1. Introduction

Over the past few years, rare-earth-doped fiber lasers have been dramatically improved and recently fiber lasers delivering more than one kW in the continuous-wave regime have been demonstrated [1, 2].

The most recent step in the trend towards higher power has been the combining of cladding pumping and Large Mode Area (LMA) fibers [3, 4] spatially well-suited to push back the non-linear effects. First, large core size decreases the spatial confinement of the guided beam. Second, it improves the core-to-cladding area ratio and enhances pump absorption reducing the fiber length. However, up to now, the numerical aperture (N.A.) is low to keep a nearly single-mode operation for large core diameters with two consequences: high bend loss [5] and limitation of rare earth ion concentration. Indeed, the rare earth (particularly Yb³⁺) together with aluminum co-doping implies an increase of the refractive index of the fiber core. Fluorine co-doping can be used to reduce this effect but rare earth concentration remains limited. In this paper, we report a fiber design that combines high rare earth ion doping level, and large doped core with single-mode propagation thanks to original guidance properties in a microstructured optical fiber. Light is guided by resonant reflections through an array of high-index rods. This specific microstructured optical fiber has a lattice constant larger than the optical wavelength and a high contrast index in the cladding. Although guidance in this kind of special fiber is not a photonic bandgap mechanism, it leads to a modulated spectral response depending on the rod geometry. Such specific guiding properties can be explained both by the standard total internal reflection guidance regime and the resonant coupling between modes of the core and of the high-index rods in the cladding. The studied fiber has a structure similar to that of anti-resonant reflecting optical waveguides (ARROW) [6–8] except the core refractive index which is higher than that of pure silica. This difference leads to specific modal and spectral behaviors compared to those obtained with the ARROW structure. Phase-matching between modes of the high-index core and cladding rods induces a complex spectral response which is well-adapted to the selection of a fundamental mode of large area as demonstrated in this paper.

2. Fiber structure description

 

Fig. 1. Fiber structure where refractive index level is given in false colors

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To enhance performances of fiber lasers, the proposed structure must combine a large and highly rare earth doped silica core with a single mode propagation. The example of structure reported in this paper (Fig. 1) consists in a microstructured cladding formed with four rings of high-index germanium doped silica rods, surrounding a hexagonal rare-earth doped silica core whose index is higher than that of pure silica. The cladding rods have a parabolic refractive index profile, with a maximum value of: n = n_Si + 16.10^-3 (n_Si: refractive index of pure silica) at their center, in accordance with manufacturing facilities. The pitch of the cladding structure is 10 μm. The core has a large area of about 500 μm² and a high step index equal to 0.01 (core/silica). It is worth to note this value of 0.01 is about two or three times higher than that of usual LMA fibers. This feature should lead to an easier fabrication of highly doped fiber.

3. Principle of modal selection by high index microstructured cladding

The principle of the modal selection is based on a total internal reflection guidance regime modified by resonant coupling with modes of microstructured cladding. To understand the suppression of high order modes of the proposed fiber, we refer to results concerning anti-resonant reflecting optical waveguides (ARROW) [6–8]. This guiding regime occurs in waveguides where silica core is surrounded by a microstructuration of high-index rods. The transmission spectrum of such a waveguide exhibits high loss dips corresponding to the cutoff wavelengths of the highest order modes of the rods. Figure 2(a) is a schematic representation of coupling phenomena between modes of silica core and high-index rods.

 

Fig. 2. Coupling mechanisms in microstructured cladding fibers with (a) silica core (ARROW structure); (b) doped core: dashed lines represent effective indexes of rod modes and solid lines represent effective indexes of modes predominantly guided in the core. Red circles and arrows indicate the coupling effect.

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Fig. 3. (a) Real part and (b) imaginary part of the effective indexes of the fundamental (circles) and second (triangles) modes of the core; the dashed line is the effective index evolution of the fundamental mode of the rods; the arrows indicate the phase-matching wavelengths.

