Enhanced Kerr electro-optic nonlinearity and its
application in controlling second-harmonic generation
Guang-Zhen Li,
1,2
Yu-Ping Chen,
1,2,
* Hao-Wei Jiang,
1,2
and Xian-Feng Chen
1,2,3
1
State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Physics and
Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
2
Key Laboratory for Laser Plasma (Ministry of Education), IFSA Collaborative Innovation Center,
Shanghai Jiao Tong University, Shanghai 200240, China
3
e-mail: xfchen@sjtu.edu.cn
*Corresponding author: ypchen@sjtu.edu.cn
Received April 2, 2015; revised May 21, 2015; accepted May 21, 2015;
posted May 22, 2015 (Doc. ID 237276); published June 18, 2015
We proposed a new scheme of controlling second-harmonic generation by enhanced Kerr electro-optic nonlin-
earity. We designed a structure that can implement the cascaded Pockels effect and second-harmonic generation
simultaneously. The energy coupling between the fundamental lights of different polarizations led to a large non-
linear phase shift and, thus, an effective electro-optic nonlinear refractive index. The effective nonlinearity can be
either positive or negative, causing the second-harmonic spectra to move toward the coupling center, which, in
turn, offered us a way to measure the effective electro-optic nonlinear refractive index. The corresponding
enhanced Kerr electro-optic nonlinearity is more than three orders of magnitude higher than the intrinsic value.
These results open a door to manipulate the nonlinear phase by applying an external electric field instead of light
intensity in noncentrosymmetric crystals. © 2015 Chinese Laser Press
OCIS codes: (160.2100) Electro-optical materials; (160.4330) Nonlinear optical materials; (190.2620)
Harmonic generation and mixing.
http://dx.doi.org/10.1364/PRJ.3.000168
1. INTRODUCTION
Third-order nonlinearities, though with weak third-order coef-
ficients [
1,2], exist in a medium with any symmetry [3–5]. One
common way to enhance the intrinsic weak third-order non-
linearity is via cascading second-order nonlinear effects [6]
because of its much higher value than the direct higher-order
nonlinearity [
7–9]. The Kerr electro-optic (EO) effect is con-
nected to the appearance of the nonlinear third-order suscep-
tibility [
1]. It takes advantage of the modulation of the electric
field and intrinsic nature of fast response time. Besides appli-
cations in electro-optic switching [
10], electro-optical detec-
tion [
11], high-speed optical shutters [12], it is also used to
measure the optical third-order susceptibility of material
[
13]. However, the Kerr EO effect is relatively weak in noncen-
trosymmetric crystals for the existence of a linear EO effect
[
1]. Therefore, it is highly demanded to enhance Kerr EO non-
linearity and broaden its applications in noncentrosymmetric
crystals.
In our previous work, we proposed a new phenomenon
named cascaded polarization coupling generated in MgO
doped periodically poled lithium niobate (PPLN) near its
phase-matching condition [
14]. However, there remains some
deficiencies: (1) the experiment cannot measure the enhance-
ment of Kerr EO nonlinearity or the effective Kerr EO coef-
ficient; (2) the equation of phase shift did not apply for
small phase-mismatching conditions; (3) it just studied the re-
lationship between the phase shift and external electric field,
and the fixed input wavelength made it difficult in practical
flexibility and adjustability.
Therefore, in this paper, we mainly propose one of its po-
tential applications in modulating second-order nonlinearity
by achieving the cascaded effects and second-harmonic gen-
eration (SHG) simultaneously in a single PPLN. We also de-
duced the exact equation of phase shift and studied its
relationship with phase-mismatching. The nonlinearity can
be either positive or negative, depending on the sign of
phase-mismatching. The induced nonlinear refractive index
effectively affected the wave-vector mismatching of SHG
and controlled the process. In turn, the shift of SHG spectra
offered a way to measure the enhancement, which is more
than three orders of magnitude higher than its intrinsic value.
In addition, we used the tunable laser for our light source, by
which we can choose different domain periods or wave-
lengths as needed to perform the experiment. Comparing with
the ordinary way to control SHG by changing the temperature,
our scheme also takes advantage of fast response time and
large tunability.
2. MATERIALS AND METHODS
When an external electric field is applied along the y axis of a
LiNbO
3
crystal [1], the principal axes of the new index ellip-
soid rotates with an angle of θ ≈ γ
51
E
y
− s
41
E
2
y
∕1∕n
ω
o
2
−
1∕n
ω
e
2
with respect to the unperturbed principal axes.
Taking linear and Kerr EO effects into account, we deduce
the refractive index of the new optical axis due to the equation
of the index ellipsoid:
168 Photon. Res. / Vol. 3, No. 4 / August 2015 Li et al.
2327-9125/15/040168-05 © 2015 Chinese Laser Press