1. Introduction

In the past decade, the science and technology on ultrashort electromagnetic pulses with a spectral content in the 0.1 to 10 THz range (THz pulses) have attracted widespread interest and evolved into a useful tool for a number of applications (see Ref. [1] for a review). Among different approaches to generate and coherently detect THz pulses, which all require femtosecond lasers, those based on nonlinear optical effects (optical rectification and electro-optic sampling, respectively [2]) are advantageous since they use optical pulses at wavelengths outside the material’s absorption range. Therefore the emitted THz field scales with both optical pulse energy and source crystal thickness up to the coherence length (see Eq. (2)), whereas the THz emission from processes that involve the excitation of free charge carriers (e.g. in photoconductive switches) is limited to the optical absorption length of the optical radiation; furthermore there is a risk of damaging the source through high optical power in the latter case.

Two prerequisites are given for a nonlinear optical material to be useful for THz applications. First is a sufficient nonlinear optical susceptibility χ ⁽²⁾ and electro-optic (EO) coefficient r. Second is velocity-matching between the optical and the THz pulse, characterized by the coherence length l_c ; the latter ought to be at least the crystal thickness, typically 0.1 to 1 mm. Due to dispersion, l_c is a function of both the optical wavelength λ and the THz frequency ν. Hence the material of choice depends on the desired range of ν and the available laser source. Up to the present, many groups use the inorganic semiconductor ZnTe with r=4 pm/V and good velocity-matching between optical pulses from Ti:Sapphire lasers (λ~800 nm) and THz pulses with ν between 0 and 2 THz [3].

Due to the progress in the telecommunications industry, compact and reliable femtosecond lasers in the wavelength range from 1.5 to 1.56 µm are becoming readily available. This may contribute to comparably compact, stable and cost-effective THz systems if an appropriate nonlinear material is found. Among inorganic semiconductors, GaAs with an optimum velocity-matching wavelength of 1.4 µm [3] is the most promising candidate and has been demonstrated as a source and detection material with 1.56 µm pulses from a fiber laser [4]. However, its electro-optic (EO) coefficient is about a factor of two lower than that of ZnTe.

Organic nonlinear optical materials offer several advantages for THz applications, namely their high nonlinear optical susceptibilites, low dielectric constants, and the almost unlimited possibility to design molecules for a specific application [5]. These molecules can be incorporated in either organic crystals or polymers. Although polymers may be efficient emitters and detectors of THz radiation [6], they suffer from fast degradation and limited thickness; disadvantages that apply for organic crystals to a much lesser extent.

In this article, we demonstrate theoretically and experimentally the velocity-matched generation and detection of THz pulses with 1.5 µm laser pulses in the organic nonlinear crystal DAST (4-N,N-dimethylamino-4’-N’-methyl stilbazolium tosylate) with an EO coefficient (r111=47 pm/V at λ=1535 nm [7]) that is more than an order of magnitude higher than that of ZnTe or GaAs. We achieved a THz-induced modulation of up to 140% using a nominally linear technique (see section 4.1). Additionally, we demonstrate that DAST and ZnTe can be combined in a single THz system if one of the optical beams is frequency-doubled, which allows more versatile detection schemes.

2. Optimal wavelength range for generation/detection of THz pulses

Optical rectification is a second-order nonlinear optical process, where two optical waves with angular frequency ω interact with each other in a noncentrosymmetric crystal to generate a dc polarisation P_OR through the nonlinear susceptibility χ ⁽²⁾(Ω=0;ω,-ω). If P_OR is induced by a short laser pulse, i.e., with a typical duration of 200 fs or less, it contains components at angular frequencies Ω≠0 that act as a source for radiation in the THz frequency range. This process may also be interpreted as the generation of the difference-frequency between the frequency components of the input pulse, thus using χ ⁽²⁾(Ω;ω,-ω-Ω). An upper limit for Ω is given approximately by the bandwidth Δω of the optical pulse.

