Optical Properties of KTP Crystals and Their Potential for Terahertz Generation

High nonlinearity, wide transparency range and optical quality allowed potassium titanyl phosphate (KTiOPO4, KTP) crystals to be used in a wide range of nonlinear applications. The success of KTP usage in the visible and infrared (IR) ranges drives interest in applying it at longer wavelengths, that is, in the terahertz (THz) range. We use THz optical properties of KTP crystals measured by terahertz time-domain spectrometer (THz-TDS) and refractive index approximated in the form of Sellmeier equations to investigate KTP application possibilities for IR-to-THz and THz-to-THz wave conversion. As a result, phase matching for s − f→ f and s − f→ s types of difference frequency generation (DFG) of Ti:Sapphire laser (at the wavelengths of 0.65, 0.8 and 1.1 μm) is found possible, as well as second harmonic generation (SHG) of THz waves by f + s→ f type of interaction in the XZ principle plane of the crystal. Terahertz wave generation by phase-matched parametric processes in KTP demonstrates evident advantages in comparison with that of widely used MgO-doped LiNbO3 crystals.


Introduction
Potassium titanyl phosphate (KTiOPO 4 , KTP) is one of the most widely used nonlinear optical crystals [1]. KTP belongs to the mm2 point group symmetry and its dielectric and crystallographic axes are assigned as X, Y, Z → a, b, c. Its structure consists of chains of connected rigid PO 4 tetrahedra and TiO 6 octahedra with alternating long and short Ti-O bonds that are responsible for its nonlinear properties [2]. KTP advantages are high nonlinear coefficients: d 15 = 1.9 pm/V, d 24 = 4.2 pm/V, d 31 = 2.2 pm/V, d 32 = 2.7 pm/V and d 33 = 17.4 pm/V, wide ranges of angles and temperatures for the phase matching, low absorption in the range of 0.35 µm to 4.5 µm, excellent mechanical stability and optical quality. One of the few KTP disadvantages is its susceptibility to photochromic damage, that is, grey-tracking, that causes slow deterioration of light conversion efficiency.
The success of KTP nonlinear applications in the visible and IR ranges drives interest in studying its terahertz dielectric and optical (THz) properties to substitute the widely used pure and MgO-doped lithium niobate crystals (LiNbO 3 , LN) in this range [15]. Previously, infrared reflectivity spectrum of KTP was studied up to the wavenumber of 4000 cm −1 (120 THz) at the temperatures of 7 K, 80 K and 293 K [16]. Later, the results were supplemented by Raman spectroscopy measurements at the wavenumbers below 4000 cm −1 [17]. Recently, THz refractive index and absorption coefficient were directly measured using growingly accessible THz time-domain spectrometers (THz-TDS) [18][19][20][21]. The most comprehensive study of its THz optical properties for the waves polarized parallel to all three optical axes of the KTP crystals was carried out in [20]. The refractive index components at room temperature were approximated in the form of Sellmeier equations [21].
In this paper, we report terahertz optical properties of KTP crystals at the room temperature of 293 K (RT) and at the liquid nitrogen temperature of 81 K and calculate phase-matching conditions for nonlinear frequency conversion into and within the THz range.

Materials and Methods
KTP single-crystal ingots were grown using the Czochralski method from a Pt crucible of 100 mm in diameter. The crucible closed with Pt cover with about 1 kg of charge was disposed in the resistivity oven. After heating, the melt was homogenized and cooled down to liquidus temperature. The crystals were grown using single-domain seed in the direction of X-axis. During the growth period of 45-55 days, the melt was cooled down by 70-120 • C. The cooling rate of the crystal was 0.1-4 • C/day while its rotation speed varied from 30 to 40 rpm. In parallel, the pulling speed changed from 0 to 1.2 mm/day. By selecting optimal growth conditions high-quality single-crystal ingots having a weight of 260 g and dimensions of X × Y × Z = 40 × 60 × 70 mm 3 were grown.
