1. Introduction

Optical fibers for high power applications have to satisfy several demands. First of all the fibers should exhibit a large mode area (LMA) to avoid that the very high optical power induces damage to the fiber glass and to steer clear of nonlinear effects such as stimulated Raman or Brillouin scattering [1]. Moreover and in most cases single mode (SM) or nearly SM regime is required to assure sufficient quality of the output laser beam. However LMA fibers require an extremely small numerical aperture to obtain SM beam. This comes with the drawback that light is weekly confined in the core and hence suffers large bending loss. Therefore commercially available fibers that meet both above mentioned demands typically come in the form of fiber rods. Due to the large bending loss these rigid rods have to be kept straight when used in lasers or amplifiers, which is detrimental to the compactness of the laser system and which prevents easy integration in material processing equipment.

Conventional fibers are difficult to fabricate with SM core diameters larger than 15 µm in a 1 µm wavelength region due to limited technological flexibility over the control of the refractive indices of core and cladding [2]. One therefore attempts at exploiting the unique features of photonic crystal fibers (PCFs) to beat the limits of conventional SM fibers. Although controlling the refractive index of the core of active PCFs is still technically challenging the effective refractive index of the PCF cladding can be tailored very precisely by controlling the air-hole diameters and lattice constants, which allows designing and fabricating such fibers with extremely large core diameter values. Since the higher order modes suffer very large propagation loss while the fundamental mode remains guided with very low loss values the fiber is said to be SM. An active rod-type PCF with a mode field area of 2000 µm² has for example already been reported in [3]. Owing to the PCF design flexibility bendable LMA fibers can be obtained as well.

To allow bending of LMA fibers several fiber structures that combine low bending loss with large mode area have been proposed in literature [4–6]. However these fibers hold limited potential for practical high power applications as we have already explained in [7]. We therefore first proposed a bendable PCF with an asymmetric air-hole structure and a 60 µm core diameter that exhibits very low propagation loss when bent around a 10 cm radius [7]. To reduce bending loss and to allow LMA fiber bending we relied on an asymmetric photonic crystal fiber structure comprising two regions with small and large air-holes on opposite sides of the fiber. This kind of fiber design helps maintaining a low propagation loss of the fundamental mode (FM) and at the same time increasing the losses for the higher order modes (HOMs) while bent. Since the fiber has to be bent over its entire length (with exception of the input and output sections) in laser or amplifier to reduce the physical dimensions, SM operation is enforced by the large bending losses of HOMs compared to the fundamental mode, although the fiber is not SM when kept straight.

In this report we propose a new solution to the problem by exploiting a photonic crystal fiber involving a double lattice constant structure. To the best of our knowledge it is the first time that such a photonic crystal fiber structure has been proposed. Our paper also reports on the features and advantages of this solution.

Our paper is structured as follows. Section 2 introduces the concept of PCF with double lattice constant structure and compares its features with the fiber presented in [7]. Section 3 then analyzes the influence of crucial parameters such as the bending radius and the bend orientation on our fiber performance. Section 4 describes the fiber fabricated according to our design and reports on the numerical simulation results that we have carried out for the fiber structure as built. We close our paper with final remarks and conclusions in Section 5.

2. Fiber with double lattice constant structure

In [7] we presented two optimized fiber designs with 657 μm² and 1065 μm² mode field areas (MFA) respectively, in a fiber bent around a constant bending radius of 10 cm. Despite its lower MFA, the first structure seems to be better suited for industrial use as it shows higher bending losses for the HOMs and better tolerances to parameter deviations. Therefore we will use this solution as a reference here and refer to it as double air-hole diameter fiber (DDF). In this paper however we propose a different approach that relies on a double lattice constant to obtain two regions with different filling factors and to achieve several important benefits. First, the fiber can be drawn with only one air-hole diameter which eases fabrication compared to a fiber with different air-hole diameters. The fiber can therefore be drawn with better accuracy, which also allows for higher flexibility during the design process. Second, and as evidenced by our simulations, a two times smaller lattice constant in the region with high filling factor allows for better control of the bending losses for the FM and HOMs. Therefore SM fibers with even larger cores can be achieved.

To analyze and to optimize our PCF designs we used the commercially available software package Lumerical Mode Solution [8] which relies on a fully-vectorial and rigorous finite difference method (see for example [9]) for solving the wave equation. All simulations were carried out for a wavelength of 1064 nm, with the assumption that the refractive index of the core equals that of pure silica. This allows investigating the properties of the proposed structures while neglecting the influence of doping. Our simulations will still be valid in a real structure as the ytterbium doped core of our fiber will be co-doped to remain close to the refractive index of pure silica. Although Lumerical Mode Solution allows calculating the loss of the bent fiber, it does not take into account stress-induced refractive index changes and the resulting contribution to overall loss. Therefore if more accurate results would be needed the method presented for example in [10] could be applied. Resulting corrections to the overall loss would however not compromise our conclusions. In addition the simulation results would still have to be verified experimentally as there are many factors that influence the fiber propagation properties and that cannot necessarily be anticipated, such as for example fiber drawing induced stress.

