# Terahertz Birefringence and Dichroism of KTA Crystal

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

_{4}(KTA) crystal measured by the means of terahertz time-domain spectroscopy in the range of 0.3–2.1 THz. The dispersion of the refractive index is approximated and presented in the form of the Sellmeier equation. We observe a large birefringence Δn

_{Z-X}≈ 0.76 and dichroism which is attributed to a strong absorption peak in the vicinity of ~1.23–1.25 THz for the Z-axis. However, the crystal can be considered as almost uniaxial due to a close value of n

_{X}and n

_{Y}as well as α

_{X}≈ α

_{Y}in the region below 0.5 THz. Moreover, KTA crystals can satisfy the phase-matching condition in principal XZ-plane for THz emission on difference frequency generation mechanism. Therefore, the crystal could be considered as an efficient candidate for terahertz wave generator under intense laser pump.

## 1. Introduction

_{4}or KTA belongs to the mm2 point group symmetry. The assignment between the dielectric and crystallographic axes is X, Y, Z → a, b, c. KTA is a popular nonlinear optical crystal for laser frequency conversion at room temperature. The optical parametric oscillator (OPO) [1,2], second harmonic [3,4], sum [5], and difference [6] frequency generator (DFG) based on KTA crystals were successfully demonstrated. This is due to the exceptional optical properties [7], including a wide transparency window in 0.35–5.25 μm at “0” transmittance level corresponding to the small absorption coefficient down to 0.05 cm

^{−1}, large birefringence up to ~0.1 at 0.638 μm, the moderate value of the nonlinear coefficients d

_{24}= 4.4 pm/V, d

_{31}= 2.8 pm/V, d

_{32}= 5.1 pm/V, d

_{33}= 16.2 pm/V, and a high damage threshold of over 1.2 GW/cm

^{2}under exposure to 8 ns pulse at 1.064 μm. In a first approximation, if we consider the maximum value among the nonlinear coefficients of other basic (by classification presented in [7]) oxygen-containing nonlinear crystals it turns out that KTA has a maximum value: d

_{33}= 16.6 pm/V, while KTP has d

_{33}= 14.6 pm/V, LBO d

_{32}= 0.85 pm/V, BBO d

_{22}= 2.2 pm/V. Thus, in comparison to with LBO, BBO, and KTP, the main advantage of KTA seems to be higher nonlinearity and lower longer infrared (IR) cutoff wavelength absorption coefficient [7].

## 2. Methods and Samples

^{−8}–10

^{−9}S. Two optically polished wafers (KTA-1 and KTA-2) were cut from an ingot orthogonal to Y and Z axes with the size of 10 × 10 × 0.627 mm

^{3}, respectively. Thus, it allows us for the first time to measure all three components of the refractive index and absorption coefficient.

^{−1}). The standard deviation of the resulting data does not exceed the boundaries of rectangular symbols and is not represented in Figure 2 and Figure 3. We estimate the accuracy of our measurements in the THz range is to be ±0.015 for the refractive index and ±1 cm

^{−1}for the absorption coefficient.

## 3. Results and Discussion

^{−1}at the wavelength of about 3 μm that further confirms the high optical quality of the wafers. Considering frequency conversion into the THz range, even chemical and CO lasers can be used as the pump source.

^{−1}, which corresponds to 1.23 THz.

^{−1}) according to the [10] or 1.73 THz for a highly resistive KTP crystal [11]. Commonly, frequencies below 6 THz (200 cm

^{−1}) for crystals of this structure are attributed to the oscillations of the K

^{+}ions with respect to TiO

_{6}and PO

_{4}atomic groups [12]. A rough estimation can be made using a model of the quantum harmonic oscillator with the frequency ${\mathsf{\omega}}_{0}=\sqrt{\mathrm{k}/{\mathrm{m}}_{\mathrm{r}}}$. Here, m

_{r}is the reduced mass, and k is the bond force constant. Assuming that the reduced mass practically does not change, since we are dealing with K

^{+}ions in both cases, we can estimate the changes of the parameter k. Since,

^{+}ions in the KTA crystal is approximately two times less than in KTP. This can be explained by the fact that the substitution of the P with the As atom leads to an increase in the interatomic distance in the chain of Ti-O bonds along with the crystallographic axis c (dielectric axis Z) [13]. As a result, the bond of potassium ion with their nearest neighbors is weakened. Of course, the other strong absorption lines in the THz range should be considered, which are located beyond the dynamic range and spectral window of the terahertz spectrometer (>2.5 THz). They will also affect the optical properties in the sub-terahertz region and determine the sharp growth of absorption curves at a higher frequency range.

_{Z-X}≈ 0.76, while it presents a small value of Δn

_{Y-X}≈ 0.03. The refractive indices of the X and Y axes become more distinct above 1 THz as well as the case in the absorption coefficients of these axes.

^{(1)}for the valid value with types of s–f → f and s–f → s, where s and f are the slow and fast wave.

