There are still very strong interests for power scaling in high power fiber lasers for a wide range of applications in medical, industry, defense and science. In many of these lasers, fiber nonlinearities are the main limits to further scaling. Although numerous specific techniques have studied for the suppression of a wide range of nonlinearities, the fundamental solution is to scale mode areas in fibers while maintaining sufficient single mode operation. Here the key problem is that more modes are supported once physical dimensions of waveguides are increased. The key to solve this problem is to look for fiber designs with significant higher order mode suppression. In conventional waveguides, all modes are increasingly guided in the center of the waveguides when waveguide dimensions are increased. It is hard to couple a mode out in order to suppress its propagation, which severely limits their scalability. In an all-solid photonic bandgap fiber, modes are only guided due to anti-resonance of cladding photonic crystal lattice. This provides strongly mode-dependent guidance, leading to very high differential mode losses. In addition, the all-solid nature of the fiber makes it easily spliced to other fibers. In this paper, we will show for the first time that all-solid photonic bandgap fibers with effective mode area of ~920μm2 can be made with excellent higher order mode suppression.
©2012 Optical Society of America
Despite significant developments in fiber laser technology in recent years, there are still great needs to scale powers in both CW and pulsed lasers for use in a wide range of industrial, scientific and defense applications. Optical nonlinear effects, such as stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS), self-phase modulation (SPM) and Four-wave-mixing (FWM) are some of the key limiting factors in power scaling. All these nonlinear effects can be mitigated by effective mode-area scaling of fibers while maintaining single-transverse-mode operation. In addition, effective mode-area scaling can also lead to a high pulse energy desired in many pulse laser systems, due to an increase in stored energy in the amplification process.
The general issue for mode-area scaling is to mitigate the waveguide’s tendency to support an increasing number of modes at large core diameters. A large number of approaches have been studied that mostly fall into three categories. The first involves reducing the numerical aperture (NA) of a waveguide. Since the number of modes supported by a waveguide is a function of both core diameter and NA, a lower NA can be used to reduce the number of guided modes. Some early approaches of mode-area scaling , photonic crystal fibers [2,3] and recent triple clad approaches  fall into this category. One major deficiency of these approaches is that a lower NA weakens fundamental mode guidance and renders it very sensitive to bending and any other mechanical perturbation on the fibers. Photonic crystal fibers with over 40μm core diameter can only be used as straight rods. The second category includes approaches based on the introduction of differential mode losses. Here, fundamental mode guidance is strong enough to allow coiling even at large core diameters while higher order modes are eliminated by introducing higher losses for these modes. Conventional step-index large mode area fibers (LMA)  fall into this category and differential mode loss in this case is from coiling. This approach exploits strong mode-dependent loss to mitigate the waveguide’s tendency to support more modes at large core diameters. One major benefit of this approach is that strong fundamental mode guidance can be maintained to allow coiling. The major challenge is to introduce very high losses for all higher order modes at the desired wavelength while maintaining good fundamental mode transmission.
Special waveguide designs can also be used to further increase differential mode loss. Some recent approaches include resonant-ring designs  and chirally-coupled-core fibers . Both rely on resonant out-coupling of higher order modes from a conventional step-index core. A low loss is ensured for the desired fundamental modes by the conventional cores. They are, however, limited in terms of scaling much beyond 50μm core diameter. The higher order mode out-coupling fundamentally relies on phase-matching typically at a different wavelength for a different mode, and spatial overlap between the modes. However, both these aspects become major limits very quickly in a large core fiber. As such, it becomes difficult to ensure that all phase-matching conditions are met at the same desired wavelength for all relevant higher order modes when there are a number of modes in consideration. As the core diameter increases, these higher modes in the core are increasingly more confined to the core center. This leads to much less mode coupling due to a reduced spatial overlap between the coupling modes and much stronger wavelength-dependence in phase-matching. Both make these designs hard to implement, especially at large core diameters.
Some more recent approaches in this second category also include leakage channel fibers [8,9]. They overcome the limitations of the resonantly-coupled approach by starting with a leaky waveguide. Because modes are no longer guided in a leaky waveguide, a significant new way for optimizing differential mode loss is possible. Since these designs do not necessarily depend on any resonant effects, they are much more tolerant in the fabrication process. Due to delocalized nature of modes, they are more scalable to much large core diameters. Single mode operation in a core diameter of 180μm has been demonstrated in leakage channel fibers .
The last category of approaches for mode area scaling is based on the operation of one of the higher order modes (HOM) in a highly multimode fiber . This approach works upon the premise that the propagation of a higher order mode can be very stable even in a highly multimode fiber. Moreover, these higher order modes can offer significantly better bending performance . The main deficiency of this approach is that, in an active highly multimode fiber, spontaneous emission populates all modes equally by fundamental quantum mechanical principles. This can significantly limit the operation of high gain amplifiers due to strong amplified spontaneous emission (ASE) in undesired modes. While complex techniques have been proposed recently to mitigate these limits , it is hard to completely eliminate this ASE problem.
