## Design considerations for a high power, ultrabroadband optical parametric chirped-pulse amplifier |

Optics Express, Vol. 22, Issue 2, pp. 1594-1607 (2014)

http://dx.doi.org/10.1364/OE.22.001594

Acrobat PDF (1645 KB)

### Abstract

A conceptual design of a high power, ultrabroadband optical parametric chirped-pulse amplifier (OPCPA) was carried out comparing nonlinear crystals (LBO and BBO) for 810 nm centered, sub-7.0 fs pulses with energies above 1 mJ. These amplifiers are only possible with a parallel development of kilowatt-level OPCPA-pump amplifiers. It is therefore important to know good strategies to use the available OPCPA-pump energy efficiently. Numerical simulations, including self- and cross-phase modulation, were used to investigate the critical parameters to achieve sufficient spectral and spatial quality. At high output powers, thermal absorption in the nonlinear crystals starts to degrade the output beam quality. Strategies to minimize thermal effects and limits to the maximum average power are discussed.

© 2014 Optical Society of America

## 1. Introduction

1. J. Rothhardt, S. Hädrich, E. Seise, M. Krebs, F. Tavella, A. Willner, S. Düsterer, H. Schlarb, J. Feldhaus, J. Limpert, J. Rossbach, and A. Tünnermann, “High average and peak power few-cycle laser pulses
delivered by fiber pumped OPCPA system,” Opt. Express **18**, 12719–12726 (2010). [CrossRef] [PubMed]

4. 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]

5. B. Faatz, N. Baboi, V. Ayvazyan, V. Balandin, W. Decking, S. Duesterer, H.-J. Eckoldt, J. Feldhaus, N. Golubeva, K. Honkavaara, M. Koerfer, T. Laarmann, A. Leuschner, L. Lilje, T. Limberg, D. Noelle, F. Obier, A. Petrov, E. Ploenjes, K. Rehlich, H. Schlarb, B. Schmidt, M. Schmitz, S. Schreiber, H. Schulte-Schrepping, J. Spengler, M. Staack, F. Tavella, K. Tiedtke, M. Tischer, R. Treusch, M. Vogt, A. Willner, J. Bahrdt, R. Follath, M. Gensch, K. Holldack, A. Meseck, R. Mitzner, M. Drescher, V. Miltchev, J. Rönsch-Schulenburg, and J. Rossbach, “Flash II: Perspectives and
challenges,” Nucl. Instr. Meth. A **635**, S2–S5 (2011). [CrossRef]

6. H. Redlin, A. Al-Shemmary, A. Azima, N. Stojanovic, F. Tavella, I. Will, and S. Düsterer, “The FLASH pump-probe laser system: Setup, characterization
and optical beamlines,” Nucl. Instr. Meth. A **635**, S88–S93 (2011). [CrossRef]

7. G. Sansone, F. Calegari, and M. Nisoli, “Attosecond technology and science,”
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8. 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,” “CLEO:2013 Technical Digest © OSA,” (2013).

4. 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]

9. M. Schulz, R. Riedel, A. Willner, T. Mans, C. Schnitzler, P. Russbueldt, J. Dolkemeyer, E. Seise, T. Gottschall, S. Hädrich, S. Duesterer, H. Schlarb, J. Feldhaus, J. Limpert, B. Faatz, A. Tünnermann, J. Rossbach, M. Drescher, and F. Tavella, “Yb:YAG Innoslab amplifier: efficient high repetition rate
subpicosecond pumping system for optical parametric chirped pulse
amplication,” Opt. Lett. **36**, 2456–2458 (2011). [CrossRef] [PubMed]

10. M. Schulz, R. Riedel, A. Willner, S. Düsterer, M. J. Prandolini, J. Feldhaus, B. Faatz, J. Rossbach, M. Drescher, and F. Tavella, “Pulsed operation of a high average power Yb:YAG thin-disk
multipass amplifier,” Opt. Express **20**, 5038–5043 (2012). [CrossRef] [PubMed]

11. B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to
subpicosceond pulses,” Phys. Rev. Lett. **74**, 2248–2251 (1995). [CrossRef] [PubMed]

9. M. Schulz, R. Riedel, A. Willner, T. Mans, C. Schnitzler, P. Russbueldt, J. Dolkemeyer, E. Seise, T. Gottschall, S. Hädrich, S. Duesterer, H. Schlarb, J. Feldhaus, J. Limpert, B. Faatz, A. Tünnermann, J. Rossbach, M. Drescher, and F. Tavella, “Yb:YAG Innoslab amplifier: efficient high repetition rate
subpicosecond pumping system for optical parametric chirped pulse
amplication,” Opt. Lett. **36**, 2456–2458 (2011). [CrossRef] [PubMed]

