Femtosecond laser pulses, which are tunable from 440 to 990 nm, are generated at MHz repetition rates by noncollinear parametric amplification (NOPA). The pulses have durations of 20 to 30 fs over the major part of the tuning range and a high energy stability of 1.3% (rms). The NOPA is pumped with ultraviolet pulses from the third harmonic of an ytterbium doped fiber laser system and seeded by a smooth continuum generated in bulk sapphire. The residual second harmonic is used to pump an additional NOPA, which is independently tunable from 620 to 990 nm. Interference experiments show that the two NOPA systems have a precisely locked relative phase, despite of being pumped by different harmonics with a random phase jitter. This demonstrates that the phase of pulses generated by optical parametric amplification does not depend on the pump phase.
© 2008 Optical Society of America
1. Introduction and overview
For the generation of intense femtosecond pulses, laser amplifiers based on fiber technology promise high peak power at high repetition rates, excellent beam quality and good stability. Such characteristics are essential in machining, nonlinear imaging, microscopy, and ultrafast spectroscopy. The combination of high peak intensities with high repetition rates allows for studying or making use of the entire range of nonlinear effects with a high processing or data acquisition rate. To apply fiber lasers in ultrafast spectroscopy, the relevant absorption and emission spectra of the investigated systems must be matched and pulse durations of~20 fs are required. Typically, molecules and condensed matter absorb in the UV, visible, and near infrared spectral region. A frequency converter for fiber lasers, typically operating around 1035 nm for ytterbium doping, into an as wide as possible tuning range is therefore essential to take advantage of the high repetition rate and stability of fiber lasers in spectroscopy.
Noncollinear optical parametric amplifiers (NOPAs) pumped by Ti:sapphire lasers are well proven devices for the generation of few-cycle tunable pulses. They allow accessing the temporal signatures of ultrafast wavepacket dynamics and structural oscillations in molecules and condensed matter. Now we investigate the use of an ytterbium-doped fiber laser operating at 1035 nm as pump source for NOPAs that allow the full coverage of the near UV, visible and NIR spectral range. In contrast to earlier work performed in our laboratory , we focus on a NOPA pumped by the third harmonic of the 1035 nm fiber laser pulses. This should allow extending the tuning range significantly to shorter wavelengths and accessing the UV with simple frequency doubling. To retain the demonstrated NIR coverage, we combine the 345 nm pumped NOPA with a NOPA pumped by the residual frequency doubled pump light.
The manuscript is outlined as follows. In Section 2, we present the experimental arrangement. In Section 3 and 4, we explain the considerations and technical details for seed and pump light generation. Section 5 addresses the NOPA processes and relevant phase matching concepts. The measured spectra, Fourier limits, pulse durations and pulse energies are presented and discussed. The results of a noise analysis and phase investigations are shown and reviewed in Section 6 and 7. We conclude with final remarks in Section 8.
2. Experimental arrangement
The two NOPAs (sketched in Fig. 1) are pumped by an Yb-doped fiber-oscillator/amplifier system (IMPULSE; Clark-MXR, Inc.), which delivers 10 to 12 µJ pulses at 1035 nm (frequency ω0, red in Fig. 1) with a pulse length of 230 fs at a selectable repetition rate between 200 kHz and 2 MHz. A half-wave plate for 1035 nm in combination with a thin film polarizing beam splitter is used to split off 1.5 µJ pulses for continuum generation (Fig. 1, grey; explained in more detail in Section 3). This scheme is chosen to be able to maintain a constant energy for continuum generation, independent of slight variations of the output energy of the fiber laser. The remaining 8.5 to 10.5 µJ pulses are focused with the lens L1 towards two BBO crystals for frequency doubling and subsequent tripling. The details of the mixing concept are discussed in section 4. The resulting light (Fig. 1, blue) is separated by a dichroic mirror (DM), which is highly reflective at 345 nm and highly transmissive at 517 and 1035 nm. After recollimation by the lens L2, a spherical mirror focuses the 345 nm pulses into a 2 mm thick type-I BBO crystal, cut at 37°, where they act as pump pulses for the NOPA process. A second dichroic mirror (highly reflective for 517 nm and highly transmissive at 1035 nm) extracts the remaining 2ω0 light (Fig. 1, green), which is likewise recollimated by a lens (L3) and focused by a spherical mirror into a 5 mm thick type-I BBO crystal, cut at 26.5°. As will be shown later in detail, the 3ω0 pumped NOPA works best in the visible part of the spectrum up to 700 nm. In contrast, the 2ω0 pumped NOPA is advantageous in the 700 to 990 nm regime. Therefore a spectral splitting of the seed continuum at approximately 700 nm, for example with a dichroic mirror, is appropriate to obtain the highest seed energy in both NOPAs. If the full tuning range from 440 to 990 nm of the 3ω0 pumped NOPA shall be exploited, a broadband 50% beam splitter can be used instead.
