1. Introduction

Intense optical pulses have attracted considerable attention due to their numerous applications ranging from fundamental science to industrial production. Over the recent decades various amplification schemes for ultrashort laser pulses have been investigated. In particular diode pumped solid-state lasers have gain attraction due to their high efficiency and robustness. Nowadays, ultrafast lasers with 100 W to kW-level average power have been reported from thin disk lasers [1], slab lasers [2] and fiber laser systems [3], respectively. On the other hand Ti:Sapphire lasers, OPCPA systems and flash-lamp pumped Nd:glass laser dominate the realm of TW and PW peak power systems (e.g. [4]). As a matter of fact, all concepts have been pushed in research laboratories to their specific limitations, among them most pronounced thermo-optical issues, available pump power, nonlinearity and damage.

In this contribution, we report on an approach which is suitable to scale the performance of ultrafast lasers independent of the geometry of the gain medium, the amplification scheme or the performance level: coherent addition of ultrashort laser pulses [5]. Figure 1 illustrates the principle of the proposed approach. One mode-locked oscillator is split to N amplification channels, the pulses are amplified in these N channels and finally re-combined. N-1 elements have to be implemented to match the path lengths. Optionally, a pulse stretcher before the splitting and a pulse compressor after combining can be implemented in order to realized a chirped-pulse amplification (CPA) scheme. Assuming an ideal combining efficiency the performance of the whole system could be scaled by a factor N compared to the maximal performance of a single amplifier setup.

 

Fig. 1 Schematic setup of coherent addition of ultrashort laser pulses; Δφ: element for path length matching.

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The concept of spatially separated gain elements is well known, e.g. wavelength and polarization combining of diode lasers. For continuous-wave and Q-switched laser systems the concept of combining several laser beams to one final beam is well investigated, theoretically and experimentally (e.g. [6–11]). The combining methods themselves can be categorized into active and passive as well as in coherent and incoherent combining techniques. However, the use of ultrashort pulses instead of continuous-wave or ns-pulses for combining experiments results in new challenges for the realization. For instance, the dispersion management, or in general the management of spectral phases which can be of linear as well as nonlinear nature, in each channel becomes an important task.

In principle the coherent addition of ultrashort laser pulses, as proposed herein, is to some extent similar to the approach of cavity enhancement of laser pulses [12], which succeeded to demonstrate an average power as high as 72 kW intracavity of ultrashort laser pulses and enhancement factors >1000 recently [13]. Cavity enhancement relies on the locking of an oscillator cavity, which can be amplified, to a passive enhancement cavity, which becomes analogous to the continuous-wave case if the mode spacing of the pulse train matches the enhancement resonator’s free spectral range. In the time domain this means that after each round trip the pulse circulating in the passive cavity interferes constructively with the next pulse from the laser. A remaining challenge is the external use of these enhanced pulses as they are only available intracavity. In contrast, the approach illustrated in Fig. 1 bases on a constructive interference of N pulses at the exit of the laser system, making the enhanced performance directly available for applications. Divided pulse amplification (DPA) is another concept to increase the achievable pulse energy while keeping the average power constant [14,15]. Besides the possibility of scaling power and energy of femtosecond laser systems coherent combination provides the interesting opportunity to enhance the bandwidth of ultrashort pulses and therefore shorten the pulse duration. Recently, single-cycle pulses have been created by coherent synthesis of two fiber generated continua [16]. However, no active stabilization has been described in that manuscript.

In this contribution, we report on a proof-of-principle experiment, combination of two femtosecond fiber-based CPA systems in a Mach-Zehnder-type configuration. A combining efficiency as high as 97% has been achieved in the CPA configuration. Fiber laser systems are known to be limited by nonlinearity. In the CPA regime self-phase modulation (SPM) creates spectral phase terms which degrade the temporal Strehl ratio to a large extent. Hence, coherent combination of ultrafast fiber lasers is an interesting way to scale the performance of compact fiber based femtosecond lasers. To the best of our knowledge this reports for the first time the locked coherent addition of fiber amplified ultrashort laser pulses.

2. Challenges of coherent combination of ultrashort pulses

In order to achieve a high combining efficiency, and consequently an optimal performance scaling, some preconditions have to be fulfilled.

Firstly, one has to ensure a temporal synchronization of the N (N equals to the number of channels) pulses to be combined. Consequently, the optical path lengths of the N branches have to be matched with sub-wavelength precision. In the case of any delay coherent addition cannot take place over the entire pulse, hence, leading to a reduction in combining efficiency or even temporally separated pulses.

Furthermore, identical pulses have to be emitted from each channel. I.e. the spectral amplitude and phase as well as the spatial intensity profile and spatial phase have to be identical in order to obtain perfect coherent addition at the combining element.

In addition, a perfect overlap in the near- and far-field is required in order to obtain a combined output not to be distinguishable from a single emission. Hence, the alignment of the individual channels towards and through the combining element is subject to challenging demands.