10. M. Schulz, R. Riedel, A. Willner, S. Düsterer, M. J. Prandolini, J. Feldhaus, B. Faatz, J. Rossbach, M. Drescher, and F. Tavella, “Pulsed operation of a high average power Yb:YAG thin-disk
multipass amplifier,” Opt. Express **20**, 5038–5043 (2012). [CrossRef] [PubMed]

12. S. T. Lin, Y. Y. Lin, Y. C. Huang, A. C. Chiang, and J. T. Shy, “Observation of thermal-induced optical guiding and
bistability in a mid-IR continuous-wave, singly resonant optical parametric
oscillator,” Opt. Lett. **33**, 2338–2340 (2008). [CrossRef] [PubMed]

13. M. Vainio, J. Peltola, S. Persijn, F. J. M. Harren, and L. Halonen, “Thermal effects in singly resonant continuous-wave optical
parametric oscillators,” Appl. Phys. B **94**, 411–427 (2009). [CrossRef]

*β*-barium borate (BBO) [14

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]

15. 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]

15. 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]

*M*

^{2}-value. From these results the pump-to-signal efficiencies and compressible pulse durations for both LBO and BBO are derived. Third, because many applications require both good near and far field beam characteristics, the critical parameters required for high spatial beam quality are analyzed. Fourth, spectral phase effects (up to the fourth order) of the nonlinear processes are discussed for both the optical parametric amplification and phase modulation. Finally, the energetics of the complete amplifier and possible maximum average power, which is ultimately restricted by thermal effects, will be discussed. The maximum power, through a single stage nonlinear crystal, is difficult to estimate, because there needs to be an exact thermal model of the crystal holder. In addition, the temperature dependence of the many optical material parameters is not well known, especially in the case of a strong varying temperature profile across the crystals. We therefore restrict our discussion to how to achieve maximum average power for a single stage and give an estimate for the maximum average power at which thermal effects start to change the optical properties of the amplifier.

## 2. Numerical modeling and material parameters

18. I. N. Ross, P. Matousek, G. H. C. New, and K. Osvay, “Analysis and optimization of optical parametric chirped
pulsed amplification,” J. Opt. Soc. Am. B **19**, 2945–2956 (2002). [CrossRef]

20. J. Moses and S.-W. Huang, “Conformal profile theory for performance scaling of
ultrabroadband optical parametric chirped pulse amplification,” J.
Opt. Soc. Am. B **28**, 812–831 (2011). [CrossRef]

18. I. N. Ross, P. Matousek, G. H. C. New, and K. Osvay, “Analysis and optimization of optical parametric chirped
pulsed amplification,” J. Opt. Soc. Am. B **19**, 2945–2956 (2002). [CrossRef]

21. S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Numerical simulations for performace optimization of a
few-cycle terawatt NOPCPA system,” Appl. Phys. B **87**, 677–684 (2007). [CrossRef]

*z*-axis along the signal propagation axis and one transverse direction (

*x*-axis) formed in the plane between the signal and pump axes. The nonlinear coupled equations, Eq. (1), within the slowly varying envelope approximation (

*S*), pump (

*P*) and idler (

*I*) pulses at center frequency

*ω*

_{0}and wavenumber

*k*

_{0}were solved using a fourth-order Runge-Kutta split-step Fourier algorithm. The nonlinear part of these equations are given below:

*k*=

*k*+

_{S}*k*−

_{I}*k*is the wavenumber mismatch,

_{P}*d*

_{eff}the nonlinear optical coefficient,

*n*(

_{m}*m*=

*S*,

*I*,

*P*) refractive indices,

*α*

_{515}is the absorption coefficient (Table 1),

*n*

_{2}

*the nonlinear refractive indices and*

_{m}*γ*and

_{PS}*γ*are the correction coefficients accounting for the cross-phase modulation effects [22]. The last terms on the right hand side represent the self- and cross-phase modulation effects, SPM and XPM, respectively. For BBO, the coefficients for the Sellmeier equations were taken from [23

_{IS}23. D. Zhang, Y. Kong, and J.-Y. Zhang, “Optical parametric properties of 523-nm-pumped
beta-barium-borate near the infrared absorption edge,” Opt.
Comm. **184**, 485–491 (2000). [CrossRef]

24. M. Bache, H. Guo, B. Zhou, and X. Zeng, “The anisotropic Kerr nonlinear refractive index of the
beta-barium borate (β-BaB_{2}O_{4}) nonlinear
crystal,” Optical Materials Express **3**, 357–382 (2013). [CrossRef]

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

15. 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]

26. M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order
χ^{(2)}materials KTiOPO_{4}, KNbO_{3},
β-BaB_{2}O_{4}, and LiB_{3}O_{5},”
Opt. Comm. **142**, 294–298 (1997). [CrossRef]

*x*-axis for the signal, idler and pump pulses, were carried out in the Fourier domain.

