Abstract

Very large mode area, active optical fibers with a low high order mode content in the actively doped core region were designed by removing the inner cladding symmetry. The relevance of the numerical approach is demonstrated here by the investigation of a standard air-silica Large Pitch Fiber, used as a reference. A detailed study of all-solid structures is also performed. Finally, we propose new kinds of geometry for 50 μm core, all-solid microstructured fibers enabling a robust singlemode laser emission from 400 nm to 2200 nm.

© 2013 OSA

1. Introduction

Over the last decade, rare-earth doped optical fibers have shown outstanding potential in increasing the average optical power (in CW operation) and energy (in the pulsed regime) delivered by fiber laser systems at 1 μm [1, 2] and more recently at 2 μm [3]. These performances were driven by the development of Very Large Mode Area Photonic Crystal Fibers (VLMA-PCFs) that exhibit a Mode Field Area (MFA) larger than 1600 μm2. This has resulted in the onset of non linearities, being pushing away by a decrease in the optical power density in the fiber core and/or a reduction in the fiber length. The presence of a pump cladding and the intrinsic nature of PCFs (composed of a solid core surrounded by a classic hexagonal array of air holes) do not lead to operation that is strictly singlemode. Nevertheless, these structures provide efficient modal discrimination by favoring the High-Order Modes (HOM) leakage through the inner cladding, thus delocalizing them out of the gain region. The fundamental mode (FM), which exhibits the largest overlap with the gain region, can be preferentially amplified. Large Pitch PCFs, referred as Large Pitch Fibers (LPFs) due to their cladding hole-to-hole spacing Λ larger than 10 times the wavelength, have initiated this technological breakthrough by enabling singlemode emission from fibers that exceed 100 μm in core diameter [2].

Unfortunately, the power scaling in such VLMA-LPFs faced new key hurdles that going beyond the sole nonlinear effects and photodarkening [4]. Indeed, fast modal instabilities were demonstrated when the pump/signal powers overcome a certain threshold above which the quality of the emitted beam is suddenly degraded. This phenomenon is due to a transversal (across the fiber section) and longitudinal (along the fiber length) temperature gradient, which modifies the refractive index profile of the structure via a thermo-optical effect, and induces a thermal long period grating into the fiber core. This grating leads to a temporally varying mode coupling between the fundamental mode and at least one undesired HOM. These disturbances influence the guiding properties of the fiber and no longer allow efficient singlemode operation [5, 6]. In this context, new fiber designs have to be proposed to circumvent these limitations, i.e. by enhancing the modal discrimination in very large core LPFs. This condition is essential to achieve the power scaling expected with these fibers. Commonly, the proposed air/silica LPFs are characterized by a cladding microstructuration preserving the symmetrical hexagonal lattice of standard PCFs. However, alternative non-hexagonal designs have recently been explored. A pentagonal lattice, in particular, was pointed out for the improvement of mode discrimination allowing the extension of the MFD to 125 μm [7].

In this paper, we propose going further by developing new kinds of LPF structures based on a symmetry reduction of the cladding lattice, allowing the improvement of the singlemode robustness, and providing a better modal discrimination than that obtained using well-known photonic crystal lattices. Moreover, the proposed fiber structures are all-solid, used to obtain efficient heat diffusion, and subsequently achieve an efficient thermal cooling. Furthermore, such fibers facilitate fiber preparation (polishing, cleaving and splicing). Unlike air/silica LPFs, the solutions presented here exhibit a core refractive index which does not have to match that of silica. This suppresses the restriction on the rare-earth concentration and makes it possible to achieve higher levels of gain. An efficient mitigation for photo-darkening can also be envisaged with the help of index raising dopants such as phosphorus, without having to compensate the final refractive index. The background material should accordingly match that the index the gain region.

This paper is organized as follows. First, we will introduce our investigation method and apply it to the well-known air/silica LPF, the fiber core of which is created by omitting only one cell of the periodical lattice. How this fiber theoretically performs will be a reference for our work. Then, we will present several fiber designs, on which the periodical lattice has been modified in order to enhance modal discrimination, giving birth to the ”Vortex” and ”Hexagonal symmetry free” fibers. Here, we will demonstrate that a reduction in the microstructured cladding symmetry is beneficial to the improvement of modal discrimination, and thus to the beam quality.

