1.1 Short Light Pulses—Motivation and Historical Background

Light plays an essential role in our everyday life. Its detection via the eye provides us with continuous information about the objects and dynamics in our surroundings. For scientists, it has been a strong motivation to surpass the capabilities of the eye by technological means in order to gain insights into natures’ structures and processes that would be otherwise too small, too fast or too weak to be observed. Over the past centuries this desire has led to great innovations on the fields of photography, microscopy, astronomy and many others.

The experimental realization of the laser (“light amplification by stimulated emission of radiation”) in 1960 [1] constitutes a major step regarding this goal and enabled a variety of new techniques and applications in the last decades such as optical tweezers [2], frequency combs [3], or highly precise interferometers [4].

One of the most interesting consequences of the laser principle is the ability to concentrate energy into very short pulses by the coherent superposition of light waves. For the study of fast physical processes this is a valuable property as it allows to resolve these processes on a time scale shorter than their temporal constants. Hence, with picosecond (1ps = 10\(^{-12}\) s) laser pulses generated in the 1970s, for the first time the vibrational dynamics of molecules could be observed [5]. The development of femtosecond (1fs = 10\(^{-15}\) s) lasers in the 1980s opened the door to the measurement (and control) of atomic motion and chemical reactions [6].

Using titanium-sapphire ( Ti:Sa ) as a gain medium, conventional laser schemes have been optimized to their limits in terms of spectral bandwidth and pulse duration. Originally developed in the late 1980s and early 1990s [7, 8], Ti:Sa-based laser systems until today constitute the main work horse in many laser labs and may provide \({\sim }{5}\,\text {fs}\) pulses on a nanojoule-level from oscillators [9]. One of the main obstacles on the route towards even shorter pulses is the fluorescence emission bandwidth of the laser gain medium [10] that limits the maximum spectral width to less than one optical octave. Moreover, this physical property also leads to a spectral narrowing of the pulses during further amplification (“gain narrowing”): as a consequence, high-energy pulses on the millijoule- to joule-level from Ti:Sa power amplifiers typically feature pulse durations only in the range of 20–30 fs [11, 12].

Hence, for the next big step towards ever shorter pulses—entering the attosecond (1as = 10\(^{-18}\) s) regime which allows the observation and control of electronic motion—a fundamentally new approach was required.

Already in 1961, one year after the first demonstration of the laser, Franken et al. exploited the temporal confinement of energy in short laser pulses to achieve electric field strengths of \({\sim }{10^{7}}\,\text {V/m}\), approaching the binding forces of electrons in matter [13]. Triggering in this way a nonlinear response in crystalline quartz, the second harmonic of the fundamental laser pulse was generated (SHG), giving birth to the field of nonlinear optics.

Thanks to advances in laser development with ever increasing peak intensities, multiple other nonlinear effects were observed in the following decades. Of particular interest for the generation of ultrashort pulses is the nonlinear spectral broadening of laser pulses in gas-filled capillaries [14]. By this technique, amplified Ti:Sa pulses with mJ energy can be compressed to sub-4 fs (about two optical cycles) [15]. While not being substantially shorter than Ti:Sa oscillator pulses (\({\sim }{5}\,\text {fs}\)), the boost in pulse energy allows to drive another nonlinear process: the generation of high harmonics ( HHG ) [16]. This process can be triggered by focusing an intense laser pulse into a gas jet which results in the ionization of the atoms. The free electrons follow the oscillations of the electric field of the pulse and generate for each re-collision with the quasi-static parent ions a short burst of extreme ultraviolet (XUV) radiation, forming a train of attosecond pulses. Due to the high nonlinearity of the process, this train can be confined to a single attosecond pulse when using few-cycle driving pulses such as the mentioned spectrally broadened Ti:Sa output (“amplitude gating”) [17]. At record pulse durations of less than 100 as [18], these isolated attosecond pulses provide until today an unrivaled temporal resolution. A common application here is the pump-probe technique where a fs-pulse triggers electronic motion in solids (“pump”) and the as-pulse serves as an ultra-fast camera to resolve the response (“probe”) [19,20,21].

