In this Letter, we present, to the best of our knowledge, the largest effective single-mode fiber reported to date. The employed waveguide is a passive large pitch fiber (LPF), which shows the core area scaling potential of such a fiber structure. In particular, we achieved stable single-transverse mode transmission at a wavelength of 1.03 μm through a straight passive LPF with a pitch of 140 μm, resulting in a measured mode-field diameter of 205 μm.
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Several scientific and industrial applications of ultrafast lasers, such as materials processing or high-harmonic generation, demand high pulse peak powers. In addition, these applications would strongly benefit from a high repetition rate (i.e., a high average power), which can be offered by fiber laser systems. However, delivering high peak powers is challenging for fiber laser technology due to the early onset of detrimental nonlinear effects. In order to increase the peak power achievable with fibers, an enlargement of the single-transverse mode areas is a very valuable path. In past years, several fiber designs, such as chirally-coupled core fibers , distributed mode filtering rod-type fibers , leakage channel fibers , multitrench fibers , photonic bandgap fibers , Bragg fibers , and large pitch fibers (LPFs) , have been developed to achieve a very large mode-field area while maintaining effective single-mode operation. The term “effective” implies that these fibers are not operating strictly single-mode in an analytical consideration. However, if the discrimination of higher-order modes (HOMs) is sufficiently high, the fundamental mode will be the most dominant mode at the output of the fiber (regardless of the modal excitation at the fiber input).
The LPF design currently holds most of the performance records in ultrafast fiber lasers [8–10]. The reason is that this design has been able to combine the ability to deliver high average output powers with large mode-field sizes and effective single-mode operation. The structure of a typical active LPF, such as the one demonstrated in , is shown in Fig. 1(a). The waveguide, which is embedded in a matrix of fused silica, consists of the doped core region (green), two hexagonally arranged rings of air holes and a surrounding low-index cladding ring. The holes with diameter are equidistant from each other with a separation (pitch). Due to the cladding ring, and its associated lower refractive index (closed barrier), this structure exhibits no losses for any transverse mode. The reason why this structure still shows effective single-mode behavior is that the fundamental mode (FM, -like) exhibits a significantly higher overlap with the doped core region than the HOMs, which results in a preferential amplification and excitation of the FM. 
In contrast, a passive LPF [Fig. 1(b)] has neither the doped core region nor the cladding ring (which is the most important distinction). The missing cladding ring, as seen in Figs. 2(a) and 2(b), leads to confinement losses for each mode due to the leaky hole structure. The symmetry and the shape of the intensity profile of the propagating modes, e.g., the -like in Fig. 2(c) or the -like mode in Fig. 2(d) strongly influences the degree of leakage. In this Letter, we study the differential confinement losses of the FM and the first HOM (i.e., the HOM with the lowest losses) in a passive LPF with varying pitch and relative hole size . A mode solver based on a full-vectorial finite-difference approach, such as the one described in , has been used. The power confinement losses (in dB/m) are deduced from the complex effective index and the wavelength , as described in 7].
Figure 3 (upper graph) shows the calculated confinement losses (in dB/m) for the FM and the first HOM (lower graph) in a logarithmic scale as a function of the pitch and the relative hole size . As expected, the propagation losses for the modes decrease with increasing pitch. This behavior can be explained by the larger mode-field diameter (MFD) and the associated lower divergence angle of the modes. An increasing also reduces the propagation losses of the FM, since the mode is more confined within the structure.
As described above, the passive LPF does not have either the doped core region or the cladding ring. Consequently, these fibers cannot benefit from the preferential amplification effect, but they still exhibit a preferential excitation of the FM (since the HOMs are largely delocalized from the core). This, together with the higher propagation losses of the HOMs, allows for effective single-mode operation up to a certain pitch (due to the waning propagation losses). Using anecdotal evidence in the lab, effective single-mode operation over one meter of fiber length can be obtained when setting an upper limit of the propagation losses of the FM to 1 dB/m and a lower limit of the propagation losses of the HOMs to 10 dB/m (see the dashed lines in Fig. 3). Under these circumstances, effective single-mode operation can be guaranteed in a certain range of the pitch. The minimum and maximum pitches depend on the relative hole size. Thus, for a of 0.4, 0.3, 0.2 and 0.1, the maximum pitch is , , , and , and the minimum pitch is , (both not shown in Fig. 3), , and , respectively. It can be seen that the working range strongly depends on the relative hole size and, finally, is limited to one point (in the case of ), where the lower limit for the FM and the upper limit for the first HOM are fulfilled at the same time.