Finally, the N amplification stages will see their own thermal, acoustic and vibrational noise sources. E.g. they are pumped by different laser diodes, they possessing different heat dissipation capabilities or they are located at different places in the laser system. Consequently, an active stabilization is required. Related to the approach which bases on polarization combining we have chosen a Hänsch-Couillaud detector [17] to measure the polarization state at the output. The error signal (deviation from linear polarization) is used to stabilize the synchronization of different channels by means of piezo-stages (or any possible phase adjustment) in N-1 channels. Details are provided in the following chapter.

3. Polarization splitting and combination of ultrashort laser pulses

The herein presented approach bases on splitting laser pulses on a polarization cube, spatially separated amplification and finally coherent superposition on a second polarization cube, hence, an interferometer with active branches. Figure 2 shows the schematic setup of polarization combining. For simplicity just two channels are considered in the following discussion.

 

Fig. 2 Illustration of polarization splitting and combining to create an active interferometer.

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The orientation of the linearly polarized light is inclined by 45° to the axis of the polarization cube, hence, the cube splits the power in two equal parts which are s- and p-polarized, respectively. These parts are directed to the different amplification stages. After amplification, the output of the two channels having an orientation of polarization perpendicular to each other are spatially and temporally overlapped on a second polarization cube. In the case of zero temporal delay the output polarization is linear, however, inclined by 45° if the laser power of both channels is equal. Any temporal delay causes an elliptical polarization state at the output of the cube. Therefore, the measurement of the polarization state by a Hänsch-Couillaud detector is a possibility to stabilize the synchronization of the two interferometer branches. A Hänsch-Couillaud detector consists of a polarizer cube and two photo diodes, the difference of the two measured signals, which is basically the sine of the phase delay, can be used as an error signal driving a piezo-stage in one of the branches. It is worth to mention that this approach can be extended to an arbitrary number of channels, because a wave-plate can be used to rotate the orientation of the polarization back to s or p. Of course, with increasing channel number the stabilization becomes more challenging.

4. Coherent combination of fiber-based chirp-pulse amplifiers

The herein presented approach bases on splitting chirped laser pulses on a polarization-dependent beam splitter, spatially separated amplification and finally coherent superposition on a second polarization cube before re-compression. Figure 3 shows the experimental setup of that configuration.

 

Fig. 3 Experimental setup of coherent addition of two femtosecond fiber-based CPA systems in a Mach-Zehnder-type configuration using polarization combining.

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The oscillator is a passively mode-locked Yb:KGW laser, delivering 400 fs pulses at a repetition rate of 10 MHz and 1030 nm wavelength. A half-wave plate and a polarizing cube are used to attenuate the average power in the range of mW and to define a linear polarization state. The 400 fs pulses are stretched to about 16 ps by means of a compact grating stretcher possessing 1450 lines/mm transmission gratings.

As described above, a polarization cube is implemented to split the oscillator into the two branches of the active interferometer. The horizontal polarization just passes the cube, the vertical polarization is by-passed and retro-reflected on a mirror on a piezo-stage. Due to a quarter-wave plate the pulses pass the cube as horizontal polarization. The piezo-stage is placed on a translation stage which is used to match the path lengths in the two branches.

Both branches employ Ytterbium-doped single-clad polarization-maintaining fiber amplifiers (Nufern Yb-YSF-HI PM980) possessing a mode-field diameter of approx.7 µm and a length of roughly 1.2 m. Pumping is achieved via standard WDMs which launch 976 nm radiation from single-mode laser diodes. Both amplifiers are seeded with 1 mW of average power. In addition to the active fiber, the input pigtail, the WDM and the output pigtail increase the total fiber length in each channel to 442 cm and 439 cm, respectively. After amplification the output is carefully collimated and directed to the combining cube. A laser window, with 0.2% of reflectivity is used to extract a minor part of the output for the Hänsch-Couillaud detection system. The two beams are furthermore overlapped in the near- and far-field to create a single output beam, which is sent through the grating compressor.

To characterize the combined output two parameters, the degree of linear polarization (DOLP) and the system efficiency, can be defined as follows:

Table 1 summarizes the obtained results. Two different power levels have been investigated, however, both amplifiers were operated at similar power levels. Firstly, the fiber amplifier output was set to 56 mW out of each channel, corresponding to a calculated B-integral of 1.3 rad. A combined power of P_comb = 110 mW has been measured after the laser window. The combined output and the combination itself are characterized by a DOLP of 97.6% and a system efficiency of 97.0%, respectively.

Table 1. Summarized experimental data of the combined fiber CPA system

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Increasing the power in each channel to 260 mW and 280 mW (i.e. B-integral is approx. 5.4 rad), respectively, leads to a combined power of P_comb = 530 mW, characterized by a DOLP of 97.2% and a system efficiency of 96.8%. Measuring the power between these measuring points results in efficiencies of approximately the same value, so no significant dependency on the output power has been observed until this power level.Figure 4 depicts the measured spectral characteristics of the individual channels and the combined output at the two different power levels. This measurement reveals a very good match of the combined and individual spectra, supporting the high combining efficiency of the system. The spectra at higher power show a self-phase modulation broadened characteristics, which is typical at that small stretched pulse duration and a B-integral of 5.4 rad. Nevertheless, as both channels experience nearly the identical nonlinearity the spectral amplitudes and phases differ not too much allowing for a constructive interference of all spectral components (under the precondition of matched and stabilized path lengths).

