Introduction. Narrowband, high-field terahertz (THz) radiation has applications in a wide range of fields, including imaging [1], linear and nonlinear THz radiation spectroscopy [2], tuned excitation of material transitions [3], and more recently in powering novel accelerators with the potential to revolutionize compact electron sources and related research areas. Until recently, research in nonlinear optical generation of THz radiation has focused on the development of broadband, single-cycle sources [2,4–7], due to their ability to provide ultrahigh peak fields which are highly sought for controlling material properties. As a result, conversion efficiencies over 2% have been demonstrated [4]. Achieving comparable peak fields with the long durations associated with narrowband THz radiation pulses requires significantly more energy, so techniques for developing these sources have therefore not seen as much development. Emerging applications, such as THz-radiation-driven electron acceleration [8,9], however, are increasingly calling for high-field pulses with high spectral purity, spurring multiple advancements which have driven efficiencies from the 10⁻⁵ to the 10⁻³ range. Together with the development f large-aperture periodically poled lithium niobate (PPLN) crystals [10,11], THz radiation pulse energies have increased from the nJ to the mJ range [11–14]. Despite these advances, low conversion efficiencies remain a limiting factor for achieving the pulse energies needed by many applications. For example, THz-radiation-driven electron accelerators require pulses with tens of millijoules of highly monochromatic radiation in the 0.1–1-THz frequency band with peak powers in the 100-MW range and focused fields of several hundred MV/m [8]. These numbers are currently approximately two orders of magnitude beyond the state of the art. This low figure can be attributed to the large discrepancy between optical and THz radiation photon energies which yields sub-percent energy conversion even for 100% photon conversion. Simulations have shown, however, that multiple-percent conversion efficiencies, far beyond the Manley–Rowe limit, are achievable if the optical pulses are tailored to promote cascading of the nonlinear interaction [15], and hence, multiple conversion processes per photon [16,17].

Key among the properties is the optical spectrum, which should be composed of a series of narrow lines separated by the THz frequency, and the pulse duration, which should match the length of the crystal. Although 2-line, mW sources are commercially available for THz radiation generation in the continuous wave (CW) regime [18], high-energy pulsed sources do not currently exist. Here, we develop a multi-millijoule, 2-line source with tunable frequency separation and pulse duration tailored for extending conversion efficiencies to those predicted by simulation. We perform difference frequency generation (DFG) experiments and demonstrate record conversion efficiencies near 1% at a frequency of 530 GHz, which is a factor of three beyond the current state of the art.

Experimental Setup. Optical pulses were provided by a home-built laser consisting of a front-end [19], a commercial Yb:KYW regenerative amplifier, and a Yb:YAG four-pass amplifier (4PA). The front-end was composed of two commercial, single-frequency CW lasers, one provided by Stable Laser Systems Inc., centered at 1.03 µm and frequency stabilized to 1 Hz, and the other by Toptica Photonics AG., tunable from 990 to 1080 nm, with specified linewidth of 1 MHz over 5 µs and temperature stability of 0.4 GHz/K, to control the wavelength separation for phase-matching in the PPLN crystal. The CW lasers were combined in a polarization-maintaining fiber, and then amplified and temporally chopped in successive steps using ytterbium-doped fiber amplifiers and acousto- and electro-optic modulators (EOM), respectively. The pulse duration and profile were thus determined by the bandwidth of the EOM, which produced flattop pulses with rise times of ∼60 ps. The output pulses had durations tunable in increments of 250 ps (i.e., 250, 500, 750 ps) and energy up to 20 mJ at 10 Hz, resulting in pulses matching the requirements for efficient THz radiation generation described by Ravi et al. [15,20]. The optical pulses were then sent into a set of z-cut MgO:PPLN crystals of varying length, poling period, and aperture (Table 1). LiNbO₃ was chosen as the nonlinear material due to its high effective nonlinear optical coefficient ${d_{eff}} = 168\; \textrm{pm/V}$ [2], and 5% MgO doping was used to lessen photorefractive effects [21]. The crystals were mounted in a cryostat and cooled using liquid nitrogen to ∼80 K to minimize THz radiation absorption [22,23].

Table 1. Dimensions of MgO:PPLN Crystals Tested

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The experimental setup as well as the measured optical spectrum and temporal profile from the 4PA output are depicted in Fig. 1. The amplified beam had a Gaussian spatial profile with dimensions of 0.8 × 1.1 mm² ($1/{e^2}$ radius), ensuring a collimated beam over a range longer than the MgO:PPLN crystals.

 

Fig. 1. (a) Laser spectrum. (b) Laser pulse temporal profile for the 500-ps case. (c) Experimental layout. HWP, half-wave plate; TFP, thin-film polarizer.

