1. Introduction

At first glance, fibers do not seem to be the best choice for the amplification of high peak power ultrashort pulses. They are undoubtedly far more restricted by nonlinearities than other laser architectures since the light propagates confined in a small core along long distances. However, this property is at the same the biggest strength of the fiber laser systems. The inherent waveguide structure guarantees an excellent beam quality nearly independent of the emitted average power. Additionally, it enables a large single-pass gain resulting in simple, environmentally stable setups. In combination with the steady improvements in Chirped-Pulse Amplification (CPA) technology and the increase in the available fundamental mode area, fiber based ultrashort pulse lasers and amplifiers have been successfully developed from systems emitting pulses with peak powers in the kilowatt range only 15 years ago to today’s gigawatt-level systems. Thus, fiber based ultrashort pulse oscillators and amplifiers have found a variety of applications covering e.g. ultra-stable frequency combs [1], high harmonic generation [2,3] and micro-machining [4].

One integral part in this performance evolution is the development of so-called very large mode area fibers, i.e. single-mode fibers with Mode Field Diameters (MFDs) beyond 50 µm. In active operation, only solid-core Photonic-Crystal Fibers (PCFs) [5] have successfully demonstrated these large mode areas so far. These fibers consist of a solid signal core defined by a surrounding cladding with a hexagonal array of air holes. In the case of a large hole-to-hole distance (pitch) their modal discrimination mechanism can be understood by a modal sieve [6], where higher order modes suffer higher losses at the open interface between core and cladding. In the following we will refer to this type of fiber as Large-Pitch PCF (LPF).

However, embedding this structure into a double clad design, a necessary step for high power pumping, is not a straightforward approach since the modal sieve explanation is not valid anymore. This is because inside the highly multimode pump cladding every mode of pump and signal propagates, in a good approximation, without losses. Thus, only passive fibers with impressive core sizes beyond 100 µm have been demonstrated so far [7], whereas active mode field diameters were still limited to values around 60 - 70 µm [8,9]. In the case of a double-clad design, all the modes of the complete structure have to be considered since no distinction between core- and cladding-modes can be established. Typically, we define the mode with the highest gain overlap, a property that usually coincides with the smallest M² value, as the fundamental mode. Despite of the difficulties, effective single-mode behavior can still be achieved in these fibers by exploiting the different overlap of the modes with the doped area.

Up to now, the highest peak power emitted directly from a fiber amplifier system was demonstrated using an 85 µm rod-type PCF (see Fig. 1b ) with a corresponding MFD of 71 µm. This type of LPF with 19 missing holes can be seen as the step-index limit of the LPF design, since the rod type fiber possesses small air holes that can be described by an effective refractive index slightly lower than that of glass. Therefore, the resulting signal core NA can be extremely low.

 

Fig. 1 Microscope images (all at the same scale) of a) standard step index fiber with 6 µm core and 125 µm outer diameter, b) 85 µm core rod type LPF with 200 µm airclad diameter, and c) 108 µm core LPF with 340 µm airclad diameter.

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Using this kind of fiber, pulses with an energy of 1 mJ and a peak power of 1 GW were demonstrated [9]. However, in [9] the output pulses were still deteriorated due to the accumulated and uncompensated nonlinear phase despite of the large stretching ratio and core size.

In this contribution we present the experimental demonstration of a CPA system that overcomes this peak power limit. This becomes possible by using an Ytterbium-doped LPF (see Fig. 1c) with a core diameter of 108 µm and an affective MFD of 105 µm as main amplifier. It can be seen from Fig. 1 that the used one-missing-hole LPF is very different from the step-index like 85 µm rod-type PCF design. Furthermore, the nonlinear phase acquired during amplification is reduced by means of circular polarized light [10] and it is compensated by using a spatial-light modulator based phase shaping technique. Thus, this CPA system is able to produce pulses with 2.2 mJ compressed energy and 480 fs duration. To the best of our knowledge, the resulting peak power of 3.8 GW is the highest ever reported value directly emitted from a fiber chirped-pulse amplification system.

The maximum compressed average power of this system is 11 W and is limited by a mode-anticrossing [7]. However, we believe that this issue can be solved by small changes in the fiber design. The resulting new generation of active fibers will allow for the first time the combination of all the advantages fiber lasers and amplifiers are known for with multi-mJ pulse energies so far only achievable by other solid-state laser concepts.

