1. Introduction

The development of an operationally robust and cost-efficient ultrashort pulse laser system at a wavelength of 1030 nm is motivated by its application for near critical density probing of relativistic laser plasma interactions [1] at full pump laser power on target. With a high contrast Petawatt-scale Ti:Sapphire laser [2] driving plasma processes in solid targets the probe has to fulfill an essential set of conditions: pulse synchronized operation at a wavelength far off the fundamental (800 nm) or any harmonic of the pump; operation at the millijoule energy level to compete with the strong plasma self-emission; and a pulse duration matching the scale of the temporal pulse contrast of the ultrafast drive laser pulse [2,3] in the 100 fs range. As average power and thus pulse repetition rate demands are limited by the driver technology to below 100 Hz no special emphasis is given to this point but instead on simplicity of the system. Femtosecond laser systems based on rare-earth doped gain media are the best candidates to fulfill the required needs. Off-the-shelf available NIR laser sources, optimized for high average power output, have previously been limited either in terms of their output pulse energy in the range of 200 $\mu$J or in their pulse duration to around 400 fs. Trivalent ytterbium doped host materials can be efficiently pumped with laser diodes operating from 940 nm to 980 nm and directly support laser pulses below 300 fs. Recently, attractive pulse parameters (2 mJ pulse energy at a duration of 200 fs) were reached with Yb$^{\textrm {3+}}$:YAG but relying on intra-cavity nonlinear spectral broadening by self-phase modulation [4] and sizeable equipment in thin disc technology supporting 200 W average power. These nonlinear effects strongly affect the temporal pulse shape and the number of round-trips has to be fixed to get a short pulse. The shortest pulse duration of 97 fs was obtained at a pulse energy of 24 $\mu$J with nonlinear spectral broadened regenerative amplifier using Yb$^{\textrm {3+}}$:CaAlGdO$_4$ as gain material [5], whereas the pulse duration remained above 300 fs at the mJ level [6] without nonlinear spectral broadening. A pulse energy of 2 mJ and a pulse duration of 112 fs were achieved with a ps-CPA system based on an Yb$^{\textrm {3+}}$:glass regenerative amplifier [7]. However, Yb$^{\textrm {3+}}$:glass is too limited in repetition rate compared to crystalline gain media. Millijoule regenerative amplifiers using Yb$^{\textrm {3+}}$:CaF$_2$ based on classical Offner stretcher / Treacy compressor concepts were so far shown with pulse duration above 180 fs [8–11], yet lack in compactness and simplicity.

Recently, the availability of chirped volume Bragg gratings (CVBG) [12] opened the path for robust, alignment free and straight forward constructions of hybrid stretcher/compressor elements. An Yb$^{\textrm {3+}}$:CaF$_2$ CPA system based on a CVBG was presented with an additional grating compressor for dispersion correction to support a pulse duration of 400 fs at a spectral bandwidth of 6 nm [6]. Alternatively, a matched pair of chirped fiber Bragg grating stretcher and CVBG compressor was applied [13].

Combining the advantages of these approaches, we present a laser system tailored to the application parameters and robust in operation. The system is designed as an Yb$^{\textrm {3+}}$:CaF$_2$ regenerative CPA system with pulse stretching and compression deploying a single CVBG. In comparison to a separate stretcher and compressor geometry any dispersion ripple [14] of a CVBG or fiber-based equivalent is thus self-compensated. A set of chirped mirrors (CM) is used for compensation of additional dispersion leading to a final pulse duration of 162 fs. To counteract gain narrowing during amplification while allowing for flexible tuning of laser parameters, linear spectral broadening using quartz-birefringent filters (QBF) [15] is applied. In the linear broadening case the gain versus wavelength is flatten by introducing spectral loss inside the cavity and the gain becomes constant for all wavelength. Robust meant that the system is insensitive to pulse duration fluctuations due to the fact that the dispersion management is only done be chirped mirrors and the CVBG. Therefore, the laser system is easily to align and do not need to optimized so often. Additionally, it has to sustain harsh environment conditions of a high intensity laser plasma experiment (e.g. EMP, vibrations, stray light).