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The pulse energy was tuned using a half-wave plate and thin-film polarizer, and the optical polarization was aligned with the crystal extraordinary c-axis to maximize the effective nonlinear coefficient. The generated THz radiation was collected and imaged onto a pyroelectric detector (Gentec-EO, SDX-1152) using a pair of 2” diameter, 4” focal length off-axis parabolic (OAP) mirrors. A 1.6-mm-thick Teflon plate and a 2-mm polyethylene (PE) plate were placed in front of the detector to reduce the noise in the THz energy measurement from the transmitted optical beam as well as parasitic second harmonic generation of the pump beam. The first OAP, which collects and collimates the THz energy, had a circular hole of 3-mm diameter in the center to separate the optical beam for monitoring the crystal output surface for damage as well as the spectral reshaping of the optical beam due to THz radiation generation.

Results and Discussion. The parameters varied in the experiments were the frequency separation of the two spectral lines, the optical pulse energy, and the pulse duration. The frequency separation, $\mathrm{\Delta }\nu ,$ was tuned first to optimize the phase matching within each crystal [Figs. 2(a) and 2(b)].

 

Fig. 2. (a) Tuning curve data and theoretical fit of crystal response function for $X_{400}^{4\textrm{x}4\textrm{x}40},$ plus the measured THz radiation spectrum and calculation of expected THz spectrum. (b) Tuning curve data and theoretical fit of crystal response function for $X_{212}^{4\textrm{x}4\textrm{x}20}$. (c) THz time-domain interferogram for the spectrum in panel(a).

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The measured THz radiation yield versus $\mathrm{\Delta }\nu $ effectively maps out the frequency response function of the crystal, which, following the approach in [17,24], is described in the undepleted-pump approximation by

The spectrum of the THz radiation emitted from the 400-µm period crystal [Fig. 2(a)], which was measured using time-domain interferometry [Fig. 2(c)], also matched well with expectations. The relative spectral width of 0.5% was significantly narrower than the crystal response function, indicating that the terahertz spectrum was defined by the properties of the optical pulses which were transform-limited with linewidths of 2.5–7.5 picometers. The THz power spectrum can be calculated using $I(\Omega )\propto {|{R(\Omega )} |^2},$ where $R(\Omega )\equiv \mathop \smallint \limits_{ - \infty }^\infty {A_{op}}({\omega + \Omega } )A_{op}^\mathrm{\ast }(\omega )d\omega $ and ${A_{op}}(\omega )$ is the spectral field of the driving optical pulse. To estimate ${A_{op}}(\omega )$, the temporal profile of the optical pulse (Fig. 1) was measured with a sampling oscilloscope and fit to a super-Gaussian function of width 500 ps and order 6. As the spectral lines were too narrow to resolve with our spectrometer, two transform-limited spectral lines centered at the peaks of the measured optical spectra were assumed. The calculated and measured THz spectra matched nearly perfectly, including the side bands from the flattop temporal profile [Fig. 2(a)].

Once the frequency separation was optimized, the THz radiation yield was characterized as a function of optical pulse energy. The metric used for the yield is the “internal” conversion efficiency (CE), i.e., the ratio of THz radiation to optical pulse energy within the crystal. The internal CE quantifies the effectiveness of the intrinsic THz radiation generation process decoupled as much as possible from the practical issues of beam input and output coupling and THz radiation transport. The internal THz radiation pulse energy was inferred from the measured energy by correcting for losses from Fresnel reflections at the uncoated crystal and cryostat window interfaces as well as from absorption in the optical attenuators. These losses were determined using calculation and characterization with a THz radiation TDS (Table 2). The optical pulse internal energy was inferred similarly.

Table 2. THz Radiation Losses in Various Optical Elements

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Figure 3 shows measurements of the CE as a function of optical peak fluence and intensity for pulse durations of 250 ps, 500 ps, and 750 ps. As expected, for a given fluence, the shorter pulses provided a higher THz radiation yield due to the higher peak intensities. However, plotting against intensity showed equivalent performance independent of pulse length. The graphs showed that despite the onset of saturation of the conversion process, it may be possible to increase yield by going to higher fluences and intensities. However, we limited our scans to a peak fluence of ∼ 500 mJ/cm² (pulse energy of 7.3 mJ), to minimize photorefraction-induced damage.

 

Fig. 3. (a) CE versus peak fluence for experiment (exp.), simulation (sim.), and analytical calculation (ana.) for crystal $X_{212}^{3x3x20}$ and varying pulse duration at cryogenic temperature. (b) Data and simulation from panel (a) plotted versus intensity.