The designed fiber with double lattice constant structure is shown in Fig. 1 . We will refer to it as to double lattice constant fiber (DLCF). It has the same number of missing air holes in its centre and the same lattice constant as the DDF, except in the region with high filling factor where the lattice constant is twice as small. Moreover the air-hole diameters were chosen to assure the same level of FM bending loss as in DDF. It therefore makes sense to compare these two fiber designs. Table 1 summarizes the features of both fibers.

 

Fig. 1 Fiber with double lattice constant structure (DLCF).

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Table 1. Comparison of DDF and DLCF Parameters

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Similarly to the DDF, the DLCF has two missing air holes in the cladding structure, localized in the region with small filling factor close to the region with doubled lattice constant. Due to the index matched coupling [11, 12], HOMs couple with lossy modes propagating in the regions created by the missing air holes and suffer high loss when the fiber is bent around a 10 cm radius.

Table 1 shows that both the MFA in bent fiber and the FM bending loss are at the same level for DDF and DLCF which allows fair comparison. Moreover Table 1 reveals that the double lattice constant structure helps increasing the MFA in straight fiber as well as achieving higher HOM bending losses. The increased MFA allows extracting higher power from the fiber without risking fiber end face damage. The higher bending loss of HOMs combined with the low bending loss of the FM ensure single mode operation in a fiber bent around a 10 cm radius. Moreover the single diameter of the air holes in the DLCF supports the reproducibility and ease of manufacturing, which is crucial from the point of view of the application.

3. Guiding properties of double lattice constant fiber

The asymmetry of the proposed structure suggests that it will influence the polarization properties of the fiber. However in such a large core fibers the birefringence caused by structural asymmetry is negligible as was confirmed by our simulations. Moreover the M² factor simulated for the FMs is close to 1 for both fibers.

Figure 2 shows the influence of the fiber bending radius on bending loss of several modes propagating in the fiber. The mode numbers are defined following their effective refractive index levels from higher to lower values. For sake of clarity polarization modes (e.g. with numbers 1, 2 or 3, 4) are presented in the plot as one mode, since their loss levels are almost the same. The images of these polarization modes propagating in DLCF bent around a 10 cm radius are depicted in Fig. 3 .

 

Fig. 2 Bending loss of FM and HOMs as a function of bend radius.

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Fig. 3 The image of the modes propagating in DLCF bent around 10 cm radius.

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In a broad range of bend radii (5-12 cm) the bending loss of the HOMs maintains a high level of 20 dB/m whereas the FM bending loss does not increase above 0.01 dB/m. The fiber will therefore exhibit SM operation while bent over different bend radii. A tighter fiber bend will result in a reduction of the fiber laser system footprint. However at the same time the MFA will decrease (see Fig. 2 where the example values of MFA for DLCF bent around 5, 10 and 15 cm radii are presented).

One can also note, perhaps counterintuitively, that the FM bending loss decreases with decreasing bending radius. The reason for such behavior is that the ability of the region with low filling factor to confine light increases when the fiber is bent in the proper plane [13]. Therefore for tighter bending the FM is pushed further towards the region with doubled lattice constant which then strongly confines the FM owing to the very high filling factor. As long as the bending radius is not too small, the bending loss of the fundamental mode then decreases.

The image of the modes (Fig. 3) propagating in DLCF bent around a radius of 10 cm clearly shows that a portion of the HOMs is located in the cladding (in particular in the regions with missing air holes) where these modes suffer high loss. Only the FM is fully sited within the core and is strongly confined by the region with double lattice constant.

Figure 4 shows how variations in bending orientation influence the properties of the DLCF. The reference orientation of 0° is assumed to be naturally induced by the asymmetry of the DLCF cross section: this asymmetry will give preferred bending of the fiber in that plane for which the region with double lattice constant remains located at the outside of the bend.

 

Fig. 4 Bending loss of FM and HOMs in DLCF bent around a radius of 10 cm as a function of bend orientation. The inset shows the angle Θ defining the orientation.

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When the bending orientation varies from the assumed plane, the bending loss of the FM increases and hence the mode slips out of the region with high air-filling factor. Nevertheless in a range within ±7° the bending loss of both FM and HOM remain at reasonable levels. The FM bending loss is lower than 1 dB/m whereas HOM bending losses are higher than 40 dB/m. Employing precise fiber rotators that allow controlling the angular rotation of the fiber with an accuracy of 2° will limit the FM bending loss to 0.02 dB/m.