*B*-integral. In this work, we modified the standard textbook definition to include SPM and XPM. Thus, the

*B*-integral can be written as: where

*l*is the length of the crystal and the intensity can be derived from

*n*(

_{m}*m*=

*S*,

*I*,

*P*). The

*B*-integral for the signal and idlers pulses could be correspondingly derived. However, this parameter is only useful in the interpretation of narrow band pulses, for example, the pump pulse. For ultrabroadband pulses it is better to analyze the actually phase across the pulse (see Section 5). For high energy NOPA stages, there are three damaging effects of SPM and XPM: (i) spatially distorted beam profiles resulting in larger

*M*

^{2}-values, (ii) frequency modulation, which may cause problems in re-compressing the signal, and (iii) the phase matching condition becomes time and position dependent (i.e. Δ

*k*(

*t*,

*x*,

*z*)). This final effect can reduce the bandwidth and energy of the signal pulse [27

27. A. Thai, C. Skrobol, P. K. Bates, G. Arisholm, Z. Major, F. Krausz, S. Karsch, and J. Biegert, “Simulations of petawatt-class few-cycle optical parametric
chirped-pulse amplification including nonlinear refractive index effects,”
Opt. Lett. **35**, 3471–3473 (2010). [CrossRef] [PubMed]

*T*(

*x*) across the transverse direction of the nonlinear crystal, Δ

*k*(

*x*) and the group velocities (

*υ*(

_{m}*x*), where

*m*=

*S*,

*I*,

*P*) become position dependent. Higher order temperature dependencies on the dispersion were not considered. Within the non-collinear optical parametric process, matching the group velocities along the direction of the signal (

*υ*(

_{S}*x*) ≃

*υ*(

_{I}*x*) cos Ω, where Ω is the spatial angle between the signal and idler pulses) is important to achieve broadband amplification. Depending on the nonlinear material, a temperature distribution across the crystals can greatly reduce the amplified bandwidth and spatial beam quality.

^{2}[3

3. 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]

_{3}O

_{7}, the interstices between the helices are small and can only accommodate small ions, such as Li

^{+}. This ensures that LBO can be grown relatively free of inclusions [28

28. C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, and S. Lin, “New nonlinear-optical crystal:
LiB_{3}O_{5},” J. Opt. Soc. Am. B **6**, 616–621 (1989). [CrossRef]

28. C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, and S. Lin, “New nonlinear-optical crystal:
LiB_{3}O_{5},” J. Opt. Soc. Am. B **6**, 616–621 (1989). [CrossRef]

## 3. Simulation results: dispersion management, conversion efficiencies and spectra

4. 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]

29. 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]

*α*(between the signal and pump pulses), and

*θ*(between the optical axis and the pump pulse), were chosen to achieve a compromise between the resulting signal gain and bandwidth, while restricting the accumulation of spatial phase of the signal pulse, which results poor beam quality. Pulse widths and spatial expansions, between stages 1 and 2, and between 2 and 3, were again chosen as a compromise between achieving the required bandwidth, and the necessary beam quality at the final output (Fig. 1). The chosen crystal thicknesses were for the three stages,

*l*

_{1}= 3.1,

*l*

_{2}= 1.5 and

*l*

_{3}= 1.2 mm, and

*l*

_{1}= 1.7,

*l*

_{2}= 0.9,

*l*

_{3}= 0.5 mm for LBO and BBO, respectively.

*kz*in Eq. (1) is smaller over a larger range of wavelengths [3

3. 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]

18. I. N. Ross, P. Matousek, G. H. C. New, and K. Osvay, “Analysis and optimization of optical parametric chirped
pulsed amplification,” J. Opt. Soc. Am. B **19**, 2945–2956 (2002). [CrossRef]

## 4. Spatial beam quality

*M*

^{2}-values will be used, and were calculated from the near-field far-field product [30]. Since the quality of the pump beam depends on the final implementation of a pump system, the simulations were carried out with Gaussian beams. With this choice, it is possible to isolate and identify the important factors determining spatial beam quality resulting from the OPCPA stages. In addition, the results for spatial beam profiles of LBO and BBO are similar, and therefore the following discussion, showing only LBO results, can be applied to both crystals.

