1. Introduction

Nowadays, ultrashort laser pulses in the few optical cycle regime can be routinely generated and have found widespread applications in science and industry [1]. For example, the generation of high-order harmonics [2] substantially depends on the availability of high-peak power laser systems with ultrashort pulses. Such harmonics have been used to generate pulses on the attosecond (10^-18 s) time scale [3]. Though, this has let to a deeper understanding of atomic and molecular dynamics the applicability of extreme ultraviolet (EUV) radiation is even more divers, e.g. for imaging purposes. Recently, a lensless imaging technique based on the coherent EUV radiation from high harmonics has been presented indicating the possibility to observe nanometer scale structures [4].

However, commonly the high harmonic generation (HHG) is driven by Ti:Sapphire based laser systems that are limited in their repetition rate to some kHz due to thermo-optical effects in the gain medium [5].

In contrast, average power scalability can be achieved by the means of amplifier systems based on optical fibers typically doped with Yb. Due to the long fiber length they offer an increased ratio of surface to active volume resulting in superb thermo-optical properties. State-of-the-art fiber chirped pulse amplification systems with 131W of average power [6] or mJ pulse energy [7] have been presented lately. Due to their limited gain bandwidth Yb-doped fiber laser systems can not provide pulses of a few tens of femtosecond, though [8].

Average power scalability and the generation of ultrashort pulses can be combined by an optical parametric amplifier (OPA). Such devices offer an enormous amplification bandwidth of up to 200 THz especially in noncollinear geometry [9] or at degeneracy [10, 11]. Additionally, they can provide high gain (10² to 10⁴) in just a few mm crystal. Consequently, nonlinear phase distortion are negligible. Moreover, due to the nonlinear interaction itself no energy is stored in the crystal. Hence, only parasitic absorption leads to heating of the crystal, but is immaterial with todays quality of nonlinear crystals so that OPA is capable of producing ultrashort pulses at high average powers.

A combination of fiber based laser systems with parametric amplifiers is promising and has been presented with typical pulse energies below 1µJ [12, 13, 14].

Recently, we have presented an optical parametric amplifier at degeneracy generating 37µJ with 52 fs pulse duration at 97 kHz resulting in 500MW of peak power [15].

 

Fig. 1. Schematic setup of the fiber amplifier pumped degenerated optical parametric amplifier.

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In this contribution we report on an improved degenerated optical parametric amplifier. The overall goal of this experiment was not only to increase the peak power, but also to generate pulse durations shorter than 30 fs, since many applications such as HHG require these pulse parameters. The OPA is pumped by the frequency doubled output of a state-of-the-art fiber chirped pulse amplification system (FCPA) similar to the one reported in [7]. A schematic of the experiment is shown in Fig. 1. Both, the FCPA and the OPA are seeded by the same Yb:KGW oscillator, in contrast to the previous experiment. Additional spectral broadening of the OPA seed in a polarization-maintaining-step-index fiber provides enough bandwidth for ultrashort pulse generation. Temporal synchronization is achieved by a multipass cell configuration with 45m optical path length. Two 1mm BBO (OPA 1 and OPA 2) crystals are used to amplify the seed to 90µJ of pulse energy. Compression with chirped mirrors results in pulses as short as 29 fs and 81µJ pulse energy yielding a peak power of 2GW.

2. Pump pulse generation for optical parametric amplification

For the generation of the pump pulses a state-of-the-art fiber chirped pulse amplification system similar to the one presented in [7] was used. In contrast to the system in [7] we replaced the seed oscillator and the compressor gratings to obtain shorter pulses and enhanced compressor throughput.

 

Fig. 2. (a) Autocorrelation trace of the FCPA system at 1 mJ compressed output energy (red) and corresponding Gaussian fit (black). (b) Autocorrelation trace of the frequency doubled output of the FCPA system. The pulse energy is 550µJ.