2. Definition of our simulation procedure - Application to an air/silica LPFs chosen as reference

One criterion that is essential to the development of high power fiber lasers/amplifiers is the robustness of the singlemode emission. However, VLMA fibers undoubtedly feature a few-modes content and some efforts have to be taken in order to devise fibers that exhibit a selective amplification of the FM, principally by HOMs efficiently leaking out the gain area. In order to qualify the quality of the beam emitted by an inherently slightly multimode fiber, we decided to compare the overlap integrals of the different modes with the gain region. For this purpose, all fiber designs discussed in this paper were simulated using software based on a full-vector finite-element method that is commercially available. Then, the overlap factors of the guided modes, designated OF and expressed in percent, were computed using the following formula:

OF=Ad|E|2dSAp|E|2dS
Here, Ad and Ap represent the areas of gain region and the pump cladding respectively, E is the electric field distribution of the guided mode with |E|2 as its intensity, and dS is referred as the cross section of integration. Due to the double clad, that is to say both core and cladding modes may be propagated without confinement losses and exhibit a significant mode overlap with the gain region. For this reason, we decided to examine at least the first 300 guided modes (identified by their refractive effective indices) throughout this study to ensure that the most competitive HOM is taken adequately into account. In order to achieve a robust singlemode emission, we are looking for the highest overlap of the FM with the gain region (maximizing its amplification) and conversely the lowest for all others (limiting the gain competition with the FM). In this way, the modal discrimination (and with it the singlemode behavior) of the designed structures is defined as the difference between the overlap factor of the fundamental mode (designated OFFM) and the most confined HOM (OFHOM):
ΔOF=OFFMOFHOM
It is commonly assumed that a ΔOF value larger than 30% ensures the preferential amplification and emission of the sole fundamental mode [8]. It is straightforward logic to establish that when the modal discrimination is larger, the beam quality better, as HOMs contribute less and less to the guided radiation. As a reference to our modus operandi, we initially considered the classic air/silica LPF described in reference [2]. The 45μm actively doped core is composed of 7 hexagons [9] (see Fig. 1(a)), and the pitch Λ is equal to 30 μm. The normalized hole diameter d/Λ is variable.

 

Fig. 1. (a) 2D refractive index repartition of the air/silica LPF described in [2]. The gain region is in red, the pure silica in blue and the air holes in yellow. (b) Overlap factor of the fundamental mode (solid lines) and modal discrimination (dashed lines) computed for the air/silica LPF. Calculations have been done for three air-clad diameters: 170 μm (black), 180 μm (red), and 190 μm (blue) and various ratio d/Λ. Insets: computed intensity distributions corresponding to the fundamental mode coupling (top), and the most disturbing HOM (bottom).

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Figure 1(b) represents the evolution of the fundamental mode confinement (solid lines) and the modal discrimination (dashed lines) for a ratio d/Λ that varies from 0.1 to 0.45, as well as for different air clad diameters: 170 μm (black), 180 μm (red) and 190 μm (blue). Solid curves confirm that the fundamental mode is more confined into the gain region for larger air holes (narrower leakage channels). The dashed lines illustrate that the modal discrimination is at its maximum when the d/Λ value is close to 0.325 for an air-clad of 170 μm. Indeed, above this limit, the LP31-like mode becomes competitive and reduces the modal discrimination. Moreover, one can note that for a d/Λ smaller than 0.325, the most restrictive HOM is the LP11-like mode. The largest discrimination obtained for this air/silica LPF is close to 45%, which is congruent to the results reported in [10], validating our simulation procedure. Finally, on the curves relating to the air-clad diameter of 190 μm, a mode coupling between the LP01 and a cladding HOM is observed, as in reference [11].

3. Design of all-solid microstructured fibers

In this section, we discuss an approach aiming to improve the HOMs discrimination in microstructured leaky fibers. Designs investigated hereinafter are based on an array of hexagonal cells as depicted in Table 1 and Table 2. In leaky fibers, the refractive index of the core has to match that of the background material in order to provide efficient leakage channels. In this way, for current air/silica fibers, the refractive index of the gain medium match that of the pure silica. Here we chose to relieve the restriction on the core refractive index (RI) and to increase the RI of the background material (silica RI is increased using an index-raising dopant). This made it possible to introduce a strong concentration of rare-earth ions (RE) into the fiber core, thus reducing the required fiber length and pushing away the non linear effects. Moreover, it offers a potential for high linear gain and finally, an appropriate composition of the core material can be envisaged to efficiently compete with photodarkening.