Wavelength tuning is achieved for large parts of the spectral range in both branches by only varying the time delay between the chirped continuum seed and the respective pump pulses. Only towards the short and long wavelength ends of the tuning ranges small changes of the phase matching angles of the BBO crystals and/or the noncollinearity angles are necessary. Most of the experiments described below were performed at 200 kHz repetition rate. Since then the system has been operated continously at 500 kHz without any noticable deterioration of performance and with unchanged output pulse energies. Scaling to the full repetition rate of the fiber laser system (2 MHz) should be straightforward and as before we do not expect any significant changes in the NOPA pulse paramters . The whole setup is placed in a box with dimensions of approximately 80×80×20 cm3, is therefore easily portable, compact and protected from the environment.
3. Seed generation
Different approaches for seed light generation with high repetition rate pump systems were reported, such as optical parametric generation in periodically poled lithium niobate  or soliton generation in a highly nonlinear photonic crystal fiber . Optical parametric generation often shows high energy fluctuations, and nonlinear fibers typically result in highly structured spectra with phase modulations .
Here we use a continuum generated by filamentation in a 4 mm thick sapphire crystal. With a lens of 75 mm focal length we focus pulses at 1035 nm into the sapphire. Collimation of the continuum is achieved by a 30 mm achromatic lens. It smoothly covers a spectral region from 430 to 1000 nm, whereof the region from 500 to 850 nm forms a nearly flat plateau (±30% spectral energy density). In contrast to earlier approaches , where a minimum energy of 2.5 µJ per pulse was needed for stable continuum generation, we now find a minimum gy of 2.5 µJ per pulse was needed for stable continuum generation, we now find a minimum threshold energy of only 1.5 µJ per pulse. This is due to an improved beam profile of the pump light, since we now directly use the output of the fiber laser and avoid prior frequency doubling. In addition, even small improvements in pulse duration seem to have significant effects on the continuum threshold. To avoid damage accumulation due to the high average power, the sapphire disc is rotated at approximately 60 Hz. Instabilities and degradation of the filament are sometimes assumed as drawbacks of continua generated in bulk materials . This was not observed; in contrary we measure energy fluctuations of the continuum as low as 1.1% rms (see Section 6).
4. Ultraviolet pump pulses
In parametric processes, the wavelength of the pump pulses limits the shortest achievable amplification wavelength for a given nonlinear crystal. If the amplified spectrum approaches the pump wavelength, energy conservation results in idler pulses with long wavelengths in the infrared, which are eventually absorbed in the nonlinear crystal. For example, when using the second harmonic of the 1035 nm pulses, amplification of wavelengths below 620 nm ceases in BBO due to idler absorption above 3.1 µm . To be able to amplify a wide spectral range of the seed light on the short wavelength side, a sufficiently short pump wavelength is needed. Therefore we choose the third harmonic at 345 nm as pump pulses.
We apply frequency doubling and subsequent sum-frequency mixing with the remaining fundamental pulses for overall tripling. In the fs-regime, group-velocity mismatch (GVM) between the three pulses plays an important role, because the difference in transit time through the nonlinear crystals becomes comparable to the pulse lengths. Therefore the pulses loose temporal overlap during propagation inside the crystals, which leads to reduced efficiency. The fundamental and second harmonic pulses exit the doubling stage at different times and have to be suitably delayed to restore the temporal overlap in the mixing stage. Conventional schemes for tripling of ultrafast pulses therefore use dichroic beam separation, mechanical delay, and recombination between the doubling and mixing stages [5, 6].