In order to test the theoretical predictions, passive LPFs were drawn and characterized using the experimental setup depicted in Fig. 4. The seed system was an all-fiber laser system emitting stretched femtosecond pulses at a 1.03 μm wavelength and an average output power of 100 mW. The laser beam was imaged to the fiber under test (rod-type with an outer diameter between 1 and 2 mm). The fiber end facet was imaged onto a CCD chip. Since the magnification of the imaging optics is well known, the effective mode-field area and the appropriate MFD of the excited mode could be determined. By offsetting the coupling lens in the - and -direction, the excitation of HOMs can be expected. If these modes exhibit sufficiently high losses in the fiber, they will not be observed at the fiber end facet, which should provide evidence of the effective single-mode operation of the fibers.
Figure 5(a) shows the emitted beam of the LPF under test, which possesses a pitch of about 140 μm. The corresponding simulated FM is depicted in Fig. 5(b). By offsetting the coupling lens in the - and -direction, almost no content of higher-order transverse modes was observed at the fiber end facet (Visualization 1). The measured MFD was determined to be . This is in excellent agreement with the theoretically calculated MFD of 205 μm, which corresponds to an unprecedented effective mode-field area of about at a 1.03 μm wavelength.
Apart from the verification of effective single-mode operation, the propagation losses of the FM of some fibers have been determined by using the cutback method. Hereby, the length of the fiber has been progressively reduced, while the transmitted power in the core was simultaneously recorded. The propagation losses of the fiber can be derived taking into account the Lambert–Beer law. 
Table 1 shows the results of three LPFs with different pitches. For the simulations of the MFD and the propagation losses, the measured fiber structure, as shown in Figs. 2(a) and 2(b), has been used. All three LPFs operated in effective single-mode regime. The measured MFDs grow with increasing pitch, whereas the measured propagation losses of the FM drop with increasing pitch, as expected. While the simulated and measured MFD agree well, the propagation losses differ slightly. Perturbations (such as defects or scattering centers) within the fiber may be the reason for slightly increased propagation losses of the FM. The propagation losses of the LPF with 140 μm pitch were not measured due to the destructive nature of the cutback method, since further tests with this fiber are not excluded.
In summary, we have presented the results on the core size scaling of passive LPFs. These fibers present transverse mode discrimination through a combination of differential propagation losses and preferential excitation of the FM. A mode solver has been used to perform simulations on the propagation losses of the FM and the first HOM in these structures. The simulations have revealed that the propagation losses of both the FM and first HOM decrease with increasing and . This, in turn, poses a limitation to the HOM discrimination while upscaling the mode area. In the experimental part of this Letter, we were able to achieve effective single-mode operation in a passive LPF with a pitch of approximately 140 μm and of 0.3, which is in good agreement with the simulation results and expectations. With a MFD of 205 μm, to the best of our knowledge, this is the largest effective single-mode fiber reported so far. This result corresponds to a mode area scaling of a factor of and a factor of , compared to the largest effective single-mode reported until now in an active fiber and a passive fiber, respectively [11,15].
In this Letter, it has been shown that the passive LPF structure provides the necessary loss mechanisms to discriminate HOMs for further mode area scaling. Considering possible applications, this passive fiber type, for example, could be used for nonlinear compression of high peak power pulses. This approach is particularly interesting in combination with Tm-fiber laser systems . In the next step, the advantages of the passive LPF structure have to be transferred to active fiber concepts. Therefore, a revised fiber design has to be developed which benefits from the loss mechanisms of the passive LPF structure for the signal light, but is still able to guide the pump light without substantial losses. This evolution could be an important next step towards further mode area scaling in active fiber amplifiers.
ACOPS, H2020 European Research Council (ERC) (617173); European Regional Development Fund (ERDF) (2015 FGR 0107); European Social Fund (ESF) (2015 FGR 0107).
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