the coercive field. (Fig. 2, B and C, and fig. S5).
The PLM images taken from the 011ðÞand 0ðÞ 11
surfaces are consistent with the simulated do-
main structure (Fig. 2A). A number of domain
walls are visible in Fig. 2B, in which the angle
between the domain walls and 0½ 11 direction
is ~35°. The domain walls presented in Fig. 2B
are mainly formed by 111½or½ 111 domain with
one of the 11½ 1 =½ 11 1 =½ 1 11 =½ 1 11 ferroelectric
domains whose polarization lies in the (011)
plane(fig.S6).Becauseofthepresenceofthese
light-scattering domain walls, a 633-nm Gaussian
beam with a circular cross section is strongly
scattered as the beam goes through the crystal
(Fig. 2D). The shape of the scattered beam spot
nearly replicates the domain pattern (Fig. 2B)
as a result of the diffraction from the refractive
indices discontinuity at domain walls ( 27 ).
Evidently, the light scattering will reduce the
transparency and adversely affect the efficien-
cy of EO devices.
We employed a high-temperature poling
approach to reduce the clamping effect and
eliminate the light-scattering domain walls.
Specifically, the crystal was heated to ~105°
to 115°C and was thus in the orthorhombic
phase. Then, by applying an electric field of
5kVcm−^1 , we can achieve orthorhombic single-
domain configuration. Finally, the crystal was
slowly cooled to room temperature with the
application of the electric field. During cool-
ing, the orthorhombic single domain with po-
larization along the 011½direction only split
into the rhombohedral 111½and½ 111 domains.
Throughout the process, other variants of
rhombohedral domains were absent (movie
S2 and fig. S7). By using the above poling
strategy, we obtained 011½-poled PIN-PMN-PT
crystals without the undesired domains (i.e.,
½ 111 ,½ 11 1 ,½ 1 11 , or 1½ 11 ; Fig. 2, E and F, and
fig. S8). We observed the extinction phenom-
enon as the incident light is along the 011½
direction with polarization along the 0½ 11 di-
rection (Fig. 2E), whereas the lamellar domain
configuration is observed from the 0ðÞ 11 (Fig.
2F) and 100ðÞ(fig. S8) planes, which echoes the
simulated domain structure under stress-free
conditions (Fig. 1A). As expected, the footprint
of the Gaussian beam remains as a circular
spot after transmitting this crystal along the
½ 011 axis (Fig. 2G), implying substantially en-
hanced light transmittance compared with
that the crystal poled at room temperature. The
PIN-PMN-PT crystals used for the discussion
of EO properties as well as device design are
poled by the high-temperature poling technique.Transparency and electro-optic properties of
the 011½-poled PIN-PMN-PT crystal
We photographed 011½-poled PIN-PMN-PT crys-
tals (Fig. 3A). The poled crystals are highly
transparent when viewed from both the 100½and 011½directions. The light transmittance
along both directions of the poled sample is
~70% in the wavelength range of 550 to 2500 nm,
which is very close to the theoretical limit if
only surface reflection is considered (Fig. 3B).
Additionally, the 011½-poled PIN-PMN-PT crys-
tal exhibits high transparency in the inter-
mediate infrared band, i.e., 2500 to 5500 nm
(Fig. 3C), except for a small absorption peak
around the wavelength of 2840 nm resulting
from the stretching vibrations of OH−ions,
which was observed in many perovskites such
as SrTiO 3 , BaTiO 3 , LiNbO 3 , and KTaO 3 ( 28 – 30 ).
We found the optical absorption to monoton-
ically decrease with increasing wavelength
(Fig. 3D). As a result of the improved poling
technique, the optical transmittance of the
present PIN-PMN-PT crystal is considerably
higher than that of previously reported relaxor
ferroelectric crystals ( 14 , 31 – 33 ). The transmit-
tance can be further improved through the
coating of antireflective film on the transpar-
ent surface, e.g., the 100ðÞsurface (blue curve
in Fig. 3B). In particular, at a wavelength of
1064 nm the optical transmittance is 99.6%,
in which the optical absorption of the crystal
and surface reflection loss are 0.16 and 0.24%,
respectively.
We measured the Pockels coefficientsr 13 and
r 33 with the Mach-Zehnder interferometer
(fig. S9A), whereas the effective EO coefficientSCIENCEscience.org 22 APRIL 2022•VOL 376 ISSUE 6591 373
A BDC
E F GClamping boundary
condition[0 11][100][011][0 11][100][011][100][011][0 11][100][011][0 11]Fig. 2. Domain structures for 011½-oriented rhombohedral PIN-PMN-32PT
crystals poled by conventional and high-temperature methods.(A) Domain
structure of the 011½-poled sample under clamped conditions from phase field
simulations. It should be noted that only two domains with polarization perpendicular
to the 011½direction are present in Fig. 2A, which is due to the fact that the scale
of phase field simulation (64 nm by 64 nm by 64 nm) is much smaller than that of
a real sample. We also conducted a phase field simulation involving the other two
domains (polarizations are along the 1 11
and 1 11
directions) (fig. S3). (BandC) PLM images on 011ðÞand 0 11
surfaces of the 011½-oriented crystals poled by
conventional poling method, respectively. (D) Output spot of a Gaussian beam which
propagates along the 011½direction of the crystal poled by the conventional poling
method. (EandF) PLM images on the 011ðÞand 0 11
surfaces, respectively, of
the 011½-oriented crystals poled by high-temperature poling method, respectively. The
width of the laminar domains of the sample in Fig. 2F is 2.77mm (SD ~±1.72mm).
(G) Output spot of a Gaussian beam that propagates along the 011½direction of the
crystal poled by the high-temperature poling method.RESEARCH | RESEARCH ARTICLES