 

Fig. 4 Measured spectra a) at 110 mW combined power (B = 1.3 rad) and b) at 530 mW combined power (B = 5.4 rad) of the individual amplifiers and the combined output.

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Figure 5 shows the autocorrelation traces measured at low and high power. At 110 mW of average power before the compressor the autocorrelation width is 820 fs, which corresponds to a pulse duration of about 610 fs assuming a deconvolution factor of 0.74 obtained from numerical simulations. At the higher power level of 530 mW the AC-trace shows a typical structure of SPM influenced CPA, the FWHM pulse duration is 810 fs. Most important, there is no measurable difference between the AC-traces of the individual channels and the combining pulses, except for the increase in power.

 

Fig. 5 Measured autocorrelation traces of the combined and compressed fiber CPA output at different power levels.

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As described above, the error signal of the Hänsch-Couillaud detection system is used to drive a piezo stage in order to stabilize the path length of channel 2 with respect to channel 1 and to ensure stable constructive interference of the combined pulses. Figure 6 shows the recorded piezo position as a function of time for the two demonstrated power levels. According to that measurement a correction of the optical path difference as high as 37 rad peak-to-peak (equal to an optical path length of about 6 wavelengths) was necessary over that time scale. Noteworthy, there is no significant difference between the two power levels. We have performed identical measurements for a similar length of just passive fibers in the interferometer branches and no fibers at all in the interferometer. A corrected peak-to-peak optical path difference of 10 rad in the case of passive fibers and 3 rad in the case of no fibers has been measured, respectively. The causes of these fluctuations are density fluctuations of the air and temperature changes of the fibers, as well as power fluctuations of the amplifiers. They were all well below the maximum sliding range of the piezo system.

 

Fig. 6 Piezo positions as a function of time for two different power levels.

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A frequency analysis of the error signal for the higher power level both for locking on and off, in a frequency range up to 1000 Hz has been performed. Switching on the stabilization reduces the intensity of the error signal by 20 to 30 dB in a frequency range below 500Hz in which the most intense noise features can be found. Above 500 Hz the error signal is partly enhanced, however, important to mention that the integrated noise power is significantly lower than at lower frequencies. The currently employed piezo stage including its electronics works up to frequencies of few kHz, which appears sufficient to compensate for the thermal, vibrational and acoustic noise sources leading to a path length change in the two branches.

Finally, to illustrate the active stabilization of the coherent addition of ultrashort laser pulses a CCD camera plus an additional half-wave plate and analyzer cube is placed 50 cm behind the combining cube. As described above, any deviation from a match of the path length would lead to elliptical polarization and hence a fluctuating power behind the analyzer cube. Furthermore, any difference in power out of the two branches would lead to an inclination of the orientation of the linear polarization, hence, a power fluctuation behind the analyzer cube. As shown by the movie (Fig. 7 ), without locking strong power fluctuations are detected, basically making the path length variation under the experimental conditions (as shown in Fig. 6) visible. On the other hand, switching the locking electronics on a stable output beam can be observed. There are minor power fluctuations visible in locked operation, but those are caused by power fluctuations of the seed laser and the amplifiers, verified by comparing with the behaviour of a single running amplifier.

 

Fig. 7 CCD Camera images (Media 1) after further analyzer cube. left: locking off, right: locking on.

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Additionally, the beam quality was measured for both channels and the combined beam. The results showed an excellent beam quality with M² values lower than 1.2 in all cases, with no measurable decrease for the combined beam.

5. Conclusion and outlook

In conclusion, we have experimentally demonstrated the coherent addition of two fiber based chirped pulse amplifiers by using polarization combining. In a proof-of-principle experiment sub-picosecond pulse duration with 0.5 W of combined average power at 10 MHz repetition rate has been obtained. The combination is characterized by a high system efficiency of 97% and a degree of polarization as high as 97%. Beam quality and amplitude noise are comparable to an individual channel.

It is worth to be mentioned that to presented approach works for any laser architecture and any performance level, as long as the combining element can withstand to power and path length differences can be detected and compensated fast enough. Of course, the noise sources are specific for each laser and power level.

To provide two examples of potential performances based on coherent addition of ultrashort pulses: Femtosecond fiber lasers might be able to produce >10 mJ pulse energies at high repetition rates (100 kHz and above) starting from demonstrated mJ level performance [18]. The laser system used in that experiment provided a bandwidth and a B-Integral in the same range as the one presented in this paper, so the combination process is expected to work in a similar way. Additionally, Petawatt lasers could be combined to multi 10 PW peak power.