1. Introduction

Conventional high-energy intense terahertz (THz) sources are defined as single pulse energy >1 μJ, peak electric field >100 kV/cm, and peak magnetic field >1 mT ultrafast THz pulses [1]. Such THz sources have already shown great applications in research fields of solids, liquids, gases and plasma. Representative works include ultrafast spin control [2], two-dimensional material THz nonlinear effects [3], THz Kerr effect in liquids [4], no DC-field assisted gas molecule alignment [5,6] and THz high harmonic generation [7]. The next goal of high-energy, strong-field THz sources is to obtain mJ-level pulse energy with the peak electric field higher than 1 MV/cm (even dozens of MV/cm), and the peak magnetic field of several Teslas [8]. By using the optical rectification in organic crystals, 0.9 mJ pulse energy with ~80 MV/cm peak electric field has already been achieved in the frequency range higher than 2 THz [9]. However, for some specific applications, such as electron acceleration [10], superconductor investigation [11] and THz biological effects [12], intense THz sources with frequency range of 0.1-2.0 THz are also important.

Tilted pulse front (TPF) technique in lithium niobate (LN) crystals is expected to fill the shortage of high energy THz sources at low frequencies [13], especially the combination of TPF and the relatively mature Joule-level Ti:sapphire laser technology [14–16]. Theoretical calculations predicate that 300-500 fs Fourier transform limit (FTL) pulses in the case of 800 nm pumping are the best for efficiently generating intense THz pulses with the TPF [17]. However, the FTL pulse duration of the Joule-level Ti:sapphire laser pulses is almost less than 50 fs. This makes it difficult to realize mJ-level THz output by using the existing Joule-level Ti:sapphire lasers for the TPF technique. The specific challenges include: (1) the propagation of high-energy ultra-short pump pulses in air will induce nonlinear effects, which leads to the destruction of the pulses. This requires the TPF setup to be placed in vacuum, resulting in difficulty for efficiency optimization; (2) The wide spectrum of the pump laser after a grating diffraction has a very large divergence angle requiring large aperture optical elements of the imaging system between the grating and the LN crystal; (3) The wide pump spectrum makes it very difficult to image all the spectral components into the same imaging plane inside LN because of chromatic aberrations; (4) The extremely short pump pulse magnifies the design imperfections of TPF setup; (5) Because of the damage threshold limit of the LN crystal, a large pump beam is needed to irradiate the LN crystal, which poses a challenge to the crystal size; (6) Due to impediment of group velocity dispersion combined with angular dispersion (GVD-AD), only a small portion of the pump beam close to the edge of the phase-matching angle in LN crystal contributes to efficient THz yields; (7) Free-carriers generation due to multi-photon absorption in LN (band-gap ~4.0 eV) decreases the output THz energy and this effect becomes more pronounced for high pump intensity [18, 19].

For the aforementioned challenge of chromatic aberrations, in 2013, Kunitski et al. proposed concave mirror imaging systems to overcome the dispersion problem caused by 35 fs laser pulses [20]. However, this method makes it very difficult to optimize the THz efficiency in real experiments, especially for dual concave mirror imaging. With regard to the short effective interaction length and the multi-photon absorption caused by ultra-short pulses, in 2014, we systematically studied the effect of pulse width on THz efficiency by introducing spectrum-cutting method in grating pairs of laser systems [14]. In the same year, Blanchard et al. also used the same method to broaden the 800 nm pump laser pulses and obtained an 800 nm-to-THz energy conversion efficiency of 0.35% at room temperature with a maximum single pulse energy of ~15 μJ [15]. In 2016, Zhong et al. employed the spectrum-cutting method combined with elliptical beam excitation and cryogenically cooling the LN to liquid helium temperature, and achieved 0.19 mJ THz output energy with a corresponding energy conversion efficiency of 0.27% [16]. Although the way of spectrum cutting is very helpful for improving the efficiency, the extracted THz energy for subsequent experiments is relatively low due to heavy waste of pump laser energy.

In this work, we systematically investigate the chirp method [21] deposited on the pump pulses for efficient THz generation. For simplicity, we used a single lens imaging system, rather than the complex concave mirror systems, to verify the above method. In order to obtain higher energy conversion efficiency at room temperature, we used elliptical beam excitation in LN crystal. In this way, we obtain 0.2 mJ THz output energy with 800 nm-to-THz energy conversion efficiency of 0.3% in non-vacuum condition at room temperature. As far as we know, the 0.2 mJ THz output energy is the highest extracted THz pulse energy in LN crystal at room temperature employing TPF technique pumped by Ti:sapphire laser pulses.

