Optical Properties of KTP Crystals and Their Potential for Terahertz Generation

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Article Optical Properties of KTP Crystals and Their Potential for Terahertz Generation

Alexander Mamrashev 1,* ID , Nazar Nikolaev 1 ID , Valery Antsygin 1, Yury Andreev 2,3, Grigory Lanskii 2,3 and Arkady Meshalkin 4

1 Institute of Automation & Electrometry, SB RAS, 1, Ac. Koptyug Ave., Novosibirsk 630090, Russia; [email protected] (N.N.); [email protected] (V.A.) 2 Institute of Monitoring of Climatic and Ecological Systems, SB RAS, 10/3, Akademicheskii Ave., Tomsk 634055, Russia; [email protected] (Y.A.); [email protected] (G.L.) 3 Siberian Physical Technical Institute of Tomsk State University, 1 Novosobornaya Sq., Tomsk 634050, Russia 4 Institute of Thermophysics, SB RAS, 1, Ac. Lavrent’ev Ave., Novosibirsk 630090, Russia; [email protected] * Correspondence: [email protected]; Tel.: +7-383-330-8378

Received: 30 June 2018; Accepted: 28 July 2018; Published: 31 July 2018

Abstract: 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.

Keywords: KTP; nonlinear crystal; frequency conversion; SHG; DFG; THz radiation; THz wave

1. Introduction

Potassium titanyl phosphate (KTiOPO4, 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 PO4 tetrahedra and TiO6 octahedra with alternating long and short Ti–O bonds that are responsible for its nonlinear properties [2]. KTP advantages are high nonlinear coefficients: d15 = 1.9 pm/V, d24 = 4.2 pm/V, d31 = 2.2 pm/V, d32 = 2.7 pm/V and d33 = 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 abovementioned properties of KTP determine its wide range of nonlinear applications such as sum [3] and difference [4,5] frequency generation (SFG and DFG), second harmonic generation (SHG) [6], optical parametric oscillation/generation (OPO/OPG) and amplification (OPA) [7–9]. Parametric generation based on stimulated polariton scattering in KTP shows superior performance in terms of gain and laser damage resistance in comparison to lithium niobate and lithium tantalate [10,11]. Other KTP applications include modulators for the near- and the mid-IR ranges [12–14].

Crystals 2018, 8, 310; doi:10.3390/cryst8080310 www.mdpi.com/journal/crystals Crystals 2018, 8, 310 2 of 8 Crystals 2018, 8, x FOR PEER REVIEW 2 of 8

The successsuccess ofof KTP KTP nonlinear nonlinear applications applications in the in visiblethe visible and IR and ranges IR drivesranges interestdrives ininterest studying in itsstudying terahertz its dielectricterahertz anddielectric optical and (THz) optical properties (THz) topr substituteoperties to the substitute widely usedthe widely pure and used MgO-doped pure and lithiumMgO-doped niobate lithium crystals niobate (LiNbO crystals3, LN) (LiNbO in this3, LN) range in [this15]. range Previously, [15]. Previously, infrared reﬂectivity infrared reflectivity spectrum ofspectrum KTP was of studiedKTP was up studied to the wavenumberup to the wavenumber of 4000 cm of− 40001 (120 cm THz)−1 (120 at THz) the temperatures at the temperatures of 7 K, 80 of K7 andK, 80 293 K and K [16 293]. Later,K [16]. the Later, results the wereresults supplemented were supplemented by Raman by Raman spectroscopy spectroscopy measurements measurements at the wavenumbersat the wavenumbers below below 4000 cm 4000−1 [cm17].−1 Recently,[17]. Recently, THz refractiveTHz refractive index index and absorption and absorption coefﬁcient coefficient were directlywere directly measured measured using using growingly growingly accessible accessible THz THz time-domain time-domain spectrometers spectrometers (THz-TDS) (THz-TDS) [18 –[18–21]. The21]. The most most comprehensive comprehensive study study of its of THz its THz optical optical properties properties for thefor the waves waves polarized polarized parallel parallel to allto threeall three optical optical axes axes of the of KTPthe KTP crystals crystals was was carried carrie outd inout [20 in]. [20]. The refractiveThe refractive index index components components at room at temperatureroom temperature were approximatedwere approximated in the in form the of form Sellmeier of Sellmeier equations equations [21]. [21]. In this paper, wewe reportreport terahertzterahertz optical propertiesproperties of KTP crystals at the room temperature of 293 K (RT)(RT) andand atat thethe liquid liquid nitrogen nitrogen temperature temperature of of 81 81 K andK and calculate calculate phase-matching phase-matching conditions conditions for nonlinearfor nonlinear frequency frequency conversion conversion into into and and within within the the THz THz range. range.

