## Abstract

We report superior terahertz parametric generation from potassium titanyl phosphate (KTP) over congruent-grown lithium niobate (CLN) and lithium tantalate (CLT) in terms of parametric gain and laser damage resistance. Under the same pump and crystal configurations, the signal emerged first from KTP, 5% Mg-doped CLN, CLN, and then finally from CLT. The signal growth rate in KTP was comparable to that in 5%-Mg-doped CLN, but the signal power from KTP reached a much higher value after all the other crystals were damaged by the pump laser. We further demonstrate seeded terahertz parametric amplification in an edge-cut KTP at 5.74 THz. The THz parametric amplifier (TPA) employs a 17-mm long KTP gain crystal, pumped by a passively Q-switched pump laser at 1064 nm and seeded by a continuous-wave diode laser tuned to the signal wavelength at 1086.2 nm. With 5.8-mJ energy in a 520-ps pump pulse and 100-mW seed signal power, we measured 5-W peak-power THz output from the KTP TPA with 22% pump depletion. In comparison, we measured no detectable THz output power from a similar edge-cut CLN TPA under the same pump power, detection scheme, and crystal configuration, when tuning the seed laser wavelength to 1072.2 nm and attempting to generate a radiation at 2.1 THz.

© 2016 Optical Society of America

## 1. Introduction

Terahertz (THz) radiation is useful for a number of scientific and industrial applications, such as molecular spectroscopy, biomedical imaging and diagnostics, high-data-rate communication, and material studies. Several methods were frequently used to generate THz radiation. To name a few, nonlinear parametric frequency mixing [1], photo-conductive switching [2], quantum cascade lasing [3], ultrafast-laser induced air plasma radiation [4], and relativistic electron radiation [5] are among the popular schemes for THz radiation generation. Among those methods, THz parametric generation (TPG) is known to be an effective means to generate coherent THz radiation at room temperature. For typical TPG, one usually employs a near-infrared pump laser to excite the so-called stimulated polariton scattering (SPS) in a polar nonlinear optical material and generate a THz wave with parametric gain [1]. Since SPS involves lattice vibrations of the material, the effective nonlinear coefficient responsible for such TPG can be greatly increased from that contributed solely from the electronic nonlinear susceptibility. Notable polar nonlinear optical materials include lithium niobate (LN), lithium tantalate (LT), and crystals from the potassium titanyl phosphate (KTP) family, like potassium titanyl arsenate (KTA) [1, 6–8].

Lithium niobate has been the most widely studied material for nonlinear frequency mixing in the THz region and LN-based THz radiation sources have primarily been demonstrated between 0.5 and 3 THz with a parametric gain peak around 2 THz [9]. It has also been shown that 5% Mg-doped LN is superior to undoped LN in terms of efficient THz generation [10]. KTP has the strongest stimulated Raman scattering response [11] among those polar nonlinear optical materials. Potentially KTP and KTA could be viable alternatives to LN as these crystals have strong second order nonlinear response as well as transverse optical phonon resonances for efficient SPS. Furthermore, the KTP family crystals are known to have a higher laser damage threshold than LN and LT [12] and the refractive indices are about 20% lower than that of LN [13,14], providing a high figure of merit and enabling a better out-coupling of the THz radiation from the crystals. The first THz parametric oscillators (TPOs) have also recently been demonstrated in KTP and KTA, however, at higher frequencies than those in LN, between 3 and 6 THz [7,8].

Usually, TPG generates a broadband output through high-gain amplification of vacuum noise. To narrow down the linewidth of the generated THz radiation, one may adopt schemes such as THz parametric oscillation or THz parametric amplification. The former is built around a cavity resonating the red-shifted signal, requiring a long pump pulse to establish oscillation in a finite-length cavity. However, as optical materials are more susceptible to damage from a long pulse pump laser, this limits the THz output power. On the other hand, with enough parametric gain, a THz parametric amplifier (TPA) is capable of generating narrow-line high-power THz radiation from the difference frequency generation of a strong narrow-line pump and a weak narrow-line signal. Tunability of the THz output wavelength can then be achieved by seeding the TPA with a wavelength-tunable signal. As a result, a TPA is usually the preferred narrow-line, high-power THz source when compared to a TPO [15].