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For comparison, we ran 1D numerical simulations which included the effects of pump depletion as well as self-phase modulation. The transverse intensity variation in the optical beam was accounted for by assuming a Gaussian profile which reduced the average efficiency by a factor of two compared to the peak. The absorption coefficients used for the simulations, $\alpha ({532\; \textrm{GHz}} )= 1.1\; \textrm{c}{\textrm{m}^{ - 1}}$ and $\alpha ({286\; \textrm{GHz}} )= 0.73\; \textrm{c}{\textrm{m}^{ - 1}}$, were taken from the literature [5]. The resulting simulations agreed quantitatively with the measured CEs within approximately 20%, which was within a range attributable to tuning variations of the highly sensitive spatial and spectral alignments as well as in the temperature which affects the THz radiation absorption. The behaviors with fluence and pulse duration were also well captured. In Fig. 3(b), the simulations predict a slight advantage for the longer pulses, which was expected due to better matching between the lengths of the optical pulse and the crystal [15]. In Fig. 3(a), analytic calculations using the formalism in [15] were also done to cross-check the validity of the simulations. The analytical and simulated values of CE agreed perfectly at low fluence where the undepleted approximation is valid.

To evaluate the effects of crystal length and poling period, measurements of THz radiation yield versus pulse energy and corresponding simulations were performed for the five crystals in Table 1 (Fig. 4). These data were taken for the shortest pulse duration of 250 ps to maximize the yield. A record conversion efficiency of 0.9% was achieved at a fluence of 475 mJ/cm² in crystal $X_{212}^{4\textrm{x}4\textrm{x}40}$. These results correspond to internal energies for the THz radiation and laser pulses of 45 µJ and 6 mJ, respectively, and a measured THz radiation pulse energy of 12 µJ. For both 4-cm crystals, the agreement between data and simulation was excellent, including the saturation at higher fluence.

 

Fig. 4. Experiment (exp.) versus simulation (sim.) for internal CE versus laser fluence with a 250-ps pulse duration and varying poling period and crystal length.

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According to both the simulations and the data, the 212-µm poled crystals provided a higher CE than the 400-µm poled crystals. This effect can be understood analytically. From Eq. (2), for optimized phase matching (i.e., $\mathrm{\Delta }k = 0$), the CE should scale roughly as $CE(\Omega )\propto {\Omega ^2}/{\alpha ^2}(\Omega )$. Using our values of frequency and absorption, we expect $CE({532\; \textrm{GHz}} )\approx 1.5 \times CE({286\; \textrm{GHz}} )$, which approximately matches the data in the lower fluence range. Equations (1) and (2) only strictly apply when the laser is unaffected by the conversion process, which is best satisfied at low fluences. At higher fluences, the simulations and data both clearly show that saturation, which is related to the pump evolution, occurs earlier for the 212-µm poling case. Similar efficiencies may thus be reachable with 400-µm poling at higher fluence, provided the crystals are not damaged.

The simulation and data also agreed that the 2-cm-long crystals provide lower CEs than their 4-cm counterparts. We note that crystals $X_{212}^{4\textrm{x}4\textrm{x}20}$ and $X_{400}^{4\textrm{x}4\textrm{x}20},$ which were used extensively in the testing phase of the experiments, showed significant signs of optical damage. Crystal $X_{212}^{3\textrm{x}3\textrm{x}20},$ which was pristine for these measurements, yielded a CE of approximately 1.6-times greater than crystal $X_{212}^{4\textrm{x}4\textrm{x}20},$ thus providing an estimate of the damage level. For this reason, crystal $X_{212}^{3\textrm{x}3\textrm{x}20}$ was the most comparable to the 4-cm crystals, which were also lightly used, despite the difference in aperture size. Unfortunately, an un-used 2-cm, 400-µm poled crystal was not available for direct comparison.

The role of cascading in achieving high efficiencies implies a strong impact of the interaction on the output optical spectrum. Indeed, the measured spectrum shows the appearance of additional distinct lines (primarily on the long-wavelength side) increasing in number with fluence to over 13 at the maximum (Fig. 5). The spectrum center-of-mass shift of >10 nm to long wavelengths thus confirms percent-level optical conversion to THz [17].

 

Fig. 5. Measured, individually normalized optical spectra after THz generation for varying optical input energies in crystal $X_{400}^{4\textrm{x}4\textrm{x}40}$.

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Conclusion. We investigated narrowband THz radiation generation using a custom two-spectral-line laser in cryogenically cooled MgO:PPLN crystals and achieved conversion efficiencies of 0.9% for 0.53 THz and 0.5% for 0.29 THz which are a factor of three above previous reports [14]. These results confirm the benefits of tailoring the laser source [15] for nonlinear optical conversion to narrowband THz and point to even higher efficiencies [24] required for mJ-scale THz applications.