1. Introduction

The generation of intense terahertz (THz) radiation has been an area of intense research in the past few decades owing to its wide range of applications in advanced sciences [1–7]. Among the various THz generation methods developed to date [8], the tilted pulse front (TPF) technique, which employs femtosecond laser pulses to generate THz pulses in a lithium niobate (LN) crystal, has been identified as an effective approach for addressing the issue of phase mismatching [9]. This method offers high-efficiency THz pulse generation through an optical rectification (OR) process, making it a promising technique for practical applications. A simple approach to generating high-energy THz pulses using the TPF technique involves increasing the pump laser energy by enlarging the pump-spot size on the LN crystal. This can overcome the limitation of the effective interaction length for phase-matching THz generation in LN crystals owing to the nonlinear distortion effect in the noncollinear geometry of the TPF scheme [10]. It has been experimentally shown that a THz pulse with a pulse energy of 1.4 mJ and a corresponding 800 nm-THz conversion efficiency of 0.7% was achieved through the shaping and enlarging of a pump-spot (80 mm (1/$e^{2}$) diameter) with a spectral chirp and cryogenically cooled LN crystal (91 K) [11].

In spite of the remarkable achievement, there are limitations when using TPF pumping by femtosecond ($\leq$ 50 fs) laser pulses with large spectral bandwidths. In a conventional TPF setup, the pump beam is produced by imaging a diffracting laser beam through an optical grating, which inevitably induces angular dispersion, which in turn leads to a large group-delay dispersion (GDD) [12,13], resulting in the rapid evolution of the ultrashort pump-pulse within the LN crystal. Consequently, the average pulse duration is significantly longer than that of the Fourier-transform-limited (FL) pump-pulse [14]. Additionally, the existence of angular dispersion can cause imaging errors, resulting in a significant increase in the pump-pulse duration at the edges of large pump spots [15]. These processes collectively contribute to a reduction in the effective THz generation length and pump-to-THz conversion efficiency of LN crystals.

A novel method has been proposed to create discrete TPF pump pulses with no angular dispersion [16–19]. This technique is expected to yield better THz-generation results than those obtained using gratings with ultrashort pump pulses. It employs a reflective echelon comprising small step mirrors arranged in a tilted plane. When a laser pulse is incident on the echelon, it splits into multiple beamlets that are delayed in time, which determines the TPF angle of the pump beam, given by tan$^{-1}(c\Delta t/\Delta y)$, where $\Delta y$ and $\Delta t$ are the spacing and time-delay due to the height (H) of each step (i.e., $\Delta t = 2$H$/c$) between beamlets, respectively. In the LN crystal, the final TPF angle that satisfies the phase-matching condition in the OR process can be obtained using a lens imaging system with demagnification.

In this study, we present the optimization of THz generation from an echelon-TPF scheme using a chirped pump pulse. The discrete TPF scheme for THz generation was previously demonstrated experimentally using fixed pump pulse durations of 70 fs [16], 20 fs [20], and 280 fs [17]. Previous studies have only reported the observed performance without optimizing the pump pulse. In contrast, our study achieved improved performance in THz radiation generation by optimizing the chirped pump. Specifically, a conversion efficiency of 0.39% was achieved using a positively chirped pump pulse with a pulse duration of 330 fs. This efficiency is approximately 1.8 times higher than the previously reported value of 0.21% under similar experimental conditions (800 nm pump wavelength at room temperature) [16]. Furthermore, we investigated the characteristics of the THz beam profiles and observed a significant variation in the near- and far-field THz beam profiles in the plane of the tilted pulse direction, whereas there was no variation in the vertical direction as the pump energy was varied. This can be explained in terms of the intensity-dependent effective interaction length for THz generation.

In Section 2, we describe the experimental setup for echelon-TPF pumping THz generation. In Section 3, we present the experimental results obtained from our study on characterizing the properties of THz generation and provide a discussion of these results. In Section 4, we present conclusions about our studies. The observations presented in this work are crucial for advancing the generation of high-energy THz pulses from the echelon-TPF scheme.