2. Materials and Methods KTP single-crystalsingle-crystal ingotsingots were were grown grown using using the the Czochralski Czochralski method method from from a Pt a crucible Pt crucible of 100 of mm100 inmm diameter. in diameter. The crucible The crucible closed closed with Pt with cover Pt with cover about with 1 about kg of charge1 kg of was charge disposed was indisposed the resistivity in the oven.resistivity After oven. heating, After the heating, melt was the homogenized melt was homogenized and cooled downand cooled to liquidus downtemperature. to liquidus temperature. The crystals wereThe crystals grown were using grown single-domain using single-domain seed in the directionseed in the of directionX-axis. Duringof X-axis. the During growth the period growth of ◦ ◦ 45–55period days, of 45–55 the meltdays, was the cooled melt was down cooled by 70–120 down C.by The70–120 cooling °С. rateThe ofcooling the crystal rate of was the 0.1–4 crystalC/day was while0.1–4 ° itsС/day rotation while speed its rotation varied from speed 30 tovaried 40 rpm. from In 30 parallel, to 40 therpm. pulling In parallel, speed changedthe pulling from speed 0 to 1.2changed mm/day. from By 0 selectingto 1.2 mm/day. optimal By growth selecting conditions optima high-qualityl growth conditions single-crystal high-quality ingots having single-crystal a weight 3 ofingots 260 ghaving and dimensions a weight of of 260X ×g andY × dimensionsZ = 40 × 60 of× X70 × mm Y × Zwere = 40 grown.× 60 × 70 mm3 were grown. 3 At ﬁrst,first, a large plateplate withwith dimensionsdimensions ofof XX × YY ×× ZZ == 11 11 × ×2828 × ×58 58mm mm3 waswas manufactured manufactured to toevaluate evaluate the the quality quality of ofthe the grown grown crystal crystal and and me measureasure its its transmission transmission spectrum spectrum in in the main transparency window. window. Then Then three three pairs pairs samples samples with with different different thickness thickness with dimensions with dimensions of 10 × 10 of 3 10× (0.28,× 10 0.35× (0.28 and, 0.351.08) and mm 1.08)3 were mm cut orthogonalwere cut orthogonal to the optical to the axes optical X (KTP axesx) andX (KTP Z (KTPx) andz) (FigureZ (KTP 1).z) (FigureSides of1 ).the Sides KTP ofx thesample KTP werex sample parallel were to parallel the Y toand the ZY axesand andZ axes sides and of sides the ofKTP thez KTPsamplez sample were wereparallel parallel to the to X the andX andY axes.Y axes. So, every So, every pair pair of samples of samples allowed allowed us usto tomeasure measure all all three three (x (x, ,yy andand zz)) components of the absorption coefﬁcientcoefficient and refractiverefractive index for waves polarized parallel to the X, Y and Z axes, respectively and select the best-thickness crystalscrystals forfor thethe study.study.

Figure 1. A pair of prepared KTP crystal samples cut orthogonal to the X and Z axes. Figure 1. A pair of prepared KTP crystal samples cut orthogonal to the X and Z axes.

