We report on the design of a novel flexible very large mode area photonic crystal fibre for short pulse high peak power fibre laser and beam delivery applications. This fibre has an extremely large mode area exceeding 2500 µm2 when kept straight and over 1000 µm2 when bent over a 10 cm radius at a wavelength of 1064 nm. In addition our fibre exhibits very small fundamental mode bending loss below 10−2 dB/m. The large difference between the propagation loss levels of fundamental and higher order modes forces efficient single-mode guidance in the fibre core while bent. This allows using the fibre to build compact high power laser systems. The paper further explores the major features of this fibre including: the dependence of the mode field area on the fibre core shape, the influence of the bending radius and of the bending direction as well as the impact of manufacturing tolerances on the fibre specifications.
©2010 Optical Society of America
Fibre-based lasers have been the subject of intensive research and development in the last decade: they can offer excellent efficiency and high single pass gain, efficient and rapid heat dissipation, immunity to thermo-optic effects and a diffraction-limited output beam with several kilowatts continuous wave power .
The development of short pulse high peak power fibre lasers however still has to cope with a number of issues. In such laser systems the power density in a relatively small core can reach extremely high levels and consequently nonlinear effects such as stimulated Raman scattering, stimulated Brillouin scattering and self-phase modulation limit efficient operation or simply prevent lasing. Furthermore catastrophic failure of the fibre will occur if the power density exceeds the material damage threshold.
Avoiding nonlinear pulse distortion resulting from self-phase modulation can for example be achieved by reducing the pulse intensity and more specifically by stretching the pulse in time using a chirped-pulse amplification (CPA) technique . Reducing the pulse peak power density during amplification also relies on mode-area scaling. Active fibres used for high peak power applications are therefore made with a large core size . While increasing the core size the numerical aperture (NA) has then to be decreased to maintain single mode (SM) propagation. It is very difficult to fabricate classical fibres (step index or graded index) with a NA lower than ~0.06 . The core diameter of conventional SM fibre is therefore limited to approximately 15 μm for the 1 µm wavelength region .
A solution to this problem can be found by exploiting the unique wave guiding properties of photonic crystal fibres (PCF) [5,6] that allow exceeding the limits of conventional SM fibres. In a PCF the effective refractive index of the cladding modes can be tailored within a very broad range which allows achieving very low NA and hence designing and fabricating a SM PCF with an extremely large core. Such a PCF is said to be single mode when the propagation loss of the higher order modes is orders of magnitude larger than that of the fundamental mode. An active large-mode-area (LMA) PCF with an effective mode area up to ~2000 μm2 has for example already been reported . Such extremely large mode area (XLMA) fibres unfortunately exhibit dreadfully large bending losses and come in the form of rigid fibre rods. Such rod-type fibre lasers can therefore not be fabricated in a compact and low footprint architecture which in turn limits the application potential. Moreover, such a rod-type fibre cannot serve as a flexible high power delivery fibre either. A few XLMA PCF structures with low bending loss have nevertheless been suggested [7–9]. Still these interesting and inspiring proposals have rather limited potential for practical high power applications. First, the small difference in bending loss for the fundamental mode (FM) and the higher order modes (HOM)  or the use of temperature sensitive stress applying parts  may prevent SM operation in high power applications. Second, fibre design such as proposed in  may prove very difficult to fabricate, due to the tight demands on the tolerances.
In this paper we report a solution to the issues mentioned above with a novel design of an XLMA PCF with low bending loss, provided the bending orientation is properly chosen. This fibre structure holds promise for constructing compact short pulse high peak power fibre lasers. The remainder of our paper is structured as follows. Section 2 introduces the basic concepts on which our PCF structure relies. This structure is gradually optimised in the subsequent sections. Section 3 deals with how we optimised the basic structure towards low bending loss. Section 4 then adds the optimisation towards both low bending loss and a larger mode-field-area. The results are summarized in section 5, which also concludes our paper.
2. Approach and basic LMA fibre concept
To analyse and optimise our PCF designs we rely on the commercially-available software package Lumerical Mode Solution . The calculations employ a fully-vectorial and rigorous finite difference method (see for example ) for solving the wave equation. The software allows numerically simulating any type of PCF cross-section and calculating the mode properties (propagation constant, loss, field distribution, etc.) in both straight and bent fibres. Bent fibre is simulated directly without any conformal mapping approximation. All our simulations were performed for the wavelength of 1064 nm. Moreover it was assumed that besides ytterbium doping, the core will be co-doped to decrease the refractive index and to preserve the refractive index level of pure silica. Therefore simulations were performed for the fibres with unchanged refractive index of the core.
