Brunner-2014

THz generation by optical rectification of
near-infrared laser pulses in the organic
nonlinear optical crystal HMQ-TMS
Fabian D. J. Brunner,1,∗ Seung-Heon Lee,2 O-Pil Kwon,2 and Thomas
Feurer1
1 Institute
2 Department
of Applied Physics, University of Bern, 3012 Bern, Switzerland
of Molecular Science and Technology, Ajou University, 443-749 Suwon, South
Korea
∗
[email protected]
Abstract:
We show that the organic electro-optic crystal HMQ-TMS
[2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium
2,4,6-trimethylbenzenesulfonate] has favorable properties for the parametric generation
of THz waves in a collinear type-0 phase-matching scheme, i.e., a low
absorption coefficient at wavelengths from 800 to 1500 nm (α < 1.5 cm−1 ),
a relatively low absorption coefficient at frequencies from 0.3 to 1.5 THz
(α < 100 cm−1 ), and a large coherence length in these spectral ranges
(lc > 0.5 mm). We demonstrate efficient generation of broadband THz
pulses through optical rectification of sub-picosecond laser pulses in a
0.2 mm thick HMQ-TMS crystal at the wavelength of 1000 nm. The energy
conversion efficiency achieved in this crystal was 41 times higher than the
one achieved in a 0.3 mm thick GaP crystal, which is an often used material
for collinearly phase-matched THz generation at this laser wavelength.
The peak amplitudes of the THz signal obtained with the HMQ-TMS
crystal were 5.4 times larger in the time-domain and 7.1 times larger in the
frequency-domain than the ones obtained with the GaP crystal.
© 2014 Optical Society of America
OCIS codes: (160.2100) Electro-optical materials; (160.4890) Organic materials; (190.4400)
Nonlinear optics, materials; (190.4710) Optical nonlinearities in organic materials; (300.6495)
Spectroscopy, terahertz.
References and links
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Received 27 May 2014; revised 7 Jul 2014; accepted 7 Jul 2014; published 14 Jul 2014
1 August 2014 | Vol. 4, No. 8 | DOI:10.1364/OME.4.001586 | OPTICAL MATERIALS EXPRESS 1586
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1.
Introduction
Optical rectification of femtosecond laser pulses in an electro-optic crystal is an often used
method for the generation of broadband THz pulses [1]. A high conversion efficiency in
this process is crucial for both THz imaging and spectroscopy applications, because it leads
to a high signal-to-noise ratio and can enable nonlinear optics experiments relying on intense THz pulses. It requires a crystal with a high transparency in the near-infrared (NIR)
and THz spectral range and a high nonlinear optical susceptibility tensor element which can
be exploited in a phase-matching scheme. For instance, collinear type-0 phase-matching is
fulfilled in the inorganic electro-optic semiconductors ZnTe, GaP, and CdTe at the wavelengths of two of the most important femtosecond laser systems, namely 800 nm (Ti:sapphire
lasers) and 1 µm (Yb-doped fiber lasers), respectively [2–4]. However, small energy conversion efficiencies of typically 3 × 10−5 are achieved in these materials [5, 6]. Up to two orders of magnitude higher conversion efficiencies can be obtained in some inorganic ferroelectric and organic molecular crystals with much higher optical nonlinearities. A conversion efficiency of 3.8 % was demonstrated in the inorganic ferroelectric crystal LiNbO3 at a laser
wavelength of 1 µm, however, a more sophisticated Cherenkov phase-matching scheme and
cryogenic cooling was required and the bandwidth of the generated THz pulses was relatively small [7]. Broadband THz pulses can be generated at room temperature in the organic
crystals DAST (4-N,N-dimethylamino-4′-N ′ -methyl-stilbazolium tosylate), DSTMS (4-N,Ndimethylamino-4′-N ′ -methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate), and OH1 {2-[3(4-hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene]malononitrile} with conversion efficiencies up to 2 % at laser wavelengths between 1.3 µm and 1.5 µm [8–12]. The organic crystals COANP (2-cyclooctylamino-5-nitropyridine), HMQ-T [2-(4-hydroxy-3-methoxystyryl)#212730 - $15.00 USD
(C) 2014 OSA
Received 27 May 2014; revised 7 Jul 2014; accepted 7 Jul 2014; published 14 Jul 2014
1 August 2014 | Vol. 4, No. 8 | DOI:10.1364/OME.4.001586 | OPTICAL MATERIALS EXPRESS 1587
1-methylquinolinium 4-methylbenzenesulfonate], and HMQ-TMS [2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium 2,4,6-trimethylbenzenesulfonate] were shown to emit more intense THz pulses than ZnTe when pumped with a femtosecond Ti:sapphire laser or with the
second harmonic of an ultrafast Er-doped fiber laser [13–15].