Mode area scaling to 20μm mode field diameter using all-solid photonic bandgap fibers was reported few years ago . A detailed theoretical investigation on the limit of mode area scaling with all-solid photonic bandgap fibers was reported recently , indicating an upper limit of ~500μm2 using a more optimized seven-cell core and operating in the first bandgap. Recently, all-solid photonic bandgap fibers with up to ~700μm2 effective mode areas have been demonstrated operating in the first bandgap [15, 16].
In all-solid photonic bandgap fibers, a mode is guided only when it falls within the photonic bandgap of the cladding lattice. This provides great potential for creating designs that support only the fundamental mode, i.e. selective mode guidance versus selective elimination of mode guidance as in some other approaches. The robust optical guidance and physical constructs of all-solid PBFs enable them to be made and used much like conventional fibers. Double-clad designs and polarization-maintaining can be added with ease. Transmission can be made with strong wavelength-dependence in these fibers for use in SRS suppression, accomplished by introducing strong loss at the Raman Stoke wavelength, in FWM suppression by providing appropriate dispersion, and in lasers at wavelengths normally dominated by much stronger transitions .
In this work, we will report, for the first time, both theoretical and experimental studies of mode-area-scaling with all-solid photonic bandgap fibers to beyond 900μm2 which has the capability to delivery 30 times of power as regular single-mode fiber without reaching the non-linear threshold. We have performed what we believed to be the first quantitative mode content analysis in all-solid photonic bandgap fibers using a S2 method . The quantitative mode content measurements show that excellent single mode output can be obtained from theses fibers in length scale close to what is required for fiber laser and amplifiers. Measured higher order mode power is less than −30dB below that of fundamental mode.
Guidance properties of all-solid photonic bandgap fibers and their fairly matured fabrication processes are well understood [19–21]. These fibers have a background glass and a cladding lattice of high index nodes (Fig. 1(a) ). The cladding is defined by node diameter d, pitch Λ, node index nh and background index nb. The photonic bandgap effect of the cladding lattice, i.e. anti-resonant effects of the cladding lattice, guides light in the core of the fiber. The bandgaps in the cladding is illustrated as the white areas in Fig. 1(b). The horizontal axis in Fig. 1(b) is the normalized frequency of the node, V/π = (d/λ)(nh2-nb2)1/2 and the vertical axis modal index minus nb. The guided modes in the defect core only exist within the cladding bandgaps, which determine the wavelength range over which the modes in the core are guided. This photonic bandgap guidance can be strongly mode-dependent. A large core all-solid PBF can potentially be designed by maximizing guidance of the fundamental mode while minimizing the guidance of all higher order modes, equivalent to the use of mode-dependent leakage losses. As in conventional fibers, the effective indices of the core modes are just slightly below the core index nb. First three modes in the first bandgap of an all-solid photonic bandgap fiber with 50μm core are illustrated in Fig. 2 , showing strong guidance of fundamental mode and weakly guided higher order modes.
A recent theoretical work has determined that a seven-cell all-solid photonic bandgap fiber can achieve an effective area of 511μm2 in a fiber with a core diameter of ~42.2μm when operating in the first photonic bandgap at ~1μm and being coiled at radius R = 10cm . Further mode area scaling is limited by significant increase of fundamental mode loss at large pitch required for larger cores, noting core diameter 2ρ = 4Λ-d for a seven-cell core. Higher order bandgaps are usually associated with shallower bandgaps and, consequently, high losses (Fig. 1(b)). However, this loss can be significantly lowered by an increase of d/Λ. Operating in the third bandgap allows choosing a much larger d/Λ, by almost a factor of three. This is more than what is required to compensate the loss caused by the reduced bandgap depth, leading to an overall lower loss for the fundamental mode and, consequently, much larger core diameters for using the third bandgap. In this work, we will demonstrate further mode area scaling is still possible with the operating in the third bandgap.
Fundamental mode (FM) and second order mode (referred to as HOM) losses versus normalized frequency V over the third bandgap are simulated using a Finite Element Method (FEM) mode solver developed at Hokkaido University for Λ = 13.0μm, 13.5μm, 14.0μm, 14.5μm, 15.0μm and 15.5μm, for each Δ = (nh2-nb2)/2nh2 = 0.5%, 1.0%, 1.5%, 2.0%, 2.5% and 3.0%, at λ = 1050nm, bend radius R = 15cm, and number of cladding layers N = 5. The results are shown in Fig. 3 , Fig. 4 , Fig. 5 , Fig. 6 , Fig. 7 , and Fig. 8 , respectively. All other higher order modes have much higher losses and are not plotted here. Node diameter d is varied to adjust V while all other parameters remain constant for each curve.
As it can be seen, the loss difference between the FM and HOM increases in general at a larger Δ. The dependence on Λ is more subtle at constant Δ. In general, larger differential mode loss can be achieved at larger Λ, if V is carefully chosen. We target our FM loss to be <0.1dB/m and HOM loss to be >10dB. Two dotted lines representing the 0.1dB/m and 10dB/m targets are also shown in the figures. It can be clearly seen in Fig. 8 that not only can these targets be met for Λ = 15.5μm, corresponding to a core diameter of ~55μm, and FM/HOM differential mode loss of over 4 orders of magnitudes can be realized. This is the highest level of HOM suppression that we have seen for core diameter of ~50μm in any known designs.