At first, a large plate with dimensions of X × Y × Z = 11 × 28 × 58 mm 3 was manufactured to evaluate the quality of the grown crystal and measure its transmission spectrum in the main transparency window. Then three pairs samples with different thickness with dimensions of 10 × 10 × (0.28, 0.35 and 1.08) mm 3 were cut orthogonal to the optical axes X (KTP x ) and Z (KTP z ) ( Figure 1). Sides of the KTP x sample were parallel to the Y and Z axes and sides of the KTP z sample were parallel to the X and Y axes. So, every pair of samples allowed us to measure all three (x, y and z) components of the absorption coefficient and refractive index for waves polarized parallel to the X, Y and Z axes, respectively and select the best-thickness crystals for the study. The success of KTP nonlinear applications in the visible and IR ranges drives interest in studying its terahertz dielectric and optical (THz) properties to substitute the widely used pure and MgO-doped lithium niobate crystals (LiNbO3, LN) in this range [15]. Previously, infrared reflectivity spectrum of KTP was studied up to the wavenumber of 4000 cm −1 (120 THz) at the temperatures of 7 K, 80 K and 293 K [16]. Later, the results were supplemented by Raman spectroscopy measurements at the wavenumbers below 4000 cm −1 [17]. Recently, THz refractive index and absorption coefficient were directly measured using growingly accessible THz time-domain spectrometers (THz-TDS) [18][19][20][21]. The most comprehensive study of its THz optical properties for the waves polarized parallel to all three optical axes of the KTP crystals was carried out in [20]. The refractive index components at room temperature were approximated in the form of Sellmeier equations [21].
In this paper, we report terahertz optical properties of KTP crystals at the room temperature of 293 K (RT) and at the liquid nitrogen temperature of 81 K and calculate phase-matching conditions for nonlinear frequency conversion into and within the THz range.

Materials and Methods
KTP single-crystal ingots were grown using the Czochralski method from a Pt crucible of 100 mm in diameter. The crucible closed with Pt cover with about 1 kg of charge was disposed in the resistivity oven. After heating, the melt was homogenized and cooled down to liquidus temperature. The crystals were grown using single-domain seed in the direction of X-axis. During the growth period of 45-55 days, the melt was cooled down by 70-120 °С. The cooling rate of the crystal was 0.1-4 °С/day while its rotation speed varied from 30 to 40 rpm. In parallel, the pulling speed changed from 0 to 1.2 mm/day. By selecting optimal growth conditions high-quality single-crystal ingots having a weight of 260 g and dimensions of X × Y × Z = 40 × 60 × 70 mm 3 were grown.
At first, a large plate with dimensions of X × Y × Z = 11 × 28 × 58 mm 3 was manufactured to evaluate the quality of the grown crystal and measure its transmission spectrum in the main transparency window. Then three pairs samples with different thickness with dimensions of 10 × 10 × (0.28, 0.35 and 1.08) mm 3 were cut orthogonal to the optical axes X (KTPx) and Z (KTPz) (Figure 1). Sides of the KTPx sample were parallel to the Y and Z axes and sides of the KTPz sample were parallel to the X and Y axes. So, every pair of samples allowed us to measure all three (x, y and z) components of the absorption coefficient and refractive index for waves polarized parallel to the X, Y and Z axes, respectively and select the best-thickness crystals for the study. Transmission spectra in the transparency window were measured by UV-2101/3101 spectrophotometer (Shimadzu, Kyoto, Japan). Terahertz optical properties were studied using a THz-TDS (IA&E SB RAS, Novosibirsk, Russia) with a cryostat described elsewhere [20] at the temperatures of 293 K and 81 K. Transmission spectra in the transparency window were measured by UV-2101/3101 spectrophotometer (Shimadzu, Kyoto, Japan). Terahertz optical properties were studied using a THz-TDS (IA&E SB RAS, Novosibirsk, Russia) with a cryostat described elsewhere [20] at the temperatures of 293 K and 81 K.