_{Z}angle (an angle between the optic axis of the crystal and z-axis) is observed for longer wave generation. Here, we should note that according to the handbook of “Nonlinear Optical Crystals: A Complete Survey” written by Nikogosyan (p. 168) [7], KTA has 2V

_{Z}= 40.4° for λ = 0.5321 μm. It is probably a typo since none of the dispersion equations set shown in the handbook could give this value. The dispersion equations from [14] used in present work only gives V

_{Z}= 16.7 for λ = 0.5321 μm and V

_{Z}= 15.0 for λ = 1.0642 µm.

_{Z}and θ < V

_{Z}. The difference between FFS and SFS phase-matching curves is almost imperceptible to the eye. For reference, the absorption coefficients for α

_{Y}and α

_{Z}in the case of FFS and SFS respectively are presented since they mainly determine the attenuation of generated THz waves. The absorption coefficient decreases with longer wavelength (in up direction on the Figure 4). Hence, the FFS type of frequency conversion is much more efficient since the absorption coefficient of the THz wave is at least four times lower than that of SFS type. The tuning range at θ < V

_{Z}is less than that value at θ > V

_{Z}since for θ → 0 the curves asymptotically approach to the wavelength λ ~ 300 μm, while for θ → 90° the curves go slightly below this value. However, the crystal thickness should also be taken into consideration for the exact tunable wavelength range in the experiment.

## 4. Conclusions

_{Z-X}≈ 0.76. The dichroism is defined by strong absorption in the direction of the Z-axis and due to the presence of a peak in the vicinity of ~1.23–1.25 THz. However, in the region below 0.5 THz, the crystal can be considered as almost uniaxial due to the low birefringence Δn

_{Y-X}≈ 0.03 and approximate equality property of the absorption coefficient α

_{X}≈ α

_{Y}. It is found that the KTA crystal could satisfy the phase-matching conditions in principal XZ-plane for THz difference frequency generation. We estimate that s−f→f type of three-wave interaction is more efficient than that of s–f → s type due to the notable lower THz-wave absorption.

_{33}= 16.6 pm/V, while KTP has d

_{33}= 14.6 pm/V, LBO d

_{32}= 0.85 pm/V, BBO d

_{22}= 2.2 pm/V. KTA also has a lower longer IR absorption coefficient [7]. Thus, according to our results, KTA is seen as a promising generator of intense tunable narrowband THz radiation under a high-power IR laser pump. Lithium niobite being also a “basic nonlinear crystal” is out of consideration in this case since it has no collinear phase matching [17] for DFG into the THz range.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Webb, M.S.; Moulton, P.F.; Kasinski, J.J.; Burnham, R.L.; Loiacono, G.; Stolzenberger, R. High-average-power KTiOAsO
_{4}optical parametric oscillator. Opt. Lett.**1998**, 23, 1161–1163. [Google Scholar] - Bai, F.; Wang, Q.; Liu, Z.; Zhang, X.; Wan, X.; Lan, W.; Jin, G.; Tao, X.; Sun, Y. Theoretical and experimental studies on output characteristics of an intracavity KTA OPO. Opt. Express
**2012**, 20, 807–815. [Google Scholar] - Zeil, P.; Zukauskas, A.; Tjörnhammar, S.; Canalias, C.; Pasiskevicius, V.; Laurell, F. High-power continuous-wave frequency-doubling in KTiOAsO
_{4}. Opt. Express**2013**, 21, 30453–30459. [Google Scholar] - Liu, Z.; Wang, Q.; Zhang, X.; Zhang, S.; Chang, J.; Fan, S.; Sun, W.; Jin, G.; Tao, X.; Sun, Y.; et al. Self-frequency-doubled KTiOAsO
_{4}Raman laser emitting at 573 nm. Opt. Lett.**2009**, 34, 2183–2185. [Google Scholar] - Huang, H.; Shen, D.; He, J.; Chen, H.; Wang, Y. Nanosecond nonlinear Čerenkov conical beams generation by intracavity sum frequency mixing in KTiOAsO
_{4}crystal. Opt. Lett.**2013**, 38, 576–578. [Google Scholar] - Kung, A.H. Narrowband mid-infrared generation using KTiOAsO
_{4}. Appl. Phys. Lett.**1994**, 65, 1082–1084. [Google Scholar] - Nikogosyan, D.N. Nonlinear Optical Crystals: A Complete Survey; Springer Science+Business Media: New York, NY, USA, 2005; pp. 168–172. [Google Scholar]
- Mounaix, P.; Sarger, L.; Caumes, J.P.; Freysz, E. Characterization of non-linear Potassium crystals in the Terahertz frequency domain. Opt. Commun.
**2004**, 242, 631–639. [Google Scholar] - Duvillaret, L.; Garet, F.; Coutaz, J.L. A reliable method for extraction of material parameters in terahertz time-domain spectroscopy. IEEE J. Sel. Top. Quantum Electron.
**1996**, 2, 739–745. [Google Scholar] - Tu, C.; Guo, A.R.; Tao, R.; Katiyar, R.S.; Guo, R.; Bhalla, A.S. Temperature dependent Raman scattering in KTiOPO
_{4}and KTiOAsO_{4}single crystals. J. Appl. Phys.**1996**, 79, 3235–3240. [Google Scholar] - Antsygin, V.D.; Kaplun, A.B.; Mamrashev, A.A.; Nikolaev, N.A.; Potaturkin, O.I. Terahertz optical properties of potassium titanyl phosphate crystals. Opt. Express
**2014**, 22, 204–210. [Google Scholar] - Kugel, G.E.; Brehat, F.; Wyncke, B.; Fontana, M.D.; Marnier, G.; Carabatos-Nedelec, C.; Mangin, J. The vibrational spectrum of a KTiOPO
_{4}, single crystal studied by Raman and infrared reflectivity spectroscopy. J. Phys. C Solid State Phys.**1988**, 21, 5565–5583. [Google Scholar] - Novikova, N.E.; Sorokina, N.I.; Verin, I.A.; Alekseeva, O.A.; Orlova, E.I.; Voronkova, V.I.; Tseitlin, M. Structural Reasons for the Nonlinear Optical Properties of KTP Family Single Crystals. Crystals
**2018**, 8, 283. [Google Scholar] - Kato, K.; Umemura, N.; Tanaka, E. 90° Phase-Matched Mid-Infrared Parametric Oscillation in Undoped KTiOAsO
_{4}. Jpn. J. Appl. Phys.**1997**, 36, L403–L405. [Google Scholar] - Mamrashev, A.; Nikolaev, N.; Antsygin, V.; Andreev, Y.; Lanskii, G.; Meshalkin, A. Optical Properties of KTP Crystals and Their Potential for Terahertz Generation. Crystals
**2018**, 8, 310. [Google Scholar] - Huang, J.; Huang, Z.; Nikolaev, N.A.; Mamrashev, A.A.; Antsygin, V.D.; Potaturkin, O.I.; Meshalkin, A.B.; Kaplun, A.B.; Lanskii, G.V.; Andreev, Y.M.; et al. Phase matching in RT KTP crystal for down-conversion into the THz range. Laser Phys. Lett.
**2018**, 15, 075401. [Google Scholar] - Takayuki, S.; Suizu, K.; Kawase, K. Widely tunable monochromatic Cherenkov phase-matched terahertz wave generation from bulk lithium niobate. Appl. Phys. Express
**2010**, 3, 082201. [Google Scholar]

