**2. Recycling the pump energy**

pump an OPCPA allows higher peak intensity in the nonlinear medium as the damage threshold intensity of materials scales with the inverse square root of the pulse duration [6]. The high pump intensity makes it possible to achieve the required gain in a shorter crystal,

Further advantage with a short crystal is that the effect of transverse walk-off is reduced, the temporal contrast can be enhanced, and stretchers and compressors can be simpler. However, the crystal length does not decrease as rapidly as the pulse duration, so the temporal walk-off relative to the pulse duration increases for short pulses. A simple analytical analysis shows that the optimum pump-pulse duration to achieve a high conversion efficiency and a broad‐

Nevertheless, all these advantages of short-pulse-pumped OPCPA remain useless without an efficient, reliable, and powerful pump source. Such pump lasers are required to deliver highenergy near-1-ps pulses with near-diffraction-limited beam quality at repetition rates in the

Heretofore, due to the lack of suitable pump lasers, the few-cycle OPCPA delivered either high-energy pulses at a low repetition rate [8, 9] or low-energy pulses at a high repetition rate [10]. Nowadays, Yb-doped lasers in the thin-disk, fiber or slab geometries [1, 11–15] are capable of delivering high-energy, high average power pulses with ps-pulse duration. Among these laser technologies, the recent advances in Yb:YAG thin-disk lasers have started to fulfill the criteria for suitable pump sources for OPCPA systems and hold promise to change the current state of the art of OPCPA systems to few-cycle pulses with higher energy and average power

This chapter is devoted to the recent progress in Yb:YAG-pumped, few-cycle OPCPA systems. In Section 1, a brief overview on the fundamentals of OPCPA is presented. In Sections 2 and 3, novel techniques for increasing the conversion efficiency are discussed. In Section 4, a

In a medium with second-order nonlinearity, a high-energy photon (called pump) can decay to two newly generated photons with lower frequencies (called seed and idler). In the presence of initial seed photons, the decay of pump photons is stimulated and consequently more photons at the seed frequency are generated. The seed photons after amplification are named signal and the process is called optical parametric amplification (OPA). The frequency of the generated signal and idler photons is defined by the conservation of energy. However, the amplification bandwidth can be increased by fulfilling conservation of momentum between pump, signal, and idler pulses, which can be tuned by the type, thickness, and temperature of

To obtain a strong pump-to-signal and idler energy conversion, the spatial and temporal overlap between seed and pump pulses in the nonlinear medium should be maximized. The optimum temporal overlap between the pump and seed pulses can be ensured by temporal stretching of the seed pulses to the temporal window of pump pulses. This technique is the combination of chirped-pulse amplification (CPA) [17] and OPA, hence called optical para‐

technique for extension of the amplification bandwidth is discussed.

the nonlinear medium and also the geometry of the three interacting beams.

which leads to greater amplification bandwidth.

band gain is around 1 ps [7].

56 High Energy and Short Pulse Lasers

metric chirped-pulse amplification.

kHz to MHz range.

[1, 16].

In optical parametric amplification, the behavior of the gain over the length of the nonlinear medium can be divided into three main regions (**Figure 1(a)**). In the beginning, the energy of the amplified signal has an exponential growth due to the generation of the idler field that enhances the amplification process (region A). In region B, the gain drops gradually as the pump energy is reduced, and the growth of the signal power becomes approximately linear. When the pump beam has been locally depleted at some point in time and space, back conversion sets in and further reduces the gain. In region C, back conversion dominates, and the signal power drops. In the case of pulses with Gaussian spatiotemporal profile, the depletion mainly occurs at the center of the pulse, where the intensity is highest. Therefore, the back conversion already starts before the complete depletion of the pump. Because back conversion depends on both signal and idler beams, it can be reduced by removing the idler between the stages of a multistage OPCPA.

To explore this option, three different designs (as shown in **Figure 1(b)**) are simulated and compared using the SISYFOS code [23]. In all designs, the amplification takes place in a type-I BBO crystal, where the angle between the Optical axis and the signal is 22°, and the noncol‐ linear angle between the pump and the signal in the tangential phase-matching geometry is 2.7°. The pump have a Gaussian beam and pulse shape, and the seed have the Gaussian beam shape and a super-Gaussian spectrum of order 4, ranging from 600 to 1100 nm and linearly chirped to 1.1 ps pulse duration. Higher-order nonlinear effects and parasitic processes were not taken into account.

**Figure 1(c)** compares the three simulated OPCPA systems. The first configuration (Design 1 in **Figure 1(b)**) consists of a single OPCPA stage using a 2 mm thick BBO crystal, with 7 mJ of pump energy at a peak intensity of 80 GW/cm2 , which results in a conversion efficiency of 14%.