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The studied fiber presents a similar structure except the core index which is higher than that of pure silica. This implies that modes guided without any loss by total internal reflection in the isolated core (i.e. surrounded by pure silica) have their spectral properties modified by the microstructured cladding. Actually, in such a case, high loss dips appear at phase matching wavelengths between the modes essentially guided in the core and the rod modes (see Fig. 2(b) and Fig. 3) when the whole structure is considered [9]. The numerical results presented Fig. 3 (and the followings) were obtained thanks to a full-vector mode solver based on the finite element method [10]. They were calculated with a mesh of 130000 nodes and an absorbent layer is employed to effectively absorb the radiation waves out of the computational window. Figure 3(b) shows that losses of fundamental and second modes propagating mainly in the core dramatically increase around 1.18 μm and 1.32 μm respectively, which are the two phase matching wavelengths between these modes and the fundamental mode propagating in the cladding rods.

Moreover, we can note that losses for the second mode around 1.5μm are higher than losses of the fundamental mode. This difference can be explained by the fact that the fundamental mode of the rods has larger overlap with the second mode of the core than with the fundamental one which is more confined in the core (Fig. 4). Actually, the Fig. 5 shows that second mode of the fiber structure has a larger spreading over the cladding than the fundamental mode.

 

Fig. 4. Overlap factor between rod modes (LP01 and LP11) and core modes (fundamental and some of high order modes).

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Fig. 5. (a) Fundamental and (b) second modes patterns of the microstructured fiber.

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In a general way, to understand coupling mechanisms, we have to take into account both phase-matching and overlap between modes of core and of cladding rods. The overlap between rod and core modes increases with mode orders (Fig. 4). So, out of phase matching conditions, theses overlaps are mainly responsible for the high order mode losses. As seen in Fig. 6, around 1.55μm, the first high order modes of the core are coupled with the LP01 modes of rods whereas the highest order modes are coupled with the LP11 ones [9, 11].

Consequently, three or four orders of magnitude separate losses of these modes and those of the fundamental mode leading to a single mode operation at 1.55 μm.

 

Fig. 6. Real part of effective indexes of some core modes (solid curves) and rod modes (dashed curves).

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Moreover as transmission spectrum depends only on properties of coupling between core and rod modes, which are driven by core and rod characteristics, it can be easily adjusted by properly choosing refractive index and diameter of the rods. This property allows, for example, to enhance cladding pumping efficiency by furthering coupling between rod modes and structure modes at pumping wavelength, and at the same time to guarantee single mode propagation at signal wavelength. Furthermore, like in ARROW waveguides [7], as long as all rods have the same characteristics, whatever the number or the position of the rod rings or rods themselves, the structure will keep the same loss dip wavelengths (see Fig. 7). Nevertheless, the loss value decreases when the number of layers is increased.

 

Fig. 7. Imaginary part of the effective index of the fundamental mode guided predominantly in the core for different cladding structures.

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Finally, we have simulated curvature influence in this fiber, using the method of conformal transformation [12, 13]. This method consists in using an equivalent linear guide whose index profile is: n_eq = n(x,y) (1 + x/Rc), n(x,y) is the index profile of the straight waveguide, Rc is the bend radius. As curvature generates a slight field displacement towards the highest index fiber area, effective index of fundamental mode increases with curvature influence [12].

We have compared the evolution of the effective index imaginary part according to the fiber bend radius for fundamental modes propagating in the studied fiber and in a step index single mode fiber with the same doped core area (about 500 μm²), but with a cladding made of pure silica. Figure 8 shows that such a microstructured cladding leads to a significant curvature loss reduction, despite a large core diameter.

 

Fig. 8. curvature influence

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6. Conclusion

We propose a new design of microstructured fiber whose guidance regime is based on total internal reflection modified by coupling with modes of resonant microstructured cladding. Thanks to the original guidance properties, this fiber combines single mode propagation with a large and highly doped area. Moreover, whereas this structure presents a large core, it remains less sensitive to curvature influence than usual LMA fibers. This fiber is particularly attractive for high power laser operation. Indeed, the non linear effects can be significantly reduced because core characteristics (large and highly doped area) induce reduction of both field confinement and fiber length. Moreover, opto-geometrical characteristics of such waveguides can be adjusted to enhance cladding pumping efficiency and to preserve single mode operation at a chosen wavelength.