Fiber oscillators operating in the normal dispersion regime allow generating high energy output pulses. The best stability of such oscillators is observed when the intracavity dispersion is close to zero. Intracavity dispersion compensation in such oscillators can be achieved using a higher-order mode fiber, which substantially reduces the higher order dispersion compared to all-normal dispersion oscillators or oscillators using intracavity gratings for dispersion compensation. Using this approach, we are able to obtain relatively high energy pulses, with high fidelity. Our modeling based on an analytic approach for oscillators operating in the normal dispersion regime predicts that at intermediate pulse energies an almost flat chirp can be obtained at the oscillator output enabling good pulse compression with a grating compressor close to Fourier limited duration. Here, we present a mode-locked ytterbium-doped fiber oscillator with a higher-order mode fiber operating in the net normal-dispersion regime, delivering 7.2 nJ pulses that can be dechirped down to 62 fs using a simple grating compressor.
© 2013 OSA
All-integrated mode-locked ytterbium-doped fiber lasers delivering high fidelity pulses are very attractive as seed sources for ytterbium fiber amplifier systems  as well as ytterbium-solid state lasers  delivering sub-200 fs pulses. The main demands for seed sources of such systems are good pulse quality and compressibility, and enough seed energy. The requirement for pulse energy and pulse compressibility becomes even more demanding for phase stabilized amplifier systems . In order to achieve a reliable phase lock, sub-100 fs pulses with a pulse energy of several nJ are required. While in many applications solid state oscillators are used to achieve this, the robustness and stability of all-fiber oscillators offer an interesting alternative. Other applications for high energy fiber oscillators delivering high-quality sub-100 fs pulses, include micromachining and microsurgery, as well as nonlinear microscopy. Collateral damages or unwanted artifacts are minimized when the pulse duration is reduced and the pulse quality is improved.
Recently, many different approaches to push the pulse compressibility and energy of fiber oscillators have been explored. In general, two different operating regimes can be distinguished: Fiber oscillators with net anomalous intracavity dispersion, and fiber oscillators with net normal intracavity dispersion. Fiber oscillators operating in the first regime can produce highly compressible pulses, down to below 30 fs , but with only very limited pulse energy (generally < 1 nJ). Fiber oscillators operating with normal intracavity dispersion can produce pulses with higher pulse energy (generally > 1 nJ) , but the pulse fidelity from such oscillators is much lower. Generally, in order to achieve a higher output pulse energy, one needs to reduce the repetition rate of the oscillator, because the available pump power is limited. Without dispersion compensation, a decrease of the repetition rate leads to an increase of intracavity dispersion, which generally leads to a reduced spectral bandwidth with consequently longer pulses after extracavity compression. Except for the longer compressed pulse duration, another disadvantage of all-normal dispersion lasers is the reduced stability in terms of timing jitter [6–8]. Thus, through reduction of the intracavity dispersion the spectral bandwidth can be increased and the stability of the oscillator will be improved.
One of the main limitations in order to achieve better pulse quality is poor intracavity dispersion control for Yb-fiber oscillators; most Yb-fiber oscillators with intracavity dispersion compensation use intracavity gratings. While the use of gratings sacrifices the robustness and long-term stability of the fiber oscillator, the main limitation posed by intracavity gratings is that no compensation of higher order dispersion can be obtained. For more stable operation and better pulse fidelity, it is important to realize good compensation of higher order dispersion and intracavity nonlinearities. As an alternative to using bulk grating in the fiber cavity, the use of chirped fiber Bragg gratings has been demonstrated successfully , and the stability of such an oscillator was shown to be excellent . However, such devices have several drawbacks, most severely that they introduce severe ripples on the intracavity dispersion, which leads to a reduction of the compressibility of the output pulses. Hence, in order to develop a serious fiber-based alternative to solid-state seed oscillators, smooth fiber dispersion compensation is needed. The first approach for smooth fiber based dispersion compensation is based on the design of the waveguide dispersion in photonic crystal fibers . However, in order to achieve the required dispersion compensation, solid-core photonic crystal fibers with very small core diameters are needed, which leads to a large increase of the intracavity nonlinearities. Moreover, up to now, monolithic integration of photonic crystal fibers in fiber oscillators is problematic, since fusion splicing tends to destroy the fiber structure. When splicing photonic crystal fibers to standard single mode fiber, generally only the outer part of the solid cladding is actually fused to the outer part of the cladding of the single mode fiber. The cores are not actually fused together, resulting in relatively high splice losses. Splicing of photonic crystal fibers with very small cores requires additionally that the single mode fiber is tapered, which complicates the procedure even more. Here we report on a fiber oscillator working with net normal intracavity dispersion using another approach to achieve smooth fiber dispersion compensation, utilizing the anomalous dispersion of a higher-order mode (HOM) in a fiber . Using such a HOM fiber in an oscillator with net anomalous intracavity dispersion, 0.5 nJ, 57 fs pulses were realized . The advantages of HOM fibers illustrate their attractiveness: Mode conversion can be achieved reliably, and integration of solid, silica-based HOM fibers is possible using standard fusion splicing techniques. Additionally, the nonlinearities in the HOM module are slightly reduced compared to those in standard single mode fiber (SMF), since the mode area in the HOM fiber is slightly larger.
