1. Introduction

In the recent years, the improvement of existing and the advent of novel sources and detectors of THz radiation was driven by an increasing number of potential applications in many fields of science and technology [1]. One field of research is the development of novel nonlinear optical materials especially designed for efficient THz generation (through difference frequency generation or optical rectification) and detection (through electrooptic sampling). The requirements for these materials are a high optical nonlinearity and a low dielectric constant, which results in small Fresnel losses at the boundaries and, more important, allows velocity-matching [2]. Particularly among organic crystals, one can find materials that exhibit both of these desired properties. The organic salt crystal 4-N,N-dimethylamino-4′-N′-methyl stilbazolium tosylate (DAST) was proven to be an excellent THz emitter and detector [3, 4]. However, a transverse optical phonon leads to a gap in the accessible THz spectrum around 1.1 THz [5]. In a recent work, the frequency and the oscillator strength of this resonance could be reduced by the use of a different anion [6]. Nevertheless, the THz absorption remains relatively strong near the resonance frequency. Instead of modifying the molecules of a salt crystal, one can circumvent the problem of the ionic resonance by using a different class of organic materials, namely hydrogen bonded organic crystals [7].

Recently, a very promising member of this class of materials, the configurationally locked polyene crystal 2-[3-(4-hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene]malononitrile (OH1) has been developed and its linear and nonlinear optical properties have been determined [8, 9]. In this article, the linear optical properties of OH1 at THz frequencies are presented, and a detailed theoretical and experimental investigation of OH1 as a THz source and detector is given, including the analysis of velocity-matching conditions.

2. Basic properties of OH1

2.1. Crystal structure

The OH1 molecule (see Fig. 1) shows a large dipole moment of µ _g=3.44×10^-29 Cm and contains an extended π-conjugated electron system, which leads to a large hyperpolarizability of β_z=765×10^-40 m⁴V^-1, as measured in chloroform solution [8]. The charge transfer within the OH1 chromophore is induced by a phenolic (Ar-OH) electron donor and a dicyanomethylidene (C=C(CN)₂) electron acceptor [8]. In the crystalline phase, the material has the point group symmetry mm2 with an acentric packing of four molecules per unit cell with hydrogen bonds between the phenolic and the cyano group (i.e. Ar-OH…N≡C) [8]. The angle between the charge transfer axis of the chromophores and the polar c-axis of the crystal is 28°, which results in a large macroscopic second-order nonlinear optical susceptibility of χ ⁽²⁾ ₃₃₃=240±20 pm/V for second-harmonic generation at a fundamental wavelength of 1.9 µm [9]. OH1 single crystals grow as a-plates, i.e. with the largest surfaces perpendicular to the a-axis [8].

 

Fig. 1. The chemical structure of the molecule OH1.

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2.2. Near infrared linear and nonlinear optical properties

Due to the orthorhombic symmetry of the crystal, the dielectric coordinate system (x ₁,x ₂,x ₃) coincides with the crystallographic coordinate system (a,b,c). OH1 crystals are highly birefringent due to a highly anisotropic linear polarizability of the chromophores and their acentric packing (n ₃−n ₂>0.5 in the wavelength range between 0.6 and 2.2 µm) [9]. The absorption coefficient for the b- and c-polarizations is below 0.3mm^-1 in the wavelength range between 680 and 1460 nm [9]. The largest linear electrooptic coefficient r ₃₃₃=52±7 pm/V [9] at a wavelength of 1300 nm and a modulation frequency of 1 kHz is similar to the largest electrooptic coefficient r ₁₁₁=53±6 pm/V of DAST [10].

3. Terahertz spectroscopic measurements

3.1. Experiments

The linear optical properties of OH1 single crystals have been determined at THz frequencies using THz time-domain spectroscopy (TTDS). The samples were OH1 a-plates with thicknesses of 0.956 and 0.365 mm, respectively. The a-plates allowed the determination of the refractive index n and the absorption coefficient α along the dielectric axes x ₂ and x ₃, where n ₃ and α ₃ are of main interest for THz applications (see Section 4).