The efficiency of the THz pulse generation depends on the phase-matching between the optical and the THz wave. It can be characterized by a function f (l,ν,λ) that contains the complete dependence of the emitted THz electric field E_THz on the length l of the nonlinear crystal in the non-depleted pump approximation and in the absence of absorption [8]:

ν=Ω/(2π) is the THz frequency, λ=2πc/ω the optical wavelength, and l_c (ν,λ) the coherence length for THz generation. It has been pointed out that in the case of THz pulse generation, the optical group index n_g (λ) rather than the refractive index n(λ) determines the coherence length [2, 3, 9], in contrast to other nonlinear conversion processes such as second-harmonic generation (SHG). Thus l_c (ν,λ) is given by [2]

with the group index

The coherent detection of the transient THz electric field E_THz (t) through electro-optic sampling (EOS) [3, 10] is a prerequisite for the unique applications of these pulses. In standard EOS, E_THz alters the polarisation state of a copropagating optical probe pulse through the linear electro-optic effect (Pockels effect). A measurement of this polarisation change as a function of the delay time between THz and probe pulse reveals the THz electric field E_THz(t). The measured probe beam modulation also depends on the phase-matching conditions; for unequal propagation velocities of THz and probe pulse, the measured waveform gets distorted [9]. In the frequency-domain, the modulation amplitude is proportional to the same factor f (l,ν,λ) from Eq. (1) as the generation efficiency.

Maximizing f for a given THz frequency range by choosing the optical wavelength λ and the crystal length l properly is thus necessary to obtain an optimal THz signal, in terms of both generation and detection. However, not all electro-optic materials are equally well suited for electro-optic sampling as for THz generation, since EOS in its standard configuration requires a material that is not or only weakly birefringent, which excludes e.g. DAST (n_a-n_b =0.53 at λ=1.5µm). One possibility to overcome this restriction is a double-pass scheme [11], another is to use a variation of EOS that is not inhibited by the birefringence, namely THz-induced lensing (TIL) [8]. Nevertheless, standard EOS is more versatile since it allows extensions such as two-dimensional real-time imaging [12] or single-shot measurements [13]. We will show in the following that a high-efficiency THz source using DAST can be combined with the standard EOS detection in ZnTe in order to profit from the respective advantages.

2.1. DAST

In the following, we determine the THz frequency range where a long coherence length l_c (Eq. (2)) allows efficient THz generation or detection for a given optical wavelength λ in DAST in the ${\mathrm{\chi }}_{111}^{\left(2\right)}$ configuration, i.e., both optical and THz waves are polarized along the crystal a-axis.

Walther et al. measured the refractive index n ₁(ν) using THz time-domain spectroscopy from 0 to 3 THz [14]. We extended this range up to 4.2 THz using the same method [15]. Above a phonon resonance at 1.1 THz, n ₁(ν) increases up to about 3 THz where it shows a small kink; above this frequency, it remains nearly constant. From 1.8 to 4.2 THz, it ranges between 2.2 and 2.3. These values match approximately the optical group index n _g,1(λ) between 1.4 and 1.8 µm that was calculated analytically from the Sellmeier function determined by Pan et al. [7]. Figure 1 shows a contour plot of the coherence length l_c (ν,λ) according to Eq. (2).

Broadband velocity-matching, i.e., a value of l_c (ν,λ) that is larger than a typical crystal thickness of 1 mm in a wide frequency range, is achieved for wavelengths λ between 1.3 and 1.6 µm, with corresponding frequencies from 1.5 to above 4 THz. From these data it can be expected that telecommunication wavelengths (~1.50 to 1.56 µm) are well suited for pulsed THz systems that use DAST as the emitter material.

2.2. ZnTe

By comparing the THz transients measured with two ZnTe crystals of a different thickness, Wu et al. [3] found experimentally that broadband THz pulses with a frequency content below 2 THz are velocity-matched to optical pulses with λ=822 nm. Due to THz dispersion, this wavelength changes with the center frequency of the THz pulse. For a quantitative analysis, we calculated the coherence length l_c (ν,λ) also for ZnTe. The index data in the THz range are taken from references [16] and [17], those in the optical range are calculated with a Sellmeier fit to the data from Sliker et al. [18]; a more elaborate function for the optical dispersion of ZnTe presented by Sato et al. [19] does not agree better with the measured values in the 600–900 nm range and was therefore not used.

 

Fig. 1. Contour plot of the coherence length l_c for THz generation and/or detection in DAST. The numbers indicate the value of the contour in millimeters.