2. Experimental setup

Figure 1 shows the setup of the regenerative CPA system. Seed pulses are generated in a Kerr lens mode-locked Yb$^{\textrm {3+}}$:KGW oscillator (Flint, Light Conversion) with a pulse duration of 60 fs, a bandwidth of 25 nm centered at 1033 nm, a pulse energy of 10 nJ, and a repetition rate of 78 MHz. Subsequently, an optical isolator, a pulse picker (DKDP Pockels cell) as well as a beam collimation telescope are placed. The pulses are then coupled into the stretcher/compressor unit (see Fig. 1(b)), which consists of a volume Bragg grating in reflecting geometry with a period that gradually varies along the direction of the beam propagation.

 

Fig. 1. Experimental setup: (a) regenerative amplifier, (b) front-end chain, (c) stretcher/compressor setup (d) chirped mirror pairs; OSC, fs oscillator; FI, FR Faraday isolator/rotator; TFP, thin-film polarizer (66 $^{\circ }$); $\lambda$/4, $\lambda$/2, quarter/half-wave plate; PC1, PC2, Pockels cells; T1, T2, spherical lens telescope; CVBG, chirped volume Bragg grating; LD, 10 W fiber coupled laser diode; QBF, quartz birefringent filter (d = 2.5 mm); L1, L2, plan-convex lenses (f1 = 75 mm, f2 = 150 mm, Ø = 25 mm, AR 0$^{\circ }$ 900–1000 nm); DM, dichroic mirror (AR 0$^{\circ }$ 920–990 nm, HR 0$^{\circ }$ 1020–1070 nm); M0, silver mirror; M1, dielectric concave mirror (HR 0$^{\circ }$ 1010–1060 nm), radius of curvature: 500 mm; M2, dielectric flat mirror (HR 0$^{\circ }$ 1010–1060 nm); M3, dielectric concave mirror (HR 0$^{\circ }$ 1010–1060 nm), radius of curvature: 2000 mm; M4, M5, dielectric plane turning mirrors (HR 45$^{\circ }$ 1010–1060 nm); CM1–CM6, dielectric plane chirped mirrors (HR 0$^{\circ }$ 940–1100 nm), GDD1,2 = 0 fs$^2$, GDD3 = -550 fs$^2$, GDD4 = -250 fs$^2$, GDD5 = 0 fs$^2$, GDD6 = -550 fs$^2$ (for optimized output pulse duration); footprint size: 900 $\times$ 600 mm$^2$.

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Here, a 45 mm long chirped volume Bragg grating (CVBG, OptiGrade Corp.) with an aperture of 5 $\times$ 5 mm$^2$ serves as a compact pulse stretcher yielding a pulse duration of 480 ps (i.e. stretching factor of 22 ps/nm). For the present design a hard clip bandwidth of 22 nm centered at 1029 nm constrains the Fourier limit to 145 fs [16].

Polarization coupling is performed by quarter-wave plates providing beam separation at the thin film polarizers (TFP). The CVBG is operated in normal incidence configuration. Chirped mirrors before and after amplification perform compensation of the remaining group delay dispersion (GDD) and a second telescope is used for mode-matching (see Fig. 1(d)).The regenerative amplifier (RA) is pumped by a 10 W fiber coupled laser diode (Lumics) with a 105 $\mu$m core diameter and a numerical aperture of 0.15. The laser medium is glued onto a water cooled copper heat sink (T$_{water}\,=\,15^{\circ }C$). A lens telescope with a magnification factor of 2.0 images the fiber output onto the gain medium. The Yb$^{\textrm {3+}}$:CaF$_2$ crystal (CIMAP, Université de Caen, France) has a thickness of 2.5 mm, a diameter of 12.5 mm, a wedge of 1$^{\circ }$ and an Yb$^{\textrm {3+}}$-concentration of 4.5 at.%. With the given laser diode (spectral width of 7 nm and center wavelength of 978 nm) approximately 95% of the pump light is absorbed. The resonator configuration of the RA with a length of 1.36 m, two concave mirrors (M1 and M3) and a distance of 265 mm between M1 and the gain medium results in a focal beam radius of 140 $\mu$m (1/e$^2$) at the gain medium. The angular dispersion of 0.1 $\mu$rad/nm due to the wedged gain medium is small enough to be neglected in comparison to the local divergence of the laser beam which is in the mrad range.