The source of the laser pulses for the generation and detection of the THz pulses was the tunable output of an optical parametric generator/amplifier (OPG/OPA) (Quantronix, TOPAS) pumped by a Ti:sapphire laser (Clark-MXR, CPA 2001). The pulses of the signal wave of the OPG/OPA at the wavelengths used in these experiments had typically an energy of 40 µJ and a duration of 150 fs full width at half maximum. The THz pulses have been generated by optical rectification of the sub-picosecond near-infrared pulses in a nonlinear optical crystal and detected by electrooptic sampling in a second nonlinear crystal [11]. In order to obtain the refractive indices and the absorption coefficients of OH1 over the broadest possible frequency range, we used two configurations of TTDS based on different nonlinear optical materials. The first covered the ranges 0.3–0.8 THz and 1.4–4 THz with a laser wavelength of λ=1400 nm using single crystals of DAST for both generation and detection [3, 12]. Anticipating the results presented in section 5.1, an OH1 crystal served as THz source in the second configuration with λ=1460 nm; for the detection, we used ZnTe with a frequency-doubled probe pulse [4]. The spectrum in these measurements spanned continuously from 0.3 to 2.2 THz.

 

Fig. 2. (a) Absorption coefficient α ₃ and (b) refractive index n ₃ of THz waves polarized along the c-axis. Diamonds: measured data. Solid lines: best fit to the measured data using a Lorentz four-oscillator model [13] (see Eqs. (1)–(3) and Table 1). Dashed line: optical group index n _g,_c calculated with parameters from Ref. [9] as a function of wavelength (upper scale).

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3.2. Results

The results are presented in Figs. 2 and 3. We use a classical Lorentz multiple oscillator model to describe the dispersion of the complex dielectric function ε(ω)=ε′(ω)+iε″(ω), whose real and imaginary parts are given by [13]

where ω_j is the resonant angular frequency, γ_j is the damping parameter, and f _j is the oscillator strength of the jth oscillator. ε∞ is the high frequency dielectric constant. The refractive index n(ω) and the intensity absorption coefficient α(ω) can be obtained from ε′ and ε″ by

where c is the speed of light in vacuum.

 

Fig. 3. (a) Absorption coefficient α ₂ and (b) refractive index n ₂ of THz waves polarized along the b-axis. Diamonds: measured data. Solid lines: best fit to the measured data using a Lorentz three-oscillator model [13] (see Eqs. (1)–(3) and Table 2).

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The functions with the oscillator parameters shown in the Tables 1 and 2 are plotted in the Figs. 2 and 3, respectively. They are in good agreement with the measured data. All the deviations of the theoretical curves from the data points are within the experimental errors. The features in the measured THz spectrum of the c-polarization can be described by four Lorentzian oscillators, whose parameters are listed in Table 1. The absorption within the THz frequency range between 0.7 and 1.0 THz is very low (i.e. α ₃<0.2mm^-1) and remains lower than 4mm^-1 in the whole range between 0.3 and 2.2 THz. Due to the fourth resonance, which is the strongest in the investigated spectral range, the transmission of the THz wave was below the detection sensitivity for frequencies above 2.5 THz.

The parameters of the Lorentz-model function for b-polarized waves as shown in Fig. 3 are listed in Table 2. Here, we observed three main resonances. In the gaps at 1.7–1.9 THz and 2.5–3.1 THz, where no data points are given in Fig. 3, the absorption coefficient α ₂ is above the detection limit.

Table 1. Parameters for the refractive index n₃ and the absorption coefficient α₃ of OH1 in the Lorentz-model.^a,b

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Table 2. Parameters for the refractive index n2 and the absorption coefficient α2 of OH1 in the Lorentz-model.^a,b

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4. OH1 for the generation and detection of THz waves: Theory

In the following, the dependence of the THz generation and detection efficiency using OH1 crystals on the laser wavelength and on the crystal thickness is discussed in terms of velocity-matching of the optical and THz waves and their absorptions. For this discussion we use the theory presented in Ref. [3], which is briefly summarized in the following.

THz pulses can be generated by optical rectification of sub-picosecond laser pulses. The optical pulses give rise to a nonlinear optical polarization of the crystal at THz frequencies, which acts as a source term in the nonlinear wave equation. The nonlinear optical susceptibility for optical rectification χ ⁽²⁾(ω,λ) is related to the linear electrooptical tensor r(ω,λ) at THz angular frequencies ω as follows [14]:

where n _o,i(λ) is the refractive index at the optical wavelength λ. In the following, we will omit the tensor notation because we are interested here in noncritical type I interactions, where only one tensor element χ ⁽²⁾ _ijj of the nonlinear optical susceptibility is involved (note that i=j is possible in optical rectification). Using the plane wave and the non-depleted pump approximations, the spectral amplitude of the electric field of the generated THz wave after the crystal length l is given by [3]

where µ ₀ is the permeability of vacuum, I(ω) is the Fourier transform of the intensity of the near-infrared pulses. n_T(ω) and α_T(ω) are the refractive index and the absorption coefficient at the THz angular frequency ω, respectively. n _o(λ), n _g(λ) and α _o(λ) are the refractive index, the group index and the absorption coefficient of the optical pulse with the central wavelength λ. The dependence of |ETHz(ω)| on the crystal length l is given by the effective generation length l _gen [3]:

where the coherence length l _c of THz generation by optical rectification can be written as [11]