To achieve ultimate temporal resolution and enable an even broader range of applications, it is desirable to use the attosecond XUV pulses not only as a probe but also as the pump. This in turn requires an increase of the pulse energy by orders of magnitude which proved to be difficult to accomplish with the described HHG technique in gas: As the peak intensity of the driving pulse is limited by the ionization threshold of the target gas medium, a loose-focusing geometry is obligatory for high-energy laser systems. This geometry becomes impractically large (several meters) when the few-cycle driving pulses approach energies of tens of mJ [22,23,24,25].

A method that circumvents the intensity limitation of HHG in gas and at the same time exhibits significantly higher conversion efficiencies, is the generation of high harmonics on plasma targets [26,27,28,29,30]. In this process an intense light pulse interacts with a solid surface (SHHG), ionizes it and creates a nearly step-like vacuum-plasma interface. Under the effect of the ponderomotive force of the incident pulse and the restoring Coulomb force of the ionized background, the free electrons perform oscillations perpendicular to the surface, forming a plasma mirror that moves at relativistic speed. The incident light pulse that creates this oscillating mirror (ROM), at the same time is reflected from it. Owing to the relativistic oscillations of the mirror, it gets Doppler-shifted resulting in high-harmonic radiation in the deep XUV and even soft X-ray region. In the temporal domain, this corresponds to the generation of one attosecond pulse per cycle of the electric field where once again amplitude gating can be used to select an isolated pulse.

To perform SHHG experiments, relativistic intensities larger than 1.37\(\times \)10\(^{18}\) W/cm\(^{2}\) \(\times \ \lambda _c^2\, [\upmu \text {m}]\) are required on target, where \(\lambda _c\) is the central wavelength of the driving pulse. For few-cycle pulses with \(\lambda _c\sim {1\,{\upmu }\text {m}}\) and a typical focal spot size of few \(\upmu \)m\(^{2}\), this calls for pulse energies of at least the order of mJ. For an efficient operation of the process and for the generation of high harmonics up to the water window (>280 eV), however, rather hundreds of mJ are necessary [27].

Even though conventional laser systems exist that provide pulses with Petawatt peak power and strongly relativistic intensities [31, 32], their long pulse duration prevents the generation of isolated attosecond pulses by SHHG. The aforementioned temporal compression to the few-cycle regime by nonlinear spectral broadening does not help here as the technique is limited in energy: so far only the generation of sub-two-cycle pulses at \({\sim }{3}\,\text {mJ}\) pulse energy [33] and sub-four-cycle pulses at \({\sim }{10}\,\text {mJ}\) [34] have been demonstrated. A recently suggested scheme for upscaling the concept to the joule-level by spectral broadening in thin foils still has to show its experimental feasibility [35, 36].

Besides the limitation in pulse duration, conventional lasers face another issue when used for plasma experiments, namely the imperfect temporal contrast: Essentially all high-energy laser pulses exhibit an amplified spontaneous emission (ASE) background and a coherent pedestal from pulse compression after chirped-pulse amplification (see for example [37]). As the intensity of these artifacts is typically of the order of \({10^{-9}}\) relative to the intensity of the main pulse, they may well exceed the threshold intensity for plasma formation of \({\sim }{10^{10}\,{\text {W}}/{\text {cm}}^{2}}\). Due to the long temporal extent of the pedestals, this occurs already tens (coherent pedestal) or hundreds (ASE) of picoseconds before the main pulse arrives, giving the generated plasma time to expand. Thus, in the case of SHHG the otherwise clean plasma-vacuum interface created by the main pulse is critically distorted, impairing the generation of high harmonics.

Next Generation Relativistic Light Sources

Mainly for the reason of contrast improvement, several large-scale systems nowadays combine the standard laser amplification with optical parametric amplification (OPA) [38,39,40]. This technique exploits the second-order nonlinearity of birefringent crystals to transfer energy from an energetic, narrowband “pump” beam to a weak, but broadband “signal” beam [41, 42]. A third beam—called “idler”—is generated in this three-wave-mixing process and guarantees conservation of energy and momentum. Being an instantaneous process, no energy is stored in the nonlinear crystal and therefore parasitic effects are limited to the duration of the pump pulse. This property makes OPA schemes an ideal frontend for systems with high contrast requirements.