In this paper, we report on the linear optical properties of the HMQ-TMS crystal for light
polarized along its polar axis in the visible and infrared spectral range from 600 to 2000 nm and
in the THz spectral range from 0.3 to 1.5 THz, discuss the phase-matching characteristics at
various laser wavelengths based on this information and demonstrate efficient THz generation
pumped at 1000 nm.
2.
Basic properties
In the following, we will summarize some basic properties of HMQ-TMS crystals, which
are of interest for nonlinear optical applications [14]. The HMQ-TMS crystal is an organic
molecular salt crystal built up of HMQ [2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium]
cations with virtually perfect parallel alignment and TMS (2,4,6-trimethylbenzenesulfonate)
counter anions. It belongs to the monoclinic point group m. The polar axis is oriented along
the dielectric x3 direction. Large area plane parallel slabs containing the polar axis can be prepared by cleaving as-grown crystals along the crystallographic ac-plane. The HMQ molecule
shows an effective first-order hyperpolarizability obtained by quantum chemical calculation
eff = 185 × 10−30 esu, which is larger than the ones of OH1 (β eff = 63 × 10−30 esu) and
of β333
333
eff = 161 × 10−30 esu) [14, 16]. Since the HMQ-TMS and DAST crystals have simDAST (β111
ilar structures and microscopic nonlinearities, it can be expected that the largest electro-optic
coefficient of the HMQ-TMS crystal is comparable to the one of the DAST crystal, which is
about one order of magnitude larger than the ones of the inorganic electro-optic semiconductors
ZnTe, GaP, and CdTe [4, 14]. However, a figure of merit for THz generation efficiency should
be calculated from measured rather than calculated material parameters for a quantitative comparison [13]. Note that the electro-optic coefficient is not required for the calculation of the
optimum crystal length in Section 4.
3.
Optical properties
The optical group index ng,3 for light polarized along the polar axis was determined by
measuring the time retardation of laser pulses transmitted through a 0.661 mm thick single
crystal relative to air (for details see [17]). The laser pulses with a wavelength λ in the range
from 600 to 2000 nm were provided by an optical parametric amplifier pumped by an amplified
Ti:sapphire laser. In this spectral range, the refractive index dispersion n3 (λ ) can be described
by a one-oscillator Sellmeier equation
n3 (λ ) = n20 +
q λ02
2
λ − λ02
1/2
,
(1)
where ν0 = c/λ0 is the resonance frequency, q is the strength of the main oscillator, and n0
takes the off-resonant contributions of all other oscillators into account. The corresponding
dispersion of the optical group index is given by
ng,3 (λ ) = n3 (λ ) − λ
dn3
(λ ).
dλ
(2)
The Sellmeier parameters listed in Table 1 were obtained by the best fit of the theoretical dispersion function to the measured group index data. These parameters are also accurate for the
#212730 - $15.00 USD
(C) 2014 OSA
Received 27 May 2014; revised 7 Jul 2014; accepted 7 Jul 2014; published 14 Jul 2014
1 August 2014 | Vol. 4, No. 8 | DOI:10.1364/OME.4.001586 | OPTICAL MATERIALS EXPRESS 1588
Sellmeier equation for the refractive index n3 (λ ), since ng,3 (λ ) was measured in a broad spectral range with a high dispersion [17]. The measured data and the fitted dispersion curves are
plotted in Fig. 1(a).