As one can see immediately from (6) and (7), for an efficient generation of THz pulses, the refractive index of the THz wave has to be close to the optical group index of the optical beam (velocity-matching), and the absorption should be low for both THz and near-infrared pulses. In the limit of zero absorption, (6) simplifies to the following expression that is well-known from other second order nonlinear optical processes [14]:

For each laser wavelength λ and THz frequency ν=ω/(2π), we can calculate the maximum effective generation length l _max(ω,λ) and the optimum crystal length l _optimum(ω,λ), which are defined as follows:

The detection of THz transients through electrooptic sampling is essentially the inverse process of optical rectification, and the dependence of the sampling signal on the length of the electrooptical crystal is the same as in (6). The sampling signal is proportional to the phase shift Δϕ of the probe pulse induced by the THz electric field E _THz(ω) in the detection crystal which is given by [3]:

where A(ω) is the normalized Fourier spectrum of the probe pulse amplitude.

From a contour plot of l _max(ω,λ), one can predict the range of the pump laser wavelengths l where a high conversion efficiency for a certain range of THz frequencies can be achieved. Figure 4 shows l _optimum(ω,λ) with the corresponding l _max(ω,λ) for THz generation and detection exploiting the largest tensor element of the nonlinear optical susceptibility χ ⁽²⁾ ₃₃₃ and the largest linear electrooptic coefficient r ₃₃₃, respectively. The refractive index and the absorption in the THz range are taken from the four-oscillator Lorentz function (see Fig. 2), and the optical data are taken from Ref. [9].

 

Fig. 4. (a) Optimum OH1 crystal length l _optimum(ω,λ) for the generation of THz pulses (see Eq. (9b)); (b) the corresponding maximum effective generation length l _max(ω,λ) (see Eq. (9a)). The values of the contour lines are in units of mm.

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The highest conversion efficiency can be expected in the velocity-matching and transparency range for THz frequencies below 2.2 THz and optical wavelengths between 1200 and 1460 nm. The upper limit for the wavelength is given by the optical absorption. Above 2.2 THz, the main limiting factor is THz absorption.

Due to the very large birefringence n ₃-n ₂>0.5 of OH1 in the THz as well as in the optical range [9], the second largest coefficient χ ⁽²⁾ ₃₂₂ cannot be used for velocity-matched generation of THz pulses. Likewise, r ₂₂₃ cannot be exploited in velocity-matched THz detection.

4.1. Figure of merit for generation and detection of THz pulses

For the comparison of the performance of two THz systems using different electrooptic crystals, one may define an overall figure of merit (FoM) for the generation and detection of THz pulses [15]:

where λ _vm is the velocity-matching wavelength. The overall efficiency of a THz system for the generation and detection of the electric field at the frequency ν using the laser wavelength λ is proportional to FoM×l ² _max(2πν,λ). The equation (11) has been derived from (5) and (10) taking into account the Fresnel losses of the optical beam at the generation crystal and of the THz beam at the generation and the detection crystals [15].

In Table 3, the figures of merit of OH1 and of the commonly used electrooptic crystals DAST, ZnTe and GaAs are shown. Additionally, the THz absorption coefficient is given at the typical frequency ν _peak of the peak spectral amplitude of THz pulses generated through optical rectification of 150 fs laser pulses at the velocity-matching wavelength. OH1 shows the highest figure of merit and a low THz absorption at the optimum conditions.

Table 3. Overall figure of merit (FoM) for generation and detection of THz pulses and other relevant parameters of OH1 in comparison with commonly used electrooptic crystals.

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5. OH1 for the generation and detection of THz waves: Experiments

5.1. Generation of THz pulses using OH1 crystals

We performed THz emission experiments using an unpolished 0.365mm thick a-plate of OH1. The pump wavelength was 1460 nm. The electric field of the generated THz pulse was measured by electrooptic sampling in a 0.5mm thick (110)-cut ZnTe crystal using a probe beam with the second-harmonic wavelength (730 nm) [4]. The wavelength was chosen to ensure nearly velocity-matching in the ZnTe crystal. Although this is not the optimum wavelength for OH1, one can see from Fig. 4(a) that l _optimum is larger than our crystal length below 2.5 THz. Hence, velocity-mismatch and THz absorption do not affect the emitted amplitude significantly. Possible distortions of the measured THz transient, which may arise if the peak electric field exceeds the linearity range of the detection, have been corrected using the algorithm from Ref. [22]. The measured signal is plotted in Fig. 5. The emission spectrum is continuous and ranges from 0.3 to 3.0 THz with a maximum at 1.3 THz.

