THz generation by optical rectification of near-infrared laser pulses in the organic nonlinear optical crystal HMQ-TMS

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 1000nm. 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 1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics1, 97–105 (2007). 2. A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett.69, 2321–2323 (1996). 3. G. Chang, C. J. Divin, C.-H. Liu, S. L. Williamson, A. Galvanauskas, and T. B. Norris, “Power scalable compact THz system based on an ultrafast Yb-doped fiber amplifier,” Opt. Express14, 7909–7913 (2006). 4. B. Pradarutti, G. Matthäus, S. 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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.

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 x 3 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 of β eff 333 = 185 × 10 −30 esu, which is larger than the ones of OH1 (β eff 333 = 63 × 10 −30 esu) and DAST (β eff 111 = 161 × 10 −30 esu) [14,16].Since the HMQ-TMS and DAST crystals have similar 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.

Optical properties
The optical group index n g,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 n 3 (λ ) can be described by a one-oscillator Sellmeier equation where ν 0 = c/λ 0 is the resonance frequency, q is the strength of the main oscillator, and n 0 takes the off-resonant contributions of all other oscillators into account.The corresponding dispersion of the optical group index is given by 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 Sellmeier equation for the refractive index n 3 (λ ), since n g,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).   1) and ( 2) with the parameters listed in Table 1 The transmission of light polarized along the polar axis of the crystal was measured in the same spectral range.The absorption coefficient α 3 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 β 3 = 2.5 ± 0.4 cm/GW at λ = 800 nm and β 3 = 0.4 ± 0.1 cm/GW at λ = 1300 nm using the method described by Bechtel and Smith [18].
The refractive index n 3 and the absorption coefficient α 3 were also measured at THz fre- quencies 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 (α 3 < 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.

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] where µ 0 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, n T (ν) and α T (ν) are the refractive index and the absorption coefficient at the THz frequency ν. n o (λ ), n g (λ ) and α o (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 where is the coherence length for optical rectification.In addition, we define the optimum crystal length l optimum as the (smallest) crystal length which gives the maximum effective generation length, i.e., l gen (ν, λ , l optimum ) = sup l>0 l gen (ν, λ , l).The effective generation length l gen is equal to the crystal length l in the case of ideal phase-matching (n T = n g ) and zero absorption (α o = α T = 0) and it is a bounded function of l if there is a phase-mismatch or absorption, in which case l optimum is finite.For a finite coherence length and zero absorption, l gen is given by the function which has a maximum of 2l c /π at l = l optimum = l c .If there is both phase-mismatch and absorption, l gen has a lower maximum than 2l c /π at l = l optimum < l c .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 l optimum for the highest conversion efficiency as a function of THz frequency and the maximum effective generation length l gen (ν, λ , l optimum ) 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/cm 2 .The energy conversion efficiency was η HMQ-TMS = 4.9 × 10 −4 for the HMQ-TMS crystal and η OH1 = 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

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.

Fig. 1 .
Fig.1.Linear optical properties of HMQ-TMS crystals for light polarized along the polar axis.(a) Optical group index n g,3 (dots).The dotted line represents the best fit to the measured data of the Sellmeier equation for the optical group index n g,3 according to the Eqs.(1) and (2) with the parameters listed in Table1.The solid line corresponds to the refractive index n 3 calculated from the Sellmeier equation.(b) Absorption coefficient α 3 .The inset shows a semilogarithmic plot of α 3 for a better readability of the graph near the absorption edge.

Fig. 2 .
Fig.1.Linear optical properties of HMQ-TMS crystals for light polarized along the polar axis.(a) Optical group index n g,3 (dots).The dotted line represents the best fit to the measured data of the Sellmeier equation for the optical group index n g,3 according to the Eqs.(1) and (2) with the parameters listed in Table1.The solid line corresponds to the refractive index n 3 calculated from the Sellmeier equation.(b) Absorption coefficient α 3 .The inset shows a semilogarithmic plot of α 3 for a better readability of the graph near the absorption edge.

Fig. 3 .
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).

Fig. 4 .
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).

Table 1 .
Parameters of the Sellmeier dispersion formula for the refractive index n 3 (λ ) of HMQ-TMS crystals in the spectral range between 600 and 2000 nm [see Eq. (1)].