Table 1. Parameters of the Sellmeier dispersion formula for the refractive index n3 (λ )
of HMQ-TMS crystals in the spectral range between 600 and 2000 nm [see Eq. (1)].
q
n0
452 ± 4
1.10 ± 0.06
1.910 ± 0.009
(a)
3.5
3.0
2.5
2.0
1.5
500
1000
1500
2000
25
(b)
20
15
10
Abs. coeff. (1/cm)
Refractive index
Optical group index
4.0
Absorption coefficient (1/cm)
λ0 (nm)
101
0.55
0.60
0.65
Wavelength (µm)
5
0
500
1000
1500
2000
Wavelength (nm)
Wavelength (nm)
2.4
(a)
2.2
2.0
0.4
0.8
1.2
Frequency (THz)
Absorption coefficient (1/cm)
Refractive index
Fig. 1. Linear optical properties of HMQ-TMS crystals for light polarized along the
polar axis. (a) Optical group index ng,3 (dots). The dotted line represents the best
fit to the measured data of the Sellmeier equation for the optical group index ng,3
according to the Eqs. (1) and (2) with the parameters listed in Table 1. The solid
line corresponds to the refractive index n3 calculated from the Sellmeier equation. (b)
Absorption coefficient α3 . The inset shows a semilogarithmic plot of α3 for a better
readability of the graph near the absorption edge.
80
(b)
40
0
0.4
0.8
1.2
Frequency (THz)
Fig. 2. (a) Refractive index n3 and (b) absorption coefficient α3 of HMQ-TMS crystals
for THz waves polarized along the polar axis.
The transmission of light polarized along the polar axis of the crystal was measured in the
same spectral range. The absorption coefficient α3 was calculated from the measured transmission data taking the Fresnel losses into account [see Fig. 1(b)]. The cutoff wavelength, which
we define for an absorption coefficient of 10 cm−1 , is 577 nm. The absorption coefficient is
smaller than 1.5 cm−1 in the whole wavelength range between 800 and 1500 nm. In addition,
we measured the two-photon absorption coefficient β3 = 2.5 ± 0.4 cm/GW at λ = 800 nm and
β3 = 0.4 ± 0.1 cm/GW at λ = 1300 nm using the method described by Bechtel and Smith [18].
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Received 27 May 2014; revised 7 Jul 2014; accepted 7 Jul 2014; published 14 Jul 2014
1 August 2014 | Vol. 4, No. 8 | DOI:10.1364/OME.4.001586 | OPTICAL MATERIALS EXPRESS 1589
The obtained value at 800 nm is approximately half the value of OH1 (β3 = 4.5 ± 0.4 cm/GW),
which we measured for comparison. At λ = 1300 nm, the two-photon absorption coefficient of
HMQ-TMS is comparable to the one of OH1 (β3 = 0.3 cm/GW) and smaller than the one of
DAST (β1 = 0.7 cm/GW) [8, 10].
The refractive index n3 and the absorption coefficient α3 were also measured at THz frequencies using THz time-domain spectroscopy. The refractive index drops from 2.3 to 2.2 as
the THz frequency increases from 0.3 to 1.5 THz and matches the NIR group index well, in
particular for wavelengths between 800 and 1000 nm [see Figs. 1(a) and 2(a)]. The absorption
is low to moderate (α3 < 100 cm−1 ) in the range from 0.6 to 1.5 THz and below the detection
limit of the measurement from 0.3 to 0.6 THz [see Fig. 2(b)]. Thus, the HMQ-TMS crystal has a
considerably lower maximum THz absorption in the shown frequency range than the molecular
salt crystals DAST (600 cm−1 ) and DSTMS (240 cm−1 ), which is necessary for the generation
of a gap-free THz spectrum [8, 9, 19]. Altogether, the HMQ-TMS crystal is a promising candidate for highly efficient THz generation in this frequency range due to its high transparency in
the NIR and THz ranges, good phase-matching properties, and high optical nonlinearity.
4.