2. Experimental setup

The experimental setup for our THz generation is illustrated in Fig. 1(a). We employed a Ti:sapphire laser system that delivered a maximum output energy of 6 mJ, a repetition rate of 720 Hz, a pulse duration of 34 fs at a central wavelength of 795 nm, and a full-width-half-maximum (FWHM) spectral bandwidth of 30 nm, as shown in Fig. 1(b). The beam from the Ti:sapphire laser system of size $\sim$10 mm (1/$e^{2}$ diameter) was divided by the beam splitter (BS) into two beams: a 90% reflected pump beam for THz generation, and a 10% transmitted probe beam for electro-optic (EO) sampling measurements [21]. The pump beam was chopped using an optical chopper at frequencies of 25 Hz and 120 Hz and directed to an echelon mirror for the THz energy and waveform measurements, respectively. The polarization direction of the pump beam was rotated from horizontal to vertical using a half-wave plate parallel to the optical axis of the LN crystal.

 

Fig. 1. (a) Experimental setup for the generation and detection of THz pulses. The pump beam for THz generation was imaged with a demagnification of $\sim$5 into the LN prism after reflecting off the echelon mirror. The THz pulse energy and temporal THz field waveform were measured by the PD and the EO sampling, respectively, in Setup 1. The far-field THz beam profile was measured by the PD with a slit in Setup 2. (b) Spectra of the pump beam were measured before incidence on the echelon. (c) Schematic diagram of the echelon mirror used for THz generation, with dimensions 20 mm $\times$ 20 mm $\times$ 5 mm, and of height (H) 100 $\mu$m and width (W) 230 $\mu$m. (d) Image of pump beam recorded with a camera placed in the image plane.

Download Full Size | PDF

The echelon mirror was fabricated by Double H R&D (Republic of Korea) by cutting a stair-step pattern on the surface of a brass block (20 mm $\times$ 20 mm), followed by 24K gold plating for high reflectivity. As shown in Fig. 1(c), the echelon mirror consists of many small stair steps with a width of 230 $\mu$m (W) and height of 100 $\mu$m (H), respectively. To optimize its performance, the echelon mirror was mounted on a platform capable of one linear motion (x-axis) and three rotational motions ($\Theta$x, $\Theta$y, and $\Theta$z; not shown in Fig. 1(a)). This configuration facilitated the generation of many time-delayed beamlets from a single-input pump beam upon reflection, leading to the collective generation of a tilted pulse-front pump. To satisfy the phase-matching condition ($\sim$63$^{\circ }$) between the pump pulse and the THz pulse, the image of the tilted pump beam from the echelon mirror is demagnified by a factor M $\approx$ 5 using a telescope imaging system consisting of two lenses of focal lengths $f_{1}$ = 500 mm and $f_{2}$ = 100 mm. For a given demagnification factor M, the final tilt angle was calculated using Eqs. (1) in [16]. The size of the pump beam on the LN crystal was approximately 2 mm (1/$e^{2}$ diameter), with 50 individual beamlets after the telescope, as shown in Fig. 1(d). The 1.3% MgO-doped stoichiometric LN crystal used for THz generation consisted of a prism-shaped cut at an angle of 62$^{\circ }$. In our experiments, we were limited to a maximum pump energy of 2.2 mJ, despite the laser system’s capability of providing up to 6 mJ of pulse energy. This limitation was attributed to energy loss resulting from laser beams transmitted or reflected from various optical components. Specifically, we observed a low reflectance of 52.5% in the echelon mirror due to its polished face falling short of optical-grade standards.

