1. Introduction

Time domain THz spectroscopy and imaging are rapidly developing research fields. Especially interesting are large area THz imaging and nonlinear THz spectroscopy [1] which need energetic THz pulses. Free electron lasers can produce THz pulses with energies in the μJ range [2]. However, the cost effective access to these large-scale facilities is limited. One scheme for tabletop generation of high-energy THz pulses is illumination of photoconductive switches by ultrashort laser pulses [3–5]. Such devices can emit up to 800 nJ [3] and 400 nJ [4] THz pulses at 10 Hz and at 1 kHz repetition rates, respectively. The spectral peak of the pulses generated in these experiments lies in the 0.3 – 0.5 THz range. Although generation of THz pulses by photoconductive switches with useful spectral content in the 1 –20 THz range has also been reported [5], no data are available concerning the THz pulse energy, which has shown to be small because of the small area between the electrodes of the switch.

Alternatively, THz pulses can be generated by optical rectification of ultrashort laser pulses. This method is effective only if the phase-matching condition is fulfilled which can be expressed as $v_{\mathit{\text{pump}}}^{\mathit{\text{group}}}$ = $v_{\mathit{\text{THz}}}^{\mathit{\text{phase}}}$ [6], and crystals with high optical nonlinearity such as LiTaO₃ and LiNbO₃ are used as the nonlinear medium. Typically $v_{\mathit{\text{THz}}}^{\mathit{\text{phase}}}$ is much smaller than $v_{\mathit{\text{pump}}}^{\mathit{\text{group}}}$ and therefore collinear phase matching is not possible. Phase-matching can, however, still be accomplished with these materials via a Cherenkov type geometry or periodic poling [7,8]. However, these methods are not useful for efficient generation of high-energy THz pulses. The Cherenkov type geometry does not allow larger pump spot sizes [9] and consequently severely limits the applicable pump pulse energy, while for periodically poled crystals the desired matching between the group velocity of the pump laser pulse and the phase velocity of the THz radiation does not exist [10].

Recently, tilting of the pump pulse front has been proposed [11] as a generally applicable velocity matching method for THz pulse generation by optical rectification. The THz radiation is emitted under an angle and with the proper tilt of the pump pulse front the THz electric field generated in different locations along the pump beam propagation can interfere constructively. As can be seen from Fig. 1b) of Ref. 12, successive contributions to the THz pulse are only shifted sideways by a small amount and not in the direction of THz propagation. The improved spatial overlap between the THz field and the pump field strongly increases the conversion rate. Using this method, MgO doped stoichiometric LiNbO₃ as the nonlinear crystal and 2.3 μJ pump pulses, THz pulses with 100 pJ and 400 pJ energy were generated at room temperature and at 77 K, respectively [10,12]. More than 3 % [10] photon conversion efficiency was demonstrated, which is according to our knowledge the highest value ever achieved in the FIR spectral range. The main advantage of the tilted pulse front excitation scheme [11] is the possibility to scale up the THz pulse energy by simply using a higher pump pulse energy and simultaneously a larger pump spot area.

An alternative method for scaling up the THz pulse energy has been proposed two decades ago [13] and demonstrated experimentally only very recently [14]. Using a cylindrical lens for tight focusing (line focusing) of the pump beam, the total area of the focal spot can be rather large, while its width can be small enough for effective generation of “two dimensional” Cherenkov radiation. Indeed, applying pump pulses with a few μJ energy, the generated THz energy was as high as for the tilted pulse front set-up [14].

In this contribution, we investigate experimentally the potential of further increasing the generated THz energy for tilted pulse front and line focusing configurations employing pump pulse energies up to 500 μJ.

2. Experimental

As the pump pulse source a Ti:sapphire amplifier (CPA 2001; Clark-MXR, Inc.) was used, which delivered 150-fs-long pulses with 780 nm central wavelength and up to 800 μJ energy at 1 kHz repetition rate. The laser beam was collimated, and its diameter was decreased by a lens telescope consisting of two lenses with f ₁ = 250 mm and f ₂ = 100 mm focal length. For the THz generation with tilted pulses a set-up very similar to that described in [10] was used: a 2000 lines/mm grating was applied to tilt the intensity front of the pump pulses, and a f = 60 mm lens was used to image the spot of the pump beam on the grating into the Mg-doped stoichiometric LiNbO₃ crystal. The crystal of about 2 mm size was cut so that both the entrance face for the 780 nm pulses and also the exit face for the THz radiation is perpendicular to the respective propagation direction (for details refer to Fig. 4 of Ref. 10). As a result of the imaging with a demagnification of 2, the horizontal and vertical sizes (FWHM) of the pump beam spot on the LiNbO₃ crystal were 1.3 mm and 0.9 mm. The horizontal size was determined using the moving slit method, while the vertical size was calculated from the pulse tilting geometry supposing a circular cross-section of the original beam. For the line focusing set-up, just a cylindrical lens with f = 65 mm focal length was used. In this case the estimated focal spot size on the LiNbO₃ crystal was 0.025 mm × 1.8 mm, that is, the spot area was about 26 times smaller than for the tilted pulse front set-up.