Tables Icon

Table 1. On the left side, the structures are numbered and named. The middle column depicts the distribution of the fiber refractive index, based on which the actively (passively) doped region is in red (clear blue) and pure silica in dark blue. On the right side, a representation of the modal confinement for the first 300 guided modes is shown for different core diameters: 50 μm (in black), 60 μm (in red) and 70 μm (in blue). The intensity distributions of the FM and the most disturbing HOM are depicted in the inset.

Tables Icon

Table 2. Similar to Table 1 with three structures based on symmetry reduction.

New fiber designs presented throughout this paper are composed of actively (red hexagons in Table 1 and Table 2) and passively (clear blue hexagons) doped rods, both of which have a positive refractive index contrast of Δn = 6·10−3 compared to that of pure silica (dark blue hexagons). This value of refractive index contrast has been arbitrarily fixed and can be adjusted without changing our approach. However, it can be pointed out that it is realistic considering the RI of current highly RE-doped silica materials. The inner cladding geometry enabling the mode discrimination is obtained by inserting pure silica rods into the passively-doped background material. According to the state-of-the-art air/silica PCF/LPF operating in a singlemode regime, the ratio d/Λ is fixed to 0.33. The 50 μm core, involving a pitch of 30 μm, is fully doped and composed of 19 actively doped rods. It should be pointed out that to mitigate the request on the volume of fabricated material, all structures we propose are limited to 7 layers of hexagons (two of them belonging to the core) [12]. Thus, the influence of a homogeneous enlargement of the fiber core from 50 to 70 μm will be studied and, by the way, an increase of the double clad diameter from 150 to 210 μm is induced. It is also important to underline that the pure silica clad (outer dark blue region, see Table 1 and Table 2) is not the outer cladding, but rather a part of the pump core. Thus, suck kind of pedestal acts on the mode’s confinement in the fiber core. An air-clad or fluorine-doped layer has to be added to propagate the pump radiation, resulting in a triple clad design. Guided modes of the different structures are computed at an emitted wavelength of 1.03 μm. The flagship all-solid designs we studied are depicted in Table 1 and Table 2 with their corresponding overlap factor graphs. These graphic representations allow the clear identification of the most competitive HOM (its intensity distribution is depicted in inset). Moreover, they provide information about the fundamental mode overlap factor and the evolution of the modal discrimination versus the core size, as calculations have been done for three core diameters: 50, 60 and 70 μm). Later, fiber designs will be referred to their numbering in the tables.

3.1. HOM leakage behavior

Structure 1 (see Table 1) is made of a single layer of low-index rods. The conventional six fold symmetry is retained and the HOMs leakage behavior examined. In order to study the cladding region where the most disruptive HOMs are delocalized, the cladding of structure 1 is divided into six identical sections, according to the minimum sector of its pattern (C6ν symmetry) [13]. Each of the cells in a section is associated with the other five cells at the same position in the other sections, forming a set of subdomains. Then, the analysis of the mode’s intensity localized in each group of cladding subdomains make it possible to strive toward an optimum cladding microstructuration for HOMs discrimination (as depicted in Table 1). Structure 1 exhibits a strong mode coupling of the fundamental core mode with the cladding mode (see inset on Table 1), reducing its confinement in the core to 50%. Nevertheless, HOMs leaky behavior can be observed (OFHOMs<50%). In addition, a conventional all-solid LPF (Structure 2) was studied and provides a reference on the performance of all-solid structures in terms of fundamental mode confinement and modal discrimination (88% and 29.4%, respectively).

Moreover, the most competitive mode is the LP31-like (depicted in inset of the Table 1). It should be pointed out that a reduction in the contrast of the refractive index in all-solid fibers (Δn = 6·10−3) compared to air/silica ones (Δn ≈ 0.45) drastically impacts the value of the modal discrimination. These performances are slightly lower than those of air-silica LPF because of this lower refractive index contrast between the inclusions and the background refractive index.