*x*-axis for LBO at the end of each of the first two OPCPA stages are shown. The highest

*M*

^{2}-value is calculated after the first stage (Table 2). This results from the optical parametric amplification process including spatial directional walk-off of the signal and pump pulses. This problem is most serious in the first stage, since the pulse diameters are relatively small compared to the length of the crystal. An additional factor is the choice of the phase matching geometry: tangential phase matching (TPM) or Poynting-vector walk-off compensation (PVWC) [31

31. A. L. Oien, I. T. McKinnie, P. Jain, N. A. Russell, D. M. Warrington, and L. A. W. Gloster, “Efficient, low-threshold collinear and noncollinear
β-barium borate optical parametric oscillators,” Opt.
Lett. **22**, 859–861 (1997). [CrossRef] [PubMed]

29. 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]

*M*

^{2}-values from Table 2). Furthermore, the spatial phase of the pump beam does not affect the beam quality of the amplified signal. This was investigated by adding an oscillatory spatial phase on the

*x*-axis of the pump beam of the form exp(

*i*cos

*ax*), where

*a*was greater than the inverse of the beam width. In this case, exactly the same results were achieved for the signal, but the idler was strongly modulated by the phase of the pump. In contrast, spatial distortions in the pump intensity are transferred into the signal intensity, as shown in Fig. 5. While the signal intensity profile is dominated by the pump intensity profile of the second stage, the spatial phase of the signal is predominantly accumulated on passing through the first, second, and third stages, and should be kept to a minimum.

*M*

^{2}(see Table 2).

*B*-integral for the pump pulse was therefore estimated for the first, second and third stages to be 0.90, 0.38, 0.31 and 1.40, 0.63, 0.25 for LBO and BBO, respectively. For the corresponding given beam widths, self-focusing should be negligible for these values.

## 5. Spectral characteristics of the signal pulse

**19**, 2945–2956 (2002). [CrossRef]

*f*= 1 −

*I*(

_{P}*z*)/

*I*(0),

_{P}*γ*=

_{S}*ω*(0)/(

_{P}I_{S}*ω*(0)); and

_{S}I_{P}*I*(

_{S}*z*) and

*I*(

_{P}*z*) are the intensities of the signal and pump, respectively. From Eq. (3), changes in the spectral phase can be minimized for a given Δ

*k*by using shorter crystals, increasing the ratio

*I*(0)/

_{S}*I*(0) and by keeping pump depletion close to zero. The latter is not possible, if pump-to-signal conversion efficiency is maximized. Thus the greatest spectral phase changes are experienced in the first stage, which has the longest crystal and the smallest

_{P}*I*(0)/

_{S}*I*(0) ratio (see Table 3). The ratios between GDD, TOD and FOD can be modified by changing the wavelength dependent form of Δ

_{P}*k*. This can be achieved by adjusting the non-collinear angle [32

32. S. Demmler, J. Rothhardt, S. Hädrich, J. Bromage, J. Limpert, and A. Tünnermann, “Control of nonlinear spectral phase induced by
ultrabroadband optical parametric amplification,” Opt.
Lett. **19**, 3933–3935 (2012). [CrossRef]

*B*-integral for the signal after the first stage is approximately 0.77 for both LBO and BBO. This result is dominated by the large intensity of the pump pulse. However, if the signal pulse duration is smaller than the pump pulse duration, the signal experiences a largely “flat” pump pulse. Therefore cross PM from pump to signal only adds a relatively constant phase to the signal. This is complicated because the pump pulse undergoes a large depletion, which adds an inverted phase modulation to the signal. The combined processes are rather complex, depending on intensity of the signal and pump pulses, length of crystals, the degree of pump depletion, and exact details of the relative timing, spatial and spectral parameters of the two input pulses (signal and pump). Therefore, instead of using Eq. (2) to measure the effects of phase modulation on the signal pulse, it is better to examine the change phase modulation adds to each dispersion order. As an example, the changes of spectral phase in LBO for the second, third, and fourth order are given in Table 3 for all three stages. The changes in phase due to phase modulation are much smaller than the contributions due to the dispersion for GDD and TOD, however, for the FOD they are similar. Using the chosen parameters in this design, phase modulation has only minor effects on both the output signal energy and bandwidth.