The second design (Design 2 in **Figure 1(b)**) has two stages, and the idler beam is removed between the two stages. This reduces back conversion in the second stage and allows operation in a regime with stronger pump depletion. Temporal and spatial overlap of the beams could be readjusted between the stages, and a further advantage with the two-stage design is that the phase-matching of the crystals can be tuned slightly differently to optimize the total bandwidth. The crystal lengths for the two stages are 1.2 and 0.7 mm, respectively. The second stage is pumped by the residual pump energy from the first stage resulting in a conversion efficiency of 34%.

**Figure 1.** (a) Qualitative behavior of OPCPA amplified energy over the length of the nonlinear medium. (b) Three OPCPA designs are discussed in the main text. Design 1 consists of one OPCPA stage. Designs 2 and 3 consist of two OPCPA stages, where the residual pump energy after the first OPCPA stage is reused in the second stage. In Design 3, the pump after the first amplification stage is resized to increase the pump peak intensity. (c) Calculated amplified sig‐ nal energy over the crystal length for the three different designs.

The third configuration (Design 3 in **Figure 1(b)**) is a two-stage OPCPA system similar to the second design except that the pump-beam size between the two stages is reduced to compen‐ sate the reduction in the pump intensity after the first stage of amplification and therefore the efficiency in the third design reaches 39%.

All three designs are capable of supporting the ultrabroad amplification bandwidth necessary for a few-cycle pulse durations. The detailed parameters of the simulations are shown in


**Table 1**. In what follows, the experimental realization of the third design is demonstrated and discussed. The third design is chosen as it supports the highest conversion efficiency in the above-mentioned study.

**Table 1.** Parameters used in simulations: *Lc*, crystal thickness; *Es* amp, amplified signal energy; *ϕp*, pump-beam diameter at full width at half maximum; *ϕs*, seed beam diameter at FWHM.

#### **2.1. System description**

#### *2.1.1. Front end*

in a regime with stronger pump depletion. Temporal and spatial overlap of the beams could be readjusted between the stages, and a further advantage with the two-stage design is that the phase-matching of the crystals can be tuned slightly differently to optimize the total bandwidth. The crystal lengths for the two stages are 1.2 and 0.7 mm, respectively. The second stage is pumped by the residual pump energy from the first stage resulting in a conversion

**Figure 1.** (a) Qualitative behavior of OPCPA amplified energy over the length of the nonlinear medium. (b) Three OPCPA designs are discussed in the main text. Design 1 consists of one OPCPA stage. Designs 2 and 3 consist of two OPCPA stages, where the residual pump energy after the first OPCPA stage is reused in the second stage. In Design 3, the pump after the first amplification stage is resized to increase the pump peak intensity. (c) Calculated amplified sig‐

The third configuration (Design 3 in **Figure 1(b)**) is a two-stage OPCPA system similar to the second design except that the pump-beam size between the two stages is reduced to compen‐ sate the reduction in the pump intensity after the first stage of amplification and therefore the

All three designs are capable of supporting the ultrabroad amplification bandwidth necessary for a few-cycle pulse durations. The detailed parameters of the simulations are shown in

nal energy over the crystal length for the three different designs.

efficiency in the third design reaches 39%.

efficiency of 34%.

58 High Energy and Short Pulse Lasers

The experimental OPCPA setup (as shown in **Figure 2**) consists of a Ti:Sa-based oscillator and amplifier followed by a broadband nonlinear seed generation scheme, a pump laser, a temporal jitter compensation system, three OPCPA stages, and a chirped-mirror compressor [24]. The Yb:YAG regenerative amplifier [25], optically synchronized with the OPCPA seed [26], delivers 16 mJ, 1.6 ps pulses at full width at half maximum (FWHM) at 3 kHz repetition rate and its frequency doubled output is used for pumping the OPCPA. However, due to the long optical beam-path difference between seed and pump pulses, timing fluctuations occur due to air turbulence, mechanical vibrations of optical components, temperature drifts, and the finite stability of the front end, which need to be compensated by an active stabilization system. The timing jitter in our system is reduced to a level of 24 fs (root mean square) by using an active stabilization system based on spectrally resolved cross-correlation between the stretched seed and the pump pulse [27].

The broadband OPCPA seed was generated by using a small portion of the output of the Ti:Sa multipass amplifier (Femtolasers GmbH), providing a spectral bandwidth of 60 nm (FWHM) centered at 790 nm. These pulses, containing 30 μJ of energy, focused on a 15 cm long hollow core fiber (HCF) with an inner diameter of 120 μm filled with 4.5 bar of krypton. The pressure of krypton in the HCF and the group delay dispersion (GDD) of the input pulse were optimized to obtain the maximum spectral broadening, covering a spectral range from 500 to 1050 nm. With this combination of parameters, an overall throughput of 10 μJ pulse energy in a neardiffraction-limited output beam containing the broad spectrum was achieved (**Figure 3(a)**).

