1
Supplemental Material
Elliptically polarized terahertz radiation from a chiral oxide
R. Takeda1, N. Kida1,*, M. Sotome1, and H. Okamoto1
1
Department of Advanced Materials Science, The University of Tokyo, 5-1-5 Kashiwa-
no-ha, Chiba 277-8561, Japan.
Content
S1. Estimation of complex optical constants in terahertz and visible frequency
regions
S2. Laser power dependence of terahertz radiation
S3. Estimation of coherence length and effective generation length for terahertz
radiation
2
S1. Estimation of complex optical constants in terahertz and visible frequency
regions
We measured the reflectance R and transmittance T spectra in the energy range of 0.55
eV by the grating monochromator. Figure S1(d) shows the measured R and T spectra. A
sharp decrease of T and the gradual increase of R are due to the presence of the chargetransfer gap around 2.2 eV. We show in Fig. S1(f) the absorption coefficient  spectrum,
1
𝑇
which was estimated from R and T data by using the relationship of  = − 𝑑 ln ((1−𝑅)2 ),
where d is the thickness of the sample. Bi12GeO20 has a transparent window below 2 eV.
 at 800 nm (the wavelength of a femtosecond laser pulse used for the terahertz radiation
experiments) was estimated to be 3 cm-1, which corresponds to the penetration depth of
3.33 mm. It exceeds the thickness of the sample (1 mm). By performing the KramersKronig transformation using the measured R and T spectra, we estimated the refractive
index n spectrum, as shown by the blue line in Fig. S1(e). As indicated by the broken line
in Fig. S1(e), we reproduced the n spectrum by using the Sellmeier relationship, given by
𝑆 𝜆20
𝑛 = √1 + 1−(𝜆0
2
0 /𝜆)
with S0 = 5.920 m-2 and 0 = 278 nm, where  is the wavelength. The
calculated optical group refractive index ng spectrum is shown by the green line in Fig.
𝑑𝑛
S1(e). ng is given by |𝑛 −  𝑑 |. ng at 800 nm was estimated to be 2.79, which is
indicated by the horizontal line in Fig. S1(b).
Figure S1(a) shows the optical spectra in the terahertz frequency region up to 10 THz.
R (circles) and T (squares) spectra were measured by Fourier-transformed infrared (FTIR) spectroscopy and terahertz time-domain spectroscopy, respectively. R and T spectra
below 2.5 THz are shown in Fig. 1(d). In order to estimate the n and  spectra up to 10
THz, we performed the dispersion analysis by assuming a Lorentz oscillator with a
damping rate  and the oscillator strength f. The measured R spectrum was able to be
reproduced by Lorentz oscillators with parameters listed in Table SI. The detailed
procedures of our dispersion analysis were reported in Refs. 18 and 32. Figures S1(b) and
3
(c) show the estimated n and  spectra (solid lines), respectively. n and  spectra indicated
by squares were directly obtained by the measured transmittance and phase spectra. The
detailed our estimation procedure was reported in Ref. 32. .
S2. Laser power dependence of terahertz radiation
To reveal the mechanism of terahertz radiation from Bi12GeO20, in addition to the
measurements of the azimuth angle dependence described in the main text, we measured
the laser power dependence of terahertz radiation. In this experiment, we used a
Ti:sapphire regenerative amplifier (the center wavelength of 800 nm, the repetition rate
of 1 kHz, and the pulse width of 25 fs) as light source. Using an optical parametric
amplifier, we obtained pump pulses with a wavelength of 1200 nm. The angle  of the
electric field of incident pump pulses was set to 139. The spot diameter was 4 mm. For
the detection of the terahertz wave, we adopted the standard electro-optical sampling
technique using a (110) ZnTe crystal. We show in Fig. S2 the laser power dependence of
the amplitude of the terahertz electric field at 0 ps ETHz (circles), which linearly increases
with laser power, as indicated by a solid line. This clearly indicates that the optical
rectification dominates terahertz radiation from Bi12GeO20.
S3. Estimation of coherence length and effective generation length for terahertz
radiation
We estimated the coherence length 𝑙c for the terahertz radiation [30]. 𝑙c is given by
𝑙c =
𝜋𝑐
𝜔THz |𝑛g − 𝑛THz |
,
(S1)
where c is the velocity of light. The estimated 𝑙c using values of n in the terahertz
frequency region [Fig. S1(b)] and ng at 800 nm (2.79) is shown by the purple line in Fig.
1(g). Strong absorptions, which were assigned to the TO F modes, exist at 1.37 THz and
1.54 THz, as seen in the  spectrum shown in Fig. 1(f). Thus, we calculated the effective
generation length for the terahertz radiation 𝑙ceff [31] by taking into account the
contributions of TO F modes. 𝑙ceff is expressed as
4
1
𝑙ceff
𝛼
𝜔
2
1 + exp(−𝛼𝑑) − 2 exp (− 2 𝑑) cos ( 𝑐 |𝑛THz − 𝑛g |𝑑)
=(
) ,
2
𝛼 2
𝜔 2
( 2 ) + ( 𝑐 ) (𝑛THz − 𝑛g )
The calculated 𝑙ceff is shown by the red line in Fig. 1(g).
(S2)
5
FIG. S1: (a) Reflectance R and transmittance T spectra measured by Fourier-transformed
infrared spectroscopy and terahertz time-domain spectroscopy, respectively. The solid
line is the result of least-square fit by the dispersion analysis with parameters listed in
Table SI. The estimated refractive index n [(b)] and the absorption coefficient  [(c)]
spectra. (d) R and T spectra measured by the grating spectroscopy. (e) The estimated
optical refractive index n spectrum (the blue line) by the Kramers-Kronig transformation.
The broken line indicates the fitting result by using Sellmeier relationship. The optical
group refractive index ng spectrum is shown by the green line. (f)  spectrum obtained
from R and T data. The vertical broken lines in (e) and (f) indicate the photon energy of
a femtosecond laser pulse used for the terahertz radiation experiments.
6
ETHz (arb. units)
0
-0.5
-1
0
10
20
30
40
50
Laser Power (mW)
FIG. S2: Laser power dependence of the laser power with the incident laser angle of 139.
Table SI. Obtained fitting parameters with ε =10.62.
Mode i
1
2
3
4
5
6
7
8
9
10
11
12
ω𝑖 (THz)
1.36
1.52
2.96
3.11
3.33
3.68
5.44
5.65
6.10
6.95
8.10
8.99
γ𝑖 (THz)
0.08
0.09
0.50
0.09
0.11
0.17
1.21
0.05
0.19
0.34
0.35
0.72
𝑓𝑖
6.33
3.47
5.35
6.47
0.73
6.37
0.99
0.01
0.19
3.26
0.85
2.91