In this work we investigated the TPG performance of four of the most promising polar nonlinear optical materials in a side-by-side comparison. The four crystals used in our experiments were KTP, congruent-grown LN (CLN), 5% Mg-doped congruent-grown LN (Mg:CLN), and congruent-grown LT (CLT). Primarily, thanks to the higher damage threshold and smaller refractive index, KTP came out as the most promising crystal and to exploit this further we built a KTP TPA seeded by a tunable diode laser in a second step.

## 2. THz parametric generation

Figure 1 shows the experimental setup of the TPG with different crystals. The pump laser starts from a passively Q-switched Nd:YAG microchip laser at 1064 nm, producing 520-ps pulses at a 10-Hz rate. The sub-ns laser pulse width, when compared with a ~10-ns one, is advantageous in reaching a high pump intensity without damaging the crystal. A double-pass, diode-pumped Nd:YAG amplifier following the microchip laser boosts up the pump energy to a few mJ. The amplified laser pulse was focused to the input surface of the nonlinear crystal with a waist radius of 0.25 mm and a polarization direction along the crystallographic *z* direction. All the crystals, KTP, Mg:CLN, CLN, and CLT, were 1-mm thick in *z* and 32 mm long in *x*. The end surfaces of the crystals were optically polished and uncoated. Figure 1 also depicts the wave-vector or *k*-vector matching diagram of the SPS ${\overrightarrow{k}}_{p}={\overrightarrow{k}}_{s}+{\overrightarrow{k}}_{THz}$, where the subscripts *p, s,* and *THz* refer to the pump, signal, and THz waves, respectively. Material dispersion determines how the condition ${\overrightarrow{k}}_{p}={\overrightarrow{k}}_{s}+{\overrightarrow{k}}_{THz}$ is satisfied. The diagram indicates that, for SPS in our crystals, the red-shifted signal beam propagates almost collinearly with the pump beam and the THz wave propagates away from the pump beam at some 65° angle. The signal wave, sometimes called the Stokes wave, can be intense in a TPG process and become a new pump wave to scatter the next higher Stokes wave in the crystal.

Figure 2(a) shows the output energy of the Stokes waves as a function of pump energy for the four crystals. At the pump wavelength, the refractive indices of KTP, CLN, and CLT are 1.8, 2.2, and 2.1, respectively [16–18]. The data shown in Fig. 2(a) have been corrected for the Fresnel losses at the crystal surfaces. The last data points for Mg:CLN, CLN, and CLT represent the highest pump energy that we could launch before the crystals were damaged by the laser. On the other hand, the KTP crystal was never damaged even at the maximum pump intensity available from our laser (>10 GW/cm^{2}). The onset of the measured Stokes energy, called the TPG threshold for what follows, depends on the sensitivity of our pyrodetector. The slope for KTP is almost as high as that for CLN and Mg:CLN and its TPG threshold is the smallest among all crystals. The Stokes pulse energy was measured to close to 0.55 mJ from the KTP sample at the maximum pump energy of 5.8 mJ. Pump depletion gradually saturates the output Stokes energy. Figure 2(b) shows that the measured wavelengths of the 1st Stokes wave in Mg:CLN, KTP, CLN, and CLT are 1073.3, 1086.0, 1072.2, and 1071.5 nm, respectively. From the frequency difference between the pump and 1st Stokes waves, it is straightforward to show the radiation frequencies of the THz waves from Mg:CLN, CLN, and CLT are 2.4, 2.1, and 2.0 THz, respectively, while that from KTP is much higher, 5.74 THz. It is also worth observing that the Stokes shift of Mg:CLN is considerably larger than that of CLN [10,19].