A quartz birefringent filter (QBF) with a thickness of 2.5 mm is used for spectral gain shaping during the regenerative amplification. The modulation depth as well as the center wavelength of the spectral losses introduced with a QBF can be controlled by tuning the tilt and rotation angle of the crystal, while its thickness determines the bandwidth of the spectral dip [17]. In addition, the RA incorporates a DKDP Pockels cell, and two CM for a coarse compensation of the total dispersion per cavity round trip. A DKDP (10.6 fs$^2$ mm) cell was chosen due to its small GDD compared to BBO (459 fs$^2$ mm) or RTP (135.7 fs$^2$ mm) at similar crystal lengths. The use of intra-cavity CM enables the compensation of accumulated GDD of up to 10$^5$ fs$^2$, although the practical limit of an optical coating is around -2000 fs$^2$.

3. Results

In the following the performance of the laser system is discussed. Fig. 2(a)) shows the near field output beam profile of the RA with a beam size of 1.5 mm (FWHM) and an ellipticity of 0.91. After propagation through the CVBG the near field was slightly intensity modulated in the x-direction (see Fig. 2(b)), while the modulation period increased at further beam propagation (see Fig. 2(c)). It has to be mentioned that the orientation of the fringes is connected to the interference pattern (of a convergent and a divergent optical beam [12]) during the recording of the CVBG on manufacturers site. A more detailed information can be found in Ref. [12]. However, the far field profile remains homogeneous and Gaussian shaped (see Fig. 2(d)), while its spot size and the M$^2$-value of the beam were slightly increased. Beam caustic analysis with a CCD behind a focusing lens gave a M$^2<1.24$ for both axes, while an M$^2<1.07$ of the RA was measured in front of the CVBG. Here, a quite good beam quality was demonstrated even after pulse compression. A maximum output energy of 1 mJ for stretched, 360 ps long pulses was achieved with the RA, while a pulse energy of 910 $\mu$J was measured after recompression (total throughput efficiency of the CVBG: 88%). Fig. 3(a) shows the pulse energy versus pump power as well as its dependence on the required number of round trips, where gain saturation was achieved at a constant seed pulse energy. The RA was pumped continuously to ensure thermal stability for minimized shot-to-shot errors at synchronized operation to the drive laser at 800 nm. Due to the fluorescence lifetime of 2.4 ms for Yb$^{3+}$:CaF$_2$ [18] the pulse energy remained constant up to a repetition rate of 200 Hz. Above 1.1 mJ laser induces damages on the gain medium increases strongly. This corresponds to fluences larger than 3.2 J/cm$^2$ on the used crystal with given surface quality. The damage threshold slightly varies over the aperture due to small polishing errors and scratches, while a relatively small beam diameter helps to find perfect spots. The spectral data was measured with an optical