For a comparison, the same experiment has been performed with DAST crystals as a source material under identical conditions. DAST has been chosen as a reference material for two reasons. On the one hand, it has been demonstrated to be one of the most efficient THz emitter materials so far; on the other hand, it is also very well velocity-matched at 1460 nm [4]. Two c-plates of DAST (thicknesses: 0.330 and 0.400 mm, respectively) were used having an average thickness which corresponds to the thickness of the OH1 crystal. The THz signals from the two DAST crystals are averaged and plotted in Fig. 5.

The peak THz amplitude from OH1 exceeds that of DAST in both time- and frequency-domain by 58 percent and 36 percent, respectively. A second advantage, that is relevant mainly for spectroscopic applications, is that the spectrum from OH1 is continuous from 0.3 to 3 THz, in contrast to DAST, where a transverse optical phonon leads to a gap at the resonance frequency of 1.1 THz. This fact is a direct consequence of the non-ionic nature of the OH1 crystal.

 

Fig. 5. THz pulse emitted from OH1 exploiting χ ⁽²⁾ ₃₃₃ and detected in ZnTe (red line). (a) Time domain and (b) frequency domain signal. THz pulse emitted from DAST exploiting χ ⁽²⁾ ₁₁₁ under identical conditions for comparison (black line; see text for details).

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5.2. OH1 for both generation and detection of THz pulses

5.2.1. Pump energy dependence

OH1 crystals were also used for the detection of the THz pulses. Although standard electrooptic sampling is not possible due to the large intrinsic birefringence of the crystals, we could use a modified detection method based on the spatial phase-modulation of the probe beam induced by the electric field of the THz wave through the linear electrooptic effect [12]. The spatial phase-modulation leads to a focusing or defocusing of the probe beam depending on the sign of the THz field. A fraction of the probe beam in its center after passing the detection crystal was coupled into a multimode fiber with a core diameter of 62.5 µm and its output was measured with an InGaAs photodiode. The relative modulation m(E)=(W(E)/W(E=0))-1 is proportional to the THz electric field E for moderate modulations (i.e. m≲0.5). As a reference, we used the light that was not coupled into the fiber by measuring its backscattering from a white screen with a second InGaAs photodiode. This reference was required to correct for the pulse-to-pulse energy fluctuations of the probe beam and thus to enhance the signal-to-noise ratio.

Figure 6 shows THz pulses generated and detected in two polished OH1 crystals (thicknesses 1.002 and 0.956 mm, respectively) at an optical wavelength of 1300 nm for several values of the pump pulse energy. For this, the pump pulses were attenuated using different neutral density filters. The maximum pump pulse energy of 45 µJ leads to a maximum relative modulation m(E) of 5.0, which is 3.6 times the maximum value reported to date (1.4 in DAST [4]). The maximum observed defocusing of the probe beam reduced the measured diode signal to the noise level. At the highest two pump pulse energies of 45 and 20 µJ, the maximum defocusing could also be observed in the reference. Thus, the ratio of the signal and the reference at the maximum defocusing is smaller for the pump pulse energy of 20 µJ than for 45 µJ (see Fig. 6).

In the following, the conversion efficiency η=W _THz/W _pump of the pulse energies is estimated. We assume a Gaussian beam profile of the THz pulse. The electric field E in the center of the THz beam can be calculated from m(E) [12]:

where l is the length of the detection crystal. We assume a diffraction limited THz beam profile within the detection crystal; for the main frequency components near 1 THz, this corresponds to a full width at half maximum ρ₀ of the THz intensity of about 0.6 mm. The THz pulse energy can be calculated by integrating the intensity over the beam profile and the spectrum:

where the intensity transmission coefficient T(ν) at the entrance of the detector crystal is in the limit of zero absorption given by

 

Fig. 6. THz pulses generated and detected in OH1 crystals using optical pulses at a wavelength of 1300 nm for different pump pulse energies. The ratio of the center intensities of the probe beam with and without THz electric fieldW(E)/W(E=0)=m(E)+1 is plotted on a logarithmic scale as a function of time.