Transmission spectra in the transparency window were measured by UV-2101/3101 Transmission spectra in the transparency window were measured by UV-2101/3101 spectrophotometer (Shimadzu, Kyoto, Japan). Terahertz optical properties were studied using a spectrophotometer (Shimadzu, Kyoto, Japan). Terahertz optical properties were studied using THz-TDS (IA&E SB RAS, Novosibirsk, Russia) with a cryostat described elsewhere [20] at the temperatures of 293 K and 81 K.

Crystals 2018, 8, 310 3 of 8 a THz-TDS (IA&E SB RAS, Novosibirsk, Russia) with a cryostat described elsewhere [20] at the temperaturesCrystals 2018, 8, x of FOR 293 PEER K and REVIEW 81 K. 3 of 8

3.3. Results TheThe resistivityresistivity ofof aa growngrown KTPKTP crystalcrystal isis oneone ofof indicatorsindicators ofof itsits quality.quality. HigherHigher valuesvalues ofof resistivityresistivity makemake the the crystals crystals applicable applicable for manufacturingfor manufacturing electro-optic electro-optic devices: devices: amplitude amplitude and phase and modulatorsphase modulators [12]. Figure [12].2 Figurea depicts 2a crystaldepicts resistivity crystal resistivity which stays which larger stays than larger 10 11 thanΩ cm 10 for11 Ω the cm applied for the electricapplied ﬁeld electric up tofield 20 kV/cmup to 20 proving kV/cm proving high quality high andquality easy and polarizability easy polarizability of the samples of the forsamples creating for periodicalcreating periodical structures. structures. Visible andVisible IR rangeand IR transmission range transmission spectrum spectrum of thick of KTP thick plate KTP for plate the for wave the propagatingwave propagating along alongX axis X and axis polarized and polarized parallel parallel to Z toaxis Z axis is presented is presented in Figure in Figure2a. The2a. The quality quality of theof the grown grown crystals crystals is additionally is additionally supported supported by theby the lack lack of a of wide a wide absorption absorption band band around around 2800 2800 nm thatnm isthat attributed is attributed to O–H to bonds. O–H Thebonds. measured The meas transmissionured transmission corresponds corresponds to absorption to coefﬁcientsabsorption belowcoefficients 10−3 cmbelow−1. Thus,10−3 cm KTP−1. Thus, crystals KTP can crystals be pumped can inbe thepumped range ofin 0.375–4.2the rangeµ mof by0.375–4.2 visible andµm IRby radiationvisible and including IR radiation chemical including lasers. Thechemical absence lase ofrs. two-photon The absence absorption of two-photon while pumping absorption by widely while usedpumping all-solid-state by widely lasers used suchall-solid- as Ti:Sapphirestate lasers (0.8–1.1such as µTi:Sapphirem), Nd:YAG (0.8–1.1 (1.064 µm),µm), Nd:YAG holmium (1.064 (2.01 µm),µm), erbiumholmium (2.94 (2.01µm) µm), and erbium Fe2+:ZnSe (2.94 (4.1 µm)µ m)and is Fe attractive2+:ZnSe (4.1 for appliedµm) is attracti systems.ve for applied systems.

(a) (b)

FigureFigure 2.2. ((aa)) AA typicaltypical dependencedependence ofof resistivityresistivity on the appliedapplied electric ﬁeldfield of the grown KTP ingot; ((bb)) TransmissionTransmission spectraspectra ofof thickthick KTPKTP plateplate forfor radiationradiation polarizedpolarized parallelparallel toto ZZ axisaxis inin thethe visiblevisible andand IRIR ranges.ranges.

Absorption of the KTP crystal recorded by THz-TDS decreases at higher wavelengths (Figure Absorption of the KTP crystal recorded by THz-TDS decreases at higher wavelengths (Figure3). 3). This behaviour arises from the presence of several phonon modes below 200 µm. X and Y axes 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 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 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 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 for terahertz wave generation (see Figure3a 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 are also free from strong water vapour absorption lines and are of interest for gas analysis with lidar. THz lidar.

