## Thermal properties of borate crystals for high power optical parametric chirped-pulse amplification |

Optics Express, Vol. 22, Issue 15, pp. 17607-17619 (2014)

http://dx.doi.org/10.1364/OE.22.017607

Acrobat PDF (1056 KB)

### Abstract

The potential of borate crystals, BBO, LBO and BiBO, for high average power scaling of optical parametric chirped-pulse amplifiers is investigated. Up-to-date measurements of the absorption coefficients at 515 nm and the thermal conductivities are presented. The measured absorption coefficients are a factor of 10–100 lower than reported by the literature for BBO and LBO. For BBO, a large variation of the absorption coefficients was found between crystals from different manufacturers. The linear and nonlinear absorption coefficients at 515 nm as well as thermal conductivities were determined for the first time for BiBO. Further, different crystal cooling methods are presented. In addition, the limits to power scaling of OPCPAs are discussed.

© 2014 Optical Society of America

## 1. Introduction

1. A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. **88**, 437–440 (1992). [CrossRef]

3. R. Butkus, R. Danielius, A. Dubietis, A. Piskarskas, and A. Stabinis, “Progress in chirped pulse optical parametric amplifiers,” Appl. Phys. B **79**, 693–700 (2004). [CrossRef]

4. R. Riedel, A. Stephanides, M. J. Prandolini, B. Gronloh, B. Jungbluth, T. Mans, and F. Tavella, “Power scaling of supercontinuum seeded megahertz-repetition rate optical parametric chirped pulse amplifiers,” Opt. Lett. **39**, 1422–1424 (2014). [CrossRef] [PubMed]

5. J. Rothhardt, S. Demmler, S. Hädrich, J. Limpert, and A. Tünnermann, “Octave-spanning OPCPA system delivering CEP-stable few-cycle pulses and 22 W of average power at 1 MHz repetition rate,” Opt. Express **20**, 10870–10878 (2012). [CrossRef] [PubMed]

6. R. Riedel, M. Schulz, M. J. Prandolini, A. Hage, H. Höppner, T. Gottschall, J. Limpert, M. Drescher, and F. Tavella, “Long-term stabilization of high power optical parametric chirped-pulse amplifiers,” Opt. Express **21**, 28987–28999 (2013). [CrossRef]

7. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. **35**, 94–96 (2010). [CrossRef] [PubMed]

8. P. Russbueldt, T. Mans, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, “Compact diode-pumped 1.1 kW Yb:YAG Innoslab femtosecond amplifier,” Opt. Lett. **35**, 4169–4171 (2010). [CrossRef] [PubMed]

9. A. Giesen and J. Speiser, “Fifteen Years of Work on Thin-Disk Lasers: Results and Scaling Laws,” IEEE Sel. Top. in Quantum Elec. **13**, 598–609 (2007). [CrossRef]

10. T. Metzger, A. Schwarz, C.Y. Teisset, D. Sutter, A. Killi, R. Kienberger, and F. Krausz, “High-repetition-rate picosecond pump laser based on a Yb:YAG disk amplifier for optical parametric amplification,” Opt. Lett. **34**, 2123–2125 (2009). [CrossRef] [PubMed]

11. G. Sansone, F. Calegari, and M. Nisoli, “Attosecond Technology and Science,” IEEE J. Sel. Top. in Quantum Elec. **18**, 507–519 (2012). [CrossRef]

12. S. Banerjee, M. Baudisch, J. Biegert, A. Borot, A. Borzsonyi, D. Charalambidis, T. Ditmire, Zs. Diveki, P. Dombi, K. Ertel, M. Galimberti, J. A. Fülöp, E. Gaul, C. Haeffner, M. Hemmer, C. Hernandez-Gomez, M. Kalashnikov, D. Kandula, A. P. Kovacs, R. Lopez-Martens, P. Mason, I. Márton, I. Musgrave, K. Osvay, M. Prandolini, E. Racz, P. Racz, R. Riedel, I. N. Ross, J.-P. Rosseau, M. Schulz, F. Tavella, A. Thai, and I. Will, “Conceptual design of the laser system for the attosecond light pulse source,” in CLEO: 2013 Technical Digest © OSA, (2013).