2. Experimental setup and results

The fiber CPA system that will be described in this section is based on the system presented in [11]. A schematic setup can be seen in Fig. 2 . Broadband seed pulses at 1028 nm central wavelength are generated from a soliton-shifted Titanium-Sapphire oscillator. The pulse energy is on the order of a few picojoules at a pulse repetition frequency of 78 MHz. After passing a first fiber stretcher using 100 m of 6 µm core diameter polarization maintaining single-mode fiber, the signal pulses are stretched to 100 ps duration. Afterwards, they are amplified to an average power of 250 mW in an all-fiber amplifier stage using an Ytterbium doped 6 µm core fiber pumped at 976 nm wavelength. Certainly, for the sake of simplicity, all these first stages originating from a pump laser used for optical parametric CPA could be replaced by a standard fiber or bulk oscillator. In a next step the seed pulses are stretched by means of an Öffner-type reflection grating stretcher (1740 lines/mm) to a pulse duration of ~3 ns. The hard-cut of the stretcher is 7 nm resulting in a nearly rectangular spectrum after passing this element. In the following stage, a commercially available phase shaping device is deployed. This device measures the overall phase of the CPA system after compression using the so called multiphoton intrapulse interference phase scan (MIIPS) technique [12].

 

Fig. 2 Schematic drawing of the experimental setup. AOM: Acousto-Optical Modulator, WDM: Wavelength Division Multiplexer, SLM: Spatial Light Modulator

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Afterwards, the output pulse quality is iteratively optimized by means of a 128 pixels spatial light modulator. Therefore, all effects that may cause pulse quality degradation, e.g. the accumulated amount of nonlinear phase during amplification, higher order dispersion or a small stretcher-compressor mismatch, can be efficiently pre-compensated. After the pulse shaper, further amplification is achieved using a two stage pre-amplifier comprising a core pumped 6 µm MFD fiber and a 1.2 m long PCF with 30 µm MFD and 170 µm airclad diameter. Both Ytterbium-doped fibers are pumped at 976 nm wavelength. Before and after each fiber amplifier an acousto-optical modulator is used to gradually reduce the pulse repetition frequency to a value of 5 kHz. In comparison to one single pulse picker, the use of a total of three pulse pickers has the advantage of an efficient suppression of intermediate pulses and providing sufficient seed for the amplifier chains. At the end of this stage, a pulse energy of 40 µJ is launched into the main amplifier.

As the main amplifier stage the 1.3 m long Ytterbium doped LPF depicted in Fig. 1c is used. For comparison in this figure also an 85 µm core rod type LPF (Fig. 1b) and a 6 µm core size standard step-index fiber (Fig. 1a) are shown. The used LPF was designed according to simulations based on a finite differences frequency domain mode solver [13]. The fiber parameters are a hole-to-hole distance (pitch) of Λ = 60 µm and a relative hole diameter of d/Λ = 0.22. The airclad diameter measures 340 µm resulting in a pump light absorption of 24 dB/m at a pump wavelength of 976 nm. During production, considerable effort has been spent on matching the refractive indexes of the doped core region n _core and the surrounding glass n _clad. At these large core sizes the index depression Δn = n _clad - n _core has to be carefully adjusted [14] in order to avoid step-index guidance (Δn < 0) or beam quality degradations at index depression values of Δn > 5·10⁻⁵. The resulting edge-to-edge core size is 108 µm. The measured mode field area is 8600 µm² corresponding to a MFD of 105 µm. Due to this large mode area, the fiber has to be kept straight and, therefore, possesses an outer diameter of 1.8 mm. Additionally, the incident polarization state in the LPF is changed from the initial linear to circular polarization and back again by placing two quarter-wave plates before and after the main amplifier. This simple procedure reduces the amount of acquired nonlinear phase by 2/3^rds due to the reduction of the nonlinear index of refraction n₂ [10].

The fiber is used in a counter-propagating pumping setup. At a maximum launched pump power of 65 W an output power of 15 W was achieved. In consequence of the negligible content of amplified spontaneous emission in the signal beam, the corresponding pulse energy is 3 mJ. At this power level the B-Integral, i.e. the maximum amount of acquired nonlinear phase, can be estimated to be B = 6 rad.

Any further increase in pump power results in beam quality degradation and in an increase of the signal power contained in the pump cladding (see Fig. 3 ). This observation was confirmed by a beam quality measurement at the fiber output using a commercial available Spiricon M²-200 device. Starting from an excellent value of M_x ² = 1.2 and M_y ² = 1.3 at 0.5 mJ pulse energy the beam quality degrades towards M_x ² = 1.5 and M_y ² = 1.8 at the maximum power level.

