![Normalized power spectra generated by OR in a sugar grain (red continuous line Dlaser~2.8×1012\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}_{laser} \sim 2.8\times {10}^{12}$$\end{document} W/cm², blue dashed line Dlaser~43×1010\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}_{laser} \sim 43\times {10}^{10}$$\end{document} W/cm²). Both spectra are normalized to a dynamic range equal to 1.](https://www.researchgate.net/publication/327551878/figure/fig5/AS:959273043492884@1605719924509/Normalized-power-spectra-generated-by-OR-in-a-sugar-grain-red-continuous-line_Q320.jpg)
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Scientific REPORTS | (2018) 8:13492 | DOI:10.1038/s41598-018-31970-w
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Sub-wavelength terahertz imaging
through optical rectication
Federico Sanjuan1, Gwenaël Gaborit1,2 & Jean-Louis Coutaz1
We record a sub-wavelength terahertz image of a caster sugar grain thanks to optical rectication in
the sample excited with a femtosecond laser beam. The lateral spatial resolution of this technique is
given by the laser spot size at the sample and here its measured value is 50 μm, i.e. ~λ/12. We give an
estimation of the ultimate resolution that could be achieved with this method.
Production of images in the terahertz (THz) spectral range with a sub-wavelength resolution is nowadays com-
monly achieved through near-eld techniques1,2. Most of the setups employ time-domain methods with femto-
second laser excitation of the THz emitting devices, but images have also been obtained with continuous THz
sources like QCL3 or even with synchrotron radiation4, allowing the study of biological tissues5. Such techniques
are extremely ecient and permit to observe nanometer details6,7. On the other hand, they require dedicated
instrumentation and know-how, which are not available in every laboratory.
Another solution is to generate, by optical means, the THz signal at the surface of the studied sample. is
has been greatly demonstrated for years8,9 by Japanese teams, who have produced THz pulses by exciting elec-
tronic integrated circuits with a femtosecond laser. Carriers are photo-excited in the semiconductor substrate
by the laser pulses and then are accelerated by any electric eld along interconnections and components of the
integrated circuit. ese accelerated free carriers radiate a THz signal, which allows one to map the electric eld
at the studied device and for example, to detect any failure in the electronic circuit. Here the spatial resolution
of this mapping is limited either by the distance over which carriers accelerate or by the laser spot size. Typically
this technique, called laser THz emission microscopy (LTEM), exhibits a micron spatial resolution7. It allows also
evaluating the surface state of semiconductors10,11 or the electrical properties of semiconductor components12.
A related technique was employed to produce THz sub-wavelength images by Lecaque et al.13. e sample is
put on the surface of a nonlinear crystal. e laser pump beam is focused in the nonlinear crystal in which it
produces a THz signal by optical rectication (OR) and the OR-generated THz pulse goes through the sample
before reaching the receiver. us the recorded THz intensity is modulated by the near-eld transmittance of the
sample. e image is obtained by scanning the laser beam over the sample and a λ/10 (30 μm) lateral resolution
is demonstrated aer a numerical deconvolution of the image. A method inverse to that of Lecaque et al.13 was
published by Blanchard et al.14: here the sample is put over an electro-optic crystal that is illuminated by a wide
THz beam. e THz eld, which is scattered and diracted by the sample, is read by the probe laser beam that
is tightly focused at the surface of the crystal. us, the THz transmission of the sample is measured in the near
eld and the authors report a λ/30 (14 μm) lateral resolution. anks to a very powerful THz beam generated by
tilted-pulse-front excitation in LiNbO3, images of 370 × 740 μm2 samples are captured at a rate of 35 frames per
second.
ese two techniques, i.e. photo-carriers acceleration in semiconductors and nonlinear eects in crystals,
dier notably because, in the rst one, the sample serves as a source of THz radiation, while in the second one, the
sample perturbs the emission or detection of THz waves in a nonlinear crystal. Here we propose to benet from
the advantages of both techniques, i.e. to employ optical rectication (OR) through or at the surface of the sample
in view of getting a THz image with a sub-wavelength resolution. us the technique is not limited to semicon-
ductor devices and it can be applied to the characterization of dielectric samples, as soon as they show a nonlinear
optical response. As compared to the techniques by Lecaque et al.13 or by Blanchard et al.14, which deliver a signal
proportional to the transmission of the sample at THz frequencies, here the recorded signal depends on both
the sample absorption at visible and THz frequencies and on sample crystallinity through the nonlinear tensor.