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A Yb:KGW laser oscillator operating at 10MHz repetition rate with 350 fs pulse duration and 380 nJ of pulse energy at 1030nm central wavelength is used as seed for the FCPA system and the parametric amplifier. After the oscillator the repetition rate is reduced by the means of a quartz-based-acousto-optical modulator (AOM) with 55% diffraction efficiency and finally set to 30 kHz for the presented experiment. Subsequently, we used a 50% beam splitter to steer the beam into the dieletric grating based Öffner type stretcher. The remainder passing through this beam splitter is used for signal generation described more in detail in section 3. The beam emerging from the stretcher has a temporal pulse duration of 2 ns and is coupled to a polarization-maintaining-photonic crystal fiber used as pre-amplifier. The power amplifier consists of a rod-type-photonic crystal fiber delivering the necessary pulse energy [16]. Finally, pulse compression is achieved by an enhanced dieletric grating compressor with 80% throughput efficiency. For this particular experiment we worked with 1mJ of compressed pulse energy with an autocorrelation width of 900 fs (see Fig. 2(a)) corresponding to a pulse duration of 650 fs assuming a Gaussian pulse shape. Estimating to have 80% of pulse energy in the central peak results in 1.2GW of peak power. For efficient second harmonic generation the beam size is set to 2mm by the means of a Gallilean telescope. This results in about 50GW/cm ² of infrared intensity in a 1mm BBO crystal used for the generation of the OPA pump. A conversion efficiency of 55% could be achieved yielding a pulse energy of 550µJ at an average power of 16.5W. The corresponding autocorrelation trace of the second harmonic pulses is shown in Fig. 2(b) and measured to be 700 fs equaling an OPA pump pulse duration of 500 fs.

3. Temporal synchronization and signal generation

As described in section 2 a beam splitter transmits a portion (~100nJ) of the oscillator whose repetition rate has already been down-counted by the AOM. For the parametric amplification process it is necessary to overlap the seed and pump pulses, both temporally and spatially. While spatial overlapping is easy to achieve in this experiment temporal synchronization is more challenging. The 50% reflected of the beam splitter are amplified in our FCPA system to generate the pump pulse energy for the parametric amplification stages passing about 45m of optical path length. Consequently, the seed signal needs to be delayed according to the optical path of the pump. To reduce required space and maintain a reasonable beam size and quality a multipass cell (MPC) was used. It consists of a focusing mirror and a flat mirror as depicted in Fig. 3. We used a focusing mirror with a radius of curvature of 750mm. It is placed 350mm away from the flat mirror, hence, the beam is imaged every roundtrip avoiding divergence due to diffraction. The MPC is operated such that the beam also rotates on the mirrors (see upper right of Fig. 3) creating sufficient optical path length. Coupling to the MPC is achieved by a small mirror that is cut to the smallest possible size. With this configuration we were able to match pump and signal temporally.

 

Fig. 3. Setup of the multipass cell delaying the OPA seed signal. The upper left sketch shows the experimental setup used. Simulations with the ray tracing software Zeemax of the optical path (bottom) and the beam positions on the focusing mirror (upper right) are shown.

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To yield ultrashort pulses emphasize is put on the generation of a suitable seed signal for the optical parametric amplifier. Most commonly a broadband signal for parametric amplification is generated either by filamentation [17] or spectral broadening via self-phase modulation in optical fibers [18]. In [15] we have presented spectral broadening with a small fraction of the FCPA output which limits the achievable pulse duration, since the temporal pulse shape is distorted due to nonlinearity during the amplification process. Hence, to have a clean temporal pulse profile for spectral broadening we decided to use the Yb:KGW oscillator itself. Furthermore, we also expect better compression of the OPA output due to the input pulse quality.

The oscillator provides near transform-limited sech² pulses with a pulse duration of about 350 fs. Those pulses are delayed by the multipass cell described above and subsequently coupled into a polarization maintaining step index fiber with 6µm core diameter. About 40 nJ of pulse energy were coupled into the fiber. To find the best experimental setup we performed numerical simulations based on a split-step-fourier method [19] including second and third order dispersion, self-phase modulation, Raman response and self-steepening. Different fiber lengths (2 cm–20 cm) were tested and compression was achieved by chirped mirrors with a group velocity dispersion (GVD) of either -100 fs ² or -250 fs ² without amplification. Better pulse quality with higher peak power was obtained by using -100 fs ² chirped mirrors (Fig. 4), since their GVD is constant over a larger spectral range (980 nm–1130 nm) compared to the -250 fs ² mirrors which have a constant GVD between 1000 nm and 1080 nm. Figure 4 shows the peak power of the compressed pulses and the shortening of the pulses with respect to the fiber length used for self-phase modulation. The value τ ₀/τ describes the ratio of the input pulse duration τ ₀ which is 350 fs to the compressed pulse duration τ. The highest peak power combined with the shortest pulses was obtained for a fiber length of 10 cm.