In contrast to these approaches, we use a sequence of two specially selected BBO crystals, which allow for group velocity matching in a simple collinear geometry without the need of additional delay elements. The concept is based on the following considerations. In type-I second harmonic generation in BBO, the fundamental pulses (o-polarized) have a larger group velocity than the second harmonic pulses (e-polarized). In our setup, using fundamental pulses with a duration of 230 fs at 1035 nm and a 0.8 mm thick BBO doubling crystal, this group velocity mismatch leads to a separation of the ω0 and 2ω0 pulses of approximately 50 fs after the doubling crystal (see Fig. 2(a)). For the following sum-frequency mixing process ω0+2ω0→3ω0, there are three phase matching possibilities in BBO (see table 1). They result in different group delays that affect the temporal synchronization between the involved pulses.
A first important consideration is the group delay between the fundamental and the second harmonic pulses (table 1, middle column). In contrast to earlier approaches, which used sum-frequency mixing of type-I (o+o→e) or type-II (e+o→e) [5,6], the third possibility, o+e→ e, offers a negative group delay between the ω0 and 2ω0 pulses. Because the ω0
pulses enter the tripling crystal 50 fs before the 2ω0 pulses, a subsequent negative group velocity mismatch in the tripling crystal, as given by the o+e→e process, allows for the second harmonic pulses to overtake the fundamental pulses during the propagation. This restores a good temporal overlap within the crystal, in order to achieve high conversion efficiency without applying external delay elements (see Figs. 2(b) and 2(c)). The nonlinear conversion coefficient, deff, is about one fifth of the type-I scheme, but the damage threshold of BBO is high enough to compensate this by slightly reducing the beam sizes for increased intensity. A second advantage of the o+e→e mixing scheme is the small group velocity mismatch between the original ω0 and 2ω0 pulses with respect to the generated 3ω0 pulses (table 1, right column). Frequency tripled light that is generated in different parts of the crystal therefore adds up without temporal pulse lengthening.
In addition, with the o+e→e scheme no rotation of the polarization between the two crystals is necessary and wave plates or geometrical polarization rotation is avoided. The generated 3ω0 pulses have the same polarization as the 2ω0 pulses and can directly be used for pumping the NOPAs.
Experimentally, an f=500 mm lens is used to focus the fundamental ω0 pulses towards the two BBO crystals (type-I, 0.8 mm, 23.5° and type-II, 1.5 mm, 62.8°). The type-I doubling crystal is placed about 70 mm before the focus and the type-II tripling crystal about 50 mm behind. This allows independent fine-tuning of the respective conversion efficiencies by moving the crystals in order to adjust the spot sizes. Total energy conversion efficiencies to the third harmonic of more than 15% are observed. In routine operation, we operated at approximately 11%, to maintain a good energy balance between the 2ω0 and the 3ω0 light, which are both used for NOPA pumping. We did not observe degradation or damage of the BBO crystals in long-term operation.
Our tripling scheme was already successfully used in ultrafast electron microscopy utilizing the same pump laser . The presented concept of group-velocity management in frequency tripling is generally applicable, if conditions can be found where the group velocity difference of ω0 and 2ω0 changes sign between frequency doubling and sum-frequency-mixing. For BBO, this is the case for type-I frequency doubling and type-II sum-frequency mixing for fundamental wavelengths above 905 nm up to about 1.5 µm.
5. NOPA design and output characteristics
For simultaneous parametric amplification in the UV pumped and green pumped NOPA unit, the collimated seed continuum is split suitably as explained in Section 2. For the UV pumped NOPA, it is then focused with an f=300 mm fused silica lens towards the corresponding BBO crystal (type-I, 2.0 mm, 37°), which is placed approximately 340 mm behind the lens, and overlapped spatially and temporally with the pump pulses.
To obtain the highest possible amplification bandwidth and thereby the shortest pulses, a noncollinear geometry is chosen. This concept has originally been demonstrated for 400 nm pumping [9–12] and is now widely used for 532 nm pumped optical parametric chirped pulse amplifiers (OPCPAs) [13,14]. The concept can be readily extended to 345 nm pumping. The external noncollinearity angle between the seed and the pump beam is set to ~5.5° for broadband amplification around 590 nm. The crystal is oriented for tangential phase matching to obtain the highest efficiency and the cleaner output beam profile, as compared to the walk-off compensated orientation. The collimated UV pump beam is focused with a spherical mirror (f=250 mm), placed approximately 260 mm before the BBO crystal, resulting in a beam diameter of about 100 µm in the crystal.