The targets for our PCF are to achieve good confinement of the FM (loss below 0.01 dB/m) and to exhibit high loss for the HOM (above 10 dB/m) for a fibre bending radius of 10 cm. These characteristics need to be maintained within the manufacturing tolerances and the output beam should have good quality for this fibre to be technologically viable.
To achieve these targets we started from a basic structure that relies on an asymmetric topology of the holes in the cross-section of the micro-structured cladding. As shown in Fig. 1 the fibre has larger air holes on one side and smaller air holes on the opposite side. This structure allows for low bending loss for the FM and high bending loss for HOM when the fibre is bent such that the large holes remain located at the outside of the bend. The large air holes then indeed prevent the FM from leaking, while the HOM are evacuated due to the presence of small holes. This yields single mode guidance during bending.
The confinement of FM and HOM in a bent fibre with the large holes kept outwards is shown on Fig. 2 . The FM is well confined by the large holes and the HOM leaks out through the small holes. This only occurs for a proper bending direction, which should not be an issue if the fibre is fixed in the laser cavity and when a short pulsed laser based on a short fibre length is considered. Fibre bending in a particular bending plane can rely on the use of an asymmetric coating that induces bending in a preferential plane. Microscope inspection  can be used to carry out the angular alignment.
The asymmetry of the proposed structure design suggests that the fibre exhibits birefringence. However due to the large core size the influence of the structural asymmetry on the polarization properties is very low. Our simulations confirm that the birefringence remains negligible. Furthermore, the simulations show that birefringence induced by fibre bending on a 10 cm radius is larger than the birefringence resulting from the asymmetry, but still at a very low level of 10−7.
The fibre structure presented in this section only served the purpose of explaining the concept of our PCF. In the next sections we will gradually optimize the structure to achieve optimal specifications and we will analyze tolerances.
3. XLMA PCF optimised for low bending loss
The cross-section of the first optimized XLMA PCF design is shown in Fig. 3 . This fibre has 7 missing air holes in its centre that create the core and 2 additional missing air holes in the cladding region. The core is surrounded by only 3 air hole rings. The small and large air holes have diameters of 5.2 µm and 9.2 µm, respectively. The lattice constant Λ is 17 µm and therefore the core diameter can be estimated: Dcore = 4·Λ - 0.5·dl - 0.5·ds ≈61 µm. The inset of Fig. 3 shows the FM of the straight fibre.
The lattice constant and the number of missing air holes in the centre of the fibre were chosen to achieve a large core diameter. The three air hole rings forming the micro-structured cladding guarantee good confinement of the FM and simultaneously allow efficient pumping when considering a double clad fibre (DCF) structure. Since only 3 rings of air holes are used for the confinement, the diameter of the outer cladding can be kept sufficiently small. This keeps the fibre bendable and facilitates coupling of the pump power to the core.
The small and large air hole diameters were optimized to obtain low bending loss of the FM and high bending loss of HOM and therefore efficient single mode operation during bending. Additionally, two missing air holes in the micro-structured cladding increase the HOM loss during bending. This stems from index-matched coupling of these HOM with cladding modes that exist in the region with missing holes. The idea of index-matched coupling was investigated in detail in [13,14].
Numerical simulations of the optimized PCF evidenced that the FM bending loss is lower than 0.01 dB/m and that the HOM bending loss exceeds 10 dB/m for a bending radius Rbend = 10 cm. The difference in bending loss together with the absolute loss values yield single mode operation, even for relatively short fibre lengths. An important characteristic is evidently the MFA, which can be calculated by means of Eq. (1):
Tolerance analysis results for our XLMA PCF structure are summarized in Fig. 4 and Fig. 5 . These figures depict the influence of the large and small air hole diameters on the FM bending loss (Fig. 4) and second order mode bending loss (Fig. 5). The black dots in these figures indicate the fibre parameters (small and large air holes diameters) for which FM bending loss is very low and HOM bending loss is high. The bending loss would still be acceptable (< 0.05 dB/m for the FM and > 5 dB/m for the HOM) if the air hole diameters would deviate by 10% from their optimal value. Since the technology allows drawing this type of fibres with tolerances better than 5%, any deviations resulting from the fabrication process should not significantly affect the fibre characteristics.