13. M. J. Prandolini, R. Riedel, M. Schulz, A. Hage, H. Höppner, and F. Tavella, “Design considerations for a high average power, ultrabroadband, optical parametric chirped-pulse amplifier,” Opt. Express **22**, 1594–1607 (2014). [CrossRef] [PubMed]

14. J. Rothhardt, S. Demmler, S. Hädrich, T. Peschel, J. Limpert, and A. Tünnermann, “Thermal effects in high average power optical parametric amplifiers,” Opt. Lett. **38**, 763–765 (2013). [CrossRef] [PubMed]

13. M. J. Prandolini, R. Riedel, M. Schulz, A. Hage, H. Höppner, and F. Tavella, “Design considerations for a high average power, ultrabroadband, optical parametric chirped-pulse amplifier,” Opt. Express **22**, 1594–1607 (2014). [CrossRef] [PubMed]

*β*-BaB

_{2}O

_{4}, BBO) [4

4. R. Riedel, A. Stephanides, M. J. Prandolini, B. Gronloh, B. Jungbluth, T. Mans, and F. Tavella, “Power scaling of supercontinuum seeded megahertz-repetition rate optical parametric chirped pulse amplifiers,” Opt. Lett. **39**, 1422–1424 (2014). [CrossRef] [PubMed]

6. R. Riedel, M. Schulz, M. J. Prandolini, A. Hage, H. Höppner, T. Gottschall, J. Limpert, M. Drescher, and F. Tavella, “Long-term stabilization of high power optical parametric chirped-pulse amplifiers,” Opt. Express **21**, 28987–28999 (2013). [CrossRef]

_{3}O

_{5}, LBO) [13

13. M. J. Prandolini, R. Riedel, M. Schulz, A. Hage, H. Höppner, and F. Tavella, “Design considerations for a high average power, ultrabroadband, optical parametric chirped-pulse amplifier,” Opt. Express **22**, 1594–1607 (2014). [CrossRef] [PubMed]

_{3}O

_{6}, BiBO) [15

15. V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I.V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB_{3}O_{6},” Laser & Photon. Rev. **4**, 53–98 (2010). [CrossRef]

*d*

_{eff}. This allows for a high single-pass gain. All three crystals support a large spectral amplification bandwidth [16

16. R. Akbari and A. Major, “Optical, spectral and phase-matching properties of BIBO, BBO and LBO crystals for optical parametric oscillation in the visible and near-infrared wavelength ranges,” Laser Phys. **23**, 035401 (2013). [CrossRef]

*E*

_{g}, which would make it susceptible to two-photon absorption at 515 nm. We would like to mention, that there are other nonlinear optical crystals with vast potential for high power applications, e.g. YCa

_{4}O(BO

_{3})

_{3}(Yttrium Calcium Oxyborate - YCOB). This crystal can be grown to few-cm size, and its temperature tolerance and thermal conductivity are very high. However, its nonlinear coefficient is low [17

17. Z.M. Liao, I. Jovanovic, C.A. Ebbers, Y. Fei, and B. Chai, “Energy and average power scalable optical parametric chirped-pulse amplification in yttrium calcium oxyborate,” Opt. Lett. **31**, 1277–1279 (2006). [CrossRef] [PubMed]

*α*) at the OPCPA-pump wavelength at values near 515 nm are given as upper limit estimates:

*α*< 10

^{4}ppm cm

^{−1}at 532 nm for BBO, and

*α*< 10

^{3}ppm cm

^{−1}at 532 nm for LBO [21]. For BiBO, a value of

*α*< 10

^{3}ppm cm

^{−1}was measured at 1064 nm [22

22. V. Wesemann, J. A. L Huillier, L. K. Friess, P. A. V. Loewis of Menar, G. Bitz, A. Borsutzky, R. Wallenstein, T. Salva, S. Vernay, and D. Rytz, “Optical properties of BiB_{3}O_{6} with different phase matching orientations,” Appl. Phys. B **84**, 453–458 (2006). [CrossRef]

*κ*) are available for BBO and LBO (see Table 2), but the thermal conductivities of BiBO along the main crystallographic axes

*x*,

*y*and

*z*, and along the phase-matching direction have not been determined. For the numerical modeling and optimization of spatial temperature changes in the investigated borate crystals, the thermal conductivity (

*κ*) and the wavelength-dependent linear absorption coefficients (

*α*) at 515 nm are the most important parameters.