Going one step further, conventional laser amplifiers can be entirely replaced by parametric amplifiers, which has already been demonstrated on a single shot basis for high energies (35 J, 84 fs) [43]. The main motivation behind this step is the ability of the OPA technique to amplify ultrashort pulses as the bandwidth depends only on the phase-mismatch between pump, signal and idler that is aggregated by propagation of the pulses inside the nonlinear crystal (assuming no strong absorption of spectral components in the medium). At multi-TW peak power, this capability has been impressively shown by the LWS20 system delivering 4.5 fs pulses with up to 80 mJ energy at a 10 Hz repetition rate [44].

This thesis is dedicated to the continued development of a light source that is planned to take the concept of parametric ultrashort pulse amplification to the Petawatt-level.

1.2 The PFS Project

The Petawatt Field Synthesizer (PFS) at the Max-Planck-Institut für Quantenoptik (MPQ) has been designed to deliver sub-two-cycle, high-contrast light pulses for the generation of high harmonics on solid surfaces as the main application [45, 46]. To reach the ambitious target parameters—a pulse duration of 5 fs, pulse energies of up to 3 J and a repetition rate of 10 Hz—the concept of this fully OPA-based system contains several key features, which will be briefly explained in the following.

In order to scale OPA systems to high pulse energies, the amplification is distributed to several consecutive OPA stages similar to the amplifier chains in conventional laser systems. The number of required stages depends on the achievable gain per stage which in turn is determined by experimental conditions such as the amplification bandwidth or the type of nonlinear crystal. To reach the PFS target energy of 3 J, the last stages have to be pumped by multi-joule pump pulses requiring large nonlinear crystals and beam diameters of the order of several centimeters to keep the fluences below the damage threshold of the medium.

At the time of design of the system in 2007, potassium dideuterium phosphate KD\(_2\)PO\(_4\) (DKDP) was the only suitable nonlinear crystal type available at this size. Due to its comparatively weak nonlinearity, high pump intensities are necessary to maintain an efficient parametric amplification—at first glance a contradiction to the prior condition of low fluences to prevent optical damage. The solution is to use short pump pulses at \({\sim }{1}\,\text {ps}\) pulse duration: Owing to the \(\sqrt{\tau }\)-scaling of the damage threshold fluence for pulse durations \(\tau \) in the nanosecond to picosecond range [47], a safe operation of the OPA stages at intensities of the order of 100 GW/cm\(^{2}\) is possible.

In the first (small) OPA stages, DKDP was later replaced by lithium triborate (LBO) owing to its superior nonlinear properties. As a result, in the design of the system the total number of required stages could be reduced from 8 to 5 [48, 49].

To reach the desired amplification bandwidth of about one optical octave, the phase-mismatch between the three interacting waves in the OPA process is kept small by employing thin nonlinear crystals. Due to the shorter interaction length, choosing this solution usually comes at the price of a reduced OPA gain. The high-intensity pump pulses, however, mostly compensate for this effect. Overall, this ansatz constitutes a notable difference to high-energy OPA systems using longer pump pulses and thicker crystals where two-color pumping is required to achieve a similar bandwidth [50].

For an efficient transfer of energy from the pump pulses to the signal, the temporal overlap between both pulses during amplification should be as large as possible [51]. This is accomplished by introducing a chirp in the 5 fs signal pulses before amplification in order to stretch them to the \({\sim }{1}\,\text {ps}\) pulse duration of the pump. After amplification, the signal pulses are re-compressed to achieve highest peak-powers.

In analogy to the chirped pulse amplification (CPA) technique known from conventional laser amplifiers [52] this method is termed optical parametric chirped pulse amplification ( OPCPA ). Compared to typical CPA schemes, the required chirp is orders of magnitude smaller—owing to the broad signal bandwidth and the short pump pulse duration. On the other hand, the 5 fs target duration for the amplified signal pulses poses high requirements to the compensation of higher order dispersion.

As mentioned before, an excellent temporal contrast is vital for HHG experiments on solid surfaces—the main application of the PFS. Considering the potential peak intensity of up to 10\(^{22}\) W/cm\(^{2}\) in the fully realized version of the system, a contrast of better than 10\(^{12}\) has to be provided to stay below the plasma formation threshold of \({\sim }{10^{10}\,{\text {W}}/{\text {cm}}^{2}}\). The PFS concept not only promises to reach and surpass such contrast ratios owing to the intrinsic temporal filtering via the OPA technique but is expected to do so even on a 1 ps time scale due to the short pump pulses, thus outperforming OPA systems with longer pump pulse durations.