To confront our DDF and DLCF designs with the state-of-the-art we were inspired by the approach suggested by Fini in [14]. Figure 5 illustrates the tradeoff between the MFA in bent fiber and the HOM/FM bending loss ratio which describes how well HOMs are suppressed. We used the data presented in [14] for different fiber families including a 6-hole uniform PCF, a step index fiber (SIF), a W-shaped index profile fiber (W3), a fiber with a parabolic refractive index distribution in the core proposed by Fini and a fiber presented by Wong in [15].

 

Fig. 5 Comparison of the different LMA fiber families distilled from simulated fibers by interpolating fiber parameters to achieve a common FM bending loss of 0.1 dB/m (adapted from [14]).

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The values for these fiber families were obtained by changing a size parameter (core radius or lattice constant) and a contrast parameter (difference in the refractive index of the core and cladding or air-hole diameter) with the value of the FM bending loss fixed at 0.1dB/m. The bending radius was assumed to be 7.5 cm. We have added the MFA and bending loss ratio for our DDF and DLCF designs bent around radii of 7.5 cm and 10 cm (nominal value) to Fig. 5. To validate the comparison we assumed the FM bending loss for the DDF and DLCF to be 0.1 dB/m, although the true value is significantly lower. We did not consider the fiber reported in [5] which has an anisotropic numerical aperture, as the bending radius (24 cm) is not comparable with the values used here, nor the fiber with an additional ring core described in [6], as we do not know its MFA and the bending loss values.

Figure 5 clearly reveals the potential of our DLCF design. Our fiber shows a much stronger HOM suppression at a 7.5 cm bending radius than the other fiber families with a MFA ≈550 µm² even though they were optimized for bending around a 10 cm radius.

4. Analysis of fabricated fiber

Figure 6 shows a scanning electron microscope (SEM) image of the DLCF fabricated according to our design and its average parameters values. Our fiber was fabricated by a stack and draw technique [16] and the double lattice constant was obtained by replacing hollow capillaries by solid glass rods.

 

Fig. 6 Scanning electron microscope image of the fabricated DLCF.

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In the fabricated fiber the lattice constant of the region with low filling factor is not exactly twice as large as in the region with large filling factor and the average air-holes diameter is smaller than in the designed fiber by a factor of approximately 11%. Nevertheless we imported the fiber image into the Lumerical MODE Solution software and calculated loss and MFA in the straight and bent fiber to test how the fiber properties changed due to the deviations of fiber parameters which are however within typical fabrication tolerance levels. Table 2 compares the parameters of designed and fabricated fiber.

Table 2. Comparison of Designed and Real DLCF Parameters

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Due to the smaller air-holes diameter and larger lattice constant in the region with small filling factor the MFA in bent and straight fiber is larger in the as built fiber. These fabrication inaccuracies additionally result in increased propagation loss in straight and bent fiber. The increased loss for HOMs is an advantage, whereas the loss of the FM is still at a very low level < 0.05 dB/m for straight and bent fiber. The fabricated fiber therefore preserves the peculiar bending properties in spite of the modified parameters.

5. Final remarks and conclusion

So far we have seen that our fiber exhibits excellent features that allow for SM operation in a LMA when bent around a radius of 10 cm. Due to the large MFA and to the short length required, the fiber should not suffer from nonlinear effects [3]. The large MFA is however also essential to avoid fiber damage. At the glass-air interface the damage threshold is several times lower than in bulk fused silica. It is therefore very important for the MFA to be much larger in straight fiber than in the bent version. In our solution the fiber is bent almost along its entire length to make the fiber laser sufficiently compact and to enforce SM operation. However both fiber ends need to be kept straight for the light to pass through the glass-air interface with increased MFA. Although the core sizes of both the DDF and the DLCF are approximately the same, the MFA in the latter is more than 110 µm² larger when kept straight. The fiber is therefore better protected against damage. However if the laser dimension is not an issue, the fiber can be kept straight to exploit the very large mode area with only a short length of fiber bent to suppress HOMs.

Finally we can comment that due to the asymmetry of the fiber cross-section, the fiber has to be bent in a proper bending plane to obtain SM operation. However this should be not an issue in the case of a short laser or amplification fiber that is fixed after proper installation. A particular bending plane can for example be enforced by an asymmetric coating or fiber rotators. Moreover microscope inspection can be used to control angular alignment [17].

In conclusion, we reported on a photonic crystal fiber for laser and amplifier applications with a double lattice constant structure that exhibits unique bending properties. The single mode regime is obtained in a fiber bent around a 10 cm radius with a mode field area of 655 µm². Tighter bending radii are also possible, however at the expense of a smaller mode field area. The extremely large mode area in the straight fiber, which is at the level of 1454 µm², allows extracting large power from the fiber without risking fiber damage. Furthermore, the double lattice constant relying on a single air hole diameter is more advantageous in terms of fabrication efficiency and repeatability. The analysis of the fiber fabricated according to our design confirms that slightly changed parameter values do not affect the special bending properties. The fiber is therefore a very promising medium for compact high optical power fiber lasers.