*T*(

*r*,

*z*) along the beam propagation (

*z*axis) [13

**22**, 1594–1607 (2014). [CrossRef] [PubMed]

23. J. Bromage, J. Rothhardt, S. Hädrich, C. Dorrer, C. Jocher, S. Demmler, J. Limpert, A. Tünnermann, and J. D. Zuegel, “Analysis and suppression of parasitic processes in noncollinear optical parametric amplifiers,” Opt. Express **19**, 16797–16808 (2011). [CrossRef] [PubMed]

24. T. Lang, A. Harth, J. Matyschok, T. Binhammer, M. Schultze, and U. Morgner, “Impact of temporal, spatial and cascaded effects on the pulse formation in ultra-broadband parametric amplifiers,” Opt. Express **21**, 949–959 (2013). [CrossRef] [PubMed]

25. F. Tavella, K. Schmid, N. Ishii, A. Marcinkevičius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B **81**, 753–756 (2005). [CrossRef]

26. C. Manzoni, J. Moses, F. X. Kärtner, and G. Cerullo, “Excess quantum noise in optical parametric chirped-pulse amplification,” Opt. Express **19**, 8357–8366 (2011). [CrossRef] [PubMed]

27. A. Alexandrovski, M. Fejer, A. Markosyan, and R. Route, “Photothermal common-path interferometry (PCI): new developments,” Proc. SPIE 7193, Solid State Lasers XVIII: Technology and Devices, 71930D (2009); doi: [CrossRef] .

28. B. Gronloh, P. Russbueldt, B. Jungbluth, and H.-D. Hoffmann, “Green sub-ps laser exceeding 400 W of average power,” Proc. SPIE 8959, Solid State Lasers XXIII: Technology and Devices, 89590T (2014); doi: [CrossRef] .

## 2. Measurement of critical thermal properties of borate crystals

### 2.1. Thermal conductivity κ

*κ*=

*Dρc*

_{cp}, where the specific heat capacity,

*c*

_{cp}, and the density,

*ρ*, were taken from literature. The thermal diffusivity,

*D*, was measured using the temperature-wave analysis method [29

29. J. Morikawa, C. Leong, T. Hashimoto, T. Ogawa, Y. Urata, S. Wada, M. Higuchi, and J.-i. Takahashi, “Thermal conductivity/diffusivity of Nd^{3+} doped GdVO_{4}, YVO_{4}, LuVO_{4}, and Y_{3}Al_{5}O_{12} by temperature wave analysis,” J. Appl. Phys. **103**, 063522 (2008). [CrossRef]

30. J. D. Beasley, “Thermal conductivities of some novel nonlinear optical materials,” Appl. Opt. **33**, 1000–1003 (1994). [CrossRef] [PubMed]

31. D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. **62**, 1968–1983 (1987). [CrossRef]

### 2.2. Linear absorption coefficients (α_{515}): the photothermal common-path interferometry (PCI) method

27. A. Alexandrovski, M. Fejer, A. Markosyan, and R. Route, “Photothermal common-path interferometry (PCI): new developments,” Proc. SPIE 7193, Solid State Lasers XVIII: Technology and Devices, 71930D (2009); doi: [CrossRef] .

28. B. Gronloh, P. Russbueldt, B. Jungbluth, and H.-D. Hoffmann, “Green sub-ps laser exceeding 400 W of average power,” Proc. SPIE 8959, Solid State Lasers XXIII: Technology and Devices, 89590T (2014); doi: [CrossRef] .

*α*

_{515}within the volume. In many surface cases, the standard deviation was larger than the averaged value. This does not stem from a poor signal-to-noise ratio of the PCI method, but rather an unequal distribution of absorption centers at the surface. In the case of BBO (C) (volume), a large error contribution came from the errors of the theoretically calculated material specific calibration factor, which relates the measured data to an absolute absorption for the bulk. In these cases, the error bars were adjusted so that no values were negative. Also stated are the ratios between absorption coefficients at 515 nm and 1030 nm. This information is important for high power second harmonic generation for OPCPA-pump pulse generation.

### 2.3. Absorption coefficients (α_{515}) from thermal imaging measurements

*α*

_{515}) was developed using thermal imaging measurements. This measurement is not as precise as PCI. However, it is used to investigate the crystal absorption under high intensities, and therefore, would include other nonlinear and defect absorption effects. In summary, a thermally isolated crystal is irradiated by laser light under conditions similar to the real application, and in the steady state a thermal image is measured using an infrared camera. Thereafter, finite element analysis (FEA) of the crystal under stead-state irradiation was carried out with known laser and material parameters, and the averaged absorption as the free parameter. Figure 2(a) shows an example thermal image of a BBO(A) crystal irradiated at 515 nm, while Fig. 2(b) shows the corresponding FEA simulation. For this work, the measurements were carried out at the Helmholtz-Institut Jena, Germany.