In the green pumped NOPA, we use an f=350 mm lens for focusing the seed continuum towards the BBO crystal (type-I, 5.0 mm, 26.5°), which is placed about 450 mm behind the lens. The collimated green pump pulses are focused with a spherical mirror (f=250 mm), which is placed about 270 mm before the BBO crystal, resulting in a beam diameter of about 220 µm on the crystal surface. The external noncollinearity angle is set to ~5° for broadband amplification around 820 nm.
Figure 3 shows typical output spectra from the UV pumped NOPA. Tuning is mainly achieved by delaying the UV pump pulses with respect to the longer (and chirped) continuum pulse (495–665 nm), and by slightly adjusting the phase matching angle and noncollinearity for parametric amplification. The resulting output pulses are continuously tunable over more than one optical octave from 440 to 990 nm (303–682 THz). Throughout all of the tuning range, the spectra are very smooth and have nearly Gaussian shape. The pulses were compressed using a sequence of fused silica prisms with an apex angle of 68.7°. Typical prism separations (edge to edge) are 500 to 1000 mm. For temporal pulse characterization, autocorrelation traces were obtained with a dispersion-free autocorrelator . Figure 4 shows typical traces, from which the pulse durations are evaluated by assuming a Gaussian pulse shape. The smooth Gaussian shaped spectra in combination with insignificant higher order chirp allow for almost Fourier-limited pulse shapes without temporal satellites, as evident from the pedestal- free autocorrelation traces.
Figure 5 summarizes the calculated Fourier-limits of measured spectra (blue squares) and the measured pulse durations (red diamonds). Between 520 and 680 nm pulse durations of sub-30 fs were measured. The observed increase of the Fourier limits towards shorter and longer wavelengths can be explained by considering phase matching and chirp effects. In the short wavelength region, estimates show that broadband noncollinear phase matching is well possible and that the residual wave vector mismatch between signal and idler allows for Fourier limits of 13 fs from 430 to 690 nm (see blue dashed line in Fig. 5). However, even with perfect phase matching, parametric amplification can only affect such spectral components of the seed light that overlap in time with the pump pulses. The seed continuum is chirped, mainly by dispersion in the achromatic lens used for collimating and the fused silica lens used for relay imaging. Because such material dispersion is particularly severe at short wavelengths, the continuum is chirped strongest in this spectral range and longer Fourier limits are observed. With a proper chirp management, e.g., by compressing the continuum and/or stretching the pump pulses, an amplification bandwidth sufficient for sub-20 fs pulses is expected all the way down to 440 nm.
Above the degeneracy point of 690 nm effective group-velocity matching by a noncollinear geometry is not possible. Therefore a collinear arrangement is advantageous and the amplification bandwidth is mainly given by the first order wave vector mismatch between signal and idler. The dashed blue line shown in Fig. 5 above 750 nm depicts the resulting lower limit for the achievable pulse duration. The somewhat higher measured Fourier limits are explained by a small residual noncollinearity angle that was used in the experiments. The second NOPA, pumped by green pulses at 2ω0≙517 nm, therefore exhibits an ideal complement as it delivers sub-30 fs over its complete fundamental tuning range from 620 to 990 nm (see green triangles in Fig. 5). In combination, the two NOPAs provide Fourier-limited pulse lengths of sub-30 fs in a spectral range from 500 to 990 nm.
The output pulse energies are in the range of 140 nJ for the UV pumped NOPA, best at the center of its tuning range. Simultaneously, the second harmonic pumped NOPA delivers pulses with up to 250 nJ energy in a broad range around 800 nm. For both NOPAs the beam profile is visually round and homogeneous. The pulse energies are well sufficient for subsequent frequency conversion processes, for example to extend the tuning range into the ultra-violet region. The generation of 34 nJ pulses at 290 nm has already been demonstrated . The octave-wide tuning range together with simple frequency doubling leads to a continuous spectral coverage from below 250 nm to nearly 1 µm without any gap.