Indeed, when the sample material is not centro-symmetric, focusing a powerful beam at its surface induces sec-
ond order optical nonlinear phenomena in the enlightened region, i.e. second harmonic generation (SHG) and
OR. e SHG technique is widely spread in laboratory and hospitals and it delivers superb images that render for
1IMEP-LAHC, UMR CNRS 5130, University Savoie Mont-Blanc, 73376 Le Bourget du Lac Cedex, France. 2Kapteos,
354 voie Magellan, 73800 Sainte-Hélène du Lac, France. Correspondence and requests for materials should be
addressed to F.S. (email: fedeezesanjuan1983@gmail.com) or J.-L.C. (email: jean-louis.coutaz@univ-smb.fr)
Received: 11 July 2018
Accepted: 17 August 2018
Published: xx xx xxxx
OPEN
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Scientific REPORTS | (2018) 8:13492 | DOI:10.1038/s41598-018-31970-w
the sample crystalline inhomogeneity15. For example, membranes of biological cells are highly symmetrical due
to the preferred orientation of their molecules and thus membranes produce a rather strong SHG signal that also
depend on the membrane potential16, while some inner parts of the cells are liquid and thus are almost amor-
phous, leading to no SHG signal or at least to a weak one. us the proposed method is complementary to SHG
imaging, since a THz photon is produced any time a SHG photon is. However, the eciencies of OR and SHG
are dierent, as recorded signals depend not only on the nonlinear tensor, but also on the susceptibility of the
material respectively in the THz and visible ranges. erefore, the two techniques should bring complementary
information on the sample. It should be also noted that, even if the number of generated THz and SHG photons
at the molecular level are the same and even without taking into account propagation and absorption eects, the
THz beam should be weaker than the SHG one, because the energy of THz photons is about 1000 smaller than
those of visible ones. In fact, OR was already used to study biological materials (bacteriorhodopsin)17: the intense
impulse polarization excitation leads to a strong resonant infrared (IR) radiation from the molecules. Such IR
light, whose wavelength is about 10 μm, is easier to detect than the THz one, because the IR photons are about
25 times more energetic than the THz ones. However, this result by Groma and colleagues17 demonstrates that
OR could deliver information on the molecular response of the samples, even if the imaging purpose was not
addressed in their work.
In this paper, we demonstrate the proof of concept of this technique by recording for rst time a THz–OR
image of a grain of caster sugar, taken from a packet of caster cane sugar (brown sugar) bought in a grocery. Sugar
presents the advantage of being an ecient and very cheap nonlinear material, which has already been used for
SHG18–21. Moreover, caster cane sugar grain are highly crystalline, with almost cleaved faces, even if they are not
single crystals and contain impurities. Furthermore, we give the ultimate performance in terms of spatial resolu-
tion of this technique.
To our knowledge, the idea of THz imaging through OR was only published by a Japanese team22–24, in view of
observing ferroelectric domains and especially domain walls in supramolecular ferroelectrics. Impressive images
were obtained, but microscopy was not the main goal of this study. As compared to their work, we address here
for rst time any kind of material with the aim of mapping the crystalline structure of the sample through its non-
linearity and we discuss about the limitations (especially the spatial resolution) of this technique.
Results
Figure1 shows a typical THz waveform and its spectrum obtained with a rather big grain (thickness ~0.8 mm).
The mean laser power is
=Plaser
3.65 mW (3.65 μJ per pulse), corresponding to a peak power density
.×
~
D28 10
laser12
W/cm2. e spectrum is maximum around 0.495 THz and spreads up to 5~6 THz where it
reaches the noise level (about −50 dB). Some strong dips are seen around 0.9 and 1.7 THz. As sugar does not
present absorption peaks at these frequencies, they may be due to water vapor absorption lines25,26 or to tiny
rebounds of the laser pulse in the rubber tape where the sugar grain was stick.