 

Fig. 3 Near field images of the LPF output beam profile for a) low output powers and b) for the maximum power level. Signal energy contained in the outer ring of the pump cladding is cut in the compressor (and therefore not included in the power measurements) and also blocked for M² measurements.

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We believe that the reason for this effect is a mode-anticrossing [7], i.e. the change of a fiber parameter results in an approach of the effective indexes of two modes which comes accompanied by a change of their shapes. In our case the influenced fiber parameter is the refractive index inside the signal core of the fiber. There are different reasons for an index increase during active operation, e.g. the temperature dependent refractive index change of the material (dn/dT ~10⁻⁵ / K), the resonant nonlinearity resulting from the inversion [15] (on the order of Δn = 10⁻⁵ for a fully inverted fiber) and the optical Kerr effect. The latter can be estimated to be Δn = 7·10⁻⁶ assuming a maximum achieved intensity in the fiber core of I _max = 23 GW/cm² (1 MW peak power). However, these mode-anticrossings can easily be avoided by small changes in the fiber design like e.g. cladding modifications.

Finally, the pulses are compressed back to an ultrashort duration by means of a dielectric reflection grating compressor. After this last stage the output pulses posses an energy of 2.2 mJ and a corresponding average power of 11 W. The pulse quality is measured with the help of a commercially available FROG device (GRENOUILLE 10-500). The retrieved pulse shape and phase is depicted in Fig. 4a . The corresponding pulse duration is 480 fs.

 

Fig. 4 a) Temporal profile (blue) and phase (green) of the output pulses at a maximum pulse energy of 2.2 mJ measured with a commercially available FROG device (GRENOUILLE 10-500). The insets show measured and retrieved FROG traces. The FROG error is 0.8%. b) Autocorrelation calculated from the FROG pulse (blue) and measured with autocorrelator (red).

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The FROG measurement has been compared with a second harmonic autocorrelation and good agreement between both measurements has been found (Fig. 4b). Figure 5a shows the spectrum before and after the main amplifier. It can be seen that the central wavelength experiences a red-shift. The reasons for that are, one the one hand, gain shaping (since the cross-section maximum is located around 1035 nm) and, on the other hand, pulse saturation inside the main amplifier. Here, the longer wavelengths at the leading edge of the chirped pulse deplete a significant amount of inversion and, therefore, experience a higher gain than the trailing edge (shorter wavelengths). The pulse spectrum and the residual nonlinear phase at the output of the system retrieved by the FROG measurement are shown in Fig. 5b. For comparison, the spectrum measured with an optical spectrum analyzer is also depicted in this figure and shows good agreement.

 

Fig. 5 a) Spectra before the main-amplifier (black) and after the compressor (red) at maximum pulse energy of 2.2 mJ measured with an optical spectrum analyzer. The Fourier-limit of the output spectrum is 415 fs. b) retrieved spectrum (blue) and residual spectral phase (green) measured at the same power level with a commercially available FROG device (GRENOUILLE 10-500). For comparison the output spectrum from a) is depicted in gray.

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According to the FROG measurements the resulting peak power of the 2.2 mJ pulses is 3.8 GW. To the best of our knowledge, this is the highest value directly achieved with a fiber amplifier system. Future steps will include modifications in the design of the large pitch fiber that avoid mode-anticrossings and, therefore, allow for both large pulse energies and average powers. Beside further mode field area scaling, even larger peak powers seem feasible by increasing the spectral bandwidth of the amplified pulses.

These improvements may include a shift of the central wavelength of the seed oscillator to longer wavelengths [16], a bandwidth increase of seed source, stretcher and compressor or spectral shaping in order to prevent gain narrowing during amplification. Consequently, a 10 GW fiber chirped-pulse amplification system comes into reach.

3. Conclusion

We presented a fiber CPA system that comprises a large pitch fiber with 105 µm mode field diameter. In combination with a reduction and compensation of the acquired nonlinear phase we extracted 2.2 mJ pulses with nearly transform-limited 480 fs pulse duration at 11 W average power. Apart from additional pulse shortening schemes like hollow fiber compression [17] or the use of such a system as pump source for few-cycle optical parametrical CPA [11], this peak power is the largest value reported so far from fiber laser or amplifier systems. Moreover, the combination of such a high peak power system with one of these techniques will enable even higher peak powers. These fiber based systems may access for the first time power levels so far only accessible by other solid-state laser concepts.