6. Fluctuation analysis
To elucidate the usability of the MHz NOPA for low-noise spectroscopic applications, we performed a detailed analysis of the pulse-to-pulse intensity fluctuations. The energy in each single pulse was measured by a moderately fast photodiode module, of which the output voltage trace was recorded in time with a fast digital oscilloscope. Such oversampling significantly decreases digitizing effects on low-noise data. To reveal fluctuation correlations between different pulse trains, two identical photodiodes were employed simultaneously. The relative deviations of the individual pulse energies Ek from the average E̅ is referred to as laser noise. For the primary fiber laser system, we obtain a total noise of 0.8% rms when recording 100,000 subsequent pulses at 208 kHz. The frequency-resolved noise density is shown in Fig. 6(a). The relative noise intensity, i.e. the spectral power density normalized to the average power, is below -85 dB/Hz throughout the frequency range of 1–100 kHz. We note that the noise spectrum of the fiber laser output is mostly composed of uniform white noise, with a resonance at about 44 kHz.
For the output fluctuations of the green pumped NOPA unit, we obtain a total noise of 1.3% rms. The spectrum of the NOPA fluctuations (Fig. 6(b)) shows an additional low frequency resonance at 355 Hz, which originates from the rotating sapphire disc and is attributed to slight changes in the overlap between the continuum and the pump pulses in the NOPA crystal, caused by not perfectly parallel surfaces of the disc. However, this rotation is found to contribute only insignificantly to the total noise of the NOPA (1.2% rms, when excluding the 355 Hz resonance). From the noise spectrum of the NOPA we conclude that a modulation frequency in the range of 5–15 kHz is most suitable for low-noise lock-in detection. The fluctuations of the UV-pumped NOPA unit were not analyzed in detail. Since the output is in the visible, the visual impression of no significant instabilities can be taken as indication for comparable fluctuations as in the green pumped NOPA.
The total NOPA output noise is only 1.6 times larger than that of the primary fiber laser, although four nonlinear optical conversion processes are involved (frequency doubling, sum-frequency mixing, continuum generation, and parametric amplification). To investigate the origin of the NOPA noise, we measured energy correlations between the different beams involved within the NOPA. Such an analysis allows for measuring the order of nonlinearity of the involved frequency conversion processes and to investigate the effects of saturation.
Correlation plots of the measured pulse energies as two-dimensional histograms are expected to show tilted ellipsoids with the slope of the main axis given by the order m of the nonlinearity. Deviations of the measured slope m* from the expected value m indicate saturation in the conversion process.
Figure 7(a) shows the noise correlation (binned into a 75×75 histogram) between the fundamental fiber laser pulse energy and the energy of the green pump pulses. For frequency doubling m=2 is expected, but experimentally we observe m*=0.75. This means that the fluctuations in the green pulses are even smaller than those of the fundamental pulses. For high input intensities and doubling efficiencies of more than 30% depletion of the input pulse becomes significant and the second harmonic pulses are partially back-converted. Exceptionally intense fundamental pulses therefore generate attenuated frequency doubled output pulses, which can result in self-stabilization when a proper intensity regime is chosen. We believe that such a mechanism is the reason for the low fluctuations of the second harmonic and consequently the remarkably high NOPA stability.
Figure 7(b) shows the noise correlation between the fundamental fiber laser pulses and the continuum pulses (800 to 840 nm band pass). For two distinct time scales of 0.5 s and 1 ms (data not shown), we find no correlation and no tilt of the ellipse is measurable. The energy of our continuum pulses has no significant dependence on the pump pulse intensity. This is the result of the threshold behavior of the self-focusing, channeling, and spectral broadening mechanisms involved in the continuum generation. Some noise of about 1.1% rms is nevertheless observed and contributes to the overall NOPA noise.
The correlation between the output of the green pumped NOPA and the green pump pulses is reasonably high (see Fig. 7(c)). A further improvement of the pump laser stability would therefore lead to an even better NOPA stability. The observed slope of m*=2.6 is below the expectation for an unsaturated parametric amplification. A similar observation was made for the UV pumped NOPA. This indicates that the two parametric amplification processes are both operated fairly close to saturation, even for the low pump pulse energies used in this setup. Stable NOPA operation is not limited to highly energetic pump pulses, when focus sizes, pulse durations, and beam diameters within the setup are properly designed.