(a) (b)

Figure 3. Measured absorption coefficient of KTP compared to 0.7% MgO-doped stoichiometric lithium niobate (LN, adapted from [23]) at: (a) Room temperature; (b) Liquid nitrogen temperature.

Crystals 2018, 8, x FOR PEER REVIEW 3 of 8

3. 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 1011 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 Fe2+:ZnSe (4.1 µm) is attractive for applied systems.

(a) (b)

Figure 2. (a) A typical dependence of resistivity on the applied electric field of the grown KTP ingot; (b) Transmission spectra of thick KTP plate for radiation polarized parallel to Z axis in the visible and IR ranges.

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 Crystals 2018, 8, 310 4 of 8 are also free from strong water vapour absorption lines and are of interest for gas analysis with THz lidar.

(a) (b)

Figure 3. Measured absorption coefficient of KTP compared to 0.7% MgO-doped stoichiometric Figure 3. Measured absorption coefﬁcient of KTP compared to 0.7% MgO-doped stoichiometric lithium lithium niobate (LN, adapted from [23]) at: (a) Room temperature; (b) Liquid nitrogen temperature. Crystalsniobate 2018, 8 (LN,, x FOR adapted PEER REVIEW from [23 ]) at: (a) Room temperature; (b) Liquid nitrogen temperature. 4 of 8

Refractive index components for the long-wavelength terahertz range measured by TH-TDS at the room and liquid nitrogen temperaturestemperatures areare shownshown inin FigureFigure4 4a,b,a,b, respectively. respectively.

(a) (b)

Figure 4. Measured (circles) and approximated (sold lines) dispersion of refractive index Figure 4. Measured (circles) and approximated (sold lines) dispersion of refractive index components components of KTP at: (a) Room temperature; (b) Liquid nitrogen temperature. of KTP at: (a) Room temperature; (b) Liquid nitrogen temperature.

Recorded dispersions were approximated in the form of Sellmeier equations by the best-fit methodRecorded within dispersions the spectral were range approximated of 142 µm to in 1500 the formµm at of the Sellmeier room temperature equations by [21]: the best-ﬁt method within the spectral range of 142 µm to 1500 µm at the room temperature [21]: λ 2 2 1.14398 =+ 2 nx 9.54967 1.14398λ , n2 = 9.54967 + λ 2 −13637, x λ2 − 13637 1.26864λλ22 2 =2 + 1.26864 (1) ny n =+9.725159.72515 2 , (0) y λ 2− 13889 , λ −13889 2.29045λ2 n2 = 13.4416 + . z 2 − λ 2 2 λ2.2904511799 n =+13.4416 . z λ 2 −11799 Corresponding Sellmeier equations for 81 K could be written as follows:

λ 2 2 1.20539 n =+9.07963 , x λ 2 −12497

λ 2 2 1.36025 n =+9.20704 , (0) y λ 2 −12264

λ 2 2 2.36823 n =+11.8979 . z λ 2 −11336 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 LiNbO3 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 Vz angle versus wavelength is calculated for the entire transparency range of KTP (Figure 5).

Crystals 2018, 8, 310 5 of 8

Corresponding Sellmeier equations for 81 K could be written as follows:

1.20539λ2 n2 = 9.07963 + , x λ2 − 12497 1.36025λ2 n2 = 9.20704 + , (2) y λ2 − 12264 2.36823λ2 n2 = 11.8979 + . z λ2 − 11336

Approximation curves calculated using sets of Equations (1) and (2) are also depicted in Figure4. It should be emphasized that the KTP refraction index is much smaller than that of LiNbO3 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 Vz angle versus Crystalswavelength 2018, 8, x is FOR calculated PEER REVIEW for the entire transparency range of KTP (Figure5). 5 of 8

Figure 5. Spectral dependence of the Vz angle in the principle XZ plane at RT and 81 K. Figure 5. Spectral dependence of the Vz angle in the principle XZ plane at RT and 81 K.

