July 10, 2009 / Vol. 7, No. 7 / CHINESE OPTICS LETTERS 601
Analysis of laser induced thermal mechanical relationship of
HfO
2
/SiO
2
high reflective optical thin film at 1064 nm
Gang Dai (戴戴戴 罡罡罡)
∗
, Yanbei Chen (陈陈陈彦彦彦北北北), Jian Lu (陆陆陆 建建建)
∗∗
, Zhonghua Shen (沈沈沈中中中华华华),
and Xiaowu Ni (倪倪倪晓晓晓武武武)
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
∗
E-mail: huma 1@163.com;
∗∗
e-mail: lujian@mail.njust.edu.cn
Received September 12, 2008
A numerical model is developed for the calculation of transient temperature field of thin film coating
induced by a long-pulsed high power laser beam. The electric field intensity distribution of HfO
2
/SiO
2
high reflective (HR) film is investigated to calculate the thermal field of the film. The thermal-mechanical
relationships are discussed to predict the laser damage area of optical thin film under long pulse high
energy laser irradiation.
OCIS co des: 140.0140, 310.0310, 160.4670.
doi: 10.3788/COL20090707.0601.
The problem of laser damage in optical materials has
been investigated for more than 40 years
[1]
because the
damage of optical components often represents a limita-
tion in laser performance. Coated components show a
lower resistance than bulk materials, therefore, analysis
is concentrated on thin film materials. Most attention is
paid to the studies of short-pulse laser irradiation dam-
age. As a result, damage mechanisms for short-pulse ir-
radiation are now well understood
[2−9]
. However, there
are little relevant reports on the millisecond long pulse
laser induced damage in optical thin films. Therefore, it
is significant to investigate the thermal-mechanical rela-
tionship of multilayer during long pulse laser irradiation.
A numerical model is established to study the thermal-
mechanical relationship of optical thin films under long
pulse laser irradiation. The electric field pattern of
HfO
2
/SiO
2
high reflective (HR) film at 1064-nm laser
is calculated. Thermal field distribution is calculated ac-
cording to the electric intensity, and the thermal-stress
is computed as well.
The electromagnetic field of laser obeys the Maxwell
Equation during the propagation in multilayer as follows:
d
dz
2
+
2πn
k
λ
2
E
k
(z) = 0, (1)
d
dz
E
k
(z) + i
2πn
k
λ
H
k
(z) = 0, (2)
where E
k
,H
k
are electric field and magnetic field in layer
k, respectively, n
k
is the refractive index of layer k , and
λ is the wavelength of the light. We take the layer next
to the substrate as layer one, and the top layer as layer
N. The typical construction of HfO
2
/SiO
2
HR film at
1064 nm is G |(HL)
∧
12H| A, as shown in Fig. 1, where,
G indicates K9 glass, H and L represent a quarter-wave
optical thickness of high (HfO
2
) and low (SiO
2
) refrac-
tive index materials, respectively, and A is air.
The characteristic matrix
[10]
of the film could be ex-
pressed as
B
j
C
j
=
cos δ
i
n
1
sin δ
in
1
sin δ cos δ
0
i
n
2
in
2
0
0
i
n
1
in
1
0
. . .
0
i
n
2
in
2
0
0
i
n
1
in
1
0
1
n
g
,
j + 1
2
= N, (3)
B
j
C
j
=
cos δ
i
n
2
sin δ
in
2
sin δ cos δ
0
i
n
1
in
1
0
0
i
n
2
in
2
0
. . .
0
i
n
2
in
2
0
0
i
n
1
in
1
0
1
n
g
,
j
2
= N, (4)
Fig. 1. Structure of the film.
1671-7694/2009/070601-04
c
° 2009 Chinese Optics Letters