The average pump power in front of the LiNbO₃ crystal was measured with a power meter and converted to pulse energy using the known repetition rate of the laser. All pump energies given below are values obtained directly before the crystal for both set-ups.

A calibrated liquid He-cooled Si bolometer was used to measure the energy of the generated THz pulses. The voltage signal of the bolometer was fed to a storage oscilloscope and the THz energy E_THz was calculated from the voltage modulation V_m of the recorded trace according to

where the sensitivity S = 96 mV/μW was obtained from calibration, while the correction factor C and the time constant τ= 0.28 ms were determined from fitting of the recorded trace.

3. Results and discussion

Figure 1 depicts on a logarithmic scale the generated THz pulse energy versus the pump pulse energy. For the tilted pulse front set-up, the THz energy increases on the whole investigated pump energy range and approaches 240 nJ for 500 μJ pump energy.

In contrast, for the line focusing set-up the THz energy approaches its maximum value of 3.1 nJ at 32 μJ pump energy. Above this pump energy value the THz energy drops and at about 70 μJ pump energy a damage of the crystal occurs. The obvious reason for the absence of a THz pulse energy drop on the investigated pump pulse energy range for the tilted pulse front set-up is due to the 26 times larger excitation area and, consequently, the 26 times smaller pump intensity. Contrary to the case of GaSe [15], the photon energy of the 780 nm pump laser is not high enough for two-photon absorption in LiNbO₃, so it cannot induce THz absorption by free carrier excitation. However, the energy of three photons is higher than the band-gap of LiNbO₃ [16]. The 1 TW/cm² pump intensity achieved for the line focusing set-up may be high enough for efficient three-photon absorption, while the one order of magnitude smaller intensity of the tilted pulse front set-up seems to be be too weak for such an effect. This is most likely the explanation for the differing saturation behavior observed for the two set-ups.

 

Fig. 1. Measured energy of THz pulses generated by the tilted pulse front (red circles) and line focusing (open blue squares) set-ups versus the energy of the 780 nm pump laser pulses (upper left part). Energy conversion efficiency versus the pump energy for the tilted pulse front set-up (lower right part).

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Self-focusing and other intensity dependent effects can probably increase this difference in the saturation behavior. Using pump pulses with an energy on the μJ level, we recently observed for a line focusing set-up an enhancement of the THz generation with increasing energy caused by this effect [14]. The enhancement was explained by the decreased average spot size throughout the LiNbO₃ crystal at high pump energies. The development of filaments, and increased three-photon absorption can result in a saturation of this enhancement. Even a drop of the THz energy is expected at pump energies (intensities) where real self-focusing develops inside the (finite length) crystal. Using the value n ₂ = 9.5 × 10^-16 cm²/W measured for the nonlinear index of refraction for LiNbO₃ crystals [16] and the 0.4 TW/cm² intensity corresponding to the THz maxima, according to a simple estimation, the self-focusing develops after 1 – 2 mm propagation in the crystal in agreement with the experimental conditions.

The pump intensity remained below 0.4 TW/cm² (see Fig. 2) for the tilted pulse front setup and accordingly a drop of the THz pulse energy did not occur. Above about 100 μJ pump energy, however, a distinct saturation of the THz pulse energy and - even more strongly - of the energy conversion efficiency develops (see lower right part of Fig. 1). We believe that these saturation effects are mainly caused by an enhanced polariton decay induced by non-thermal acoustic phonons [17]. In spite of the saturation the energy conversion efficiency approaches 5 × 10^-4 at 300 μJ pump pulse energy. This value corresponds to 10 % photon conversion efficiency since the frequency of the THz radiation is 200 times smaller [12] than the frequency of the pump light. This photon conversion efficiency is exceptionally large. According to our knowledge until now the highest reported value was 3.4 % [10]. It was reached also using a tilted pulse front set-up, but at 77 K temperature. It is expected that cooling down the crystal in the present experiment from ambient temperature to 77 K will result in a significant increase of the photon conversion efficiency. In the earlier experiments [10,12], a three times increase was observed for a similar temperature change.

 

Fig. 2. Measured energy of THz pulses generated by the tilted pulse front (red circles) and the line focusing (blue squares) set-ups versus pump intensity. The THz pulse energy values for the line focusing set-up are multiplied by 26.

