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,N-dimethylamino-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)-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 of ${\beta }_{333}^{\text{eff}}=185\times {10}^{-30}\text{esu}$, which is larger than the ones of OH1 ( ${\beta }_{333}^{\text{eff}}=63\times {10}^{-30}\text{esu}$) and DAST ( ${\beta }_{111}^{\text{eff}}=161\times {10}^{-30}\text{esu}$) [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.

3. 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 n₃(λ) can be described by a one-oscillator Sellmeier equation

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)].

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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 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.

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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]. 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.

 

Fig. 2 (a) Refractive index n₃ and (b) absorption coefficient α₃ of HMQ-TMS crystals for THz waves polarized along the polar axis.

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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]

From the measured dispersion, we deduce that HMQ-TMS crystals have good type-0 phase-matching 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 phase-matching 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.

 

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).

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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.

 

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).

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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 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 can estimate the nonlinear optical susceptibility of HMQ-TMS from the ratio of the conversion efficiencies, ${\chi }_{\text{HMQ-TMS}}^{(2)}/{\chi }_{\text{OH}1}^{(2)}\ge \sqrt{{\eta }_{\text{HMQ-TMS}}/{\eta }_{\text{OH}1}}=37\%$, where ${\chi }_{\text{OH}1}^{(2)}=560\text{pm}/\text{V}$ [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.