2. Experimental setup
Here, we present a 20 MHz fiber ring oscillator [sketched in Fig. 1(a)] that works in the net normal dispersion regime and uses an HOM fiber for dispersion compensation. The fiber length of the HOM module (3.6 m) is chosen such that its dispersion (in the HOM the pulses propagate in the LP02 mode) matches the dispersion of most of the SMF (6.2 m) in the oscillator, and its insertion loss is only 1.6 dB. As a result, only a limited amount of group delay dispersion (GDD) and third order dispersion (TOD) are accumulated per cavity roundtrip, as can be seen from Fig. 1(b). Modelocked operation in the oscillator is based on nonlinear polarization evolution (NPE), thus stable operation is ensured using fiber polarization controllers (PCs). Although the birefringence of the HOM fiber is negligible, stable modelocked operation requires strict control of the polarization state at its input and output, hence PCs are installed directly before and after the HOM fiber. The oscillator has two output ports: The first serves for pulse cleaning, and is, together with the NPE and the spectral filter, responsible for maintaining the modelocked operation. Because of its role, we will refer to this port as NPE port from here on. The output ratio at the second (main) output port is controlled with a half wave plate. The pulses are subsequently compressed using a transmission grating pair. The overall transmission of the compressor is about 50 percent, but with state-of-the-art gratings a transmission of more than 90 percent is feasible. We have characterized the output pulses from both output ports, which in combination with our calculations, allows us to gain insight in the pulse dynamics in the oscillator and the pulse-cleaning effect of the NPE port. Modelocked operation can be sustained over a wide range of pump powers, from ∼100 mW to the maximum available pump power of ∼450 mW. At higher pump powers broader output spectra and shorter compressed pulses can be achieved, however at pump powers close to the maximum available pump power we observed a decrease in compressed pulse quality. In addition to this, the output spectra and consequently compressed pulse duration can be reproducibly controlled by adjusting the PCs before and after the free space section, and by varying the output coupling ratio. The PCs right before and after the HOM fiber do not need to be adjusted after stable modelocked operation is achieved. It is worth to notice that the free space section in the oscillator is constructed such that the pulses circulating in the cavity are not deflected, thus minimizing the possible effect of mechanical instabilities on the operation of the oscillator.
3. Theoretical considerations
The pulse evolution in normal dispersion (fiber) lasers has been the subject of many theoretical (analytical and numerical) studies [14–19]. Since we aim at obtaining pulses with a high fidelity, we have looked at the chirp of pulses obtained in different regions where stable pulsed operation is feasible. The analytic calculations based on [14, 20] result in a master diagram which is shown in Fig. 2(a). Figure 2(b) shows the spectrum and chirp, obtained for solutions in the three regions in the master diagram labeled A, B, and C. In the low energy region A, the chirp increases rapidly away from the central frequency ωc, and in the high-energy region C, when looking from the spectral edges to the center the chirp first decreases, and then increases again to have a local maximum at the central frequency. When increasing the energy from region A to region C, the output chirp varies slowly with frequency, such that at intermediate energies a chirp of the output pulses is obtained that has a bi-quadratic dependence on the distance from the central frequency. The red line in Fig. 2(a) shows where the analytical calculations yield exactly this comparatively “flat” (i.e. frequency-independent) output chirp, i.e. where the pulses can be compressed to almost Fourier limited duration by a device that just subtracts a constant chirp with respect to frequency. In this region, to a good approximation, the best pulse fidelity can be expected after recompression with a simple grating compressor. The analytical theory predicts the maximum compressibility of a high-fidelity pulse on the stability border, where an approximately three-fold excess of compensating dispersion with respect to the intracavity dispersion is required for the pulse chirp compensation. The compression degree increases with weakening saturation of self-amplitude modulation (ζ-parameter in Fig. 2).
The analytic calculations have been performed assuming a flat group velocity dispersion, i.e. assuming absence of higher order dispersion. While in all-normal dispersion oscillators, a substantial third order dispersion is inherently present, in our oscillator, the third order dispersion has been greatly reduced. The main effect that can be expected of the presence of higher order dispersion, is that the region where stable pulsed operation can be obtained shrinks . While in the absence of higher order dispersion, stable operation is expected up to infinite pulse energies, higher order dispersion leads to an upper limit of the pulse energy that can be obtained.