## 6. Pulse Energetics and Thermal Effects

*f*, where

_{r}*f*is the pulse repetition rate (discussed below).

_{r}*f*), is then finally determined by the thermal properties of LBO and BBO. Although the OPCPA process does not involve direct absorption of energy through a change of quantum numbers, there is residual absorption modeled by the Beer-Lambert law with coefficients (

_{r}*α*) that are frequency dependent (Table 1). A rough estimate of the amount of power (

*P*) to be dissipated through a crystal is given by the equation

*P*=

*f*(

_{r}τI_{max}αLπ*D*/2)

^{2}, where

*L*is the length of the crystals and the other parameters are defined in Tables 1 and 2. In the simulations, narrow band pump-pulse absorption was calculated within the solution of the nonlinear equations (Eq. (1)). The frequency dependent absorption parameters of the signal and idler pulses were taken from [17] (see Fig. 6), and were calculated in the frequency domain. For both LBO and BBO the full bandwidth of the Ti:sapphire oscillator (i.e. the signal pulse) has almost 100% transmission across its full bandwidth. However, the idler pulse, calculated by 1/

*λ*= 1/

_{I}*λ*− 1/

_{P}*λ*, extends well into wavelengths above 2000 nm, if the full bandwidth of the oscillator is used. Therefore, in the simulations, a lower wavelength cut-off was used on the initial signal pulse to restrict large attenuation of the idler pulse. Note: BBO allows a slightly greater bandwidth window, with reduced signal and idler adsorption, compared to LBO (Fig. 6). However, there are less restrictions on the idler attenuation, if the signal pulse from the Ti:sapphire oscillator could be broadened beyond wavelengths of 1100 nm. This is not considered in this work, but has been experimentally achieved [3

_{S}3. 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]

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]

*x*-axis), minimizing changes in temperature might be realized by a careful design of the crystal holder. Keeping a near constant temperature along the

*z*-axis can be achieved by balancing heat profiles from the signal, idler and pump. Towards the end of the crystal, the pump pulse becomes depleted, while the energy of the signal and idler pulses increases. In Fig. 7, the maximum temperature increase at the input side of the crystals was 8.9 K, and increases to 11.5 K at the output side for LBO, due to a greater increase of heating from the signal and idler pulses compared to the pump pulse. Applying this temperature profile in the simulation code, only minor changes (∼1%) to the critical parameters, signal energy, bandwidth, and

*M*

^{2}, were observed, compared to a flat temperature profile at the maximum temperature. Thus, we can predict a lower conservative limit where thermal effects start to affect the laser performance. Using the LBO parameters from Table 2, the simulated OPCPA amplifier can achieve 181 W at 100 kHz with 7 fs pulses with minimal temperature effects, requiring an OPCPA-pump of around 1.6 kW at 1030 nm.

*f*. Thus for the same pulse energy

_{r}αE/κ*E*and repetition rate

*f*, BBO has approximately 26 times greater temperature increase as LBO at 515 nm (Table 1). Repeating the thermal simulation for BBO, the maximum change in temperature for BBO was 205 K, at 100 kHz. In compensation to this large change of temperature, the phase matching temperature tolerance

_{r}*δT*·

*l*is 8.7 times better than LBO (Table 1). However, what is not considered with this simple model is the effect of a large temperature gradient within the crystal, which will cause large differential expansion resulting in large strains. These considerations, including a more detailed thermal model of the crystal holder, are beyond the scope of this paper. We therefore suggest that BBO would be ideal for burst-mode operation. In addition, BBO has a larger gain bandwidth compared to LBO. For example, at the new FEL, FLASH 2 at Hamburg, a three-stage BBO OPCPA system is planned for burst-mode operation (up to 1 MHz for 800 μs at 10 Hz). The average power of this system effectively corresponds to a repetition rate of 8 kHz, where thermal effects can be neglected.

## 7. Discussion and Conclusion

*M*

^{2}-values were calculated at the end of each stage. Final

*M*

^{2}-values of 1.2 can be achieved, assuming Gaussian pump beams. The relationship between the signal and pump beam profiles has been explored at each of the three stages. It is expected that the final beam quality is largely determined by the intensity of the pump beam through the nonlinear crystal and not its spatial phase. Thus, with careful adjustment of the OPCPA system and good near-field pump beam quality, a three-stage OPCPA can provide good spatial beam quality of the signal. The spectral phase of the signal does not appear to be adversely affected by either the OPCPA process or by self- and cross-phase modulation, provided that each stage is correctly adjusted (Section 5) and is not driven too hard causing back conversion. Note: This is a highly complex system to optimize and no attempt was made to find the maximal optimum efficiency within the given goals and restrictions.