spectrum analyzer (Yokogawa AQ6370D) having a resolution of 20 pm. Figure 3(b) shows the input spectrum of the RA (osc + CVBG), the output spectrum for the amplified ultrashort pulses (amplified), the output spectrum for the cavity-dumped mode (cavity-dumped) of the RA as well as the spectral transmission of the CVBG for cavity-dumped mode (cd + CVBG). The maximum input spectrum is $22\,$nm, which corresponds to the hard clip of the used CVBG. An output spectrum of the amplified pulses with a bandwidth of $16.2\,$nm (FWHM) and two local peaks at $1029\,$nm and $1040\,$nm was obtained with the RA at spectral gain shaping with an attenuation centered at $1037\,$nm. A similar spectral shape with a total bandwidth of $20\,$nm (FWHM) was measured in cavity-dumped operation mode, unrestricted by the spectral hard clip due to the CVBG. Here, the CVBG band can be better matched to the gain band of the laser material for further improvement. However, the minimum pulse duration of a $22\,$nm rectangular spectrum (CVBG hard clip) is approx. $145\,$fs. Without spectral shaping the laser tends to operate at a center wavelength of close to 1032 nm with a bandwidth of $<$6 nm or a Fourier limit of $>$270 fs, respectively (not shown in the figure). We used a single shot second-order autocorrelator (called TiPA from Light Conversion) to determine the intensity AC traces. Figure 4(a) shows the influence of the group delay dispersion (GDD) of the intra-cavity chirped mirrors CM5 and 6 on the output pulse duration leading to a minimum at -550 fs$^2$. This corresponds to a GDD = -1100 fs$^2$ per round trip or 3 $\cdot$10$^5$ fs$^2$ in total, incorporating two reflections on the mirrors as a coarse chirp compensation. The data in Fig. 4(a) was obtained by measuring the autocorrelation (AC) width as function of the number of cavity round trips for different GDD configurations of CM5 and 6. The plotted values represent linear fit parameters of these curves. A certain independence of the pulse duration from the number of round trips would be favorable for a flexible adjustment of the output pulse energy (in analogy to Fig. 3(a)). With a fine adjustment around the identified minimum, we found a GDD = -800 fs$^2$ (or -1600 fs$^2$ in total) for further compression with the following additional chirped mirrors CM1 – 4 (see Fig. 4(b)). The fitting curves in Fig. 4(a) and (b) correspond to the square root function of the pulse duration vs. the applied GDD (or $\phi ''$ of eq. (12.26) in [16]). Here, the GDD-values of the available CM varied from 0, -250, -550, to -1300 fs$^2$. A combination of the individual CM was chosen to generate the desired GDD. Numerical estimation gave a GDD of +715 fs$^2$ per round trip for all transmission optics of the RA, including GDD$_o$ = 10.6 fs$^2$/mm at 1030 nm for DKDP. It has to be mentioned that the GDD values of the optical coatings apart from the CM were unspecified and might vary up to 100 fs$^2$ per component.