Let us notice that the sample is almost transparent at the pumping laser wavelength and that we didn’t observe
any two-photon absorption eect: therefore THz emission by photo-generated carriers can be ignored. However,
to denitively demonstrate that the observed THz signal is originating from OR, we performed measurements of
the polarization state of the generated THz beam. As expected, we found an angle dependency between the rela-
tive positions of the sugar crystal with regards to the pump laser polarization angle, which is the signature of OR.
e recorded spectra obtained with grains of dierent thicknesses or for dierent pump powers present simi-
lar results. is is shown in Fig.2 where the THz power spectral density (log scale, with a dynamic range normal-
ized to 1), is plotted for the largest and weakest recorded signals, generated with
=.P365
laser
mW
(
.×
~
D28 10
laser12
W/cm2) and
=.P0056
laser
mW (
.×
~
D0043 10
laser12
W/cm2) respectively.
e weakest THz pulse energy is thus about 4200 smaller than the largest one. e spectra are rather similar,
but the weakest one is of course noisier.
is allows us to record only the peak amplitude of the THz waveforms, which makes the image recording
time much shorter. erefore, the eective experimental frequency is the one of the maximum of the THz spec-
trum, i.e. ~0.5 THz. e OR-THz image of a sugar grain is depicted on Fig.3. Points are recorded every 10 μm in
both directions. At the center of the grain, the OR-THz signal magnitude is almost constant, while it decreases
strongly at the crystal border.
Figure4 presents a photography of the grain (le) and the superposition of the sugar crystal outline from pho-
tography (black dashed line) with the OR-THz 2D plot extracted from Fig.3 (right). e THz signal is generated
Figure 1. THz waveform (le) and corresponding power spectrum (right) generated by OR in a sugar grain.
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Scientific REPORTS | (2018) 8:13492 | DOI:10.1038/s41598-018-31970-w
Figure 2. Normalized power spectra generated by OR in a sugar grain (red continuous line
.×~
D28 10
laser12
W/cm2, blue dashed line ×~
D43 10
laser10
W/cm2). Both spectra are normalized to a
dynamic range equal to 1.
Figure 3. 3-D surface plot of the recorded THz OR image.
Figure 4. Image (le side): Photography of the studied caster sugar grain. Image (right side): THz OR image.
e border of the grain sugar deduced from the photography, is shown as a black dashed line.
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Scientific REPORTS | (2018) 8:13492 | DOI:10.1038/s41598-018-31970-w
only by the sugar grain and thus the OR-THz map resembles the grain shape. However, the OR-THz image reveals
details at the crystal border that are not seen on the photography and that could be attributed to the sides of the
grain that are not sharp or vertical, for example because of slivers. Moreover, nearby the top of the sample, the
decrease of the THz signal does not follow the sample border: this could be due to impurities, to a lack of crystal-
linity or to the presence of water at these locations. Since we are making an imaging proof-of-concept, we don’t go
further in this analysis. However, this new information about the crystal could be useful to test its quality.
e decrease of the THz signal at the grain border depends on the shape of the grain side, but also on the waist
of the laser beam and on the diraction of both laser and THz beams by the sample edge and thus it reveals the
lateral spatial resolution of the measurement. To determine this spatial resolution, we have measured the waist of
the laser beam at the grain surface location using a razor blade technique. e measured data (Fig.5 le) are well
tted with a complementary error function, which attests that the laser beam is Gaussian and permits us to deter-
mine the laser beam waist (radius) equal to wlaser = 30 μm (the Gaussian shape of the laser beam is plotted as a
dashed line in Fig.5 le). We have also applied the razor blade technique to the generated THz signal. e data
are almost superimposed with the laser ones, i.e. wlaser = wTHz which proves that the THz signal is only generated
by the illuminated part of the sugar grain and that the THz beam is also Gaussian. is is conrmed by similar
data (see Fig.5 le) recorded using a perfectly at ZnTe wafer, for which scattering and diraction eects do not
perturb the THz beam shape. erefore, following the Rayleigh criterion, the lateral resolution of our record is
δ==w2ln(2) 50
THzTHz
μm.
Figure5 right depicts the prole of the OR-THz signal versus the position along a line that crosses the grain s(a
horizontal line roughly at the center of the grain shown in Fig.5). As already seen in Fig.3, the THz signal is prac-
tically constant at the center of the grain, which reveals that the grain thickness as well as the grain homogeneity
are also regular. e decrease of the OR signal at the grain border occurs over a distance of 300~400 μm. is is
not due to the spatial resolution of the experiment, since both laser and THz beams are much narrower (see con-
tinuous red line on Fig.5 right): this is validated by performing the deconvolution of the OR prole, which does
not show noticeable dierences with the prole plotted here. is smooth decrease is thus attributed to the shape
of the sugar grain and thus to a reduction of the grain thickness nearby its borders.