Figure 5 shows that Vz angle is weakly dependent on the crystal temperature, that is, Figure5 shows that V angle is weakly dependent on the crystal temperature, that is, phase-matching should be also zinsensitive to the temperature variations in contrast to LiNbO3 [15]. It phase-matching should be also insensitive to the temperature variations in contrast to LiNbO [15]. It is is interesting to note that Vz position in the long wavelength region of the THz range3 is not dependentinteresting on to notethe thatwavelength,Vz position that in theis, longeffectiv wavelengthe nonlinearity region ofis thenot THz dependent range is not on dependent the pump on wavelengththe wavelength, for frequency that is, effective conversion nonlinearity processes is within not dependent it. on the pump wavelength for frequency conversionPhase matching processes for within difference it. frequency generation into the THz range under visible and Phase matching for difference frequency generation into the THz range under visible and near-IR near-IR pump is found possible only in the principle XZ plane (at θ > Vz and θ < Vz) at RT and 81 K bypump s − f → is foundf and s possible− f → s types only inof theinteractions. principle Here,XZ plane s and (at f symbolsθ > Vz and denoteθ < V slowz) at and RT and fast81 interacting K by s − f waves,→ f and respectively.s − f → s types For ofexample, interactions. phase-matching Here, s and f curvessymbols for denote frequency slow and conversion fast interacting of tunable waves, (0.65–1.1respectively. µm) Ti:Sapphire For example, laser phase-matching are presented curves in Figure for frequency6. conversion of tunable (0.65–1.1 µm) Ti:Sapphire laser are presented in Figure6. It is seen in Figure6 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 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

(a) (b)

Figure 6. Phase-matching curves for DFG (a) s − f → f and (b) s − f → s types of Ti:Sapphire laser (at 0.65, 0.8 and 1.1 µm): optical rectification or mixing of two close wavelength lasers in the XZ principle plane of KTP crystal at RT (solid lines) and 81 K (dashed lines) versus θ angle.

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

Crystals 2018, 8, x FOR PEER REVIEW 5 of 8

Figure 5. Spectral dependence of the Vz angle in the principle XZ plane at RT and 81 K.

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 Crystals 2018, 8, 310 6 of 8 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 Academywaves, respectively. of Sciences: λFor= 475example, nm (wavelength), phase-matchingτ = 50 curves fs (pulse for duration), frequencyd = 25conversion cm (pulse of aperture), tunable P(0.65–1.1= 14 TW µm) (pulse Ti:Sapphire power) and laserE =are 1 Jpresented (pulse energy) in Figure [24]. 6.