 

Fig. 2. Near field beam profiles of the regenerative amplifier with a beam size of 1.5mm (FWHM): (a) in front of the CVBG, (b) directly behind the CVBG, (c) after CVBG and 150 mm propagation; (d) far field beam profile after the CVBG focused with a spherical lens (f = 400 mm).

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Fig. 3. (a) Output pulse energy and round trips vs. pump power of the regenerative amplifier, (b) input (black) and output pulse spectra of the regenerative amplifier in cavity-dumped (cd) and amplifying (red) operation while the CVBG defines the hard clip.

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Fig. 4. (a) The autocorrelation (AC) width increase per cavity round trip vs. the GDD introduced by different configurations of CM5 and 6, (b) AC width of the ACF vs. the total GDD of CM1–4, (c) AC trace of the amplified pulses (TiPA) and of the pulses obtained with the Wizzler, values given in FWHM.

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The shortest intensity AC trace with 245 fs is given in Fig. 4(c). A pulse duration of 162 fs (FWHM) was obtained by self-referenced spectral interferometry [19] with a Wizzler (Fastlite) adapted for the NIR spectral range. Numerical AC of the temporal Wizzler data gave an AC width of 242 fs, which is in good agreement with the TiPA result. The fundamental spectrum, the corresponding spectral phase and the calculated output pulse are shown in Fig. 5. After recompression a typical pulse shape with a remaining third order dispersion term was measured. TOD causes asymmetry of the pulse shape with post or pre pulses depending on its sign, which can be clearly seen in Fig. 5(b). Here, the amplitude of the first post pulse is smaller than 5% compared to the main peak due to the residual spectral phase. The spectra obtained with the Wizzler (see Fig. 5(b)) and the Yokogawa spectrometer (see Fig. 3(b)) result in a Fourier limit of 145 fs and 143 fs, respectively. Although, the measuring instruments show different spectra, which is due to the different measuring methods, the resulting pulse duration is almost the same. These values are in a good agreement with hard clip of the CVBG, which corresponds to a pulse duration of approx. $145\,$fs. We calculated a total B-Integral for the stretched pulses (360 ps) of 0.69 rad accumulated in the amplifier. Thereby, the main contribution originates from the propagation through the gain material of the RA where the laser beam is small due to the focusing mirror M1. Additionally, 0.1 rad is generated within the CVBG for the highest output pulse energies.

 

Fig. 5. (a) spectral amplitude and phase, GDD = -2.8 $\cdot$ 10$^3$ fs$^2$, TOD = 2.9 $\cdot$ 10$^6$ fs$^3$ (b) pulse shape and Fourier limit (FL); data recorded with a Wizzler, values given in FWHM.

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4. Summary

In summary, we demonstrated a peak power of 5.6 GW of a regenerative Yb$^{\textrm {3+}}$:CaF$_2$ CPA system based on a single CVBG operating at the millijoule level. We achieved a minimum pulse duration of 162 fs corresponding to 1.12 times of its Fourier limit. Furthermore, the intensity autocorrelation of the output pulses corresponds to the numerical autocorrelation of the pulse shape derived from self-referenced spectral interferometry.

The optical setup proves a straight forward and reliable control of the overall spectral phase in a femtosecond laser system by the use of chirped Bragg gratings and mirror coatings. The remaining spectral phase of higher order dispersion terms is mainly owed to the transmission through the DKDP-Pockels cell. Already compact in its presented form the concept can be further reduced in size by a finer selection of the intra-cavity chirped mirrors, making the extra cavity mirror pre-compression obsolete. This again allows a more flexible adjustment of the cavity round trip number to vary the operation point of a regenerative amplifier without any adaption of the spectral phase for instance in a grating compressor.

We compensated gain narrowing with a low cost quartz birefringent filter and obtained a spectral bandwidth of 16 nm (FWHM), which is more than twice of the typical bandwidth of a regenerative Yb$^{\textrm {3+}}$:CaF$_2$ amplifier. The Fourier limit of the spectrum achieved with cavity dumped output pulses even corresponds to a pulse duration of 106 fs. Therefore, a pulse duration of 130 fs (assuming similar spectral phase terms as achieved here) or even shorter of such a regenerative CPA system seems feasible when adapting the hard clip bandwidth of the CVBG as well as the length or crystal type of the Pockels cell. During ongoing experimental campaigns we have observed a shot-to-shot stability of less than 3% peak-to-valley and a long term (several months) drift of less than 5% (P-V) regarding the output pulse energy.

The presented amplifier concept shows potential for power scaling when changing to a full thin-disk design operating at mJ level and kHz repetition rates. In case of disk thicknesses in the 200 $\mu$m range supporting improved thermal conditions a multi-pass pump setup is required in order to maintain efficient pump absorption as well as single-pass gain of the RA [20]. Alternatively, a subsequent booster amplifier (e.g. single crystal fibers [21] or multi-pass amplifiers [22,23]) could perform power scaling, while single chirped mirrors compensate the additional GDD ($\sim$ 10$^3$ fs$^2$ for a path length of 50 mm in Yb$^{\textrm {3+}}$:CaF$_2$).

5. Conclusion

In conclusion, we found that an exclusive use of chirped optical elements enables a compact and collinear probe laser design with a high reliability with respect to uptime, geometrical beam stability and synchronization as, e.g., mandatory for a probe system in a complex high intensity laser driven plasma environment [1]. In comparison to classical grating stretchers and compressors CVBGs tend to be less sensitive to pointing and therefore temporal instabilities such as jitter and long term drifts.