Results
The resistivity of a grown KTP crystal is one of indicators of its quality. Higher values of resistivity make the crystals applicable for manufacturing electro-optic devices: amplitude and phase modulators [12]. Figure 2a depicts crystal resistivity which stays larger than 10 11 Ω cm for the applied electric field up to 20 kV/cm proving high quality and easy polarizability of the samples for creating periodical structures. Visible and IR range transmission spectrum of thick KTP plate for the wave propagating along X axis and polarized parallel to Z axis is presented in Figure 2a. The quality of the grown crystals is additionally supported by the lack of a wide absorption band around 2800 nm that is attributed to O-H bonds. The measured transmission corresponds to absorption coefficients below 10 −3 cm −1 . Thus, KTP crystals can be pumped in the range of 0.375-4.2 µm by visible and IR radiation including chemical lasers. The absence of two-photon absorption while pumping by widely used all-solid-state lasers such as Ti:Sapphire (0.8-1.1 µm), Nd:YAG (1.064 µm), holmium (2.01 µm), erbium (2.94 µm) and Fe 2+ :ZnSe (4.1 µm) is attractive for applied systems.

Results
The resistivity of a grown KTP crystal is one of indicators of its quality. Higher values of resistivity make the crystals applicable for manufacturing electro-optic devices: amplitude and phase modulators [12]. Figure 2a depicts crystal resistivity which stays larger than 10 11 Ω cm for the applied electric field up to 20 kV/cm proving high quality and easy polarizability of the samples for creating periodical structures. Visible and IR range transmission spectrum of thick KTP plate for the wave propagating along X axis and polarized parallel to Z axis is presented in Figure 2a. The quality of the grown crystals is additionally supported by the lack of a wide absorption band around 2800 nm that is attributed to O-H bonds. The measured transmission corresponds to absorption coefficients below 10 −3 cm −1 . Thus, KTP crystals can be pumped in the range of 0.375-4.2 µm by visible and IR radiation including chemical lasers. The absence of two-photon absorption while pumping by widely used all-solid-state lasers such as Ti:Sapphire (0.8-1.1 µm), Nd:YAG (1.064 µm), holmium (2.01 µm), erbium (2.94 µm) and Fe 2+ :ZnSe (4.1 µm) is attractive for applied systems. Absorption of the KTP crystal recorded by THz-TDS decreases at higher wavelengths ( Figure  3). This behaviour arises from the presence of several phonon modes below 200 µm. X and Y axes demonstrate the lowest absorption (<5 cm −1 for wavelengths >360 µm) especially after cooling down to 81 K (<1 cm −1 for wavelengths >250 µm). The measured absorption coefficient of KTP crystal is significantly lower compared to 0.7% MgO-doped stoichiometric lithium niobate which is preferable for terahertz wave generation (see Figure 3a for comparison) [22,23]. The wavelengths above 500 µm are also free from strong water vapour absorption lines and are of interest for gas analysis with THz lidar.
(a) (b)  Absorption of the KTP crystal recorded by THz-TDS decreases at higher wavelengths ( Figure 3). This behaviour arises from the presence of several phonon modes below 200 µm. X and Y axes demonstrate the lowest absorption (<5 cm −1 for wavelengths >360 µm) especially after cooling down to 81 K (<1 cm −1 for wavelengths >250 µm). The measured absorption coefficient of KTP crystal is significantly lower compared to 0.7% MgO-doped stoichiometric lithium niobate which is preferable for terahertz wave generation (see Figure 3a for comparison) [22,23]. The wavelengths above 500 µm are also free from strong water vapour absorption lines and are of interest for gas analysis with THz lidar.