Crystals 2018, 8, x FOR PEER REVIEW 6 of 8 (a) (b) shortest pump wavelength. Thus, ultrashort pulse conversion can be more efficient, for example, FigureFigure 6.6. Phase-matchingPhase-matching curvescurvesfor for DFG DFG ( a()a)s s− − ff →→ ff and ((bb)) ss −− ff → s types of Ti:Sapphire laserlaser (at(at under the pump of THL-100 hybrid laser system built in the Institute of High Current Electronics, 0.65,0.65, 0.80.8 and and 1.1 1.1µm): µm): optical optical rectification rectification or mixing or mixing of two of close two wavelength close wavelength lasers in lasers the XZ inprinciple the XZ Siberianplaneprinciple Branch of KTP plane crystalof of Russian KTP at RTcrystal (solidAcademy at lines)RT (sol andofid 81lines)Sciences: K (dashed and 81λ K lines)= (dashed 475 versus nm lines) θ(wavelength),angle. versus θ angle. τ = 50 fs (pulse duration), d = 25 cm (pulse aperture), P = 14 TW (pulse power) and E = 1 J (pulse energy) [24]. ByIt isusing seen relations in Figure (1) and6 that (2), type phase I andmatching type foII rinteractions collinear second have harmon very closeic generation phase-matching of THz By using relations (1) and (2), phase matching for collinear second harmonic generation of THz wavesconditions. is also For found interactions possible inby thetype XZ I ( splane, + s → whenf) and Kleinmantype II (f + symmetrys → f) of three-wave conditions interactions are not valid, in waves is also found possible by type I (s + s → f ) and type II (f + s → f ) of three-wave interactions in theeffective XZ plane. nonlinear Figure coefficient 7 plots the is phas ds−f→e-matchingf = d32·sinθ for curves θ < V forz and type ds −IIf→ SHG.s = d24 ·Phase-matchingsinθ for θ > Vz [1]. conditions At 1.064 the XZ plane. Figure7 plots the phase-matching curves for type II SHG. Phase-matching conditions forµm typed24 ≈ Id 32and = 3.7type pm/V. II SHG So, ofDFG lo ngerat larger THz angleswaves isare preferable found close for bothto each processes other, duethat tois, higher their for type I and type II SHG of longer THz waves are found close to each other, that is, their efficiencies efficienciesnonlinear coefficient also should and be close.smaller Cooling absorption. down GroupKTP crystal velocity to 81 matching K results at in θ◦a small> Vz is (1°) better increase for the of also should be close. Cooling down KTP crystal to 81 K results in a small (1 ) increase of Vz angle Vz angle (Figure 5) but it provides with efficient control of group velocity matching conditions. (Figure 5) but it provides with efficient control of group velocity matching conditions.

Figure 7. Phase-matching curves for SHG of THz waves by ff + s → f typetype of of interaction in in the XZ principle plane of KTP versus θ andand ϕφ anglesangles thatthat isis identiﬁedidentified inin thethe ﬁgurefigure inset.inset.

4. Discussion It cancan bebe proposed proposed that that minimal minimal absorption absorption coefﬁcient coefficient of KTP of crystalKTP crystal is determined is determined by the residual by the domainresidual structuredomain structure that can bethat decreased can be bydecreased application by application of higher voltage of higher and furthervoltage optimizationand further ofoptimization the growth of process. the growth Further proc coolingess. Further below cooling 81 K can below narrow 81 K the can phonon narrow lines the andphonon decrease lines theirand 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 LiNbO3 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.

Funding: This research was funded by Russian Foundation for Basic Research (RFBR) grant number 17-32-80039 and complex program of basic academic research of Russian Ministry of Science and Higher Education (State Registration No. АААА-А17-117052410033-9).

Crystals 2018, 8, 310 7 of 8 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 LiNbO3 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.

Author Contributions: Conceptualization, Y.A.; Methodology, A.M. (Arkady Meshalkin) and V.A.; Software, A.M. (Alexander Mamrashev) and G.L.; Formal Analysis, A.M. (Alexander Mamrashev), N.N. and G.L.; Investigation, N.N. and A.M. (Arkady Meshalkin); Data Curation, A.M. (Alexander Mamrashev), N.N., G.L.; Writing-Original Draft Preparation, Y.A.; Writing-Review & Editing, A.M. (Alexander Mamrashev), N.N. and Y.A.; Visualization, G.L.; Supervision, Y.A. and V.A. Funding: This research was funded by Russian Foundation for Basic Research (RFBR) grant number 17-32-80039 and complex program of basic academic research of Russian Ministry of Science and Higher Education (State Registration No. AAAA-A17-117052410033-9). Acknowledgments: The terahertz spectroscopy measurements were carried out on the time-domain terahertz spectrometer at the Shared Equipment Center “Spectroscopy and Optics” of the Institute of Automation and Electrometry SB RAS, Novosibirsk, Russia. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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