32. A. Klenke, S. Breitkopf, M. Kienel, T. Gottschall, T. Eidam, S. Hädrich, J. Rothhardt, J. Limpert, and A. Tünnermann, “530 W, 1.3 mJ, four-channel coherently combined femtosecond fiber chirped-pulse amplification system,” Opt. Lett. **38**, 2283–2285 (2013). [CrossRef] [PubMed]

*P*= 120 ± 4 W, 1.5 ps pulse duration (∼1 nm bandwidth), M

^{2}<1.5 at a repetition rate of 1 MHz. The beam diameter was

*d*= 2.8 ± 0.2 mm at 1/e

^{2}. The crystals were placed on a 8 mm thick teflon sheet for thermal insulation. The temperature distribution on the crystal surface in thermal equilibrium was imaged using an infrared camera (FLIR-SC645).

^{5}nodes. The main parameters used for the simulation were the thermal conductivity,

*κ*, the emissivity,

*ε*, the temperature at the crystal center,

*T*

_{max}(Fig. 2(a)), and the boundaries,

*T*

_{top}(Fig. 2(a)), and the heat transfer coefficient,

*h*. A Neumann boundary condition was specified (same as the convective heat transfer) with a heat transfer coefficient

*h*at the interface between the crystal and the boundary (air or heat sink). For an air boundary, free convection between the crystal surface and a static layer of air was assumed. The heat transfer coefficient was estimated using

*h*=

*Q*/(

*A ·*

*δT*), where

*Q*is the heat flow rate,

*A*is the heat transfer surface, and

*δT*is the difference between crystal surface and surrounding air temperature. The initial temperature for air or heat sinks was between 295–297 K. The initial crystal temperature was 295.9 K. The error for the measured peak temperature T

_{max}in the crystal center was estimated over a 3×3 pixel area around the maximum. The measured temperature at the crystal boundary,

*T*

_{top}, was estimated at the crystal top (see thermal image in Fig. 2(a)) and has a large spread. This large spread results in a large error of the temperature change, Δ

*T*, between the crystal center and the boundary. The remaining free parameter in the simulation, the heat flow rate

*Q*, was optimized to fit the simulated temperature distribution to the experimentally measured distribution. From the optimum heat flow rate, the absorption coefficient could be estimated according to

*α*

_{515}=

*Q*/(

*Pl*

_{c}). The results of this analysis for all crystals are given in Table 4.

### 2.4. Discussion of the absorption coefficients at 515 nm

33. F. Zhuang, B. Jungbluth, B. Gronloh, H.-D. Hoffmann, and G. Zhang, “Dual-wavelength, continuous-wave Yb:YAG laser for high-resolution photothermal common-path interferometry,” Appl. Opt. **52**, 5171–5177 (2013). [CrossRef] [PubMed]

*α*

_{515}were observed, and Table 3 lists only the mean values. In contrast, in the thermal imaging experiment, a high power, high intensity laser (2.25 GW cm

^{−2}) was used and a large crystal volume was irradiated, which is more sensitive to local absorption maxima within the volume as well as on the surfaces. Furthermore, two-photon absorption (TPA) may occur at crystal defects due to bandgap lowering. Also at the crystal surfaces TPA might be possible. Most importantly, the absorption coefficients measured in our work were a factor of 10–100 lower than the upper limit values reported in the literature (BBO:

*α*

_{515}< 10

^{4}ppm cm

^{−1}, LBO:

*α*

_{515}< 10

^{3}ppm cm

^{−1}) [21].

14. J. Rothhardt, S. Demmler, S. Hädrich, T. Peschel, J. Limpert, and A. Tünnermann, “Thermal effects in high average power optical parametric amplifiers,” Opt. Lett. **38**, 763–765 (2013). [CrossRef] [PubMed]

*α*

_{515}= 127 ppm cm

^{−1}, is very close to the absorption coefficient of LBO,

*α*

_{515}= 86 ppm cm

^{−1}.