Generation of THz pulses in HMQ-TMS crystals
The conversion efficiency of THz generation in a nonlinear optical crystal depends on the linear
and nonlinear optical properties and thickness of the crystal and on laser parameters. For a theoretical calculation of the conversion efficiency, the nonlinear wave equation for the generated
THz signal is typically solved in the frequency domain. An exact solution can be found if plane
waves and a non-depleted pump wave are assumed and cascaded second order and higher order
nonlinear optical effects are excluded [20]. If only forward traveling waves are considered, the
spectral amplitude at the THz frequency ν is given by [8]
(2)
(
µ
χ
ν
,
λ
)
2
πν
I(
ν
)
0
h
i lgen (ν , λ , l),
|ETHz (ν )| = (3)
α T (ν )
c
no (λ ) 2πν
2 + αo (λ ) + i (nT (ν ) + ng (λ ))
where µ0 is the permeability of vacuum, c is the speed of light in vacuum, χ (2) (ν , λ ) is the
nonlinear optical susceptibility for optical rectification, I(ν ) is the Fourier transform of the
intensity profile of the laser pulse, nT (ν ) and αT (ν ) are the refractive index and the absorption
coefficient at the THz frequency ν . no (λ ), ng (λ ) and αo (λ ) are the refractive index, the group
index and the absorption coefficient at the NIR wavelength λ . The dependence of the generated
THz field amplitude on the crystal length l is described by the effective generation length
lgen (ν , λ , l) =

i h
1/2
α T (ν )
πl
l
cos
exp
(−2
α
(
λ
)l)
+
exp(−
α
(
ν
)l)
−
2
exp
−
α
(
λ
)
+
o
T
o
2
lc (ν ,λ ) 


 ,
2 2
α T (ν )
π
−
α
(
λ
)
+
o
2
lc (ν ,λ )
where
lc (ν , λ ) =
c
2ν nT (ν ) − ng(λ )
(4)
(5)
is the coherence length for optical rectification. In addition, we define the optimum crystal
length loptimum as the (smallest) crystal length which gives the maximum effective generation
length, i.e., lgen (ν , λ , loptimum ) = supl>0 lgen (ν , λ , l). The effective generation length lgen is equal
#212730 - $15.00 USD
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Received 27 May 2014; revised 7 Jul 2014; accepted 7 Jul 2014; published 14 Jul 2014
1 August 2014 | Vol. 4, No. 8 | DOI:10.1364/OME.4.001586 | OPTICAL MATERIALS EXPRESS 1590
(a)
4
3
2
1
0
0.4
0.8
1.2
Frequency (THz)
Max. generation length (mm)
Optimum crystal length (mm)
5
3
(b)
2
1
0
0.4
0.8
1.2
Frequency (THz)
Fig. 3. (a) The optimum crystal length for the highest conversion efficiency and (b)
the maximum effective generation length for THz pulse generation in HMQ-TMS
crystals for the laser wavelengths 800 nm (black solid line), 1000 nm (red dotted line),
and 1500 nm (blue dashed line).
to the crystal length l in the case of ideal phase-matching (nT = ng ) and zero absorption (αo =
αT = 0) and it is a bounded function of l if there is a phase-mismatch or absorption, in which
case loptimum is finite. For a finite coherence length and zero absorption, lgen is given by the
function
πl
(6)
l ,
lgen (ν , λ , l) = sinc
2lc (ν , λ )
which has a maximum of 2lc /π at l = loptimum = lc . If there is both phase-mismatch and absorption, lgen has a lower maximum than 2lc /π at l = loptimum < lc . The nonlinear absorption of
the pump beam at very high pump intensities, which leads to smaller optimum crystal lengths
is not included in this simple model.
From the measured dispersion, we deduce that HMQ-TMS crystals have good type-0 phasematching properties for THz pulse generation through optical rectification of laser pulses from
any of the most important fiber or solid-state femtosecond laser systems operating at wavelengths between 800 and 1500 nm. The coherence length is larger than 0.5 mm for the generation of frequencies between 0.3 and 1.5 THz in this range of laser wavelengths. The phasematching is nearly ideal for THz frequencies between 0.3 and 0.8 THz at the laser wavelength
of 800 nm and between 0.8 and 1.5 THz at 1000 nm. Figure 3 shows the optimum crystal length
loptimum for the highest conversion efficiency as a function of THz frequency and the maximum
effective generation length lgen (ν , λ , loptimum ) for the three laser wavelengths 800, 1000, and
1500 nm.