A better fiber design was obtained by acquiring an understanding of the HOMs leakage. Structure 3, also referred to as ”Vortex” fiber, is composed of 6 low-index ”arms”. It is worth noting that this design clearly improves modal discrimination: from 29.4% for a 50 μm conventional all-solid LPF to 46.2% for a 50 μm Vortex fiber. Although a Vortex fiber is an all-solid fiber featuring a lower refractive index contrast than air/silica LPFs, an appropriate fiber microstructuration has enabled to reach an equivalent modal discrimination. Moreover, although a homogeneous increase in the structural dimensions affects the modal discrimination, an efficient singlemode operation is maintained at least up to 70 μm of core diameter, using the criterion defined in [8]. Furthermore, the fiber symmetry has been reduced: a reflection plane does not exist in the Vortex fiber. Here, we will in the next section check the effect of a further symmetry reduction on the core modal content.

3.2. Reduction of cladding symmetry

In Table 1, modal discrimination is limited by the presence of the LP31-like mode, the intensity pattern of which is in accordance with the inner cladding symmetry (C6ν) and maxima of intensity of which rely on the six inner low-index inclusions. To enhance the modal discrimination, solutions must be found to efficiently delocalize this kind of HOM. As the mode intensity distribution is directly induced by the structural geometry/symmetry [14, 15, 16], it is obvious that modes can be delocalized out of the fiber core by acting on the cladding microstructuration. This impacts the resonance of the leaky modes with the double clad interface. Air/silica fibers showing a reduction in symmetry (reflection and/or rotation) have been reported recently by shifting the fiber core [17] or using two size of air holes, resulting in C3ν symmetry structures [1820]. The most interesting theoretical result comes from the use of a pentagonal periodic cladding [7], demonstrating a modal discrimination enhancement. At the sight of the Vortex and pentagonal structure performances, a step-by-step investigation of the effect of cladding symmetry was conducted. The following discussion is based on fiber structures presented in Table 2, to which a symmetry reduction has been applied. First, the symmetry between the inner and the outer cladding has been broken by applying a rotation on the whole periodic lattice (Structure 4). In this case, reflection symmetries are no longer displayed and the leakage channels are narrowed (d/Λ ≈ 0.4), strengthening the fundamental mode confinement (as much as 95.6%) and enhancing the linear gain. The modal discrimination is also improved compared to all-solid LPFs. Nevertheless, this structure is slightly less efficient than the Vortex fiber as the LP11 is relocalized in the fiber core. So, to enhance further the modal discrimination, this mode has to be weakened.

To move this investigation forward, a symmetry free fiber was devised. Structure 5 features a rotated periodic lattice, as for the previous structure, but some low-index inclusions have been added judiciously to break the symmetry, weakening the overlap of the LP11 and LP31-like modes with the fiber core. The modal discrimination obtained for this fiber is close to 55%, which is even larger than for the recently proposed air-silica Spiral fiber [20], whereas the FM is heavily confined (OFFM ≈ 96%). To the best of our knowledge, this level of discrimination has never been reported before, in particular in VLMA fibers exhibiting a core diameter larger than 50 μm and such strong confinement of the FM. In this proposed design, the inner cladding acts efficiently on the HOMs delocalization. Henceforth, modal discrimination is no longer limited by the LP11 or LP31-like modes but rather by a LP02-like mode (see Table 2). Finally, a modification of the first ring shape was investigated. Structure 6, whose fiber core is now surrounded by five low-index inclusions and an aperiodic lattice, demonstrates another improvement, by displaying over 60% of discrimination. Nevertheless, the quasi-pentagonal first layer of inclusions is not as efficient as the hexagonal one in strongly confining the fundamental mode. The advantage in regard to the linear gain is lowered. Depending on the final application, designers can make a trade-off and choose the appropriate structure among those proposed here.