3). This behaviour arises from the presence of several phonon modes below 200 µm. X and Y axes demonstrate the lowest absorption (<5 cm −1 for wavelengths >360 µm) especially after cooling down to 81 K (<1 cm −1 for wavelengths >250 µm). The measured absorption coefficient of KTP crystal is significantly lower compared to 0.7% MgO-doped stoichiometric lithium niobate which is preferable for terahertz wave generation (see Figure 3a for comparison) [22,23]. The wavelengths above 500 µm are also free from strong water vapour absorption lines and are of interest for gas analysis with THz lidar.
(a) (b)  Refractive index components for the long-wavelength terahertz range measured by TH-TDS at the room and liquid nitrogen temperatures are shown in Figure 4a,b, respectively.  Recorded dispersions were approximated in the form of Sellmeier equations by the best-fit method within the spectral range of 142 µm to 1500 µm at the room temperature [21]: Corresponding Sellmeier equations for 81 K could be written as follows:  Recorded dispersions were approximated in the form of Sellmeier equations by the best-fit method within the spectral range of 142 µm to 1500 µm at the room temperature [21]: (1) Approximation curves calculated using sets of Equations (1) and (2) are also depicted in Figure 4. It should be emphasized that the KTP refraction index is much smaller than that of LiNbO 3 crystals (~5.2) [22] and collinear velocity-matching appears to be possible in contrast to LN crystal.
By using known dispersion equations for the refractive index for the main transparency window and its temperature dependence [1] and Equations (1) and (2), the dependence of V z angle versus wavelength is calculated for the entire transparency range of KTP ( Figure 5).  Figure 5 shows that Vz angle is weakly dependent on the crystal temperature, that is, phase-matching should be also insensitive to the temperature variations in contrast to LiNbO3 [15]. It is interesting to note that Vz position in the long wavelength region of the THz range is not dependent on the wavelength, that is, effective nonlinearity is not dependent on the pump wavelength for frequency conversion processes within it.
Phase matching for difference frequency generation into the THz range under visible and near-IR pump is found possible only in the principle XZ plane (at θ > Vz and θ < Vz) at RT and 81 K by s − f → f and s − f → s types of interactions. Here, s and f symbols denote slow and fast interacting waves, respectively. For example, phase-matching curves for frequency conversion of tunable (0.65-1.1 µm) Ti:Sapphire laser are presented in Figure 6.  Figure 5 shows that V z angle is weakly dependent on the crystal temperature, that is, phase-matching should be also insensitive to the temperature variations in contrast to LiNbO 3 [15]. It is interesting to note that V z position in the long wavelength region of the THz range is not dependent on the wavelength, that is, effective nonlinearity is not dependent on the pump wavelength for frequency conversion processes within it.
Phase matching for difference frequency generation into the THz range under visible and near-IR pump is found possible only in the principle XZ plane (at θ > V z and θ < V z ) at RT and 81 K by s − f → f and s − f → s types of interactions. Here, s and f symbols denote slow and fast interacting waves, respectively. For example, phase-matching curves for frequency conversion of tunable (0.65-1.1 µm) Ti:Sapphire laser are presented in Figure 6.
It is seen in Figure 6 that type I and type II interactions have very close phase-matching conditions. For interactions in the XZ plane, when Kleinman symmetry conditions are not valid, effective nonlinear coefficient is d s−f→f = d 32 ·sinθ for θ < V z and d s−f→s = d 24 ·sinθ for θ > V z [1]. At 1.064 µm d 24 ≈ d 32 = 3.7 pm/V. So, DFG at larger angles is preferable for both processes due to higher nonlinear coefficient and smaller absorption. Group velocity matching at θ > V z is better for the shortest pump wavelength. Thus, ultrashort pulse conversion can be more efficient, for example, under the pump of THL-100 hybrid laser system built in the Institute of High Current Electronics, Siberian Branch of Russian Academy of Sciences: λ = 475 nm (wavelength), τ = 50 fs (pulse duration), d = 25 cm (pulse aperture), P = 14 TW (pulse power) and E = 1 J (pulse energy) [24].
phase-matching should be also insensitive to the temperature variations in contrast to LiNbO3 [15]. It is interesting to note that Vz position in the long wavelength region of the THz range is not dependent on the wavelength, that is, effective nonlinearity is not dependent on the pump wavelength for frequency conversion processes within it.