**Figure 2.** Block diagram of the OPCPA system. The OPCPA broadband seed pulses are generated from a Ti:Sa regener‐ ative amplifier. The output of a Yb:YAG thin-disk amplifier, after frequency doubling, is used to pump the three OPC‐ PA stages. Finally, a chirped-mirror compressor is used for pulse compression of the broadband amplified pulses.

In order to measure the amount of introduced material dispersion, which needs to be com‐ pensated after the final OPCPA stage, the broadband seed was sent through the entire beam path without any pump. Pulse dispersion was caused over merely 5.5 mm beam path in BBO, 4 mm path length in SF57 glass, and over 10 m propagation in air. The stretched seed pulses were characterized by a multishot, second harmonic generation (SHG)-XFROG device incorporating a 20 μm thick BBO crystal cut at 29° as the nonlinear medium, while a fraction of the multipass amplifier's output provided the reference beam. From these measurements, a second-order spectral phase of 1433 fs2 evaluated at 850 nm was retrieved. This is in excellent agreement with the GDD introduced by the above components, evaluated as 1403 fs2 . The pulse duration of the seed pulses assuming a Gaussian fit for the retrieved time structure is 1.1 ps (FWHM), which ensures a sufficiently good temporal matching between the seed and pump pulses in the OPA stages.

For frequency doubling of the pump laser, a BBO crystal was used. Its high nonlinearity allowed the use of a relatively short crystal keeping the accumulated B-integral in the system negligible. Using a BBO crystal of 1.5 mm length, a conversion efficiency as high as 70% with a good beam quality was obtained. The high SHG efficiency confirms the excellent beam quality and clean output pulses of the regenerative amplifier. However, in order to definitely avoid problems related to the B-integral in the OPCPA stages, a 1 mm BBO crystal for the SHG was chosen, which resulted in a conversion efficiency of 57%.

#### *2.1.2. OPCPA stages and pulse compression*

The OPCPA setup consists of three stages. We added an OPCPA-based preamplifier stage in the experiment in order to boost the seed energy before the two power amplifier stages. This

With this combination of parameters, an overall throughput of 10 μJ pulse energy in a neardiffraction-limited output beam containing the broad spectrum was achieved (**Figure 3(a)**).

**Figure 2.** Block diagram of the OPCPA system. The OPCPA broadband seed pulses are generated from a Ti:Sa regener‐ ative amplifier. The output of a Yb:YAG thin-disk amplifier, after frequency doubling, is used to pump the three OPC‐ PA stages. Finally, a chirped-mirror compressor is used for pulse compression of the broadband amplified pulses.

In order to measure the amount of introduced material dispersion, which needs to be com‐ pensated after the final OPCPA stage, the broadband seed was sent through the entire beam path without any pump. Pulse dispersion was caused over merely 5.5 mm beam path in BBO, 4 mm path length in SF57 glass, and over 10 m propagation in air. The stretched seed pulses were characterized by a multishot, second harmonic generation (SHG)-XFROG device incorporating a 20 μm thick BBO crystal cut at 29° as the nonlinear medium, while a fraction of the multipass amplifier's output provided the reference beam. From these measurements,

duration of the seed pulses assuming a Gaussian fit for the retrieved time structure is 1.1 ps (FWHM), which ensures a sufficiently good temporal matching between the seed and pump

For frequency doubling of the pump laser, a BBO crystal was used. Its high nonlinearity allowed the use of a relatively short crystal keeping the accumulated B-integral in the system negligible. Using a BBO crystal of 1.5 mm length, a conversion efficiency as high as 70% with a good beam quality was obtained. The high SHG efficiency confirms the excellent beam quality and clean output pulses of the regenerative amplifier. However, in order to definitely avoid problems related to the B-integral in the OPCPA stages, a 1 mm BBO crystal for the SHG

The OPCPA setup consists of three stages. We added an OPCPA-based preamplifier stage in the experiment in order to boost the seed energy before the two power amplifier stages. This

agreement with the GDD introduced by the above components, evaluated as 1403 fs2

was chosen, which resulted in a conversion efficiency of 57%.

evaluated at 850 nm was retrieved. This is in excellent

. The pulse

a second-order spectral phase of 1433 fs2

*2.1.2. OPCPA stages and pulse compression*

pulses in the OPA stages.