7. Experimental investigation of phase dependencies in optical parametric amplification
The overlapping amplification regions of the two differently pumped NOPA units allow for an instructive interference experiment that renders information about the phase dependencies in the parametric amplification process. The two NOPA units, seeded by the same continuum, are tuned to the same center wavelength of 720 nm and brought to interference with a small angle on a distant screen (see schematic Fig. 8(a)). Such an interferogram yields information about the relative phase jitter between the two NOPAs. In earlier experiments it was demonstrated that stable interference is observed, when two NOPAs are pumped by replicas of the same blue pulse, i.e. pulses with equal phase fluctuations [17,18]. In contrast, the presented experiment involves pump pulses that are derived from different harmonics (2ω0 and 3ω0) of the primary fiber laser, which is not phase stabilized. The second and third harmonic pulses therefore have carrier-envelope phases with twice or threefold the original phase fluctuations, which makes their relative phase jitter random. Hence, if the phase of the pump pulse has influence on the phase of the amplified pulse in optical parametric amplification, the phase of the interference pattern, i.e. the position of the minima and maxima, should change statistically from shot to shot.
To test this, we recorded the time dependence of the interference pattern with a linear detector array operated at 1 kHz. A typical measurement is depicted in Fig. 8(c). Over times of several seconds, the position of the interference pattern is extremely stable (see Fig. 8(b)). The associated relative phase between the two NOPAs, shown in Fig. 8(d) and 8(e), has fluctuations of less than 20 mrad rms in the measured frequency range of 0.1 to 1000 Hz. This means that the relative phase of the two parametrically amplified pulses is extremely stable and independent of the phase of the pump pulses.
8. Concluding remarks
The presented results show that a NOPA based on a MHz fiber laser system is capable of generating sub-20 fs pulses with energies above 100 nJ and is tunable from 440 to 990 nm without a gap. This more than octave wide tuning range is made possible by pumping the parametric amplification with the frequency tripled pump pulses at 345 nm. With simple and straight forward frequency doubling the range from below 250 nm to nearly 1 µm is accessible. Ti:sapphire based systems have so far not been shown to allow this complete spectral coverage. Attempts to pump a NOPA with the third harmonic of the Ti:sapphire system at 267 nm were hampered by the strong two photon absorption in the BBO crystal and the large group velocity mismatch between the three interacting waves . Additionally, the Yb-doped fiber laser system allows at least a tenfold higher repetition rate than Ti:sapphire based amplifier systems. The present rate around 1 MHz is ideal for applications as it provides sufficiently intense pulses for nonlinear interactions, high averaging capability and still ample time for sample exchange or relaxation. The sub-250 fs pulse duration of the used pump system allows direct generation of a high quality continuum in bulk sapphire. This permits a much wider tuning range and smoother spectra than obtained with precompression of longer pump pulses [20,21] or seeding by a spectrally broadened Ti:sapphire laser .
The presented NOPA is based on a single stage traveling wave amplifier. Since the parametric amplification depends on the pump intensity and higher pump energies can be accommodated by an increased pump diameter, nearly arbitrary power scaling of the device seems realistic. This opens up the route to UV-pumped OPCPAs at the millijoule or even joule level and OPCPAs with combined green and UV pumping for increased spectral width and pulse durations approaching 5 fs.
The demonstrated phase stability in the optical parametric amplification is an important requirement for many future experiments, such as light wave synthesis. The measured phase stability between the two NOPAs of 20 mrad corresponds to a temporal jitter of only 8 atto-seconds. Since our measurement averaged over 200 pulses, we expect a true pulse-to-pulse jitter of not more than 110 attoseconds. The presented amplification concept with its tunability of more than an octave is most promising for generating single attosecond pulses in recently proposed schemes based on a strong pulse with frequency ω and a phase-locked second pulse slightly off the second-harmonic, e.g., 2.2ω .
The two NOPAs pumped by the second and the third harmonic have their best performance in different spectral regions and therefore provide powerful sources for two-color ultrafast pump-probe spectroscopy. The high repetition rate is expected to advance for example spectroscopy on surfaces, where extremely weak signals have to be detected and long averaging is needed. As a consequence of the phase stability, the full temporal resolution corresponding to the reported short pulse durations can be utilized even for long averaging times.
We thank Clark-MXR, Inc. and HORIBA Jobin Yvon for the generous loan of the IMPULSE system. This work was supported by the Austrian Science Fund within the framework of the Special Research Program F16 (Advanced Light Sources) and by the DFG-Cluster of Excellence: Munich-Centre for Advanced Photonics. The International Max Planck Research School on Advanced Photon Science (C. H.) is gratefully acknowledged.
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