**Figure 1.**Combined transmission spectra of the KTA samples measured by three spectroscopic methods. Orange and sky-blue lines represent UV/VIS and FTIR data for KTA-1 and KTA-2 samples, respectively. Yellow and navy-blue lines represent adapted THz-TDS data for KTA-1 and KTA-2 samples, respectively. Gray arrows indicate spectral ranges of the spectrometers and used detectors (for FTIR). Insets (

**a**,

**b**) show zoomed regions of UV and IR cutoff edges.

**Figure 2.**The absorption coefficient of KTA crystal for THz-wave polarized in the direction of different optical axes (indicated by letters). The inset shows the zoomed long-wavelength range.

**Figure 3.**Measured refractive index (square symbols) of KTA crystal for THz-wave polarized in the direction of different optical axes (indicated by letters). Solid lines represent the fitting results in the form of the Sellmeier equation.

**Figure 4.**(

**a**) Simulated s–f→ f; (b) s–f → s phase-matching curves for DFG of the laser radiation with the wavelength close to 1.0642 μm, where k

_{DFG}– resulting terahertz wavevector, k

_{pump}, and k

_{OPO}are pumping waves with fixed (pump) and detuned via optical parametric conversion process (OPO) wavelengths lying in the vicinity of 1.0642 μm, ${\theta}_{\mathrm{int}}^{\mathrm{o}}\text{}$ is the internal phase matching angle inside crystal with the unite of degree.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huang, J.; Li, Y.; Gao, Y.; Huang, Z.; Nikolaev, N.; Mamrashev, A.; Lanskii, G.; Andreev, Y.
Terahertz Birefringence and Dichroism of KTA Crystal. *Crystals* **2020**, *10*, 730.
https://doi.org/10.3390/cryst10090730

**AMA Style**

Huang J, Li Y, Gao Y, Huang Z, Nikolaev N, Mamrashev A, Lanskii G, Andreev Y.
Terahertz Birefringence and Dichroism of KTA Crystal. *Crystals*. 2020; 10(9):730.
https://doi.org/10.3390/cryst10090730

**Chicago/Turabian Style**

Huang, Jingguo, Yang Li, Yanqing Gao, Zhiming Huang, Nazar Nikolaev, Alexander Mamrashev, Grigory Lanskii, and Yury Andreev.
2020. "Terahertz Birefringence and Dichroism of KTA Crystal" *Crystals* 10, no. 9: 730.
https://doi.org/10.3390/cryst10090730