60 High Energy and Short Pulse Lasers

**Figure 3.** (a) The seed spectrum and the amplified spectra of three OPCPA stages, normalized to the output energy of each stage. (b) and (c) Conversion efficiencies after the second and third stages, respectively. The conversion efficiency is defined as the net increase in signal energy divided by the input pump energy of stage two. (d) The detailed parame‐ ters of each OPCPA stage. The total efficiency after each stage is defined as the net increase in signal energy after the stage divided by the total pump energy of the OPCPA chain. Inset: amplified beam profile after the third stage [7].

stage is necessary to drive the following stages into saturation [7]. Therefore, 1 mJ of the frequency doubled output of the thin-disk amplifier was used to pump a 1.5 mm BBO crystal, and an amplified energy of 120 μJ and a 350 nm broad spectrum were achieved in the first stage (**Figure 3(a)**). Here, the OPCPA crystal length was chosen to minimize the superfluor‐ escence at the third stage [28].

The following two stages were designed for reaching the highest possible pump-to-signal conversion efficiency by controlling the idler energy and recycling the pump energy. Up to 7.3 mJ of the pump energy with the peak intensity of 80 GW/cm2 at 515 nm was used for the second OPCPA stage that employed a 2 mm thick BBO crystal. In this stage, an amplified pulse energy of 1.77 mJ was obtained. The thickness of the crystal at this stage is adjusted to stop amplification slightly below the saturation while preserving a good residual pump-beam quality.

Subsequently, the size of the remaining pump beam was reduced to increase the peak intensity to 80 GW/cm2 in the third amplification stage. Here, by employing a 2 mm thick BBO crystal, the amplified energy reached 2.5 mJ. In the last two OPCPA stages, an optical-to-optical conversion efficiency of >32% was achieved (**Figure 3(b)** and **(c)**), which to the best of our knowledge is the highest reported conversion efficiency for few-cycle OPCPA systems [9, 10, 29, 30]. No measurable superfluorescence background was observed when blocking the signal beam in front of the first stage.

The simulated boost efficiency in our design study is in good agreement with the experimental results. Quantitative comparison shows, however, that higher conversion efficiencies were yielded for a shorter crystal in the simulation than in the experiment. We relate the deviation from the theoretical prediction to a slight ellipticity in our pump beam, caused by the com‐ pressor of the Yb:YAG amplifier, which limited the effective interaction area between pump and signal beams.

**Figure 4.** (a) Retrieved temporal intensity of the compressed pulses after 12 reflections in a double-angle chirped-mir‐ ror compressor measured by SH-FROG. The pulse is compressed to 9.5 fs and holds Fourier transform limit of 5.7 fs. (c) The calculated GD of retrieved spectral phase for the pumped (blue curve) and unpumped (green curve) OPCPA chains.

The 350 nm broad amplified signal measured with the Si-based spectrometer supports a transform-limited pulse duration of 5.7 fs. Preliminary compression, by using 12 reflections on double-angle chirped mirrors with −30 fs<sup>2</sup> GDD per reflection, resulted in a pulse duration of 9.5 fs (FWHM). The compressor had a total throughput of 80%. The retrieved temporal intensity profile and retrieved residual group delay (GD) of the pulses are shown in **Fig‐ ure 4(a)** and **(b)**. Our analytical study shows that the pulse can be compressed to 7 fs by adding the GD of a 0.5 mm thick fused silica to the measured GD of the pulse. However, to investigate the origin of the fine oscillation in the retrieved GD, a frequency resolved optical gating (FROG) measurement of the whole OPCPA chain was performed, but this time without any pumping. The comparison between two cases in **Figure 4(b)** shows that oscillations were enhanced by amplification but did not originate from the OPCPA phase [31]. The peak of the GD is at 760 nm, which coincides with the wavelength of Ti:Sa amplifier's pulses and the peak in the spectral intensity of the seed pulses after the HCF. Therefore, it can be concluded that the measured residual higher-order chirp is due to the self-phase modulation in the HCF, OPCPA phase, and the residual oscillations in group delay dispersion of the double-angle chirped-mirror compressor [32, 33]. The higher-order dispersion and the satellite pulses can be compensated by using specially designed chirped mirrors for this system along with the implementation of spectral smoothing techniques, such as cross-polarized wave generation [34] after the HCF.

The demonstrated highly efficient compact OPCPA system delivers broadband pulses with 2.5 mJ energy supporting a two-cycle pulse at a repetition rate of 3 kHz. Our simple OPCPA design shows that, by extraction of the idler energy and optimization of the pump peak intensity, a higher conversion efficiency can be achieved. The output of the system ensures to be compressible to its two-cycle transform limit by using specially designed chirped mirrors. The system also has the capability to operate with a stabilized carrier envelope phase (CEP) by stabilizing the Ti:Sa oscillator. These features make the reported OPCPA system a suitable driver for high harmonic generation (HHG) [35].

In the next section, an alternative method to achieve high conversion efficiency as well as uniform amplified spectrum is discussed.