## 3. Thermal simulations of high power OPCPAs and crystal heat-sink geometries

^{−1}for LBO is assumed. In the case of LBO, this value is justified (see Table 3 and Table 4). The code is described in more detail in [13

**22**, 1594–1607 (2014). [CrossRef] [PubMed]

### 3.1. Simulation of a high power OPCPA stage

*λ*

_{P}= 515 nm with a pump power

*P*

_{P}= 1 kW. The pump pulse duration was 0.6 ps. The LBO crystal (OPCPA stage) under consideration was pumped with an intensity of 85 GW/cm

^{2}. Two signal (

*λ*

_{S}) bandwidths between 650–1000 nm and 700–1000 nm were compared, for cases (b.1) and (b.2), respectively (see Fig. 3). As a result, the corresponding idler bandwidth (

*λ*

_{I}with 1/

*λ*

_{I}= 1/

*λ*

_{P}− 1/

*λ*

_{S}) was between 1062–2480 nm or 1062–1949 nm. The seed (starting signal) power was 1 W and the OPCPA gain was approximately a factor of 100, corresponding to 10% pump-to-signal conversion efficiency in a single pass. The crystal length was 2.3 mm. The radial crystal dimensions,

*r*

_{c}, were chosen to best fit the pump beam with low diffraction at the end facets and to reduce the radial temperature change to

*d/r*

_{c}= 0.62, where

*d*is the beam diameter at 1/

*e*

^{2}intensity.

### 3.2. Simulations of different heat-sink geometries

^{3}was assumed. For this evaluation, BBO and LBO were considered owing to their superior thermal properties. For simplicity, the analysis was performed with a constant heat transfer coefficient for crystal-to-air,

*h*= 10 W m

_{MA}^{−2}K

^{−1}. Further parameters were a thermal conductivity

*κ*= 401 W m

^{−1}K

^{−1}and

*κ*= 35 W m

^{−1}K

^{−1}for copper and sapphire, respectively, and a heat transfer coefficient for crystal-to-copper of

*h*≈ 400 W m

_{MC}^{−2}K

^{−1}. The radial temperature change, Δ

*T*=

_{r}*T*

_{max}(center) −

*T*(boundary), was simulated between crystal center (maximum temperature) and the crystal boundary. In Fig. 4, the calculated temperature distributions of three different cases are shown for an absorbed optical power of 0.1 W. The cases are free standing geometry (a.1), copper heat sinks at the side boundaries (a.2), and a sandwich structure with optically bonded sapphire plates at the front and back surface (a.3).

*T*

_{max}= 332K with a radial change of Δ

*T*= 19K. In case (a.2), efficient heat removal off the crystal sides is achieved by mounting copper heat sinks at the sides of the crystal. Compared to case (a.1), this reduces the peak temperature to

_{r}*T*

_{max}= 319K, while the radial change is slightly increased, Δ

*T*= 23K. The limitations were given by the large crystal aperture (front and back surfaces), which in the case discussed here led to a large uncooled surface area. A significant improvement can be achieved by optical bonding thin sapphire plates at the front and rear surface of the BBO crystal, as recently suggested in [14

_{r}14. J. Rothhardt, S. Demmler, S. Hädrich, T. Peschel, J. Limpert, and A. Tünnermann, “Thermal effects in high average power optical parametric amplifiers,” Opt. Lett. **38**, 763–765 (2013). [CrossRef] [PubMed]

35. C. Rothhardt, J. Rothhardt, A. Klenke, T. Peschel, R. Eberhardt, J. Limpert, and A. Tünnermann, “BBO-sapphire sandwich structure for frequency conversion of high power lasers,” Opt. Mater. Express **4**, 1092–1103 (2014). [CrossRef]

*T*

_{max}= 303K, and Δ

*T*= 3K (Fig. 4(a)).

_{r}*T*are simulated for different absorbed optical power

_{r}*P*

_{abs}(blue lines). The total absorbed power depends linearly on the crystal length, if only pump wave absorption is considered. The cases discussed above are marked as triangles (see legend). In addition, the simulation for LBO in free standing geometry (case (a.1)) is also shown (red line). In free standing geometry, the heat removal in LBO is more efficient than in BBO. Because of the higher thermal conductivity of LBO, a lower peak temperature and a smaller radial temperature was attained. The best configuration is the sandwich structure (Fig. 4(a), case (a.3)).

## 4. Discussion on power scaling limits

36. J. Matyschok, T. Lang, T. Binhammer, O. Prochnow, S. Rausch, M. Schultze, A. Harth, P. Rudawski, C. L. Arnold, A. L’Huillier, and U. Morgner, “Temporal and spatial effects inside a compact and CEP stabilized, few-cycle OPCPA system at high repetition rates,” Opt. Express **21**, 29656–29665 (2013). [CrossRef]

*T*= 293–353 K for BBO [31

31. D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. **62**, 1968–1983 (1987). [CrossRef]

*T*= 293–383 K for LBO [37

37. K. Kato, “Temperature-Tuned 90° Phase-Matching Properties of LiB_{3}O_{5},” IEEE J. Quant. Elec. **30**, 2950–2952 (1994). [CrossRef]

*T*= 303–443 K [38

38. H. Lingxiong, L. Xiang, Z. Ge, H. Chenghui, and W Yong, “The accurate refractive indices of BIBO crystal at different temperatures,” J. Phys. D: Appl. Phys. **42**, 225109 (2009). [CrossRef]

*T*

_{peak}= 373K (Fig. 4(b), black rectangles).