In Setup 1, the emitted THz radiation was collected and focused using a pair of off-axis parabolic (OAP) mirrors with a diameter of 50.8 mm and an effective focal length of 76.2 mm. The output THz pulse energy was measured using a pyroelectric detector (PD, Gentec THz5B-BL-DZ), and the waveform was characterized using EO sampling. For the latter, the probe beam was attenuated using a 2 mm diameter circular iris and neutral-density filters and then time-delayed using a delay line. Subsequently, it was directly passed through a hole ($\sim$3 mm diameter) in the second OAP mirror and overlapped with THz radiation in a 0.3 mm thick ZnTe (110) crystal. The EO signal was detected and analyzed using balanced photodiodes and a lock-in amplifier after passing through a quarter-wave plate and Wollaston prism, respectively. The two-dimensional far-field THz beam profile was measured in Setup 2 using a PD mounted on the xyz-linear motion stages. A diaphragm of a small slit aperture of 500 $\mu$m was placed in front of the PD, which allowed the PD to adequately measure the THz signal, even at large distances from the source. The slit aperture was lesser than that of the THz beam, thereby ensuring that the spatial averaging effect was disregarded. The 300 $\mu$m thick, 50.8 mm diameter silicon wafer was used to block the pump beam and its second harmonic from entering the PD for all THz energy measurements (not shown in our setup).

3. Results and discussion

3.1 Optimization of THz generation with chirped pump pulses

In the first measurement, we investigated the influence of the chirped pump pulse duration on the THz radiation generation, for which, we varied the GDD of the pump pulse by tuning the distance between the grating pairs in the laser compressor [22]. Figure 2(a) shows the pump pulse duration as a function of the grating distance, as measured using a single-shot second-harmonic autocorrelator. At a grating distance of 300 mm, the minimum pulse duration was measured to be 34 fs (FWHM), which is comparable to the transform-limited pulse duration of 31 fs [23]. The measured pulse duration corresponded to the presence of negative (-) and positive (+) chirps for grating distances > 300 and < 300 mm, respectively.

 

Fig. 2. (a) Measured (black dotted line) and fitted (red solid line) pulse duration of the pump beam as a function of the distance between the grating pairs in the laser system. (b) Measured output THz radiation energy as a function of the chirped pump pulse duration for different pump energies: 2.18 mJ (purple solid line), 0.94 mJ (blue solid line), 0.47 mJ (red solid line), and 0.052 mJ (black solid line). For comparison, the THz curves at 0.47 and 0.052 mJ are multiplied by 4 and 160 times, respectively. (c) The optimal pulse duration of the pump beam for THz radiation generation as a function of the pump energy. The estimated output THz energy and the corresponding conversion efficiency as a function of the pump energy are shown in (d) and (e), respectively; “+” and “-” represent the “positive chirp” and “negative chirp” of the pump beam.

Download Full Size | PDF

Figure 2(b) shows the dependence of the THz output energy on the chirped pump pulse duration for four different pump energies. When the pump energy was below 0.37 mJ, the optimized THz energy exhibited a peak for a negatively chirped pump pulse. For a pump energy of 0.052 mJ, the optimal pulse duration for negative chirp was 300 fs. However, for pump energies greater than 0.37 mJ, longer pulse durations of both negative and positive chirps resulted in higher yields of THz radiation as shown in Fig. 2(b). This behavior was previously observed in experiments utilizing a TPF scheme with an LN prism [24,25], and a scheme in which the pump laser was directly sent to a bulk LN crystal [26]. The observations can be attributed to variations in the effective interaction length, which is an important parameter in THz radiation generation. The effective interaction length was defined as the propagation length within the generation crystal where the THz radiation intensity increased from 5% to its peak value [14]. At low pump energies, the effective interaction length is influenced by the variation in the pump pulse duration with the propagation distance owing to material dispersion and absorption at THz frequencies. A negatively chirped pump pulse undergoes temporal compression by propagation, resulting in a higher peak intensity of the pump and consequently enhancing the THz radiation generation [24–26]. However, at higher pump energies, the effective interaction length is significantly reduced by the combined effects of the self-phase modulation (SPM) [27–30], pump energy depletion, and free-charge carrier absorption (FCA) by three-photon absorption (3PA) [14,26,31], as well as a spectral broadening of the pump pulse due to cascading effects [27,32–34]. Therefore, a short pulse duration results in increased pump intensity, which leads to a more robust nonlinear process for reducing the effective interaction length. However, a long pump pulse was insufficient for THz radiation generation. Thus, the interplay between these processes resulted in the characteristic curves for the pump chirp and energy, as shown in Fig. 2(b).