Furthermore, the evolution of the modal discrimination was calculated over a wide spectral range (from 400 to 2200 nm) for all design fibers presented above (see Fig. 2). Structures are classified in two groups: the all-solid LPFs in Fig. 2(a) and fibers that feature a further symmetry reduction on Fig. 2(b). The air/silica LPF previously chosen as reference is also shown in the two graphs to quantify the potential of our structures. First of all, it is worth noting that the modal discrimination was efficiently enhanced thanks to an appropriate cladding microstructuration (Vortex fiber), which equals the performances of air/silica LPFs. Moreover, the structure 4 has the same symmetry (C6) and demonstrates also a discrimination close to 40%, which is competitive with the air-silica LPF. Figure 2(b) shows that a suppression of the symmetries allows an in-depth improvement of the modal discrimination (Symmetry free fibers). Indeed, these fibers exhibit outstanding modal discrimination. Over a wide wavelength range spanning from 800 to 2200 nm, they confirm their potential for scalability. This makes them quite useful in fiber amplifiers and lasers doped with Ytterbium, Erbium, Thulium and Holmium ions. Moreover, the change in refractive index does not seem to modify the modal discrimination drastically. The ability to efficiently delocalize HOMs appears to be conversely proportional to the number of existing symmetries (reflection or rotation ones). More precisely, the pentagonal symmetry free fiber shows a modal discrimination of more than 53%, across almost the entire investigated spectral range,even for the long wavelengths (beyond 2 μm), although the fundamental mode leaks more heavily out of the core. However, a homothetic enlargement of the fiber dimensions should make it possible to retrieve the maximum modal discrimination. Notably, 100 μm core thulium-doped fiber should demonstrate the same behavior as a 50 μm core ytterbium-doped fiber, because the mode expansion is proportional to the wavelength, maintaining efficient singlemode operation.

 

Fig. 2 Spectral evolution of the modal discrimination for the whole 50 μm all-solid structures proposed: (a) LPF structures (air/silica LPF and structures n°2 and 4), (b) Vortex (n°3), hexagonal symmetry free (n°5) and aperiodic quasi-pentagonal (n°6) fibers. The latter two fibers feature two different refractive index contrasts.

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4. Conclusion

In this article, we report on our study of novel all-solid fibers that aim to enhance modal discrimination, and thus make the singlemode operation more robust. Two strategies were followed to fulfill this goal: an appropriate cladding micro-structuration stemming from the understanding of HOMs leakage, and then the reduction of the cladding symmetry. Hence, a demonstration of the very low modal content into the gain/core region was performed, making it possible to achieve unmatched theoretical performance, outperforming the state-of-the-art LPFs and the recently reported Spiral fibers. It has been clearly evidenced that the cladding symmetry suppression allows an efficient delocalization of HOM whereas the shape of the first ring of inclusions acts strongly on the fundamental mode confinement by defining the thickness of the leakage channels. Finally, the development of all-solid symmetry-free fibers having an extremely low HOM content in the core as well as an enhancement of the fundamental mode confinement have been pointed out, strengthening the linear gain. These fibers should be experimentally relevant and compete with the state-of-the-art rod-type LPF.

Acknowledgments

This work, conducted under the AVANTAGE project, was co-funded by the European Union and Eolite Lasers. EC is involved in the Région Limousin with the ”Fonds européen de développement économique et régional”.

References and links

1. D. Gapontsev, “6kW CW single mode ytterbium fiber laser in all-fiber format,” Proc. Solid State and Diode Laser Technology Review (2008).

2. F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26mJ, 130W Q-switched fiber laser system with near-diffraction-limited beam quality,” Opt. Lett. 37(6), 1073–1075 (2012). [CrossRef]   [PubMed]  

3. P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580 , paper 7580112 (2010).

4. S. Jetschke, S. Unger, A. Schwuchow, M. Leich, and J. Kirchhof, “Efficient Yb laser fibers with low photodark-ening by optimization of the core composition,” Opt. Express 16(20), 15540–15545 (2008). [CrossRef]   [PubMed]  

5. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011). [CrossRef]   [PubMed]  

6. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 3997–4008 (2013). [CrossRef]  

7. F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “Non-hexagonal large-pitch fibers for enhanced mode discrimination,” Opt. Express 19(13), 12081–12086 (2011). [CrossRef]   [PubMed]  

8. M. M. Jørgensen, S. R. Petersen, M. Laurila, J. Lægsgaard, and T. T. Alkeskjold, “Optimizing single mode robustness of the distributed modal filtering rod fiber amplifier,” Opt. Express 20(7), 7263–7273 (2012). [CrossRef]   [PubMed]  

9. F. Jansen, F. Stutzki, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “High-power thermally guiding index-antiguiding-core fibers,” Opt. Lett. 38(4), 510–512 (2013). [CrossRef]   [PubMed]  

10. J. Limpert, F. Stutzki, F. Jansen, H. J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science & Applications 1, e8, (2012). [CrossRef]  