Phase matching for difference frequency generation into the THz range under visible and near-IR pump is found possible only in the principle XZ plane (at θ > Vz and θ < Vz) at RT and 81 K by s − f → f and s − f → s types of interactions. Here, s and f symbols denote slow and fast interacting waves, respectively. For example, phase-matching curves for frequency conversion of tunable (0.65-1.1 µm) Ti:Sapphire laser are presented in Figure 6. It is seen in Figure 6 that type I and type II interactions have very close phase-matching conditions. For interactions in the XZ plane, when Kleinman symmetry conditions are not valid, effective nonlinear coefficient is ds−f → f = d32·sinθ for θ < Vz and ds−f → s = d24·sinθ for θ > Vz [1]. At 1.064 µm d24 ≈ d32 = 3.7 pm/V. So, DFG at larger angles is preferable for both processes due to higher nonlinear coefficient and smaller absorption. Group velocity matching at θ > Vz is better for the By using relations (1) and (2), phase matching for collinear second harmonic generation of THz waves is also found possible by type I (s + s → f ) and type II (f + s → f ) of three-wave interactions in the XZ plane. Figure 7 plots the phase-matching curves for type II SHG. Phase-matching conditions for type I and type II SHG of longer THz waves are found close to each other, that is, their efficiencies also should be close. Cooling down KTP crystal to 81 K results in a small (1 • ) increase of V z angle ( Figure 5) but it provides with efficient control of group velocity matching conditions.  [24]. By using relations (1) and (2), phase matching for collinear second harmonic generation of THz waves is also found possible by type I (s + s → f) and type II (f + s → f) of three-wave interactions in the XZ plane. Figure 7 plots the phase-matching curves for type II SHG. Phase-matching conditions for type I and type II SHG of longer THz waves are found close to each other, that is, their efficiencies also should be close. Cooling down KTP crystal to 81 K results in a small (1°) increase of Vz angle ( Figure 5) but it provides with efficient control of group velocity matching conditions.

Discussion
It can be proposed that minimal absorption coefficient of KTP crystal is determined by the residual domain structure that can be decreased by application of higher voltage and further optimization of the growth process. Further cooling below 81 K can narrow the phonon lines and decrease their wavelength extending the THz transparency range toward shorter wavelengths. Furthermore, cooling can increase the damage threshold leading to improved frequency conversion efficiency that is a subject of future study. THz wave energy can be seriously scaled up by using large aperture KTP samples pumped by ultrashort pulse terawatt (TW) laser systems that should be studied experimentally.

Discussion
It can be proposed that minimal absorption coefficient of KTP crystal is determined by the residual domain structure that can be decreased by application of higher voltage and further optimization of the growth process. Further cooling below 81 K can narrow the phonon lines and decrease their wavelength extending the THz transparency range toward shorter wavelengths. Furthermore, cooling can increase the damage threshold leading to improved frequency conversion efficiency that is a subject of future study. THz wave energy can be seriously scaled up by using large aperture KTP samples pumped by ultrashort pulse terawatt (TW) laser systems that should be studied experimentally.
Finally, low absorption at visible-IR pump wavelengths and long THz wavelengths (≥500 µm at RT and 125 µm at 81 K) together with the exceptional set of known physical properties render KTP crystal amongst the most prospective ones for long wavelength THz generation by phase-matched parametric processes. It demonstrates evident advantages in comparison with widely used MgO-doped LiNbO 3 crystals. Available growth technology for producing large-size KTP crystals and TW-level pump systems can allow generation of high-power ps-scale THz pulses.