Figure 2(c) shows the optimal pump pulse duration as a function of the pump energy. In the range of 0.052–2.18 mJ, the optimal pulse duration increased monotonically with the pump energy. Specifically, at a negative chirp, the pulse duration varied in the range of 300–600 fs, whereas at a positive chirp, it varied approximately in the range of 96–330 fs. It is important to note that the pump intensity has a significant impact on the effective interaction length [10]. Thus, the tradeoff between the pump energy and pulse duration is important for maintaining a consistent pump intensity, which accounts for the variation in the optimal pulse duration.

Figures 2(d) and 2(e) show the measurements of the output THz radiation energy and the corresponding THz conversion efficiency, respectively, as a function of the pump energy. It is worth noting that we maintained the pulse duration at the optimal value for both negative and positive chirps during all THz radiation energy measurements. As in a previous numerical analysis [19], the THz conversion efficiency (and THz energy) in the discrete TPF scheme is expected to increase linearly (and quadratically) with the pump energy. This increase can be observed for pump energies below 0.37 mJ with a negative chirp. However, when the pump energy exceeds 0.37 mJ, the THz conversion efficiency saturates even when an optimal pulse duration is used. The maximum THz output energies of 8.1 $\mu$J and 7 $\mu$J are achieved for positive and negative chirps, respectively, when the pump energy is 2.18 mJ. Furthermore, the highest THz conversion efficiency of 0.39% was achieved at a positive chirp with a 1.8 mJ pump energy and pulse duration of 330 fs.

3.2 Near-field THz beam profile measurements

In a previous study [10], it was shown through near-field THz beam profile imaging that the effective interaction length and pump energy are related. Similarly, we investigated the effect of the effective interaction length on the pump energy using the knife-edge (KE) method to measure the one-dimensional near-field THz beam profile. To perform this experiment, a sharp rectangular blade was placed near the output surface of the LN prism, as shown in Fig. 3(a). The blade was moved along the x-axis in increments of 200 $\mu$m, and the THz energy of the unblocked beam was measured using the PD in Setup 1. Figure 3(b) shows a near-field THz beam profile obtained at a pump energy of 0.052 mJ. The extracted beam profile (blue solid line) was obtained by differentiating the measured THz energy (cyan circle dotted line) from the KE measurement after fitting it to the error function [35]. We observed a Gaussian beam profile of the THz radiation with a diameter of $D_{\textrm{FWHM}}$ = 1.63 mm. As we increased the input energy to 2.1 mJ, we observed a decrease in the beam diameter to $D_{\textrm{FWHM}}$ = 0.83 mm and 1.03 mm for negative and positive chirps, respectively, as shown in Figs. 3(c) and 3(d). Moreover, we also observed a horizontal displacement of the THz beam center of approximately 0.67 mm and 0.47 mm in the positive x-direction for negative and positive chirps, respectively, as shown in Figs. 3(c) and 3(d).

 

Fig. 3. (a) Schematic of the measurements of the near-field THz beam profiling using the KE method. The measurements were carried out in Setup 1 as shown in Fig. 1(a). The gap between the blade and output surface of LN prism is $\sim$500 $\mu$m. (b–d) Measured THz beam profile for pump energies of 0.052 mJ and 2.1 mJ, and chirps. The extracted beam profiles (solid line) were obtained by differentiating the measured THz energy (cyan circle dotted line). (e) The estimated beam diameters and (f) the beam centers as a function of the pump energy.

Download Full Size | PDF

Figure 3(e) shows the measured THz beam diameter as a function of pump energy. As mentioned earlier, reductions in the horizontal beam size from 1.63 mm at 0.053 mJ to 0.83 mm at 2.1 mJ for negative chirp, and from 1.38 mm at 0.74 mJ to 1.03 mm at 2.1 mJ for positive chirp are observed. Figure 3(f) shows the horizontal beam center position as a function of the pump energy. The center of the horizontal beam shifts towards the apex of the LN prism in the positive x-direction, from 0 mm at 0.053 mJ to 0.67 mm at 2.1 mJ for a negative chirp, and from 0.21 mm at 0.74 mJ to 0.47 mm at 2.1 mJ for positive chirp. This trend closely followed the changes in the beam size. These results can be explained in terms of a reduction in the thickness of the active THz radiation generation area within the LN prism, which corresponds to the effective interaction length. This phenomenon is consistent with the findings reported in [10]. With an increase in pump energy, the reduction in the effective interaction length leads to a decrease in the THz beam size and a shift in the center of the THz radiation towards the apex of the LN prism at the output surface. In the pump energy range 0.37–0.67 mJ for a positive chirp, a reciprocal correlation was observed for both the THz beam size and center, as shown in Figs. 3(e) and 3(f). A possible mechanism is an enhancement in the effective interaction length being more pronounced with an increase in the pump pulse duration (96–137.7 fs) than with an increase in the pump energy.