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In the 2 to 3 THz range, the largest values of l_c (ν,λ) are obtained for wavelengths λ between 750 and 850 nm (see Fig. 2), i.e. frequency-doubled pulses from lasers at telecom wavelengths may be used for velocity-matched electro-optic sampling in ZnTe.

 

Fig. 2. Contour plot of the coherence length l_c for THz generation and/or detection in ZnTe. The numbers indicate the value of the contour in millimeters.

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Taking the results of the paragraphs 2.1 and 2.2, one finds that a THz spectroscopy or imaging system combining the advantages of highly efficient generation in DAST and velocity-matched EOS in ZnTe may be built using a telecom laser if the probe pulse is frequency-doubled. Figure 3 resumes the data of Fig. 1 and Fig. 2 to show which combinations of THz frequency and optical wavelength are expected to give the highest detectable THz signal in a setup using DAST at the fundamental wavelength as the source and ZnTe at the frequency doubled wavelength for the detection. One finds that the broadest THz frequency range is accessible with a fundamental wavelength near 1500 nm.

 

Fig. 3. Color plot of the coherence length l_c for THz generation and detection; a darker shade corresponds to a lower l_c . Red: DAST at fundamental wavelength (lower x-scale), no coloring for l_c >1.5 mm. Green: ZnTe at SHG wavelength (upper x-scale), no coloring for l_c >0.75 mm.

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3. Experiments

The laser source in our experiment was an amplified Ti:Sapphire laser that generated pulses with a duration of 160 fs (full width at half maximum, FWHM) and a repetition rate of 1 kHz. Pulses in the desired wavelength range were obtained by means of an optical parametric generator/amplifier (OPG/OPA) whose signal wave was tunable from 1100 to 1600 nm, with a typical pulse energy of several tens of microjoules, depending on the wavelength. The signal wave with the angular frequency ω was separated from the idler wave and the fundamental Ti:Sapphire wave by dichroic mirrors and appropriate filters.

The setup that was used with a frequency-doubled probe beam is shown in Fig. 4. The incoming laser pulses at ω pass a nonlinear optical crystal (BBO) in which a fraction of the pulse energy is converted to the second-harmonic frequency 2ω. The two frequencies are then split by a dichroic mirror into a pump pulse at the fundamental frequency ω and a probe pulse at 2ω. Note that the energy of the probe pulse may be two to three orders of magnitude lower than that of the pump pulse since it only has to lead to an ample signal on the photo detectors. Thus a high SHG conversion efficiency is not required, or even not desired, since a reduction of the pump pulse energy at the frequency ω would decrease the emitted THz field.

The polarisation change that the electric field E of the THz pulse induced on the probe pulse in the electro-optic detection crystal (ZnTe) was high enough to be measured directly by taking the ratio of the two polarisation components (two photo diodes in Fig. 4), without the need of lock-in detection.

In the measurements with the probe beam at the fundamental frequency ω, the dichroic mirror in Fig. 4 was replaced by a conventional beamsplitter. The THz pulses were detected by THz-induced lensing in DAST with the necessary changes in the detection setup described in Ref. [20].

 

Fig. 4. Experimental setup using a pump beam at ω and a frequency-doubled probe beam at 2ω. EM: Ellipsoidal mirror; PBS: Polarizing Beam Splitter.

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4. Results

4.1. Detection in DAST crystals

In Fig. 5, we show a THz pulse generated and detected in DAST crystals with 150 fs laser pulses at a wavelength of 1.50 µm and a pulse energy of 25 µJ. The time-domain signal is the relative intensity modulation m(t)=ΔI(t)/I ₀ in the center of the probe beam caused by the lensing effect that the THz electric field ETHz(t) exerts on the probe beam profile in the far field after the electro-optic detection crystal (THz-induced lensing [20]). The relation between m(t) and E_THz(t) is intrinsically linear for a relative modulation well below unity; the signal presented in Fig. 5 however exceeds the linearity range. As an estimation, we calculated the maximum electric field of the THz pulse in the linear regime using Ref. [20] and obtained a value of 50 kV/cm.