For the experimental realization of the PFS concept, three main challenges have to be mastered:

  1. (I)

    The generation of 1 ps pump pulses featuring energies of more than 10 J in the fundamental beam at a repetition rate of 10 Hz. Not being commercially available, a system delivering such pulses based on ytterbium-doped gain media (1030 nm central wavelength) had to be newly developed at the MPQ.

  2. (II)

    The generation of high-energy, broadband signal (“ seed ”) pulses for the OPA chain from a commercial Ti:Sa frontend. The required spectral range of 700–1400 nm for these pulses is defined by the frequency-doubled pump wavelength of 515 nm and the phase-matching properties of the DKPD and LBO crystals.

  3. (III)

    The combination of pump and signal for parametric amplification. This involves the installation and optimization of the OPA system as well as the dispersion management for the signal pulses, i.e. the temporal stretching before and re-compression after amplification.

Regarding all three pillars significant achievements have been attained by co-workers, namely (in approximately historical order) the installation of the PFS frontend including a preliminary scheme for broadband seed generation [53, 54], the development of an Yb-based CPA pump amplifier chain delivering up to 0.8 J compressed energy at a pulse duration of \({\sim }{800}\,\text {fs}\) [55,56,57,58,59] as well as first proof-of-principle OPA experiments at a reduced pump energy [48, 49].

Building on these earlier works, we will describe in the following chapters new developments, modifications and improvements to the PFS system, with the main focus on seed generation (pillar II) and OPA development (pillar III). The overall goal of these measures is to reach for the first time relativistic intensities exceeding 10\(^{19}\) W/cm\(^{2}\) that allow to perform SHHG experiments.

1.3 Structure of the Thesis

Chapter 2—Fundamentals

This chapter provides an introduction into the mathematical description of ultrashort light pulses. The linear and nonlinear physical effects relevant to this work are discussed and experimental tools for temporal characterization are presented.

Chapter 3—The Petawatt Field Synthesizer System

This chapter gives an overview over the PFS system, summarizes previous works and explains new or modified parts of the system. In particular the initial seed generation scheme is described which delivered the broadband pulses for the OPCPA chain by spectral broadening in two cascaded hollow-core fibers (HCF). The shortcomings of this scheme provide the motivation for Chap. 4.

Main modifications to the system:

  • The replacement of the master oscillator with an updated version simplifies the pump chain owing to an additional 1030 nm output.

  • The rebuild of the pump compressor in vacuum slightly reduces the timing jitter and allows the compression of high-energy pump pulses (potentially >10 J).

  • The rebuild of the currently last pump amplifier enables a stable long-term operation and improves the maintainability of the setup, the beam profile and the output energy.

Chapter 4—Seed Generation Schemes

In this chapter the principle ideas and experimental realizations of alternative schemes for the generation of broadband seed/signal pulses for the OPCPA chain are explained. In total three different schemes are tested that use a Ti:Sa amplifier (1.5 mJ, 30 fs, 1 kHz) as a common frontend.

4.1   Idler Generation

  • In this scheme the Ti:Sa pulses are split into two channels, where one channel is frequency-doubled and the other broadened in a HCF. By recombination in a non-collinear OPA stage, a broadband idler is produced. Theoretical considerations and experiments are presented, aiming at the compensation of the intrinsic angular chirp of this idler.

Main results:

  • The generated idler pulses feature energies of up to 15 \(\upmu \)J and a spectral range of 680–1400 nm.

  • The experimentally achievable compensation of the angular chirp is not sufficient to allow the use of the generated pulses as a seed.

4.2   Cross-Polarized Wave Generation

  • Reusing the original seed generation scheme consisting of two HCFs, the broadband pulses are temporally gated and spectrally smoothed in a cross-polarized wave (XPW) generation stage.

Main results:

  • 4 \(\upmu \)J pulses are generated that feature a smooth spectrum spanning 680–1600 nm with an almost Gaussian shape.

  • The reliability of the setup makes it the scheme of choice for daily operation as an OPA seed source.

4.3   Cascaded Difference-Frequency Generation

  • After pulse compression of the Ti:Sa pulses in one HCF, strong broadening into the infrared is achieved by cascaded second-order intra-pulse interactions in a BBO crystal.

Main results:

  • Generation of 10 \(\upmu \)J pulses with extremely broad spectra from 600 nm to more than 2400 nm (\({\sim }{8}\,\upmu \)J in the relevant range of 700 nm to 1400 nm).