In SPS, the growth of the Stokes wave strongly depends on the competition of the parametric gain and THz absorption loss in the crystal [20]. Furthermore, the extracted pulse energy of the Stokes wave finally also depends on available pump to and the damage threshold of a crystal. THz parametric generation is a high-gain process that amplifies vacuum noise photons to an energy level comparable to the pump energy. For our pyrodetector with a detection limit of ~1 μJ/pulse at the optical frequencies, the amplification gain exceeds 10^{11}. The measured signal pulse width is shortened from the 520-ps pump pulse width to a 200 ps one, also indicating a very strong gain in the TPG process [21]. In such an exponential-gain regime, the output signal energy from a crystal of length *L* is described by the expression [1,20]

*g*is the signal power gain coefficient and

_{s}*P*=

_{si}*hν*Δ

_{s}*ν*is the initial noise photon energy with

_{s}*h*,

*ν*, Δ

_{s}*ν*being the Planck constant, signal frequency, and signal bandwidth, respectively. For SPS, the gain coefficient

_{s}*g*is given by [1]:

_{s}*α*is the power absorption coefficient of the THz wave in the crystal,

_{Τ}*ϕ*~65° is the phase-matching angle between the pump and THz wave, and Γ is the lossless parametric field gain coefficient. The approximation in Eq. (2) is made with the assumption $16\mathrm{cos}\phi {(\Gamma /{\alpha}_{T})}^{2}>>1$, which is usually valid in the high-gain regime with Γ >

*α*. The specific form of the parametric gain coefficient is given by

_{T}*ε*is the vacuum permittivity,

_{0}*c*is the speed of light in vacuum,

_{0}*ω*is the angular frequency of the mixing waves,

*I*is the pump intensity,

_{p}*n*is the refractive index,

*d*is the effective nonlinear coefficient, and the subscripts

_{eff}*s*,

*T*,

*p*denote the signal, THz, and pump waves, respectively. By using Eqs. (2) and (3), we can recast Eq. (1) into the formwhere the normalized parameters, ${\overline{d}}_{eff}\equiv {d}_{eff}{L}_{eff}$ and ${\overline{\alpha}}_{T}\equiv {\alpha}_{T}{L}_{eff}$, are introduced along with an effective crystal length

*L*

_{eff,}and

*A*,

*B*coefficients are from known from material parameters [14,22,23] and experimental conditions. The effective crystal length

*L*is a reduced length from

_{eff}*L*due to wave walkoff and diffraction. The nonlinear coefficient ${\overline{d}}_{eff}$ can now be obtained from the differentiation of the measured output signal energy with respect to $\sqrt{{I}_{p}}$, given by

*th*, is to point out that Eq. (5) is only valid without pump depletion and is applicable to the data near the TPG thresholds in Fig. 2(a). By plotting Eq. (5) versus $\sqrt{{I}_{p}}$ and taking the initial slope of the curves from the experimental data, one can deduce the nonlinear coefficient ${\overline{d}}_{eff}$.

The absorption coefficient can be derived from Eq. (4), given by

The TPG threshold in Fig. 2(a) depends on our detector sensitivity and therefore the nonlinear coefficient ${\overline{d}}_{eff,th}$ obtained from Eq. (5) near the TPG thresholds is under estimated. To compensate it, a modification factor *m* for the system is introduced to write

To determine *m*, we first derived *L*_{eff} = 8.4 mm from Eqs. (1) and (2) by using the measured TPG data at threshold together with the well-known *d*_{eff} = 168 pm/V and ${\alpha}_{T}$ = 40 cm^{−1} for CLN at 2.1 THz [24–26]. We then obtained *m* = 3.23 by again forcing the *d*_{eff} and ${\alpha}_{T}$ extracted from Eqs. (5) and (6) to match the known values for CLN. With *m* deduced from such a self-consistent loop, Eqs. (5)–(7) become the theoretical basis to extract both ${\overline{d}}_{eff}$ and ${\overline{\alpha}}_{T}$ from the measured TPG data for all the other materials. To calculate ${\overline{\alpha}}_{T}$ from Eq. (6), we chose the threshold values for *I _{p}* and

*P*from the experimental data. To estimate the initial noise power

_{so}*P*, we used the measured signal bandwidths in Fig. 2(b) for the expression

_{si}*P*=

_{si}*hν*Δ

_{s}*ν*. The logarithm function ln(

_{s}*P*/

_{so}*P*) is insensitive to slight changes in the estimated ratio

_{si}*P*/

_{so}*P*.