A tolerance analysis was also carried out for variations of the bending orientation and of the bending radius. Figure 6 shows how bending loss of the fundamental, second and third order modes changes when the bending orientation deviates from its predefined optimal value. At a ± 5° deviation from this orientation the bending loss remains at reasonable levels for all modes. The order of the modes (1st, 2nd, 3rd and 4th) is defined following the level of the effective refractive indices for the propagating modes from higher to lower values. The two polarization states of these modes have approximately equal bending loss and therefore they are taken as a single mode order. Figure 7 shows that for a bending radius varying between 8 and 12 cm the FM bending loss stays within the same range. The HOM bending loss is more sensitive to the bending radius but remains sufficiently high to maintain SM operation.
Our XLMA PCF structure shown in Fig. 3 can still be further optimized to maintain low bending loss for bending radii smaller than 10 cm. However the MFA decreases with the bending radius. The inset of Fig. 7 summarizes MFA values for different bend radii. In the next section we therefore investigate another possible fibre structure allowing larger MFA for the same bending radii yet at the expense of lowering the difference in bending loss between the FM and the HOM.
4. XLMA PCF optimised for low bending loss and high MFA
Bending XLMA PCF over too small a radius significantly reduces the MFA. Nonlinear effects and/or glass damage can then appear as they would do in fibres with small core diameters. Furthermore increasing the outer diameter of XLMA fibres would mechanically limit the bending radius. Fini proposed to introduce doped fibre regions to counteract the decrease of the MFA in bent fibre . However modifying the refractive indices of the core and cladding by introducing such doped regions may spoil single mode guidance. By studying the evolution of the MFA for different bending directions and different PCF core shapes and dimensions we find another possibility for limiting the bending-induced decrease of the MFA.
The MFA expansion in a hexagonal core fibre bent over a 10 cm radius in two orthogonal directions as a function of the hexagon radius (Rhex) is illustrated in Fig. 8 . To neglect the influence of the air hole diameters on the MFA during bending the simulations were performed for a fibre in which the hexagonal silica core is surrounded by air as shown in the upper left inset in Fig. 8. The calculated FM field distributions of such a fibre bent in two orthogonal planes are presented in the insets of Fig. 8.
When the core hexagonal radius is relatively small the FM field distribution fills the entire core of the fibre. The MFA then increases with Rhex 2 since it is proportional to the surface of the hexagonal fibre core. One sees that for core radii below 20 µm (assuming a wavelength of 1064 nm) the MFA is independent on the bending direction for a 10 cm bending radius. For larger fibre hexagonal radii the FM field distribution does no longer fill the core (see insets to Fig. 8). For a horizontal bending direction (see Fig. 8) the MFA is limited in two dimensions, since the mode is located in a corner of the hexagon. The MFA then remains constant with increasing core diameter. In this case it is pointless to increase the hexagonal fibre core further as enlarging the MFA for the bent fibre is not possible. However, for the vertical bend the mode field distribution is limited only in one dimension, since the mode is now located against a side of the hexagon. This results in a linear MFA increase with the core diameter.
The MFA does not only depend on the bend direction, but also on the size and on the shape of the core region. We therefore investigated micro-structured fibres with different core shapes and sizes. The simulation results for the MFA as a function of the radius of the micro-structure (RPCF) for a vertical fibre bend with a 10 cm radius is shown in Fig. 9 . The lower right inset of this figure explains the meaning of the micro-structure radius – RPCF and the upper left inset depicts five micro-structures with different core sizes and shapes, each represented by the number of missing holes in the core. The air hole diameters for these structures were chosen to provide low FM bending loss for a given micro-structure radius and a 10 cm vertical bend radius. Moreover the diameter of the air holes has a minor influence on the MFA. RPCF was enlarged for consecutive simulations by changing the lattice constant of the micro-structure, while the number of missing air holes in the core and the number of air hole rings in the cladding remained fixed for every investigated structure. Insets a and b in Fig. 9 reveal the shape of the FM in straight fibre with triangular and hexagonal lattice structure, respectively.