4. Pulse characterization
We have performed a complete characterization of the oscillator output pulses. First, using a high bandwidth oscilloscope and matching photodiode, and a long range (±100 ps) second harmonic frequency resolved optical gating (SH-FROG) scan, we have confirmed the oscillator works in a single pulse mode. The spectral filter ensures the modelocked pulse train is stable, i.e. that every pulse has the same energy. The role of the characteristics of the spectral filter in the oscillator will be the subject of future investigations and is beyond the scope of this paper. The results of a finer short range SH-FROG scan after compression of the pulses from the main output port with a transmission grating pair are presented in Fig. 3. By appropriately setting the fiber polarization controllers to achieve stable single pulse operation the oscillator delivers up to 7.5 nJ pulses that can be dechirped to 62 fs. The measured spectral bandwidth corresponds to a Fourier-transform limited duration of 61 fs. In Fig. 3(c) we compare the Fourier transform limited and measured pulse profile, indicating the excellent pulse quality delivered from our oscillator. The small discrepancies between the Fourier transform limited and measured pulse profile are mainly due to the higher order dispersion that is not compensated by the grating compressor.
At a slightly lower pulse output energy, and with a slightly narrower output spectrum, we have measured SH-FROG traces of the uncompressed and the compressed output pulses from both the NPE and main output ports. The measured pulse energy from the NPE output port was 2.5 nJ, and the pulse energy obtained from the main output port was 7 nJ. The measured SH-FROG traces of the uncompressed pulses are shown in Fig. 4, together with the retrieved pulse profiles and spectra. From Fig. 4(a) it becomes clear, that even with phase shaping, it will not be possible to compress the output from the NPE port to a single pulse. The output pulses from the main port however, can be compressed to a single pulse with high fidelity. Figure 5 shows the results of SH-FROG scans after compression of the pulses from both output ports. As can be clearly seen from Figs. 4 and 5, the spectrum obtained from the NPE port is more structured, and as well slightly broader than the spectrum obtained from the main output port. Especially close to the long wavelength edge of the spectrum, the spectrum from the NPE output port is strongly structured, and a weak modulation is visible on the spectrum from the main output port. This modulation increases when the pulse energy right before the NPE output port is increased, and causes secondary pulses at both outputs. Since the modulation increases with pulse energy, it implies that at higher pulse energies the pulse quality will degrade due to excess nonlinearities in the oscillator. Here, the NPE output port actually plays a critical role in suppressing the secondary pulses from the main output port, which becomes clearly visible when looking at the compressed pulses in Fig. 5.
Recently, an all-normal dispersion ytterbium doped fiber oscillator that delivered 22 nJ pulses that could be recompressed to 42 fs was demonstrated  (the energy after compression was 10 nJ). In contrast to the oscillator with dispersion compensation described here, that oscillator used no anomalous dispersion components, and an adaptive pulse shaper was needed to obtain the optimal pulse compression, while in the experiments presented here, only diffraction gratings were used to compress the pulses, which greatly reduces the complexity of the setup. Another difference is that the oscillator in  uses fiber components with a 10 μm core diameter, instead of the standard SMF used in our oscillator. In  high energy pulses with similarly broad spectra were reported from an oscillator that utilizes standard SMF and intra-cavity diffraction gratings for dispersion management. A fundamental difference of [22, 23] compared to the work presented here, is that the main output is taken from the NPE port, from which the pulses are known to have a lower quality . For many applications, this does not matter, since nonlinear effects are utilized that only the main pulse can generate. But, when for example such pulses are further amplified, it can lead to unwanted detrimental effects, as was demonstrated in .
In conclusion, we have presented a fiber oscillator with all-fiber dispersion compensation with record performance delivering pulse parameters comparable to solid state oscillators. The use of an HOM fiber for dispersion compensation allowed us to dramatically reduce the intracavity higher order dispersion in the oscillator compared to oscillators using other means of dispersion compensation. The combination of that, with using an output coupler residing right after the NPE ejection port results in a high output pulse energy with high pulse fidelity. Since the net intracavity dispersion in our oscillator is close to zero, that aside from the demonstrated excellent pulse quality, also the pulse-to-pulse energy and carrier-envelope phase stability are expected to be superior compered to all-normal dispersion oscillators. Our modeling based on an analytic approach substantiates that control over the experimental parameters such as the dispersion and pulse energy allows to obtain pulses with good compressibility using a simple compressor. The reported pulse energy is 14 times higher than that of a previous oscillator using an HOM fiber delivering pulses with comparable duration .
This work has been supported by the Austrian Science Fund (FWF), grants U33-N16 and F1619-N08, and by the Austrian Research Promotion Agency (FFG), grant Eurostars 4319. A.F. acknowledges support from a Hertha Firnberg Fellowship by FWF (project T420-N16).
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