*et al.*[31

31. D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. **62**, 1968–1983 (1987). [CrossRef]

*θ*= 22° and

*ϕ*= 90°, which is used for phase matching of the OPAs. However, in our case, the temperature changes are mainly in radial direction. Further, the fracture toughness depends strongly on surface defects. For example, BBO crystal damage was observed in [14

**38**, 763–765 (2013). [CrossRef] [PubMed]

*T*= 50 K over a crystal aperture of 5 mm.

_{r}*k*(

*λ*

_{signal},

*T*)| is the absolute phase mismatch at the signal wavelength,

*λ*

_{signal},

*T*is the crystal temperature and

*l*

_{c}is the nonlinear crystal length. Using broadband phase-matching, a large signal bandwidth is amplified if

*δ*(

*λ*

_{signal},

*T*) <

*π*/2. A thermally induced change of the phase-matching will result in a decrease of the gain for certain wavelengths with

*δ*(

*λ*

_{signal},

*T*+ Δ

*T*(

*r*)) >

*π*/2, where Δ

*T*(

*r*) =

*T*

_{max}−

*T*(

*r*) is the radial temperature change. This causes a radially dependent thermal dephasing,

*δ*(

*λ*

_{signal},

*r*), and thus a radially varying bandwidth Δ

*λ*

_{signal}(

*r*), pump-to-signal conversion efficiency

*η*(

*r*), and radially dependent group velocity

*v*

_{g}(

*r*). For a signal bandwidth of Δ

*λ*= 300 nm, around 820 nm center wavelength, thermal dephasing limits were calculated for 1.2 mm BBO, 2.3 mm LBO and 0.82 mm BiBO (typical values for single-stage high power OPCPAs). These limits, 〈Δ(

*T*)〉 =

*π*/2, were estimated to be about Δ

*T*= 125 K for BBO, 36 K for LBO, and 17 K for BiBO. These values provide rough estimates of allowed maximum changes in crystal temperature.

*α*

_{515}= 127 ppm cm

^{−1}and

*l*

_{c}= 1.2 mm would lead to an absorbed heat of

*P*

_{abs}= 0.15 W, resulting in a radial change of Δ

*T*= 30 K. In the case of a

_{r}*l*

_{c}= 2.3 mm long, free standing LBO (case (a.1)) with

*α*

_{515}= 86 ppm cm

^{−1}pumped at 10 kW average power, about

*P*

_{abs}= 0.2 W are absorbed, leading to an uncritical radial change of Δ

*T*= 16 K. This result for LBO is supported by detailed numerical simulations, which demonstrate a negligible change to critical laser parameters, such as, signal energy, bandwidth and beam profile for a similar radial change in temperature [13

_{r}**22**, 1594–1607 (2014). [CrossRef] [PubMed]

*P*

_{abs}= 1.2 W, resulting in an uncritical radial change of Δ

*T*= 30 K. At these OPCPA-pump powers, the radial changes in temperature are well below the thermal dephasing limits calculated above. Finally, if we assume a pump-to-signal conversion efficiency of 10%, a few-cycle laser pulse could be generated with kW-level of average power for free standing BBO and LBO (case (a.1)), and above 10 kW for a BBO sandwich structure (case (a.3)).

_{r}*G*=

_{T}*α*

_{515}/(

*TT*

_{300}·

*κ*) in units kW

^{−1}cm

^{−1}: a lower value is better. The corresponding values are 0.33 kW

^{−1}cm

^{−1}for BBO(B), 0.41 kW

^{−1}cm

^{−1}for LBO(A) and 160 kW

^{−1}cm

^{−1}for BiBO(A) using the thermal conductivities in the phase-matching direction (Table 2.1) and the absorption coefficients from Table 4.

