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Supplemental Material
Visualization of ferroelectric domains in a hydrogen-bonded molecular
crystal using emission of terahertz radiation
M. Sotome1, N. Kida1, S. Horiuchi2,3 , and H. Okamoto1
1Department of Advanced Materials Science, The University of Tokyo, 5-1-5 Kashiwa-
no-ha, Chiba 277-8561, Japan.
2National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba
305-8562, Japan.
3CREST, Japan Science and Technology Agency (JST), Tokyo 102-0075, Japan.
Content
S1. Sample preparations
S2. Terahertz-radiation experiments
S3. Mechanism of terahertz radiation
S4. Coherence length for terahertz radiation
S5. Terahertz-radiation imaging experiments
S6. Terahertz-radiation vector images
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S1. Sample preparations
Single crystals of croconic acid were grown by slow evaporation of the solution of
raw materials in 1 N hydrochloric acid and purified in repeated crystallization
procedures, as followed by the recipe in Ref. 5 (In Ref. 5, it was reported that the
obtained single crystal is of single phase, which was confirmed by four-circle X-ray
diffractometer). Yellowish crystals with a typical size of 0.6 mm 1 mm 0.4 mm
were obtained. The crystal orientation was checked by a back Laue photograph.
S2. Terahertz-radiation experiments
In the terahertz radiation experiments, we used single crystals with large ac
surfaces, which were obtained by cleaving as-grown crystals. The thickness of the
crystal along the perpendicular direction to the ac plane is 80800 m. We detected
radiated terahertz waves in the time domain using the photoconducting sampling
technique with a photoswitching device made on low-temperature-grown GaAs (LT-
GaAs) coupled with a dipole antenna. The experimental setup is schematically shown in
Fig. S1. The femtosecond laser pulses delivered from a mode-locked Ti:sapphire laser
(the central wavelength of 800 nm, the repetition rate of 80 MHz, the pulse width of 100
fs) were divided into two beams; one beam is used for pump pulses and the other beam
is used for trigger pulses for the detection of terahertz radiations. The pump pulses were
irradiated on ac plane of the sample in the normal incidence [Fig. S1(a)].
The polarization direction of the incident light was set parallel to the horizontal (X)
axis. The radiated terahertz electromagnetic wave was collimated by a pair of off-axis
paraboloic mirrors and was focused on the LT-GaAs detector. In order to enhance the
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collection efficiency of the terahertz waves, we attached a Si lens on the backside of the
LT-GaAs detector. The gap of the antenna was also set parallel to X axis, so that the X-
components of the terahertz electric fields were detected. The induced photocurrents
were measured by a lock-in method. By changing the arrival time of the trigger pulse at
the detector, we recorded the terahertz electric fields in the time domain.
S3. Mechanism of terahertz radiation
When a non-centrosymmetric medium is irradiated by a femtosecond laser pulse
with a finite width of frequency, the electric polarization P is modulated via the
difference frequency mixing within the pulse. This process is expressed as P()=0(2)(-
; 1, -2)E1E2 (=1-2), where E is the electric field of the incident light at
frequency and (2) is the second-order nonlinear optical susceptibility. The frequency
width of the femtosecond laser pulse is 10 THz, resulting in a radiation of
electromagnetic wave in the terahertz frequency region. In Fig. S2, we show electric-
field-amplitude spectra obtained from the time evolutions of the radiated electric fields
shown in Fig. 1(c) by Fourier transformations. The spectra range from 0.2 THz to 3.5
THz.
According to the X-ray diffraction data, the space group of croconic acid is Pca21
[5]. Within the electric dipole approximation, non-zero tensor components of (2) are
aac, aca, bbc, bcb, caa, cbb, and ccc. In our experimental geometry [Fig. 2(b)], only ccc,
caa , and acc survive. We confirmed that caa and acc are negligibly small, as compared
to ccc . Then, the terahertz eclectic field ETHz can be expressed as
ETHz∝❑ccc cos3 θ EX EX . ( S 1 )
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S4. Coherence length for terahertz radiation
The coherence length lc for the terahertz radiation was defined as
lc=λTHz
2|ng−nTHz|, (S 2 )
where THz is the wavelength of the radiated terahertz wave, nTHz is the refractive index
in the terahertz frequency region, and ng is the optical group refractive index of the
incident light. In order to estimate the nTHz spectrum along the c-axis, we performed the
standard terahertz time-domain spectroscopy in transmission geometry. We used ac
surface crystal with the thickness of 980 m. Figure S3(a) shows the nTHz spectrum; we
only obtained the nTHz spectrum below 1.5 THz due to the presence of the strong
absorption above 1.5 THz. In croconic acid, ng at 800 nm used for the excitation was
evaluated to be 2.4 by visible optical spectroscopy [15]. Using these values, we
obtained lc in the terahertz frequency region, as shown in Fig. S3(b). lc at 1 THz was
416 m, which is about 1/10 of lc of ZnTe (3 mm at 1 THz) [10].
S5. Terahertz-radiation imaging experiments
The setup of the terahertz-radiation imaging experiments is schematically shown in
Fig. S1. The sample was attached to a holder placed on a two dimensional stepping
stage, which can independently move in X- and Z-directions [Fig. S1(a)]. The pump
pulses were focused on a sample by a lens (focal length f = 70 mm) or an object lens
(N.A. = 0.3, f = 5 mm). The corresponding spatial resolution was 16 m or 6 m,
respectively, which was evaluated by a conventional knife edge method. We fixed the
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delay time, at which the amplitude of the radiated terahertz wave reaches a maximum,
and monitored its magnitude. Using a raster scan over the entire crystal area, we
obtained a terahertz radiation image. In the raster scan, data were accumulated for 200
msec in each 6 m 6 m area. For the measurements under external electric fields
(Eex), two gold wires were attached on both sides (ab planes) of a crystal with carbon
paste and a bias voltage of up to 1 kV was applied along c.
S6. Terahertz-radiation vector images
Full vector images of the polarization of the crystal shown in Fig. 3(a) are presented
in Fig. S4. The main panel of Fig. S4 is the image of the entire crystal, which
corresponds to the visible image of Fig. 3(a) and the terahertz radiation image in Fig.
(b). Right three panels show the magnified vector images of the boxed areas in the main
panel. Each arrow indicates the direction of the polarization at each position. These
results indicate that the red and blue regions shown in Fig. 3(b) have polarizations
directed right and left, respectively; the polarizations are directed along c axis not only
inside domains but also near DWs.
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Figure S1 A schematic of the experimental setup to directly detect radiated terahertz
electromagnetic waves in the time domain. (a) Magnified view near the sample. is
defined as the angle between the crystallographic c and X axis. The electric field of the
incident light was set parallel to the X axis. The sample is placed in a X-Z stage in order
to measure the spatial image of the terahertz radiation. (b) Overview of the experimental
setup with the photoconducting sampling technique with a low- temperature-grown
GaAs (LT-GaAs) antenna detector. A wire grid polarizer (WG1) is set between off-axis
parabolic mirrors in all the measurements to detect horizontal (X) components of the
radiated terahertz electric fields. For the vector imaging of electric polarization P,
another wire grid polarizer (WG2) is inserted in front of WG1.
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Figure S2 Fourier spectra of electric-field amplitudes of the terahertz radiations with the
external electric field of ± 33.3 kV/cm shown in Fig. 1(c).
Figure S3 (a) Refractive index and (b) coherence length for the terahertz radiation with
800 nm excitations in the terahertz frequency region.
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Figure S4 Terahertz vector image of the polarization in the same area shown in Fig.
3(b). Right three panels show the expanded views of boxed areas in the main panel.