R
dV
4π |r|
2
exp
µ
Z
[g (l) − α] dl
¶
#
+ I
f
(x, y, z) . (3)
For the laser light propagating along the z axis, the
equation of the coherent laser flux is expressed as
dI
f
(x, y, z)
dz
= [g (x, y, z) − α] I
f
(x, y, z), (4)
for which the gain coefficient is defined as
g (x, y, z) =
g
0
(x, y, z)
1 + I/I
s
, (5)
Fig. 1. Model of ASE calculations.
1671-7694/2010/080764-04
c
° 2010 Chinese Optics Letters