 

Fig. 4. Numerical simulation for optimized pulse compression using chirped mirrors with a GVD of -100 fs ². The peak power (black squares) of the compressed pulses and the ratio of the input pulse duration τ ₀=350 fs to the compressed pulse duration τ (red triangles) with respect to the fiber length are shown.

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However, for compression at least 48 bounces on the chirped mirrors (-100 fs ²) are necessary. Since we decided to use a chirped mirror compressor for a simple experimental setup this value seems not practical. Additionally, the compressor losses are expected to be far beyond the theoretical optimum of 95 %, since beam clipping can occur in the mirror stage.

 

Fig. 5. Spectrum broadened by self-phase modulation in 6 cm of polarization maintaining step index fiber with 6µm core diameter (black) and corresponding numerical simulation (red dots).

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Finally, we decided to use a combination of -100 fs ² and -250 fs ² chirped mirrors for compression and a fiber length of 6 cm as tradeoff between ultrashort pulses and experimental simplicity. Our numerical simulations indicate that such a setup is in principle capable of generating pulses in the 30 fs range with clean temporal pulse shape. Figure 5 shows the experimental spectrum of a 40 nJ input pulse after 6 cm of polarization maintaining step index fiber with the corresponding numerical simulation indicating a spectral bandwidth of 68 nm.

4. Two stage optical parametric amplifier

For efficient conversion in an optical parametric amplifier the design of this device has to be optimized carefully. Due to the Gaussian profile of the interacting pulses, both temporally and spatially, conversion efficiency is reduced. Moreover, the nonuniform parametric gain caused by the spatial Gaussian profile can lead to an effect called gain-narrowing [20]. Since, the parametric gain is higher in the central parts of the Gaussian pump beam the signal beams tend to narrow during the amplification process. This can cause poor beam quality, because of backconversion in the central parts, or lead to reduced conversion efficiency, since the tails of Gaussian beams are not converted.

This problem can be overcome in a two stage optical parametric amplifier. In [20] it is suggested to work with a pre-amplifier operating in the high gain regime and a power amplifier with low gain and high conversion. Lately, we have shown that this approach can yield superb conversion efficiency and good beam quality [15].

The concept of a two stage parametric amplifier is even more important for the experiment presented here. Since we decided to use the oscillator output for spectral broadening (see section 3) the available seed power is about 1.2mW at 30 kHz. Considering the outcome that is desired an overall gain factor of more than 30 dB is necessary.

 

Fig. 6. Experimental setup of the two stage degenerated parametric amplifier. (HWP: Half wave plate, QWP: Quarter wave plate)

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The experimental setup of the degenerated parametric amplifier stages is shown in Fig. 6. The first amplifier stage consists of a 1mm BBO crystal and is pumped by the frequency doubled output of the FCPA system at an average power of 16.5W. To achieve a high gain in the short crystal length a Gallilean telescope is used to reduce the pump beam diameter to about 450µm resulting in a peak intensity of 300GW/cm ² which is close to the damage threshold. This high intensity is necessary to achieve a high gain and maintain a good seed signal quality [20]. Due to the interaction of gain-guiding and diffraction the seed signal remains nearly Gaussian (Fig. 8). This first stage is capable of amplifying the seed signal to 60µJ of pulse energy corresponding to 1.8W of average power which is already a gain factor of 31 dB. However, due to the large pump depletion of 22% the spatial beam profile of the pump is clearly distorted. Since the remainder of the pump is used to pump another optical parametric amplifier the first stage was optimzed for the best depleted pump beam profile.

 

Fig. 7. (a) Spectra of the seed (black) after the first amplifier (red) and after the second amplifier (blue). (b) Autocorrelation trace of the compressed OPA output(black), Fourier transform of measured spectrum (red dots) and Fourier transform with additional third order dispersion (blue).