  • Being conceptually simple and scalable in energy, the scheme is recommended as the future seed source for the PFS.

Chapter 5—OPCPA Experiments with Two OPA Stages

This chapter describes the OPCPA experiments carried out in vacuum on two OPA stages with LBO crystals.

5.1   Performance of Alternative Seed Generation Schemes

  • The seed pulses from the idler generation and the XPW generation scheme are parametrically amplified and compared to prior experiments with the initial seed generation scheme. Furthermore, the temporal compressibility of the amplified XPW pulses is tested in air.

Main results:

  • Compared to the initial seed generation scheme, both alternative schemes yield (at a comparable gain) significantly less modulated spectra of the amplified pulses promising better compressibility.

  • Seeding with the XPW scheme, energies of 180 \(\upmu \)J and 9.8 mJ are achieved after the first and second OPA stage respectively (4.5 and 81 mJ pump energy at 1 Hz).

  • Test compression of the amplified pulses with chirped mirrors in air results in a pulse duration of 7 fs.

5.2   High-Energy OPCPA Experiments

  • For the first time the full 1.2 J fundamental pulse energy available from the last pump amplifier are used for OPA experiments at 10 Hz

Main results:

  • The pump SHG efficiency is improved from previously 45% to 55% by the implementation of a fast-switching Pockels cell in the amplifier chain to suppress amplified spontaneous emission. This results in frequency-doubled pump pulse energies of 14 and 400 mJ respectively for the two OPA stages.

  • The parametric amplification of the broadband seed pulses generated by the XPW scheme yields pulse energies of 1.0 mJ after the first and 53 mJ after the second OPA stage.

  • These amplified signal pulses are compressed to approximately 6.4 fs (sub-2.5-optical cycles) with chirped mirrors in vacuum, resulting in a peak power of 4.9 TW.

  • The temporal contrast of the amplified signal pulses is measured to be better than \(10^{11}\) on a 1 ps time scale.

Chapter 6—Preparations for a Third OPA Stage

In this chapter the preparations for the next upgrade of the PFS system are presented. This includes the basic design considerations for the system, experimental tests of nonlinear crystals and an examination of potential schemes to match the pulse fronts of pump and signal in the upscaled system.

  • 6.1   General Layout The designed layout for the system upgrade is discussed.

Main planned modifications:

  • The existing system will be extended with a third (using pump recycling possibly even with a fourth) OPA stage.

  • A new pump amplifier is planned to deliver the required energy of 10 J in the fundamental beam. After splitting this beam into a 9 J and a 1 J arm, the pulses will be individually compressed and frequency-doubled, providing 4 J and 400 mJ + 15 mJ pump energy for the OPA stages.

6.2   Evaluation of Nonlinear Crystals

  • Possible options regarding the nonlinear crystal type (DKDP or LBO) to be used for pump SHG and OPA in the upgraded system are examined.

Main results:

  • Owing to the measured four times higher damage threshold, the superior nonlinear properties and a comparable pricing, LBO is preferred over DKDP as a crystal material. For the size of the LBO crystals, the largest commercially available diameter of 80 mm will be used.

  • Measurements with small test crystals give an optimal thickness of 1.5 mm for the SHG crystal at the planned peak fluence of 0.19 J/cm\(^{2}\) (fundamental beam).

  • Testing different crystal thicknesses for OPA reveals a trade-off between energy, stability and spectral smoothness. A final decision will be made based on the results of a second campaign in the near future.

6.3   Pulse Front Matching

  • A detailed analysis of the required pulse front matching of pump and signal beam in large non-collinear OPA systems is presented. Different schemes are discussed that introduce a pulse front tilt (PFT) in the pump beam.

Main results:

  • Matching the pulse fronts of pump and signal at the second and third OPA stage is crucial to ensure spatio-temporal overlap and efficient amplification.

  • A potential scheme that tilts the pump pulse front with a pair of large transmission gratings is discarded due to the low damage threshold of the tested gratings.

  • Instead, an alternative scheme is suggested that introduces the required PFT by a controlled misalignment of the pump compressor. This method allows an independent control of the pump PFT at the second and third OPA stage. An additional pair of transmission gratings will adjust the tilt for the (weak) pump pulses at the first OPA stage.