## 5. Conclusion

22. V. Wesemann, J. A. L Huillier, L. K. Friess, P. A. V. Loewis of Menar, G. Bitz, A. Borsutzky, R. Wallenstein, T. Salva, S. Vernay, and D. Rytz, “Optical properties of BiB_{3}O_{6} with different phase matching orientations,” Appl. Phys. B **84**, 453–458 (2006). [CrossRef]

35. C. Rothhardt, J. Rothhardt, A. Klenke, T. Peschel, R. Eberhardt, J. Limpert, and A. Tünnermann, “BBO-sapphire sandwich structure for frequency conversion of high power lasers,” Opt. Mater. Express **4**, 1092–1103 (2014). [CrossRef]

## References and links

1. | A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. |

2. | I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, “The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers,” Opt. Commun. |

3. | R. Butkus, R. Danielius, A. Dubietis, A. Piskarskas, and A. Stabinis, “Progress in chirped pulse optical parametric amplifiers,” Appl. Phys. B |

4. | R. Riedel, A. Stephanides, M. J. Prandolini, B. Gronloh, B. Jungbluth, T. Mans, and F. Tavella, “Power scaling of supercontinuum seeded megahertz-repetition rate optical parametric chirped pulse amplifiers,” Opt. Lett. |

5. | J. Rothhardt, S. Demmler, S. Hädrich, J. Limpert, and A. Tünnermann, “Octave-spanning OPCPA system delivering CEP-stable few-cycle pulses and 22 W of average power at 1 MHz repetition rate,” Opt. Express |

6. | R. Riedel, M. Schulz, M. J. Prandolini, A. Hage, H. Höppner, T. Gottschall, J. Limpert, M. Drescher, and F. Tavella, “Long-term stabilization of high power optical parametric chirped-pulse amplifiers,” Opt. Express |

7. | T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. |

8. | P. Russbueldt, T. Mans, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, “Compact diode-pumped 1.1 kW Yb:YAG Innoslab femtosecond amplifier,” Opt. Lett. |

9. | A. Giesen and J. Speiser, “Fifteen Years of Work on Thin-Disk Lasers: Results and Scaling Laws,” IEEE Sel. Top. in Quantum Elec. |

10. | T. Metzger, A. Schwarz, C.Y. Teisset, D. Sutter, A. Killi, R. Kienberger, and F. Krausz, “High-repetition-rate picosecond pump laser based on a Yb:YAG disk amplifier for optical parametric amplification,” Opt. Lett. |

11. | G. Sansone, F. Calegari, and M. Nisoli, “Attosecond Technology and Science,” IEEE J. Sel. Top. in Quantum Elec. |

12. | S. Banerjee, M. Baudisch, J. Biegert, A. Borot, A. Borzsonyi, D. Charalambidis, T. Ditmire, Zs. Diveki, P. Dombi, K. Ertel, M. Galimberti, J. A. Fülöp, E. Gaul, C. Haeffner, M. Hemmer, C. Hernandez-Gomez, M. Kalashnikov, D. Kandula, A. P. Kovacs, R. Lopez-Martens, P. Mason, I. Márton, I. Musgrave, K. Osvay, M. Prandolini, E. Racz, P. Racz, R. Riedel, I. N. Ross, J.-P. Rosseau, M. Schulz, F. Tavella, A. Thai, and I. Will, “Conceptual design of the laser system for the attosecond light pulse source,” in CLEO: 2013 Technical Digest © OSA, (2013). |

13. | M. J. Prandolini, R. Riedel, M. Schulz, A. Hage, H. Höppner, and F. Tavella, “Design considerations for a high average power, ultrabroadband, optical parametric chirped-pulse amplifier,” Opt. Express |

14. | J. Rothhardt, S. Demmler, S. Hädrich, T. Peschel, J. Limpert, and A. Tünnermann, “Thermal effects in high average power optical parametric amplifiers,” Opt. Lett. |

15. | V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I.V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB |

16. | R. Akbari and A. Major, “Optical, spectral and phase-matching properties of BIBO, BBO and LBO crystals for optical parametric oscillation in the visible and near-infrared wavelength ranges,” Laser Phys. |

17. | Z.M. Liao, I. Jovanovic, C.A. Ebbers, Y. Fei, and B. Chai, “Energy and average power scalable optical parametric chirped-pulse amplification in yttrium calcium oxyborate,” Opt. Lett. |

18. | A. V. Smith, |

19. | R. H. French, J. W. Ling, F. S. Ohuchi, and C. T. Chen, “Electronic structure of β-BaB |

20. | Z. Lin, Z. Wang, C. Chen, and M.-H. Lee, “Mechanism for linear and nonlinear optical effects in monoclinic bismuth borate (BiB |