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Since the relative modulation m(E) exceeds the linearity range of the detection for the higher pump pulse energies by far, we calculated η for THz pulses generated by 3 µJ pump pulses. The peak electric field of this THz transient of E _peak=8 kV/cm is reached at a maximum value of the relative modulation of m _max=0.46, i.e. the whole waveform is in the linear regime. Using (13)–(14), we calculated an energy conversion efficiency of η=6×10^-5, which corresponds to a photon conversion efficiency η _photon=ηc/(λ$\overline{\nu }$) of 1 percent, where $\overline{\nu }$=∫|E(ν)|² νdν/∫|E(ν)|² dν is the average generated THz frequency. Since the generated THz field is proportional to the pump pulse energy, we can extrapolate the THz electric field measured for 3 µJ to the pump pulse energy of 45 µJ. This extrapolation yields a peak electric field of 120 kV/cm, an energy conversion efficiency of η=1×10^-3 and a photon conversion efficiency of 15 percent.

So far, the effect of two-photon absorption of the pump beam has not been taken into account. We measured a two-photon absorption coefficient β ₃=0.3 cm/GW for c-polarized light with a wavelength of 1300 nm using the method described by Bechtel and Smith [23]. Two-photon absorption of the pump beam is insignificant for the THz pulse generated with a pump pulse energy of 3µJ, where the peak intensity was I _{pump, max}=3 GW/cm². However, it becomes relevant for the 45µJ pump pulse, where I _{pump, max}=41 GW/cm². To estimate the effect of two-photon absorption on the THz conversion efficiency, we averaged the pump pulse energy—which is proportional to the THz electric field—over the crystal length, and obtained a reduction of η by a factor of 0.74, resulting in a photon conversion efficiency of 11 percent for the 45 µJ pump pulse.

5.2.2. Pump wavelength dependence

We investigated the wavelength dependence of the THz spectra generated and detected using OH1 crystals in the velocity-matching and transparency range between 1200 and 1460 nm. The intensity of the pump beam has been attenuated to obtain a THz signal in the linear detection regime (m≤0.5). Figure 7(a) shows the normalized spectra obtained with a 1.002mm thick source crystal and a 0.956mm thick detector crystal. For all these wavelengths, the spectral amplitudes reach their maxima near 1.3 THz. Below 1.4 THz, all spectra normalized to their maximum values are almost identical. The spectral amplitude is reduced around the resonance near 1.5 THz (oscillator 3, see Table 1), however it is still large enough for spectroscopic applications. This is in contrast to DAST crystals, for which the absorption at the resonance frequency of 1.1 THz is more than 10 times larger than that of OH1 at 1.5 THz. The position and the amplitude of the second local maximum in the normalized spectra depends on the pump wavelength. A calculation of the spectra according to the theory from [3] leads to the same result (see Fig. 7(b)). The plane-wave approximation has been used in the calculation for both the optical and the THz wave. However, the diffraction of the THz beam due to the finite pump beam diameter decreases the spectral amplitudes at low frequencies [3]. This explains the discrepancy between the measured and the calculated spectra below about 0.8 THz.

Although all the experiments were carried out in a box purged with dry air, there was some residual humidity. The additional features in the measured spectra compared with the calculated ones stem from this residual water vapor, visible mainly at 1.1, 1.7 and 2.2 THz [24].

 

Fig. 7. THz spectra generated and detected in 1mm thick OH1 crystals using different wavelengths, normalized to their maximum values. (a) Measurements; (b) calculation.

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6. Conclusions

The refractive indices n ₂ and n ₃ and the absorption coefficients α ₂ and α ₃ of the organic crystal OH1 have been measured in the spectral range between 0 and 4 THz using THz time-domain spectroscopy. Based on these results, we found that the largest element χ ⁽²⁾ ₃₃₃ of the nonlinear optical susceptibility tensor can be exploited for high efficiency generation and detection of THz pulses, thanks to a low absorption α ₃ for frequencies below 2.5 THz and to velocity-matching with a large range of pump laser wavelengths (1200–1460 nm). The peak spectral amplitude from OH1 was found to be 36 percent larger than that from DAST under identical conditions. For a pump pulse energy of 45 µJ, we achieved a conversion efficiency of pulse energies of 7×10^-4, corresponding to a photon conversion efficiency of 11 percent.

The results presented in this article are also valid for tunable narrowband THz generation through difference frequency generation of two lasers with slightly different wavelengths. Difference frequency generation of frequencies around 1 THz will be especially efficient due to the very low absorption of OH1.