*α/κ*ratio compared to BBO. BBO is a good choice for burst-mode operation, because it has a broader gain-bandwidth and a broader transmission window (Fig. 6). Additionally, in this three-stage OPCPA, the second stage suffers the highest heat load, and therefore this stage was analyzed in more detail (Fig. 7). In continuous mode operation, no attempt was made to find a maximum final output power, because this would require a detailed model of the crystal holder and knowledge of the behavior of the nonlinear crystal with large temperature variation across the crystal. This latter effect will lead to differential expansion and large strains within the crystal, which are difficult to predict: most parameters are measured at constant temperature. We have therefore decided to restrict the maximum change in temperature for LBO to ∼ 10 K, where only minor changes were observed in the critical laser parameters. We also provide strategies for minimizing heat absorption, demonstrating an almost constant temperature through the length of the crystal along the

*z*-axis, which is achieved by a careful balance of the signal and corresponding idler spectrum (Figs. 6 and 7). Using these assumptions and a conservative estimate of the material parameters (Table 2), an estimate of the final signal output power of 181 W with sub-7 fs pulses can be achieved using LBO at 100 kHz repetition rate. At these powers, we expect thermal effects to have negligible affects on the critical laser parameters.

## Acknowledgments

## References and links

1. | J. Rothhardt, S. Hädrich, E. Seise, M. Krebs, F. Tavella, A. Willner, S. Düsterer, H. Schlarb, J. Feldhaus, J. Limpert, J. Rossbach, and A. Tünnermann, “High average and peak power few-cycle laser pulses
delivered by fiber pumped OPCPA system,” Opt. Express |

2. | F. Tavella, A. Willner, J. Rothhardt, S. Hädrich, E. Seise, S. Düsterer, T. Tschentscher, H. Schlarb, J. Feldhaus, J. Limpert, A. Tünnermann, and J. Rossbach, “Fiber-amplifier pumped high average power few-cycle pulse
non-collinear OPCPA,” Opt. Express |

3. | 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 |

4. | 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 |

5. | B. Faatz, N. Baboi, V. Ayvazyan, V. Balandin, W. Decking, S. Duesterer, H.-J. Eckoldt, J. Feldhaus, N. Golubeva, K. Honkavaara, M. Koerfer, T. Laarmann, A. Leuschner, L. Lilje, T. Limberg, D. Noelle, F. Obier, A. Petrov, E. Ploenjes, K. Rehlich, H. Schlarb, B. Schmidt, M. Schmitz, S. Schreiber, H. Schulte-Schrepping, J. Spengler, M. Staack, F. Tavella, K. Tiedtke, M. Tischer, R. Treusch, M. Vogt, A. Willner, J. Bahrdt, R. Follath, M. Gensch, K. Holldack, A. Meseck, R. Mitzner, M. Drescher, V. Miltchev, J. Rönsch-Schulenburg, and J. Rossbach, “Flash II: Perspectives and
challenges,” Nucl. Instr. Meth. A |

6. | H. Redlin, A. Al-Shemmary, A. Azima, N. Stojanovic, F. Tavella, I. Will, and S. Düsterer, “The FLASH pump-probe laser system: Setup, characterization
and optical beamlines,” Nucl. Instr. Meth. A |

7. | G. Sansone, F. Calegari, and M. Nisoli, “Attosecond technology and science,”
IEEE J. Sel. Topics Quant. Elect. |

8. | 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,” “CLEO:2013 Technical Digest © OSA,” (2013). |

9. | M. Schulz, R. Riedel, A. Willner, T. Mans, C. Schnitzler, P. Russbueldt, J. Dolkemeyer, E. Seise, T. Gottschall, S. Hädrich, S. Duesterer, H. Schlarb, J. Feldhaus, J. Limpert, B. Faatz, A. Tünnermann, J. Rossbach, M. Drescher, and F. Tavella, “Yb:YAG Innoslab amplifier: efficient high repetition rate
subpicosecond pumping system for optical parametric chirped pulse
amplication,” Opt. Lett. |

10. | M. Schulz, R. Riedel, A. Willner, S. Düsterer, M. J. Prandolini, J. Feldhaus, B. Faatz, J. Rossbach, M. Drescher, and F. Tavella, “Pulsed operation of a high average power Yb:YAG thin-disk
multipass amplifier,” Opt. Express |