Discussion
Let us evaluate the limit of the spatial resolution in the OR imaging technique. We suppose that OR occurs at the
surface of the sample and thus phase-matching eect may be neglected (in the present case, the sample thickness
is more or less equal to the THz wavelengths, which justies that propagation eects -phase-matching- may be
ignored). As well, because we only derive order of magnitude, thus we forget about the tensorial behavior of the
nonlinear phenomenon (the nonlinear susceptibility tensor
χ
↔
is simply written as a scalar χ). It follows that the
magnitude ETHz of the THz eld is proportional to the pump laser eld power Plaser:
χχχ∝↔
→
⋅
→
∝∝.EEEE
P
S
:
(1)
THzlaser laserlaser laser
laser
2
Here Elaser is the laser eld magnitude (note that we use here only peak values of either the laser or THz pulses and
not averaged values) and
∝S w
laserlaser
2
is the laser spot surface at the sample surface. e radiated THz power PTHz
is given by:
χ∝∝∝.PSESEP
S(2)
THzTHz THzlaser THzlaser
laser
222
2
To derive this expression, we state that, at the sample surface, the THz spot size is the same as the laser one, i.e.
Slaser = STHz since the THz signal is generated by the illuminated area of the sample. Because this illuminated area
Figure 5. Le: Razor blade signal of the laser beam (red circles) and of the OR THz beam, either generated by a
sugar grain (green squares) or by a ZnTe wafer (blue triangles), together with a complementary error function t
(continuous line, wlaser = wTHz = 30 μm) (the corresponding Gaussian prole is plotted as a dashed line); Right:
OR THz signal prole versus the distance along the sugar grain (blue circles and dashed line). e continuous
red line represents the laser or THz beam prole at the sample, given by the razor blade experiment.
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Scientific REPORTS | (2018) 8:13492 | DOI:10.1038/s41598-018-31970-w
is much smaller than the THz wavelength, the radiated THz eld is almost a spherical wave. is wave is collected
by a lens of section Slens located at distance r from the sample. e collected THz is then focused onto the receiver.
e THz power PTHz,d impinging the receiver is:
χχ∝∝ ∝Ω .PS
P
r
S
r
P
S
SD
(3)
THzd lens THzlens laser
laser
lens laserlaser,222
2
22
lens is the solid angle subtended at the sample source by the entrance aperture of the THz optical system
and Dlaser is the laser power density at the sample surface. It follows that the laser waist wlaser at the sample can be
expressed as a function of PTHz,d, the nonlinearity χ and Dlaser:
χ
∝Ω.w
P
D
1
(4)
laserTHzd
lens laser
,
Two limits are imposed in the OR experiment: (1) the power PTHz,d at the receiver must be larger than the
noise equivalent power NEP and (2) the power density Dlaser must be smaller than the sample material damage
threshold Ddamage. erefore, in this OR experiment, the laser beam can be focused to a minimum waist given by
the following expression:
χ
∝Ω.
wNEP
D
1
(5)
lasermin lens damage
,
setupsample
Because the THz light is generated in the sample area illuminated by the laser, the THz lateral resolution δTHz
is proportional to the minimum laser waist wlaser,min. As expected, when Ddamage is high, the laser beam can be
strongly focused while keeping the laser power constant, resulting in a better THz resolution (δTHz decreases). As
well, using highly sensitive THz detectors (NEP small) like superconducting devices (hot electron bolometers,
kinetic inductance detectors, etc.) may improve the THz signal detection threshold by 2 ~ 4 orders of magnitude27
and thus it would lead either to a sub-micron resolution, or to the study of fragile samples, like biologic tissues.
However, because of the square root in Eq. (5), the resolution depends more on the sample damage threshold.