2. Experimental setup

The TPF setup in our experiment is shown in Fig. 1(a). The Ti:sapphire laser system (Pulsar 20, Amplitude Technologies) we used is capable of generating ~500 mJ laser pulses with 30 fs pulse duration (transform limited) at 10 Hz repetition rate. After the compressor, the laser beam size is ~40 mm diameter (1/e²). In our experiment we only used the maximum pulse energy of 70 mJ for THz generation due to damage limitation of the vacuum window of the laser system and the LN crystal. We introduced the second-order dispersion by altering its GVD value of an acousto-optic programmable dispersive filter (AOPDF, Dazzler, Fastlite) located after the stretcher to impose positive or negative chirp onto the pump laser pulses. We characterize the compressed pulse with a commercial frequency resolved optical gating (FROG, Swamp Optics, Model: 8-20-USB) device just before the TPF setup while we tune the distance between the grating pair in the compressor and change the GVD value of the AOPDF. The transform limited pulse is obtained at an intermediate GVD value which is shown in Fig. 1(b). Based on the temporal Gaussian shape and constant phase the chirped pulse duration can be calculated (Fig. 1(c)) with the formula ${\tau }_{out}={\tau }_{in}\sqrt{1+{(4\ln 2{\phi }_2/{\tau }_{in}^2)}^2}$, where ${\tau }_{out}$ is the chirped pulse duration; ${\tau }_{in}$ is 30 fs; and ${\phi }_2$ is the GVD. In our case, the transform limited pulse duration is 30 fs at a GVD value of 38000 fs². The “negative” chirp is defined as the GVD lower than 38000 fs², while the “positive” chirp is defined as the GVD higher than 38000 fs². The chirped pulses are obtained by varying the GVD value through the Dazzler, while the distance between the grating pair in the compressor is fixed.

 

Fig. 1 (a) Schematic of the high energy THz source with TPF technique and EOS setup. HWP: Half-wave plate; LN: lithium niobate; OAP: 90°off-axis parabolic mirror; IS: Integrating sphere; BPD: balanced photodiode. (b) Autocorrelation measurement of the pump laser pulses at its shortest duration of 30 fs. (c) Calculated chirped pulse duration as a function of the GVD. (d) Input IR spectra for different GVDs measured before the laser beam entering the TPF setup. (e) The pump beam position relative to the edge of the LN prism.

Download Full Size | PDF

The TPF setup includes a grating with density of 1480 lines/mm and size of 140 × 100 × 20 mm³ (length × width × height), a half-wave plate (HWP) and a plano-convex lens with f = 85 mm focal length. The grating is used to tilt the intensity front of the pump laser with a designed incidence angle of 21°. The beam is diffracted into order m = −1 with a diffraction angle of 57°. The HWP is used to rotate the polarization of the pump laser pulses from horizontal to vertical, which is parallel to the optical axis of the LN crystal. The lens is used to image the grating into the LN for phase matching. The distance between the grating to the lens and the lens to LN are ~255.0 mm and ~127.5 mm, respectively, giving a demagnification factor of −0.5. After the imaging, the pump laser pulse on the crystal becomes elliptical with diameters in horizontal and vertical directions of 10 mm and 20 mm, respectively.

A z-cut congruent LN crystal is fabricated in a triangle prism shape with the dimensions of 68.1 × 68.1 × 64 mm³ in x-y plane, which gives two 62°angles for high energy THz generation. The height of the LN prism in z-axis is 40 mm. In order to increase the damage threshold and reduce the photo-refraction effect, the LN is doped with 6.0 mol% MgO and the tested damage threshold in our TPF setup is up to ~10¹² W/cm² for 800 nm laser pulse with 30 fs pulse duration. The LN is anti-reflection (AR) coated at 700~1060 nm wavelength range on two rectangular surfaces (68.1 × 40 mm²) to overcome the ~15% Fresnel losses. The THz output surface of the prism is AR coated for the THz wave with ~96 μm thick of three stacked Kapton tape layers (polyimide, Thorlabs, KAP22-075). The stacked layers have a transmission of ~95% at 0.1-2.5 THz [22]. The measured enhancement of the out-coupled THz energy compared to that without the AR coating is ~30%. The IR input spectrum is acquired on the reflection beam from the grating, i.e. before the delay stage. The IR output spectra after generating THz pulses are collected by two parabolic mirrors and focused into an optical fiber coupled integrating sphere. All of the measurements are carried out at room temperature.