11. | B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to
subpicosceond pulses,” Phys. Rev. Lett. |

12. | S. T. Lin, Y. Y. Lin, Y. C. Huang, A. C. Chiang, and J. T. Shy, “Observation of thermal-induced optical guiding and
bistability in a mid-IR continuous-wave, singly resonant optical parametric
oscillator,” Opt. Lett. |

13. | M. Vainio, J. Peltola, S. Persijn, F. J. M. Harren, and L. Halonen, “Thermal effects in singly resonant continuous-wave optical
parametric oscillators,” Appl. Phys. B |

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. | 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. |

16. | D. N. Nikogosyan, |

17. | A. V. Smith, |

18. | I. N. Ross, P. Matousek, G. H. C. New, and K. Osvay, “Analysis and optimization of optical parametric chirped
pulsed amplification,” J. Opt. Soc. Am. B |

19. | D. N. Schimpf, J. Rothhardt, J. Limpert, A. Tünnermann, and D. C. Hanna, “Theoretical analysis of the gain bandwidth for noncollinear
parametric amplification of ultrafast pulses,” J. Opt. Soc. Am.
B |

20. | J. Moses and S.-W. Huang, “Conformal profile theory for performance scaling of
ultrabroadband optical parametric chirped pulse amplification,” J.
Opt. Soc. Am. B |

21. | S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Numerical simulations for performace optimization of a
few-cycle terawatt NOPCPA system,” Appl. Phys. B |

22. | R. W. Boyd, |

23. | D. Zhang, Y. Kong, and J.-Y. Zhang, “Optical parametric properties of 523-nm-pumped
beta-barium-borate near the infrared absorption edge,” Opt.
Comm. |

24. | M. Bache, H. Guo, B. Zhou, and X. Zeng, “The anisotropic Kerr nonlinear refractive index of the
beta-barium borate (β-BaB |

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

26. | M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order
χ |

27. | A. Thai, C. Skrobol, P. K. Bates, G. Arisholm, Z. Major, F. Krausz, S. Karsch, and J. Biegert, “Simulations of petawatt-class few-cycle optical parametric
chirped-pulse amplification including nonlinear refractive index effects,”
Opt. Lett. |

28. | C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, and S. Lin, “New nonlinear-optical crystal:
LiB |

29. | 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 |

30. | A. E. Siegman, “How to (maybe) measure laser beam
quality,” OSA TOPS |

31. | A. L. Oien, I. T. McKinnie, P. Jain, N. A. Russell, D. M. Warrington, and L. A. W. Gloster, “Efficient, low-threshold collinear and noncollinear
β-barium borate optical parametric oscillators,” Opt.
Lett. |

32. | S. Demmler, J. Rothhardt, S. Hädrich, J. Bromage, J. Limpert, and A. Tünnermann, “Control of nonlinear spectral phase induced by
ultrabroadband optical parametric amplification,” Opt.
Lett. |

33. | S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystals for high average power second harmonic generation,” Proc. SPIE2989 (1997). |

**OCIS Codes**

(190.4400) Nonlinear optics : Nonlinear optics, materials

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 30, 2013

Revised Manuscript: November 27, 2013

Manuscript Accepted: November 27, 2013

Published: January 16, 2014

**Citation**

M. J. Prandolini, R. Riedel, M. Schulz, A. Hage, H. Höppner, and F. Tavella, "Design considerations for a high power, ultrabroadband optical parametric
chirped-pulse amplifier," Opt. Express **22**, 1594-1607 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1594