11. F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Avoided crossings in photonic crystal fibers,” Opt. Express 19(14), 13578–13589 (2011). [CrossRef]   [PubMed]  

12. R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012). [CrossRef]  

13. J. M. Fini, “Improved symmetry analysis of many-moded microstructure optical fibers,” J. Opt. Soc. Am. B 21(8), 1431–1436 (2004). [CrossRef]  

14. P. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides,” IEEE Trans. Microwave Theory Tech. 23(5), 421–433 (1975). [CrossRef]  

15. R. Guobin, W. Zhi, L. Shuqin, and J. Shuisheng, “Mode classification and degeneracy in photonic crystal fibers,” Opt. Express 11(11), 1310–1321 (2003). [CrossRef]   [PubMed]  

16. M. Steel, “Reflection symmetry and mode transversality in microstructured fibers,” Opt. Express 12(8), 1497–509 (2004). [CrossRef]   [PubMed]  

17. P. M. Agruzov, K. V Dukelskii, and V. S. Shevandin, “Three types of microstructured large core fibers : development and investigation,” Conference on Lasers and Electro-Optics, paper CE.P.28 (2009).

18. V. V Demidov, K. V Dukelskii, and V. S. Shevandin, “Novel bend-resistant design of single-mode microstructured fibers,” Conference on Lasers and Electro-Optics, paper CE.P35 (2011).

19. M.-Y. Chen, Y. Li, J. Zhou, and Y.-K. Zhang, “Design of asymmetric large-mode area optical fiber with low bending loss,” J. of Lightwave Technol. 31(3), 476–481 (2013). [CrossRef]  

20. J. Limpert, “Large-pitch fibers: pushing very large mode areas to highest powers,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper T2A.1 (2012). [CrossRef]  

References

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  1. D. Gapontsev, “6kW CW single mode ytterbium fiber laser in all-fiber format,” Proc. Solid State and Diode Laser Technology Review (2008).
  2. F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26mJ, 130W Q-switched fiber laser system with near-diffraction-limited beam quality,” Opt. Lett.37(6), 1073–1075 (2012).
    [CrossRef] [PubMed]
  3. P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).
  4. S. Jetschke, S. Unger, A. Schwuchow, M. Leich, and J. Kirchhof, “Efficient Yb laser fibers with low photodark-ening by optimization of the core composition,” Opt. Express16(20), 15540–15545 (2008).
    [CrossRef] [PubMed]
  5. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express19(14), 13218–13224 (2011).
    [CrossRef] [PubMed]
  6. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 3997–4008 (2013).
    [CrossRef]
  7. F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “Non-hexagonal large-pitch fibers for enhanced mode discrimination,” Opt. Express19(13), 12081–12086 (2011).
    [CrossRef] [PubMed]
  8. M. M. Jørgensen, S. R. Petersen, M. Laurila, J. Lægsgaard, and T. T. Alkeskjold, “Optimizing single mode robustness of the distributed modal filtering rod fiber amplifier,” Opt. Express20(7), 7263–7273 (2012).
    [CrossRef] [PubMed]
  9. F. Jansen, F. Stutzki, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “High-power thermally guiding index-antiguiding-core fibers,” Opt. Lett.38(4), 510–512 (2013).
    [CrossRef] [PubMed]
  10. J. Limpert, F. Stutzki, F. Jansen, H. J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science & Applications1, e8, (2012).
    [CrossRef]
  11. F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Avoided crossings in photonic crystal fibers,” Opt. Express19(14), 13578–13589 (2011).
    [CrossRef] [PubMed]
  12. R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
    [CrossRef]
  13. J. M. Fini, “Improved symmetry analysis of many-moded microstructure optical fibers,” J. Opt. Soc. Am. B21(8), 1431–1436 (2004).
    [CrossRef]
  14. P. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides,” IEEE Trans. Microwave Theory Tech.23(5), 421–433 (1975).
    [CrossRef]
  15. R. Guobin, W. Zhi, L. Shuqin, and J. Shuisheng, “Mode classification and degeneracy in photonic crystal fibers,” Opt. Express11(11), 1310–1321 (2003).
    [CrossRef] [PubMed]
  16. M. Steel, “Reflection symmetry and mode transversality in microstructured fibers,” Opt. Express12(8), 1497–509 (2004).
    [CrossRef] [PubMed]
  17. P. M. Agruzov, K. V Dukelskii, and V. S. Shevandin, “Three types of microstructured large core fibers : development and investigation,” Conference on Lasers and Electro-Optics, paper CE.P.28 (2009).
  18. V. V Demidov, K. V Dukelskii, and V. S. Shevandin, “Novel bend-resistant design of single-mode microstructured fibers,” Conference on Lasers and Electro-Optics, paper CE.P35 (2011).
  19. M.-Y. Chen, Y. Li, J. Zhou, and Y.-K. Zhang, “Design of asymmetric large-mode area optical fiber with low bending loss,” J. of Lightwave Technol.31(3), 476–481 (2013).
    [CrossRef]
  20. J. Limpert, “Large-pitch fibers: pushing very large mode areas to highest powers,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper T2A.1 (2012).
    [CrossRef]