3.3 THz beam divergence measurements

For the beam divergence measurements, we examined the changes in the two-dimensional THz beam profiles along the propagation direction, starting from 21.9 mm away from the output surface of the LN prism in Setup 2, as depicted in Fig. 1(a). Figure 4 summarizes the THz beam measurements for three pump energies. Figures 4(a) and 4(b) show the far-field THz beam profiles in the horizontal direction at a distance of 53 mm. The results showed a significant increase in the THz beam size as the pump energy increased for both negative and positive chirps. This finding differs from the near-field THz beam profiles shown in Fig. 3, which indicates an increase in the divergence angle of the THz beam. To determine the THz beam divergence, we used the Gaussian beam propagation theory [36], which gives a relation between the beam diameter and the propagation distance. The divergence angle was defined as the full opening angle of the THz beam. As shown in Fig. 4(c), the divergence angle of the THz beam in the plane of the tilted pulse direction increased with the pump energy from approximately 4.5$^{\circ }$ (at 0.21 mJ) to 14$^{\circ }$ (at 2.1 mJ) and from approximately 9$^{\circ }$ (at 1.16 mJ) to 11.3$^{\circ }$ (at 2.1 mJ) for the negative and positive chirps, respectively. It is evident that the energy-dependent (intensity-dependent) near-field THz beam profile change is directly related to the THz beam divergence. Figures 4(d) and 4(e) show the vertical THz beam profiles at a distance of 53 mm. In contrast to the horizontal direction, the vertical divergence angle was almost unchanged with the pump energy and remains in the range of 10.3$^{\circ }$–11$^{\circ }$ for all chirp signs and pump beam energies, as shown in Fig. 4(f). Based on these results, we expected no variations in the near-field THz beam profiles in the vertical direction. The beam profile in a direction perpendicular to the non-collinear phase coincident plane (x-direction) is not expected to change because it is only affected by the divergence of the image of the pump beam as determined by the telescope lens system.

 

Fig. 4. (a, b, d, e) Far-field THz beam profile at 53 mm from the output surface of the LN prism for different energies: 0.21 mJ (black line), 1.16 mJ (blue line), and 2.1 mJ (red line), and chirps. The measured horizontal (c) and vertical (f) THz beam diameter as a function of the propagation distance along the y-direction in Setup 2. The dotted and solid lines represent the positive and negative chirps, respectively.

Download Full Size | PDF

3.4 Pump beam and THz pulse characterizations

In this section, we investigate the effect of the pump beam on THz generation. Figure 5(a) shows the spectrum of the pump beam before (blue line) and after (red line) interaction with the LN prism, with a pump energy of 2.1 mJ and pulse duration of 34 fs. The initial pump spectrum exhibits strong modulation with a period of 3.12 $\pm$ 0.18 nm, arising from temporally delayed beamlets generated after the reflection from the echelon mirror. The corresponding pulse delay was determined to be 682 fs, whereas the expected delay owing to the step height (H = 100 $\mu$m) of the echelon mirror was 667 fs. This discrepancy is due to the slight tilt ($\Theta$z) of the echelon mirror present in the experimental setup. After the interaction, we can clearly observe significant spectral broadening as well as a red-shift from 795 nm to 822 nm in the spectrum in Fig. 5(a), owing to the cascading effects in THz generation [37–39]. From the observed redshift, we estimated the corresponding THz conversion efficiency to be approximately 3.28% [37,38,40]. This was approximately 12 times higher than the measured efficiency of 0.27%, as shown in Fig. 5(a). This difference can be attributed to the THz absorption in the LN crystal ($\alpha \approx$ 25 cm$^{-1}$ at 1 THz [41]) and the reflection loss of both THz field ($n_{\textrm{LN}}$(1 THz) $\approx$ 4.9) and pump beam ($n_{\textrm{LN}}$(800 nm) $\approx$ 2.2) at the air interface of the LN crystal.