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### References

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- F. Tavella, A. Willner, J. Rothhardt, S. Hädrich, E. Seise, S. Düsterer, T. Tschentscher, H. Schlarb, J. Feldhaus, J. Limpert, A. Tünnermann, J. Rossbach, “Fiber-amplifier pumped high average power few-cycle pulse non-collinear OPCPA,” Opt. Express 18, 4689–4694 (2010). [CrossRef] [PubMed]
- J. Rothhardt, S. Demmler, S. Hädrich, J. Limpert, 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]
- R. Riedel, M. Schulz, M. J. Prandolini, A. Hage, H. Höppner, T. Gottschall, J. Limpert, M. Drescher, F. Tavella, “Long-term stabilization of high power optical parametric chirped-pulse amplifiers,” Opt. Express 21, 28987–28999 (2013). [CrossRef]
- B. Faatz, N. Baboi, V. Ayvazyan, V. Balandin, W. Decking, S. Duesterer, H.-J. Eckoldt, J. Feldhaus, N. Golubeva, K. Honkavaara, M. Koerfer, T. Laarmann, A. Leuschner, L. Lilje, T. Limberg, D. Noelle, F. Obier, A. Petrov, E. Ploenjes, K. Rehlich, H. Schlarb, B. Schmidt, M. Schmitz, S. Schreiber, H. Schulte-Schrepping, J. Spengler, M. Staack, F. Tavella, K. Tiedtke, M. Tischer, R. Treusch, M. Vogt, A. Willner, J. Bahrdt, R. Follath, M. Gensch, K. Holldack, A. Meseck, R. Mitzner, M. Drescher, V. Miltchev, J. Rönsch-Schulenburg, J. Rossbach, “Flash II: Perspectives and challenges,” Nucl. Instr. Meth. A 635, S2–S5 (2011). [CrossRef]
- H. Redlin, A. Al-Shemmary, A. Azima, N. Stojanovic, F. Tavella, I. Will, S. Düsterer, “The FLASH pump-probe laser system: Setup, characterization and optical beamlines,” Nucl. Instr. Meth. A 635, S88–S93 (2011). [CrossRef]
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- 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, I. Will, “Conceptual design of the laser system for the attosecond light pulse source,” “CLEO:2013 Technical Digest © OSA,” (2013).
- M. Schulz, R. Riedel, A. Willner, T. Mans, C. Schnitzler, P. Russbueldt, J. Dolkemeyer, E. Seise, T. Gottschall, S. Hädrich, S. Duesterer, H. Schlarb, J. Feldhaus, J. Limpert, B. Faatz, A. Tünnermann, J. Rossbach, M. Drescher, F. Tavella, “Yb:YAG Innoslab amplifier: efficient high repetition rate subpicosecond pumping system for optical parametric chirped pulse amplication,” Opt. Lett. 36, 2456–2458 (2011). [CrossRef] [PubMed]
- M. Schulz, R. Riedel, A. Willner, S. Düsterer, M. J. Prandolini, J. Feldhaus, B. Faatz, J. Rossbach, M. Drescher, F. Tavella, “Pulsed operation of a high average power Yb:YAG thin-disk multipass amplifier,” Opt. Express 20, 5038–5043 (2012). [CrossRef] [PubMed]
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- R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
- D. Zhang, Y. Kong, J.-Y. Zhang, “Optical parametric properties of 523-nm-pumped beta-barium-borate near the infrared absorption edge,” Opt. Comm. 184, 485–491 (2000). [CrossRef]
- M. Bache, H. Guo, B. Zhou, X. Zeng, “The anisotropic Kerr nonlinear refractive index of the beta-barium borate (β-BaB2O4) nonlinear crystal,” Optical Materials Express 3, 357–382 (2013). [CrossRef]
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- A. Thai, C. Skrobol, P. K. Bates, G. Arisholm, Z. Major, F. Krausz, S. Karsch, J. Biegert, “Simulations of petawatt-class few-cycle optical parametric chirped-pulse amplification including nonlinear refractive index effects,” Opt. Lett. 35, 3471–3473 (2010). [CrossRef] [PubMed]
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- J. Bromage, J. Rothhardt, S. Hädrich, C. Dorrer, C. Jocher, S. Demmler, J. Limpert, A. Tünnermann, J. D. Zuegel, “Analysis and suppression of parasitic processes in noncollinear optical parametric amplifiers,” Opt. Express 19, 16797–16808 (2011). [CrossRef] [PubMed]
- A. E. Siegman, “How to (maybe) measure laser beam quality,” OSA TOPS 17, 184–199 (1998).
- A. L. Oien, I. T. McKinnie, P. Jain, N. A. Russell, D. M. Warrington, L. A. W. Gloster, “Efficient, low-threshold collinear and noncollinear β-barium borate optical parametric oscillators,” Opt. Lett. 22, 859–861 (1997). [CrossRef] [PubMed]
- S. Demmler, J. Rothhardt, S. Hädrich, J. Bromage, J. Limpert, A. Tünnermann, “Control of nonlinear spectral phase induced by ultrabroadband optical parametric amplification,” Opt. Lett. 19, 3933–3935 (2012). [CrossRef]
- S. Seidel, G. Mann, “Numerical modeling of thermal effects in nonlinear crystals for high average power second harmonic generation,” Proc. SPIE2989 (1997).

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