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According to Fig. 1, the energies of the THz pulses generated by the tilted pulse front and the line focusing set-ups are very similar for low pump energy. This similarity, however, is accidental. Actually, for the tilted pulse front set-up the observed THz energy strongly depends on the ratio of the pump spot size along the y-direction (see Fig. 3) to the length (in z-direction) of the crystal. For the line-focusing set-up, it depends on the ratio of the focal line diameter to the wavelength of the THz radiation. The THz pulse energies for both configurations are plotted in Fig. 2 as a function of the pump intensity. The measured THz energy values for line focusing set-up are multiplied by 26, the ratio of the spot areas for the two set-ups. For a usual second order frequency conversion process in the absence of saturation, we should expect the same square dependence for both set-ups. Figure 2 reveals such dependence for the tilted pulse front case and for pump intensities smaller than 0.1 TW/cm². At higher intensities the saturation mentioned above becomes decisive. Even after taking into account the different pump areas, the THz pulse energy values for the line focusing set-up are about 4 times smaller than the values obtained for the tilted pulse front set-up. This difference can be explained by the finite width of the pump line for the line focusing set-up. This width must be small compared to the wavelength (Cherenkov condition).

In order to illustrate the very different type of development of the THz pulse inside the LiNbO₃ crystal, model calculations were performed and the results are shown in Fig. 3 and the underlying movie. For these calculations the analytic solution (Eq. 18 of Ref. 13) of a Cherenkov type emission from a line source was convoluted with the actual intensity distribution of the pump pulse. In order to keep the calculation time small, a 0.5-mm-long crystal and a 160-μm-wide (FWHM) spot were assumed for the tilted pulse front set-up. These values are about 3 to 8 times smaller than the actual ones, but the qualitative picture obtained can well illustrate the situation of the experiment. For the line focusing set-up, a 6-μm-wide (FWHM) focal line was assumed. In the figure and the underlying movie, the intensity of the pump pulse (pink color) and the amplitude of the THz electric field are shown, red and yellow denote a positive amplitude of the electric field, blue a negative one.

The 780 nm pulses propagate along the z-axis and enter the crystal (shown in green) from the left. At 0.0 ps (first frame of the movie) the line focus (perpendicular to the plane of display in the upper part of Fig. 3) is at the entrance face and half of the tilted pulse (lower part of Fig. 3) has already entered the crystal. Inside the crystal, the THz electric field develops and propagates away from the z-axis (horizontal) at the angle given by the phase-matching condition [10–12]. For the line focus (see upper part of Fig. 3), the spatial overlap between the pump and THz fields is quickly lost and the typical Cherenkov pattern results. For the pump pulse with the tilted front (see lower part of Fig. 3; the two doted lines mark the pulse edges) the THz radiation again propagates away from the pump beam propagation direction. Due to the proper tilt angle this now corresponds to a sliding of the THz radiation disk relative to the pump disk at a small rate compared to the transversal dimensions. This ensures an excellent spatio-temporal overlap between the pump and the THz fields and therefore a high conversion efficiency.

 

Fig. 3. (1.3 MB) Numerical simulation of THz pulses generated in LiNbO₃. Top panel: the pump pulse is focused from the left to a line perpendicular to the plane of display. Bottom panel: tilted pulse front set-up with an input pulse extending from -80 to + 80 μm. Red and yellow denote a positive amplitude of the electric field, blue a negative one.

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According to the calculation (see movie accompanying Fig. 3), the energy of the THz radiation increases by increasing its area at constant intensity during the propagation inside the crystal for the line focusing set-up. In contrast, for the tilted pulse front set-up, the energy of the THz radiation increases mainly because of the increased intensity during the propagation. For the line focusing set-up the calculation predicted a 16 times smaller THz energy when the pump linewidth is increased from 1.5 μm to 25 μm.

4. Conclusion

The energy of sub-ps THz pulses generated by tilted pulse front excitation has been scaled up by using increased pump pulse energy and pump spot area. Employing 150-fs-long 500 μJ pump pulses at 780 nm, up to 240 nJ THz energy was achieved at room temperature. The energy conversion efficiency from pump to THz radiation has a maximum of 5 × 10^-4 at 300 μJ pump energy. The corresponding photon conversion efficiency amounts to 10 %. Using line focusing excitation for comparison, the maximum THz energy was 3.1 nJ. This value was obtained at 32 μJ pump energy. At larger pump energy, the THz energy drops for this geometry. The experimental results are in good agreement with model calculations. The tilted pulse front excitation allows further up-scaling of the THz energy if the pump spot size is increased. We believe that this set-up is an attractive source of THz pulses applicable for linear and nonlinear spectroscopic investigations as well as for large area THz imaging.