February 10, 2009 / Vol. 7, No. 2 / CHINESE OPTICS LETTERS 169
Formation of domain reversal by direct irradiation
with femtosecond laser in lithium niobate
Haisheng Zhu (
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), Xianfeng Chen (
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∗
, Hongyun Chen (
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), and Xuewei Deng (
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Department of Physics, the State Key Laboratory on Fiber Optic Local Area Communication Networks and
Advanced Optical Communication Systems, Shanghai Jiao Tong University, Shanghai 200240
∗
E-mail: xfchen@sjtu.edu.cn
Received June 16, 2008
We propose that domain inversion can be directly induced by femtosecond laser both theoretically and
experimentally, which opens a path to achieve three-dimensional (3D) nonlinear crystal with a period in
sub-micron-scale. A simulation of domain inversion is modeled by considering the temporal distribution
of femtosecond pulses. The calculation results clarify that the domain inversions can happen within or
after the interaction with the laser pulse, and the response time of domain inversion is in the picosecond
level depending on the intensity and the materials. The domain reversal windows of lithium niobate by
femtosecond laser are observed which agrees with theoretical predictions qualitatively.
OCIS codes: 320.0320, 160.0160, 310.0310.
doi: 10.3788/COL20090702.0169.
Periodically poled lithium niobate (PPLN), as a man-
ual nonlinear optical crystal, has been widely used for
frequency conversion in the past decade. In order to
obtain short wavelength coherent optical sources by
second harmonic generation (SHG) or sum frequency
generation, micrometer scale periodic domain structure
is necessary, which is out of the ability of conven-
tional room temperature electrical poling techniques. As
the technique of the femtosecond ultrafast laser devel-
ops, interactions between femtosecond laser and vari-
ous materials have drawn more and more attentions.
Femtosecond laser shows unique potential applications
in micro-machining
[1,2]
, optical storage
[3]
, and optical
processing
[4,5]
. As we know, femtosecond laser can be
focused to micrometer scale, so if it can induce domain
inversion in ferroelectrics crystals, domain inversion with
micron-period can be realized. On the other hand, be-
cause the domain inversion happens under certain inten-
sity, and the laser can be focused inside the crystal, it is
expected that three-dimensional (3D) domain inversion
can be achieved. In 1994, Fahy et al. suggested that
reversal of ferroelectric domains can be directly achieved
by ultrafast laser pulses
[6]
, and recently optical poling by
short ultraviolet (UV) pulses has been demonstrated
[7,8]
.
Here we use a more detailed model to propose a method
for domain inversion by femtosecond laser with the wave-
length of 800 nm, the mechanism of which is different
from Refs. [7,8].
Different models have been used to study ferroelectric
materials driven by ultrafast optical pulses. As men-
tioned above, a simple model from Fahy et al. indi-
cates properties of domain inversion subjected to a high-
intensity optical pulse
[6]
. Another one from Montakhab
et al. investigates the behavior of domain walls
[9]
. In
this letter, followed by their works, we theoretically simu-
late the domain inversion process considering spatial and
temporal distributions of femtosecond pulses with an os-
cillating electric field, in which ion accelerating process
is studied. Different from the previous works, our sim-
ulations can provide the information about the energy
threshold of domain inversion as functions of crystal pa-
rameters.
In the x-y plane, a model of an n × n oscillator array
is considered, in which the oscillators, representing the
lithium ions of lithium niobate, are harmonically coupled
and damped
[10]
. Only the nearest neighbor coupling with
a coupling spring constant k and an anharmonic double-
well potential u (z) = −az
2
+ bz
4
(z is the amplitude
of the oscillator, a and b are coefficients) are taken into
account
[6,11]
. When the laser pulse gives the oscillator
enough energy to climb over the potential barrier, the
system will be stable at another equilibrium position,
then the inversion happens
[12]
. To start the oscillation
of the ion oscillators, the polarization direction of the
laser pulse should be parallel to the c axis (spontaneous
polarization axis) of the single crystal congruent lithium
niobate. The electric field of the laser pulse acting on
the crystal is described as follows (generally, we choose
Gaussian distribution):
E
ij,0
=
A
u
0
exp
"
−
i
2
+ j
2
u
2
0
#
t
0
= E
0
exp
−B
i
2
+ j
2
, (1)
where E
ij,0
is the electric field amplitude at the peak
value of the laser pulse at (i, j) in the array
[13]
, u
0
is the
radius of the laser waist spot, and B = 1/u
2
0
is the mod-
ulus decay of laser spot. Equation (1) describes the elec-
tric field spatially, which is also applied in Montakhab’s
model
[9]
. In order to investigate the influence of laser
pulse parameters (response time, threshold, and dura-
tion, etc.), the temporal term should be considered. So
we have
E
ij
(t) = E
ij,0
exp[−α(t − t
c
)
2
] cos(w
0
t − ϕ), (2)
where α is the modulus decay of the laser pulse in tem-
poral distribution, t
c
is a constant, w
0
is the angular fre-
quency of the electric field, and ϕ is the carrier envelop
1671-7694/2009/020169-04
c
2009 Chinese Optics Letters