The generated THz waves are characterized in three ways. (1) We employed a pyroelectric detector (Gentec SDX-1152) to measure the extracted single pulse THz energy and its corresponding efficiency. This fast THz detector has a response curve from the factory and we further confirmed the calibration in our lab, both of which agree very well. (2) For the out-coupled THz spectrum measurement, we used indirect electro-optic sampling (EOS) method and direct frequency domain measurement. The EOS setup includes four 90°off-axis parabolic mirrors (OAP) for collimating and focusing the THz beam. The probing beam from the zero-order reflection of the grating is focused after a mechanical delay stage together with the THz beam into a ZnTe (0.5 mm thickness) detection crystal. The THz time-domain waveform is recorded by moving the delay stage and Fourier transform gives the output THz spectrum. The direct spectrum measurement consists commercial THz band-pass filters (Thorlabs) and the THz energy detector. By replacing the band-pass filter with different designed central THz frequencies, we can record the emitted THz spectrum. In our case, we have only three band-pass filters by hand with the central frequencies of 0.75 THz, 1.0 THz and 2.0 THz, which can, to some extent, be used to deduce the central frequency in a range. However, this direct spectrum measurement method can be used to compare with the results from EOS. For the THz polarization measurement, we used a well-calibrated commercial THz polarizer (Tydex). (3) A home-built three-dimensional translation stage combined with the THz energy detector is employed to measure the divergence angle of the output THz beam at horizontal and vertical directions. In order to avoid the averaging effect, an aluminum film with a hole of 2 mm diameter in the center is covered on the THz detector. This measurement is carried out with the THz detector facing to the emission facet of the LN crystal.

3. Results and discussions

3.1 Optimization of the 800 nm-to-THz energy conversion efficiency

In order to investigate the influence of chirped laser pulses on the THz efficiency, we first fixed the pump energy at 30 mJ in the LN crystal corresponding to a pump fluence of ~40 mJ/cm², and then optimized the TPF setup for each negative and positively chirped pulse duration. The optimization is very sensitive to the pump pulse duration because of the variable pump peak intensity and the change of the effective interaction length inside LN crystal. As shown in Fig. 2 (a), we obtained a maximum 800 nm-to-THz energy conversion efficiency of ~0.3% for both 450 fs positively chirped and 105 fs negatively chirped pulse duration. This conversion efficiency is already close to the record number of 0.35% obtained in LN driven by Ti:sapphire laser systems [15]. However, the record number of 0.35% was obtained under TFL laser pulse pumping, while we simply chirped the pump pulses and achieved the close result. In our case, the extracted THz efficiency for 30 fs duration is about 0.25%, although the pump peak intensity is 15 times higher than that of 450 fs and >3 times higher than that of 105 fs, respectively. Further increasing the pulse duration for both negative and positively chirped pulses, the extracted energy conversion efficiency decreases. However, it decreases much faster for the negative chirp than that of the positive chirp. At ~280 fs negatively chirped pulse duration, the extracted efficiency has already decreased to ~0.17%, while the efficiency keeps ~0.25% even the positive chirped pulse duration has already been stretched to 2 ps.

 

Fig. 2 (a) Extracted 800 nm-to-THz energy conversion efficiency as a function of the pump pulse duration for negative and positive chirp, respectively. (b) Extracted THz single pulse energy and its corresponding 800 nm-to-THz energy conversion efficiency dependence on the pump energy. (c) Input IR pump spectrum and IR output spectra for different chirped pump pulses, and (d) IR input spectrum and output spectra for different pump energies.

Download Full Size | PDF

The chirp method has been proposed in contact-grating schemes [23, 24], and the previous work also presented enhanced THz efficiency under chirped pulses [21]. The possible mechanism for the asymmetrical behavior in Fig. 2(a) could be attributed to the variation of the input pump spectrum (Fig. 1(d)) for different chirped pump pulses. When tuning the GVD with the Dazzler in the laser system, the output spectra from the laser are changed for different GVDs. The generation efficiencies are asymmetric with respect to the signs of applied chirp because pulse duration (peak power) evolved differently during the generation process. The dispersion comes from the chirp applied to the input pulses (normal/anomalous), grating (anomalous) and lithium niobate crystal (normal). They have different signs and the combination of these can either extend or shorten the temporal overlap between the THz efficiency and pump. The THz efficiency is influenced by the combination of the pump intensity, effective interaction length, multi-photon absorption and so on. Therefore, the competition between these processes lead to the asymmetrical efficiency curves for negative and positive chirp.