Also, if the sample is highly nonlinear (large χ), the resolution is better. It follows from relation (5) that the spatial
resolution depends on both the sample (Ddamage, χ) and the setup (NEP, lens). In the present experiment, we
observe damage in the sugar sample for .×~
D32 10
laser12
W/cm2 and we measure both the OR prole and the
THz beam waist with
.×
~
D28 10
laser12
W/cm2. We selected this pump power density in order to have a large
measurement dynamics and actually the generated THz signal (power) was about 1600 times larger than NEP.
erefore, the reported 50-μm resolution could have been decreased by a factor
=1600 40
, i.e. down to a few
μm, at the expense of a strong lack of dynamics.
About the depth resolution of the technique for a bulk sample (d ≫ λ), we can simply estimate it from
Gaussian optics. Typically, when using a focused pump beam, the nonlinear signal is generated in a material
region whose thickness is equal to the Rayleigh length ZR (
πλ=Zwn/
Rlaser laser
2
)28, where nlaser is the refractive
index of the nonlinear material. For thin samples, the depth resolution is the minimum among ZR and the crystal
thickness. In the present work, ZR ~ 5 mm, therefore the depth resolution is equal to the crystal thickness. It is why
the prole given in Fig.5 right is directly proportional to the sugar grain thickness prole, assuming the material
is homogeneous.
In conclusion, we have demonstrated that sub wavelength THz images can be obtained by OR in the sample.
Here, while testing a sugar grain, we achieve a λ/12 lateral resolution. We also give an estimation of the limits
of this technique, in terms of spatial resolution which is determined by both the sample (damage threshold and
nonlinearity) and the setup (collecting optics and detector sensitivity).
Methods
e studied grains are taken in a packet of commercial caster cane sugar (brown sugar). Caster cane sugar is made
at 85–90% of sucrose and the rest (10–15%) includes fructose, glucose and impurities29. Sucrose belongs to the
space group P21 (monoclinic)30. e size of the sugar grains is typically of the order of millimeters. We chose
grains that exhibit as at as possible upper and lower faces, which appear as if they have been cleaved. e studied
sugar grains are stick on a transparent rubber tape. In the laser beam, the tape is located before the grain. us,
the generated THz beam does not propagate through the tape. We have checked that the tape does not produce
a noticeable THz signal when illuminated by the laser. e experimental THz set up is similar to a classical THz
time-domain system, in which the emitting antenna has been substituted by the nonlinear sample, i.e. the sugar
grain stick on the rubber tape (Fig.6). e setup includes an amplied femtosecond laser system (Coherent Libra)
that delivers 5 mJ pulses of 50 fs duration at a repetition rate of 1 kHz. e central wavelength of the laser pulses is
λ = 800 nm. e power of the pumping beam is adjusted with a half-wave plate (HWP) and a polarizer. In front of
the sample, a second HWP permits to rotate the laser polarization. e detection of the THz signal produced by
the sample is recorded with an electro-optic antenna, which consists of a 200 μm thick [111] ZnTe crystal, a HWP,
a Wollaston prism and a balanced photodiode system. e parabolic mirrors used to collect the THz wave have
a 2″ (~5.1 cm) diameter. e one close to the sample has a reected focal length of 6″ (~15.2 cm) and the other
ones 4″ (~10.2 cm). e THz signal was recorded with a lock-in amplier (time constant: 1 s). We performed the
measurements with spatial steps of 10 microns, taking in average 1 minute for each point. e total recording time
of the whole image was around 3.5 hours.
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Scientific REPORTS | (2018) 8:13492 | DOI:10.1038/s41598-018-31970-w
Since all the sugar crystal axes directions are unknown, we changed the pump beam polarization angle by
rotating the HWP situated in front of the sample, in order to maximize the detected signal. en, we optimized
the signal by rotating the HWP close to the balanced photodiodes. is allows to put the detection axis in the
same direction of the THz electric eld. Because the detecting ZnTe crystal is [111] cut, there is no need to rotate
it to maximize the detected signal31.
Data Availability
e datasets generated during and/or analysed during the current study are available from the corresponding
author on reasonable request.
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Acknowledgements
is research and especially the work of Dr. F. Sanjuan, was supported by the French Research Agency (ANR)
through the LabEx FOCUS ANR-11-LABX-0013 project.
Author Contributions
J.-L.C. proposed this study, F.S. performed the experimental work and F.S., J.-L.C. and G.G. analyzed the results
and wrote the manuscript. All authors reviewed the manuscript.
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