_{si}We summarize in Table 1 the relative values of the extracted normalized nonlinear and absorption coefficients with respect to those for congruent lithium niobate. Unlike the generic nonlinear and absorption coefficients, those normalized quantities take into account the wave walkoff and diffraction in a SPS experiment. We also list in the same table relevant material properties for all the crystals. It is seen from the table that the normalized THz nonlinear coefficient of KTP is about 60% that of lithium niobate. Given the superior TPG from KTP, one would expect KTP has less THz absorption. However, Table 1 shows a comparable normalized absorption coefficient for KTP and CLN. A further investigation reveals that KTP has the shortest THz radiation wavelength and smallest refractive indices among all the materials. The ratio (Γ/${\alpha}_{T}$)^{2} in Eq. (2) plays a crucial role in separating the gain regime of SPS [20]. We therefore define the figure of merit (FOM) for SPS as

*λ*and

_{s}*λ*are the signal and THz wavelength, respectively. Unlike the usual

_{THz}*FOM*for nonlinear laser frequency conversion, the SPS

*FOM*defined here is a function of mixing wavelengths and absorption, as SPS is strongly influenced by the dispersion of the transverse phonon modes of a polar material. The 7th row of Table 1 shows that KTP has the largest

*FOM*due to its shortest THz radiation wavelength and smallest refractive indices; CLT has the poorest

_{SPS}*FOM*due to its very large THz refractive index and slightly smaller nonlinear coefficient. Although KTP has the smallest normalized nonlinear coefficient and slightly larger material absorption compared with Mg:CLN, its largest

_{SPS}*FOM*explains the lowest TPG threshold among all and a fast TPG growth rate comparable to Mg:CLN.

_{SPS}## 3. KTP terahertz parametric amplifier

Given the superior TPG performance from KTP, we carried out a TPA experiment to compare KTP and CLN side by side. Figure 3(a) shows the experimental setup for the TPA experiment. We pump the TPA with the same laser system used for the TPG experiment, except that a self-made tunable external-cavity diode laser (ECDL) seeds the crystal at about 2.5° from the pump beam. For the KTP TPA, the seed laser power, wavelength, and bandwidth were 100 mW, 1086.2 nm, and 0.24 nm, respectively. For the CLN TPA, the seed laser wavelength was tuned to 1072.2 nm. Both the KTP and CLN crystals were cut and polished into a trapezoid in the x-y plane, as shown in Fig. 3(b). The pump and signal beams were focused to a THz-wave extraction point in the crystal, which is 17 mm from the crystal’s entrance surface. Therefore, the useful crystal length for the THz wave is 17 mm, as shown in the plot. Upon reflection from the THz-wave extraction point, the amplified signal, along with the pump, propagates toward the exit surface of the crystal. The signal gain length between the entrance the exit crystal surfaces consists of two sections, one coinciding with the 17-mm THz gain length and the other is measured to be 18 mm from the THz-wave extraction point to the crystal’s exit surface. The photograph in Fig. 3(a) shows a typical view on an infrared detection card when multiple Stokes waves are generated at different emission angles from the KTP crystal under an intense pump. Without the seed signal, the output dots are symmetrically distributed about the pump dot. With the signal seed on one side, the Stokes outputs on the right hand side of the photograph are apparently much stronger. The THz wave was measured by a Golay cell (GC-1P, TYDEX) with a 2-mm high-density polyethylene THz filter. The filter has about 20% and 52% transmittance at 6 and 2 THz, respectively.

For non-collinear phase matched polariton scattering, generation of high-order Stokes waves is sometimes undesirable. The correspondingly generated THz radiations propagate at different angles and could mostly be absorbed in the crystal. Figure 4(a) shows the measured Stokes wave energy as a function of pump energy. At 5.8-mJ pump energy, the first 3 Stokes waves from the KTP crystal account for ~25% pump depletion. The seeded 1st Stokes wave contributes most to the generation of the desired narrow-line THz radiation at the output. Once the 1st Stokes wave grows to an appreciate amplitude, it becomes a pump wave to generate high-order broad-band Stokes through TPG. This can be seen from Fig. 4(b), wherein a narrow-line spectrum of the seeded 1st Stokes output from the KTP TPA is plot together with a broad-band spectrum of the unseeded 1st Stokes output from the KTP TPG. Both the spectra were measured with a pump energy of 1.1 mJ at 1064 nm. The spectral peak of the KTP TPA signal is set at 1086.2 nm by the seeding ECDL, corresponding to a THz radiation frequency of 5.74 THz. The linewidth of the KTP TPA signal spectrum is 0.18 nm, which is comparable to the 0.24-nm spectral width of the seeding ECDL. This reduced spectral width is a consequence of a smaller pump beam size in a spatially chirped large-diameter seeding signal. Since the pump laser is a single-frequency microchip laser, the radiation bandwidth of the THz radiation is expected to be about the spectral width of the 1st Stokes wave or the seeding signal.