We generated THz pulses in a 0.2 mm thick HMQ-TMS crystal through optical rectification
of 100 fs laser pulses at 1000 nm, which were frequency-doubled idler pulses from an optical
parametric amplifier pumped by an amplified Ti:sapphire laser (see Fig. 4). The THz pulses
were detected by electro-optic sampling in a 1 mm thick ZnTe crystal using a probe beam at
800 nm [2]. For comparison, THz pulses were generated in a 0.3 mm thick GaP crystal under
identical conditions. The THz pulses emitted from the HMQ-TMS crystal showed a 41 times
higher energy, a 5.4 times higher peak amplitude [see Fig. 4(a)], and a 7.1 times higher peak
spectral amplitude [see Fig. 4(b)] than the ones emitted from the GaP crystal.
We also generated THz pulses in a 0.661 mm thick HMQ-TMS crystal and in a 0.731 mm
thick OH1 crystal using laser pulses with a central wavelength of λ = 1300 nm, a duration of 100 fs and a peak intensity of 100 GW/cm2 . The energy conversion efficiency was
ηHMQ-TMS = 4.9 × 10−4 for the HMQ-TMS crystal and ηOH1 = 3.6 × 10−3 for the OH1 crystal. The coherence length of both crystals is sufficiently large, they have comparable linear and
nonlinear NIR absorption, and HMQ-TMS has a larger THz absorption than OH1. Thus, we
#212730 - $15.00 USD
(C) 2014 OSA
Received 27 May 2014; revised 7 Jul 2014; accepted 7 Jul 2014; published 14 Jul 2014
1 August 2014 | Vol. 4, No. 8 | DOI:10.1364/OME.4.001586 | OPTICAL MATERIALS EXPRESS 1591
0
–4
0
5
Time (ps)
10
Spectral amplitude (norm.)
THz amplitude (norm.)
4
(a)
8
(b)
6
4
2
0
0.0
0.5
1.0
1.5
2.0
Frequency (THz)
2.5
Fig. 4. THz pulse generated in a 0.2 mm thick HMQ-TMS crystal and detected in a
1 mm thick ZnTe crystal (red solid line). (a) Time-domain and (b) frequency-domain
signal. THz pulse emitted from a 0.3 mm thick GaP crystal under identical conditions
for comparison (black dotted line).
can estimate the nonlinear optical susceptibility of HMQ-TMS from the ratio of the conversion
p
(2)
(2)
(2)
efficiencies, χHMQ-TMS /χOH1 ≥ ηHMQ-TMS /ηOH1 = 37 %, where χOH1 = 560 pm/V [10].
5.
Conclusions
We have measured the refractive index and absorption coefficient of the organic ionic crystal
HMQ-TMS for light polarized along its polar axis in the optical wavelength range from 600
to 2000 nm and in the THz frequency range from 0.3 to 1.5 THz. The linear absorption is very
low for wavelengths of femtosecond lasers and relatively low for THz waves. The HMQ-TMS
crystal shows good phase-matching properties for THz generation, in particular for the generation of frequencies between 0.3 and 0.8 THz at the laser wavelength of 800 nm and between
0.8 and 1.5 THz at 1000 nm. We have shown that the HMQ-TMS crystal allows more efficient
THz generation than the often used GaP crystal at the laser wavelength of 1000 nm.
Acknowledgments
This work was supported by the National Centre of Competence in Research Molecular Ultrafast Science and Technology (NCCR MUST)—a research instrument of the Swiss National Science Foundation (SNSF), Mid-career Researcher Program (NRF-2013R1A2A2A01007232),
Priority Research Centers Program (2009-0093826) through the National Research Foundation
of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning, and the Ministry
of Education.
#212730 - $15.00 USD
(C) 2014 OSA
Received 27 May 2014; revised 7 Jul 2014; accepted 7 Jul 2014; published 14 Jul 2014
1 August 2014 | Vol. 4, No. 8 | DOI:10.1364/OME.4.001586 | OPTICAL MATERIALS EXPRESS 1592

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