Two fibers were fabricated for this work (see Table 1 .). The nodes in the cladding of Fiber 1 are made from a graded index MM preform with germanium doped core with peak Δ = 1.72%. The nodes of Fiber 2 are made from a step-index preform with germanium doped core with peak Δ = 1.52%. Fibers 1 and 2 have respective core diameters of 55.1μm and 49.1μm. The cross sections of the two fibers are shown in Fig. 9 . Effective mode area of Fiber 1 is simulated at various coiling diameters and is shown in Fig. 10 , showing an effective area of ~900μm2 at wavelength of 1050nm and coil diameter of 30cm. An effective are of ~920μm2 can be achieved when using 50cm coil diameter. There is no significant variation in mode areas when wavelength is changed within the bandgap (see Fig. 10).
The bend-dependent loss was measured for Fiber 1 by setting the coil diameters to 20cm, 30cm and 35cm and performing cut-back measurements. The result is shown in Fig. 11(a) . The target coil diameter is 30cm. At the center of the third bandgap at ~1.05μm, very little bend dependent loss was measured at the target coil diameter. At 20cm, significant bend-induced loss was seen throughout the band. Also shown is the much stronger bend-induced loss in the second bandgap at ~1.55μm. This is expected, due to the shallower band depth for this even bandgap  (Fig. 1(b)). Single mode output of 2m Fiber 1 coiled at 30cm diameters was tested qualitatively by monitoring the near field output pattern while the launch beam is moved across the front face of the fiber (Fig. 12 ). No sign of higher order modes is present during the entire process, indicating fairly robust single mode operation.
The loss of Fiber 2 is shown in Fig. 11(b). The fiber was loosely coiled for the measurement in Fig. 11(b). It was also confirmed that the loss in the center of the third band around 1050nm was hardly changed when the fiber was coiled down to 30cm. More quantitative mode analysis on Fiber 2 was performed with a S2 setup  implemented with a rapidly tunable external cavity diode laser from 1020nm to 1085nm, a wave meter and a CCD camera. In all our measurements, an input and output polarizers were used and both were aligned to the birefringence axis in the fiber. We have found that our all-solid photonic bandgap fibers have a weak birefringence due to asymmetries introduced during fiber fabrication. The setup is capable of performing necessary S2 measurement quickly and resolving mode power below −35dB of fundamental mode. S2 measurements were performed on 6m Fiber 2 coiled at 30cm, 40cm, 50cm and 80cm while efforts were made to ensure launch is not altered while changing coil diameter. The normalized power versus total relative delay is plotted in Fig. 13 for the 30cm coil diameter at two positions on CCD, one at peak of LP11 mode intensity (solid black line) and one at LP02 mode peak intensity (dotted red line). The plot in Fig. 13 shows the Fourier transform of power beating between high order modes and fundamental mode in which, the beating amplitude is proportional to the ratio of their electric field. The mode image and content were calculated using the peak in the curves for respective modes. The two sharp peaks at 7.7ps and 11.8ps are from interferometers formed by bulk optics in the system. These features were well characterized prior to these measurements. The broad peaks at ~4ps and ~12ps are from LP11 and LP02 modes respectively. The resolved mode patterns are plotted in Fig. 14 . The measured LP11 and LP02 mode contents are shown in Fig. 15 at various coiling diameters. Below 40cm coil diameters, the LP11 and LP02 mode contents do not seem to vary very much and the mode contents are below −33dB for both observed modes. No other higher order modes are observed. Over 30dB higher order mode suppression can be achieved at coil diameter of 50cm as shown in Fig. 15, demonstrating a record effective mode area of ~920μm2 for all-solid photonic bandgap fibers.
Fiber birefringence can also be measured using the S2 setup by aligning both input and output polarizers at 45 degree angle to the fiber birefringence arises. The polarization mode beating leads to a sharp peak in the delay curve. The group birefringence can then be calculated from this measured polarization mode delay. This was done for Fiber 2, resulting in a measured birefringence of 3.1 × 10−6. Polarization mode extinction ratio (PER) was measured for 6m Fiber 2. This is given in Fig. 16 . It is interesting to note that PER as high as 14dB were achieved in this nominally non-PM fiber. This birefringence is a result of geometry asymmetry introduced during the fabrication process.
4. Discussions and conclusions
We have studied both theoretically and experimentally the possibility of further mode area scaling using all-solid photonic bandgap fibers. Our theoretical studies have shown that all-solid photonic bandgap fibers have the potential to provide significant higher order mode suppression. Our experimental studies have confirmed this to a large extent. We have demonstrated a record effective mode area of ~920μm2 in all-solid photonic bandgap fibers with higher order mode content below −30dB. Recently, it was observed that mode instability can be initiated by very small amount of higher order modes when combining with thermal effects . Fibers with strong higher order mode suppression are critical for further power scaling of single mode fiber lasers to beyond kW levels. We are currently working on ytterbium-doped all-solid photonic bandgap fibers.
This material is based upon work supported in part by the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF-10-1-0423 through a Joint Technology Office MRI program.
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