Figure 5(a) shows the measured amplified 1st Stokes efficiency and the THz wave peak power from the KTP TPA as a function of pump energy. When the pump energy exceeds 2 mJ, higher-order Stokes waves start to build up and the generation of the 1st Stokes wave reaches the maximum efficiency of 22%. The THz wave output therefore starts to saturate between 2 and 3 mJ pump energy. At 5.8-mJ pump energy, the measured peak power of the THz output wave is about 5 W at 5.74 THz with 17-mm gain length in the KTP crystal. Figure 5(b) shows the oscilloscope traces of the measured THz pulses from the Golay cell, indicating a signal-noise-ratio of about 10.

As a comparison, with the same setup, we replaced the KTP crystal with a CLN crystal with exactly the same dimensions and tune the ECDL wavelength to 1072.2 nm for a phase-matched CLN TPA at 2 THz. Unfortunately, we were unable to detect a conclusive THz- radiation in our Golay cell until we damaged the CLN crystal at about 2.2-mJ pump energy. Given the signal-to-noise ratio of ~10 in Fig. 5(b), the peak power of the THz radiation from the CLN TPA, has to be less than 0.5 W. The relatively poor performance of the surface-emitted CLN TPA can be explained by the 30% smaller *FOM _{SPS}* for CLN relative to that for KTP, as shown in Table 1.

## 4. Conclusions

We have compared the TPG performance for KTP, Mg:CLN, CLN, and CLT crystals under the same experimental conditions. First of all, KTP is the best and CLN is the worst in terms of laser damage resistance. We successfully developed a theoretical model to extract the effective THz nonlinear and absorption coefficients from the TPG experimental data for all the materials relative to CLN. The result is listed in Table 1. Although KTP has the smallest THz nonlinearity among all the tested materials and a comparable THz absorption to CLN, the SPS figure of merit for KTP is the largest, 1.2, 1.7, 2.6 times that of Mg:CLN, CLN, and CLT, respectively. The superior *FOM _{SPS}* for KTP is attributable to KTP’s relatively smaller refractive indices and shorter THz radiation wavelength. As a result, KTP has a TPG threshold smaller than Mg:CLN and a TPG growth rate comparable to Mg:CLN.

We also reported a KTP TPA in comparison with a CLN TPA under the same experimental conditions, except that the seeding signal wavelengths for KTP and CLN are 1086.2 and 1072.2 nm, respectively. While we measured a 5 W peak power at 5.74 THz from the KTP TPA, we were unable to detect a conclusive THz radiation from the CLN TPA until we damaged the CLN crystal with a pump intensity about 1/3 that on the KTP crystal.

This work focuses on the comparison of KTP, Mg:CLN, CLN, and CLT crystals for THz radiation generation through nonlinear frequency mixing. The edge-cut out-coupling scheme of the THz radiation from the crystals in our TPA is apparently not optimal. It is our next effort to optimize the THz-radiation extraction, such as using a Si-prism output coupler [27], and demonstrate high-power THz radiation from KTP.

## Funding

Ministry of Science and Technology of Taiwan (MOST-103-2221-E-007-062-MY2 and MOST-105-2112-M-007-021-MY3); Swedish Research Council through the Linnaeus center ADOPT.

## Acknowledgments

The authors appreciate helpful discussion with Ulf Österberg of Norwegian University of Science and Technology. Y.-C. Chiu acknowledges a matching graduate scholarship from HC Photonics Corp. (http://hcphotonics.com/).

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