A direct comparison of this value with those obtained by other groups in different materials is difficult, since absolute values of the transient THz electric field are often not published. However, the ratio between the induced modulation per pump pulse energy and crystal thickness may serve as a measure for the conversion efficiency. Nagai et al. reported 12 (mm mJ)^-1 for their experiment with 1.56 µm pulses in GaAs (ΔI/I ₀=2·10^-5, pulse energy 3.4 nJ, 0.5 mm crystal [4]), compared to 93 (mm mJ)^-1 in our experiment. Considering that the negative effect of two-photon absorption on the THz amplitude is stronger for the higher energy optical pulses in our setup, one can conclude that the THz generation efficiency using DAST crystals at telecommunication wavelengths is an order of magnitude higher than that using GaAs at comparable wavelengths.

The Fourier spectrum of the THz pulse in Fig. 5 extends from 0 to 6.5 THz, where the upper frequency limit is mainly determined by the duration of the optical probe pulse. Absorption of the THz wave in the DAST crystals reduces the amplitude at the resonance frequencies 1.1 THz [14], 3.1 THz, and 5.2 THz [21]. However, the second resonance at 3.1 THz is weak enough not to reduce the amplitude to the noise level, such that a continuous spectrum without gaps is obtained in the central part of the spectrum from 1.3 to 4.8 THz.

 

Fig. 5. THz pulse generated through optical rectification in a 0.60 mm thick DAST crystal and detected using THz-induced lensing [20] in a 0.69 mm thick DAST crystal, at an optical wavelength of 1.50 µm. Left panel: Signal in time-domain. The indicated modulation is in first order proportional to the THz electric field, limited by nonlinear effects (see text for details). Right panel: Fourier transform of the same THz pulse. Absorption by the residual ambient water vapor leads in time-domain to the oscillation that persists for t>1 ps, in frequency-domain to the numerous dips; thus the effectively emitted THz spectrum is given by the envelope.

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4.2. Detection in ZnTe using a frequency-doubled probe beam

In Fig. 6 we present a measurement of the same THz pulse in time and frequency-domain, detected by EO sampling in a ZnTe crystal with a frequency-doubled probe beam (λ=0.75µm). The spectrum extends from 0 to 4 THz, again with a gap at 1.1 THz due to the phonon resonance in DAST. Here, the upper frequency limit is given by the properties of the detection material, on the one hand since the coherence length becomes shorter than the crystal thickness above 3.5 THz (see Fig. 2), on the other hand due to the THz absorption in ZnTe that strongly increases above 4 THz [16]. The residual velocity-mismatch in ZnTe for the major part of the spectrum leads to a reduction of the maximum THz amplitude compared to that in Fig. 5, such that the linearity range of the detection is not exceeded.

It is remarkable that the observed upper frequency limit of 4 THz lies higher than that measured with e.g. 800 nm probe pulses [2], even though the optimum probe wavelength for ZnTe was considered to be 822 nm so far [3]. This can be explained by the increased coherence length for frequencies above 3 THz at λ=750 nm compared to 800 nm (see Fig. 2).

5. Conclusions

In conclusion, we demonstrated a highly efficient generation and detection of few-cycle THz pulses using optical pulses at a wavelength of 1.5 µm and the nonlinear optical crystal DAST. Its large nonlinear optical susceptiblity can be fully exploited due to a coherence length l_c above 1 mm from 1.5 to 4.5 THz at this wavelength. Alternatively, nearly velocity-matched detection in ZnTe crystals was achieved for a frequency-doubled probe beam, resulting in a continuous spectrum from 1.3 to 4 THz. This is important since the detection by conventional electro-optic sampling in ZnTe is more versatile than by THz-induced lensing as it was used with DAST.

 

Fig. 6. THz pulse generated through optical rectification of 1.5 µm pulses in a 0.60 mm thick DAST crystal and detected by electro-optic sampling in a 0.5 mm thick ZnTe crystal using a frequency-doubled probe beam (λ=0.75µm). Left panel: Time-domain. Right panel: Frequency-domain. The effect of water vapor absorption is the same as in Fig. 5.

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Together with compact and stable femtosecond lasers originally built for the telecommunications industry, DAST-based systems are an efficient and cost-effective alternative for any application of short THz pulses.