21. | D. N. Nikogosyan, |

22. | V. Wesemann, J. A. L Huillier, L. K. Friess, P. A. V. Loewis of Menar, G. Bitz, A. Borsutzky, R. Wallenstein, T. Salva, S. Vernay, and D. Rytz, “Optical properties of BiB |

23. | J. Bromage, J. Rothhardt, S. Hädrich, C. Dorrer, C. Jocher, S. Demmler, J. Limpert, A. Tünnermann, and J. D. Zuegel, “Analysis and suppression of parasitic processes in noncollinear optical parametric amplifiers,” Opt. Express |

24. | T. Lang, A. Harth, J. Matyschok, T. Binhammer, M. Schultze, and U. Morgner, “Impact of temporal, spatial and cascaded effects on the pulse formation in ultra-broadband parametric amplifiers,” Opt. Express |

25. | F. Tavella, K. Schmid, N. Ishii, A. Marcinkevičius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B |

26. | C. Manzoni, J. Moses, F. X. Kärtner, and G. Cerullo, “Excess quantum noise in optical parametric chirped-pulse amplification,” Opt. Express |

27. | A. Alexandrovski, M. Fejer, A. Markosyan, and R. Route, “Photothermal common-path interferometry (PCI): new developments,” Proc. SPIE 7193, Solid State Lasers XVIII: Technology and Devices, 71930D (2009); doi: [CrossRef] . |

28. | B. Gronloh, P. Russbueldt, B. Jungbluth, and H.-D. Hoffmann, “Green sub-ps laser exceeding 400 W of average power,” Proc. SPIE 8959, Solid State Lasers XXIII: Technology and Devices, 89590T (2014); doi: [CrossRef] . |

29. | J. Morikawa, C. Leong, T. Hashimoto, T. Ogawa, Y. Urata, S. Wada, M. Higuchi, and J.-i. Takahashi, “Thermal conductivity/diffusivity of Nd |

30. | J. D. Beasley, “Thermal conductivities of some novel nonlinear optical materials,” Appl. Opt. |

31. | D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. |

32. | A. Klenke, S. Breitkopf, M. Kienel, T. Gottschall, T. Eidam, S. Hädrich, J. Rothhardt, J. Limpert, and A. Tünnermann, “530 W, 1.3 mJ, four-channel coherently combined femtosecond fiber chirped-pulse amplification system,” Opt. Lett. |

33. | F. Zhuang, B. Jungbluth, B. Gronloh, H.-D. Hoffmann, and G. Zhang, “Dual-wavelength, continuous-wave Yb:YAG laser for high-resolution photothermal common-path interferometry,” Appl. Opt. |

34. | J. H. Jang, I. H. Yoon, and C. S. Yoon, “Cause and repair of optical damage in nonlinear optical crystals of BiB |

35. | C. Rothhardt, J. Rothhardt, A. Klenke, T. Peschel, R. Eberhardt, J. Limpert, and A. Tünnermann, “BBO-sapphire sandwich structure for frequency conversion of high power lasers,” Opt. Mater. Express |

36. | J. Matyschok, T. Lang, T. Binhammer, O. Prochnow, S. Rausch, M. Schultze, A. Harth, P. Rudawski, C. L. Arnold, A. L’Huillier, and U. Morgner, “Temporal and spatial effects inside a compact and CEP stabilized, few-cycle OPCPA system at high repetition rates,” Opt. Express |

37. | K. Kato, “Temperature-Tuned 90° Phase-Matching Properties of LiB |

38. | H. Lingxiong, L. Xiang, Z. Ge, H. Chenghui, and W Yong, “The accurate refractive indices of BIBO crystal at different temperatures,” J. Phys. D: Appl. Phys. |

**OCIS Codes**

(140.3280) Lasers and laser optics : Laser amplifiers

(190.4400) Nonlinear optics : Nonlinear optics, materials

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: February 18, 2014

Revised Manuscript: May 8, 2014

Manuscript Accepted: May 8, 2014

Published: July 14, 2014

**Citation**

R. Riedel, J. Rothhardt, K. Beil, B. Gronloh, A. Klenke, H. Höppner, M. Schulz, U. Teubner, C. Kränkel, J. Limpert, A. Tünnermann, M.J. Prandolini, and F. Tavella, "Thermal properties of borate crystals for high power optical parametric chirped-pulse amplification," Opt. Express **22**, 17607-17619 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-17607

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### References

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