The triangular lattice structure with 15 missing air holes exhibits the largest MFA. However this fibre yields a deformed FM field distribution (inset a in Fig. 9) and would be difficult to manufacture. For a hexagonal lattice the largest MFA is obtained – counterintuitively – for the fibre structure with 16 missing holes instead of the fibre with 19 missing holes in the core. In general the MFA strongly depends on the shape of the micro-structured fibre core which has to be taken into account when designing XLMA fibre, instead of only considering the number of missing holes.
The fibre with 16 missing air holes in the core confines the FM very well and exhibits low propagation loss for straight and vertically bent fibre. However the HOMs are also well confined. This structure must therefore be adapted to obtain single-mode operation. Since such fibre is supposed to be bent while guiding and amplifying light we increased the HOM loss by removing some of the holes which do not participate to the confinement of the FM. HOMs then become leaky modes as their effective indices are matched with the badly confined cladding modes existing in the regions with missing holes. The mode effective index is a function of wavelength and hence index matching occurs over a certain wavelength range. However the coupling of cladding with unwanted modes increases the loss of the latter, even if their indices are not perfectly matched. Therefore, for wavelengths that differ from the design wavelength, the loss of unwanted HOM is still increased.
The optimized design is depicted in Fig. 10 . This micro-structure confines the FM for the vertically bent fibre and simultaneously exhibits large HOM loss. In addition it provides a larger MFA than the structure shown in Fig. 3. The inset of Fig. 10 shows the FM of the straight fibre.
When the fibre from Fig. 10 is bent vertically over a 10 cm radius the MFA is 1065 µm2 while the MFA of the straight fibre is 2524 µm2. In comparison to the structure shown in Fig. 3 the MFA of the new fibre is more than 400 µm2 larger during bending and almost 1200 µm2 larger when kept straight. However this new fibre has smaller HOM bending loss and a weaker tolerance to deviations from the optimal bend orientation. This is shown in Fig. 11 : the FM loss increases significantly when the bend orientation changes from vertical. Furthermore the loss of the second order mode is around 2 dB/m. For a 3° deviation from the vertical direction the loss difference between FM and HOM is only one order of magnitude. The bend orientation of such an active fibre in the laser cavity must therefore be precisely controlled to maintain single mode operation.
Due to the close proximity of missing air holes to the core, modes propagating in these regions may be excited during launch. This may also affect the coupling efficiency into the FM and therefore excellent control over light launching is required. These modes should however not largely affect the M2 value since they have very large propagation loss and hence they will not reach the end of the fibre. On the other hand the very large bending loss of HOM should assure SM operation. We have calculated the M2 values for the x and y directions, Mx 2 and My 2. We find Mx 2 = 1.07 and My 2 = 1.07 for the fibre corresponding to Fig. 3 and Mx 2 = 1.07 and My 2 = 1.09 for the fibre corresponding to Fig. 10.
5. Summary of and conclusion on XLMA fibre designs
We reported on two optimized micro-structured fibre designs that exhibit exceptional properties for fibre laser and amplifier applications, including an extremely large mode field area, single-mode operation and low bending loss. The parameters of these structures are summarized in Table 1 . The first structure (shown in Fig. 3) reveals smaller MFA and higher FM bending loss than the fibre design shown in Fig. 10. The latter is more appropriate for very high power applications. However the first structure provides larger HOM loss and therefore gives easier single-mode operation. Furthermore it has better tolerance to structural imperfections and bending orientation. Only 3 air hole rings around the core are needed to sustain strong confinement of the fundamental mode. Our fibre designs also remain flexible due to the relatively small thickness even when adding the air clad that traps the pump power. A final advantage lies in the reasonably small amount of air holes, the majority of which has a small diameter, which allows very efficient pumping of the active core surrounded by these holes.
To conclude we have shown that maximizing the MFA for a straight and bent micro-structured fibre can be achieved by a proper choice of the shape of the fibre core, of the number of missing air holes in the core and of the bending directions. This allows guiding very high optical power. Our fibre designs can therefore open possibilities for the construction of high power pulsed fibre lasers with a small footprint.
The authors would like to acknowledge financial support from the European Commission 7th Framework Programme, the Agency for Innovation by Science and Technology (IWT), the Research Foundation – Flanders (FWO), the Methusalem and Hercules Foundations Flanders, the Vrije Universiteit Brussel research Council (OZR) and the Interuniversity Attraction Poles (IAP) – Belgian Science Policy.
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