 

Fig. 5. (a) Spectra of the pump pulse with a pump energy of 2.1 mJ and a pulse duration of 34 fs before (blue line) and after (red line) interaction with the LN prism. (b) Measured temporal THz field waveform using the EO sampling method. (c) Normalized amplitude of spectral THz field for pump energies: 0.36 mJ (black line), 1.0 mJ (blue line), and 2.1 mJ (red line).

Download Full Size | PDF

In Fig. 5(b), we present the temporal THz waveforms for three pump energies obtained through EO sampling, with temporal ranges and steps of 60 ps and 200 fs. The pulse durations of both the probe and pump beams were fixed at their minimum values during the THz waveform measurements to achieve a high temporal resolution ($\sim$34 fs) in subsequent EO measurements. The results in Fig. 5(b) demonstrated that the pulse generated in the echelon-TPF setup was a single-cycle THz waveform. The Fourier-transformed THz spectra corresponding to the EO-sampled waveforms are shown in Fig. 5(c). The peak frequency and spectral bandwidth of the THz spectra decreased with increasing pump energy. Specifically, with the increase in pump energy in the range 0.36–2.1 mJ, the peak and bandwidth of the THz spectra varied in the range 0.95–0.75 THz and 0.88–0.61 THz, respectively. A possible explanation for the observed changes in the THz spectrum is due to the correlation between the phase-matching condition and the spectral components for the OR process owing to the cascaded spectral broadening of the pump beam. This effect becomes more pronounced for highly efficient THz generation [11,38].

4. Conclusion

In conclusion, we optimized the single-cycle THz generation in an echelon-TPF scheme using a chirped pump pulse. Our optimized approach resulted in a maximum THz conversion efficiency of 0.39% at a pump energy of 1.8 mJ achieved using a positively chirped pump. The onset of saturation behavior for THz conversion efficiency was observed at a pump energy of 0.37 mJ, corresponding to a fluence of 10 mJ/cm$^{2}$ and an intensity of 22 GW/cm$^{2}$. We also observed that the optimal pulse duration of the chirped pump increased with the pump’s energy. The nonlinear behavior of the THz generation from the echelon-TPF scheme was attributed to the intensity-dependent interaction length. To investigate this, we measured the near-field THz beam profile and corresponding THz divergence angle. Our results indicated that the effective interaction length decreased as the pump energy increased. This decrease is evident from the reduction of the near-field THz beam size in the plane of the tilted pulse direction and the increase in the corresponding divergence angle. However, no variations in the THz divergence angle were observed perpendicular to the plane of the tilted pulse direction. We made an important observation in the echelon method without angular dispersion, where we observed nonlinear distortion similar to the results demonstrated in [10]. This observation holds significant meaning as it contributes significantly to the saturation behavior in THz generation, even in the presence of other nonlinear effects such as SPM, depletion, absorption due to 3PA, and spectral broadening caused by cascading effects.

Our study provides evidence that the efficiency of intense THz sources can be improved by using a pump beam with a fluence or intensity value that remains below the saturation threshold. This can be accomplished by increasing the spot size of the pump beam on the face of the LN prism. An approach to achieve this is to use a cylindrical lens imaging system or to increase the pump beam size by enlarging the LN crystal size. An issue that needs to be addressed is the low reflectivity of the echelon mirror used in our experiments. The reflectance of the pump beam from the echelon mirror is only 52.5%, resulting in a significant loss of pump energy for THz generation. Achieving higher reflectivity requires delicate polishing techniques on the surface of the echelon mirror.

The results of our study have important implications for the advancement of the echelon-TPF THz generation scheme, with the potential to enhance the pulse energy to mJ levels. Further, these findings can lead to further research in nonlinear THz science.