To further increase the THz output energy, we fixed the pulse duration to be the optimal 450 fs and scaled up the pump energy up to 70 mJ. Note that we optimized the TPF setup as well as the THz detector collecting efficiency for each pump energy. The optimization of the TPF setup for different pump energy is slightly different, because the effective interaction length due to nonlinear distortion for different pump energy is varied [25]. Therefore, the competition between the THz absorption length and effective interaction length inside LN influences the THz efficiency. Meanwhile, the relative position between the pump beam and the edge of the LN prism is also very sensitive for the efficiency. As is shown in Fig. 1(d), the edges of both the pump beam and the LN are overlapped for the optimal condition. As can be seen in Fig. 2 (b), for the pump energy lower than 20 mJ, the extracted THz energy increases following a quadratic behavior, corresponding to a linearly increase of the extracted energy conversion efficiency. However, the extracted THz efficiency starts to show obvious saturation when the pump energy is higher than 20 mJ. Fortunately, the efficiency does not decrease when further increasing the pump energy till the maximum pump energy of 70 mJ. The maximum THz output energy of 200 μJ is achieved, with a corresponding maximum efficiency of 0.3%, as already presented in Fig. 2 (a). This THz energy is a record number generated in LN via optical rectification at room temperature driven by Ti:sapphire laser systems at 800 nm wavelength range.

According to the conversion efficiency formula of the optical rectification, it is straightforward that the efficiency increases linearly with the pump peak intensity. However, the pulse duration influences not only the peak intensity, but also the effective interaction length, and multi-photon absorption. Theoretical calculations reported that highly efficient THz generation in LN crystal should be only obtained under optimal temporal shape with FTL pulses of the pump pulses. However, in our case, the short FTL pulses of 30 fs does not guarantee the highest conversion efficiency due to competition between the aforementioned three effects, especially, decreasing the effective interaction length and generating free-carrier due to multi-photon absorption in LN crystal [18, 19]. By introducing the controlled temporal chirp to the pump laser pulses in the TPF setup, we not only decrease the pump peak intensity to overcome the efficiency decreasing due to free-carrier generation, but also compensate for some unidentified imperfections in the TPF setup, like fine-tuning the TPF angle, temporally stretching or compressing the pump pulses at the imaging plane, optimizing the TPF in the transverse projection and adding a group delay dispersion into the system. All these effects are inherently inter-coupled in the TPF setup. By detuning the temporal dispersion of the pump pulse off FTL, we find locally optimal chirped pulse durations of 450 fs and 105 fs that yield maximum 800 nm-to-THz conversion efficiency. Our method introduces a new and simple approach for highly efficient THz generation in LN especially driven by high energy, ultra-short pulses delivered from Ti:sapphire laser systems.

Figure 2(c) exhibits the IR output spectra from LN crystal pumped at chirped pulse durations of 105 fs (negative chirp), 30 fs (transform limited), 450 fs (positive chirp) and 1.85 ps (positive chirp). The four broadened and red-shifted IR output spectra show no obvious differences. In Fig. 2 (d), we can see obvious spectrum redshift and broadening depending on pump pulse energy. However, the output spectrum stops broadening itself when the pump energy is scaled up to 50 mJ, corresponding to the efficiency of 0.25% in Fig. 2 (b). Due to cascading effect for highly efficient THz generation, the IR photons continuously down converted to THz photons as long as the phase matching condition is satisfied, resulting in the IR output spectrum redshift and broadening. The IR output spectrum stops varying when the efficiency saturates. For the optimization of the chirped pump pulse duration, we fixed the pump laser energy at 30 mJ and optimized the extracted efficiency at different pulse duration. In this case, the efficiencies for the above mentioned four pulse durations in Fig. 2 (c) are already higher than 0.25%. That is why we did not observe pronounced variations of the IR output spectra for the four pulse durations.

3.2 Characterization of the output THz spectrum, polarization and divergence

Figure 3 (a) shows the measured THz time-domain waveform and its corresponding spectrum. The single-cycle THz output waveform has a pulse duration of ~1.5 ps, which is also used to estimate the peak field. The peak frequency of the output THz wave locates at 0.4 THz and the frequency range covers from 0.1 THz to 2.5 THz. Employing THz band-pass filter and energy detector, we measured the emission spectrum in a direct way, shown in Fig. 3(b). Due to the limitations of the filters, we only measured the minimum frequency down to 0.75 THz. The spectrum obtained by direct measurement shows that the peak frequency is below 0.75 THz, which is in agreement with the results obtained by the EOS measurement. Congruent LN has strong linear absorption in THz region [26]. This makes the generated THz wave absorbed by the crystal and cannot be successfully coupled out, especially for higher frequencies. Cryogenically cooling crystal can greatly reduce the absorption of the THz wave and increase the emission efficiency, and can also extend the out-coupled THz spectrum to higher frequencies. For different application requirements, the realization of tunable THz central frequency can be realized by means of temperature control.