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The power amplifier stage consists of another 1mm BBO crystal. The pulse duration of the seed signal after the first stage is matched to the pump pulse duration by a pair of chirped mirrors with a GVD of -250 fs ² and the beam diameters are adjusted for efficient conversion. The pump intensity is set to 30GW/cm ². Finally, we were able to amplify the signal to 90µJ of pulse energy which corresponds to 16% conversion efficiency from pump to signal. The lower conversion efficiency is due to the degraded pump beam quality, both temporally and spatially, after the first amplifier stage which is inevitable, because a high gain is needed. Figure 7(a) shows the corresponding spectra of the seed signal (black), the signal after the pre-amplifier (red) and after the power amplifier (blue). Since, the optical parametric amplifiers are operated in a saturated amplification regime and typically have a large amplification bandwidth the spectral modulation of the seed spectrum is reduced. Furthermore, the bandwidth is increased to 74 nm.

After collimating the output of the second amplifier stage the pulses are compressed by a sequence of chirped mirrors. As mentioned in section 3 a combination of mirrors with a GVD of -100 fs ² and -250 fs ² is used. Applying a GVD of -3600 fs ² results in pulses with an autocorrelation width of 42 fs (black line in Fig. 7(b)). A deconvolution factor of 1.45 is found by stretching the Fourier transform of the measured spectrum to the autocorrelation width by third order dispersion. Therefore, the pulse duration is 29 fs which is only slightly above the transform limit of 27 fs (red dots in Fig. 7(b)). The compressor efficiency is measured to be 90% yielding a pulse energy of 81µJ. The blue curve in Fig. 7(b) shows the autocorrelation trace of the Fourier transform of the measured spectrum that is stretched by TOD to the corresponding width. According to our simulations this blue curve corresponds to a pulse peak power of 2.16GW. The black curve shows some additional wing structure that is due to higher order phase terms. Based on this a pulse peak power of 2GW is estimated corresponding to 78% of the Fourier limit.

Far field beam profiles of the seed signal after the spectral broadening, the first amplifier and the second amplifier are shown in Fig. 8. No significant superfluorescence has been observed and all amplifier stages have been optimized for best signal beam quality. A measurement of the beam quality was performed with a commercial device (4σ-method) resulting in M ² values of M ² _x=1.79 and M ² _x=1.77. With this outstanding beam quality HHG is feasable, e.g. focus a 2mm collimated beam with a corresponding peak power of 2GW with a focal length of about 55mm to an intensity of 10¹³ W/cm ². Fig. 8. Far field beam profiles of the signal after the spectral broadening a), the first amplification stage b) and the second amplification stage c). Note that beam diameters are different due to scaling of the images.

 

Fig. 8. Far field beam profiles of the signal after the spectral broadening a), the first amplification stage b) and the second amplification stage c). Note that beam diameters are different due to scaling of the images.

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5. Conclusion and outlook

A two stage degenerated optical parametric amplifier driven by a state-of-the-art FCPA system with 1mJ pulse energy and a pulse duration of 650 fs is presented. It deliveres 81µJ with a pulse duration of 29 fs at 30 kHz resulting in a peak power as high as 2GW. The conversion efficiency of pump to signal is 16% with an optimzed two stage design.

In addition to a pulse shortening factor of 22 we also increased the peak power of the FCPA to 2GW after the chirped mirror compressor. Major improvements compared to our recent experiment [15] have been successfully demonstrated. Especially further scaling towards the 100µJ level combined with even shorter pulses has been shown. To our knowledge this is highest peak power and pulse energy ever reported for a fiber laser based ultrashort optical parametric amplifier.

Yet, further scaling is possible such as increasing the conversion efficiency. As mentioned in section 4 the degradation of the pump pulse lowers the conversion in the second amplifier stage. To overcome this obstacle the generation of several pump beams with different pump pulse energies is possible and commonly used in todays high peak power optical parametric chirped pulse amplification (OPCPA) systems [21]. Scaling to shorter pulses with pulse durations below 20 fs and clean temporal pulse shape can be achieved by an OPCPA system based on a Ti:Sapphire oscillator synchronized with a FCPA system [13]. Further increase of the average power is feasible by the use of kW scale FCPA systems. In summary, ultrashort pulse systems with high repetition rates and high peak powers are within reach.