 

Fig. 3 Extracted THz output spectrum measured with EOS and band-pass filters. (a) Measured THz time-domain waveform and its corresponding Fourier transform spectrum. (b) Frequency-domain characterization with commercial THz band-pass filters. The inset shows the THz polarization characterized by the commercial the THz polarizer together with the THz energy detector.

Download Full Size | PDF

The polarization characteristics of the THz wave are also very important for applications. For example, THz electron acceleration requires good linear polarization. The THz polarization direction needs to be in accordance with the electron flight direction. The inset of Fig. 3(b) exhibits the measured THz signal as a function of the rotation angle of THz polarizer. The perfect cosine pattern shows very good linear polarized THz wave. Its polarization direction is vertical and parallel to the optic axis of the LN emitter.

In the process of producing intense THz radiation using TPF technique, the generated THz beam size and position change with the pump fluence due to nonlinear distortion effect. Meanwhile, different imaging systems between the grating and LN crystal also make the THz beam size and position varied, resulting in different divergence angle of the generated THz waves [27]. It is reported that an approximately collimated THz beam could be obtained by using a double-lens telescope method [28]. However, the telescope imaging system is complex for optimizing the energy conversion efficiency. Single lens imaging system is simpler and more convenient. Moreover, an elliptical pump laser beam can be prepared and used to irradiate the LN generator for higher efficiency at room temperature. In our case, we used an elliptical pump laser beam with a horizontal direction of ~10 mm and a vertical direction of ~20 mm (see Fig. 1(e)). The elliptical beam excitation enables the pump pulses to be closer to the cutting edge of the 62°phase matching angle of the LN crystal in the horizontal direction [29]. It is better for optimizing the effective interaction length and for overcoming the propagation absorption. This is very helpful for optimizing the efficiency.

Figure 4 shows the measured divergence angle and the recovered THz beam spot on the emission plane of the LN crystal. It can be seen from Figs. 4(a) and 4(b) that the THz beam presents Gaussian distribution in both horizontal and vertical directions. For the horizontal case, the THz beam profile has an asymmetry resulting from the imaged grating curvature inside the LN crystal, which has been predicted in Ref [24]. As the propagation distance increases, the THz beam continues to diverge. However, in the horizontal and vertical directions, the divergence is different. The measured horizontal and vertical divergence angles are 13.6°and 5.0°, respectively, both of which agree very well with the results in Ref [25]. The diameters of the THz emission spot on the emission plane of the LN are 4.9 mm in the horizontal and 10.4 mm in the vertical direction, respectively. The THz beam size is much smaller than that of the pump laser beam. This is due to the nonlinear distortion effect. In our case, the TPF setup is optimized at pump energy of ~70 mJ with the efficiency of 0.3% for the divergence measurement. A large number of THz photons are generated when the pump pulses enter the LN crystal, resulting in redshift and broadening of the IR spectrum. In the subsequent propagation process of the pump pulses, the changed IR spectrum could no longer efficiently convert to more THz photons, resulting in shorter effective interaction length inside LN and smaller THz beam size compared to that for lower energy pump. Figure 5 shows the knife-edge measurement of the focused THz beam size. The THz beam is further focused to ~1.0 mm diameter (FWHM), resulting in a THz peak field of ~4.0 MV/cm [30].

 

Fig. 4 Divergence characterization of the output THz pulses with 3D scan. Normalized THz signal depends on (a) the horizontal position and (b) vertical position at different propagation distance, respectively. (c) Calculated divergence angle at horizontal and vertical directions. (d) Calculated and recovered THz beam profile in LN crystal.

Download Full Size | PDF

 

Fig. 5 (a) The knife-edge measurement, and (b) its corresponding Gaussian fit for characterization of the focused THz beam spot size.

Download Full Size | PDF

4. Conclusion

At room temperature, we achieve the highest THz output energy of 0.2 mJ in LN pumped by 800 nm laser pulses through TPF method. The corresponding 800 nm-to-THz energy conversion efficiency is optimized to 0.3% by chirping the pump laser pulses. This method overcomes the multi-photon absorption and increases the effective interaction length in LN crystal. The out-coupled THz beam pulse duration, spectrum, polarization, and divergence are fully well characterized. Combining these parameters, we obtain the focused THz peak electric field of ~4.0 MV/cm. This robust, stable, and tabletop intense THz source is ready for various applications.