2013 (3)

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 3997–4008 (2013).
[CrossRef]

M.-Y. Chen, Y. Li, J. Zhou, and Y.-K. Zhang, “Design of asymmetric large-mode area optical fiber with low bending loss,” J. of Lightwave Technol.31(3), 476–481 (2013).
[CrossRef]

F. Jansen, F. Stutzki, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “High-power thermally guiding index-antiguiding-core fibers,” Opt. Lett.38(4), 510–512 (2013).
[CrossRef] [PubMed]

2012 (3)

2011 (3)

2010 (1)

P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).

2008 (2)

2004 (2)

2003 (1)

1975 (1)

P. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides,” IEEE Trans. Microwave Theory Tech.23(5), 421–433 (1975).
[CrossRef]

Agruzov, P. M.

P. M. Agruzov, K. V Dukelskii, and V. S. Shevandin, “Three types of microstructured large core fibers : development and investigation,” Conference on Lasers and Electro-Optics, paper CE.P.28 (2009).

Alkeskjold, T. T.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 3997–4008 (2013).
[CrossRef]

M. M. Jørgensen, S. R. Petersen, M. Laurila, J. Lægsgaard, and T. T. Alkeskjold, “Optimizing single mode robustness of the distributed modal filtering rod fiber amplifier,” Opt. Express20(7), 7263–7273 (2012).
[CrossRef] [PubMed]

Benoit, A.

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

Broeng, J.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 3997–4008 (2013).
[CrossRef]

Chen, M.-Y.

M.-Y. Chen, Y. Li, J. Zhou, and Y.-K. Zhang, “Design of asymmetric large-mode area optical fiber with low bending loss,” J. of Lightwave Technol.31(3), 476–481 (2013).
[CrossRef]

Dauliat, R.

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

Demidov, V. V

V. V Demidov, K. V Dukelskii, and V. S. Shevandin, “Novel bend-resistant design of single-mode microstructured fibers,” Conference on Lasers and Electro-Optics, paper CE.P35 (2011).

Dukelskii, K. V

V. V Demidov, K. V Dukelskii, and V. S. Shevandin, “Novel bend-resistant design of single-mode microstructured fibers,” Conference on Lasers and Electro-Optics, paper CE.P35 (2011).

P. M. Agruzov, K. V Dukelskii, and V. S. Shevandin, “Three types of microstructured large core fibers : development and investigation,” Conference on Lasers and Electro-Optics, paper CE.P.28 (2009).

Ehrenreich, T.

P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).

Eidam, T.

J. Limpert, F. Stutzki, F. Jansen, H. J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science & Applications1, e8, (2012).
[CrossRef]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express19(14), 13218–13224 (2011).
[CrossRef] [PubMed]

Fini, J. M.

Gaponov, D. A.

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

Gapontsev, D.

D. Gapontsev, “6kW CW single mode ytterbium fiber laser in all-fiber format,” Proc. Solid State and Diode Laser Technology Review (2008).

Grimm, S.

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

Guobin, R.

Hansen, K. R.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 3997–4008 (2013).
[CrossRef]

Jansen, F.

Jauregui, C.

Jetschke, S.

S. Jetschke, S. Unger, A. Schwuchow, M. Leich, and J. Kirchhof, “Efficient Yb laser fibers with low photodark-ening by optimization of the core composition,” Opt. Express16(20), 15540–15545 (2008).
[CrossRef] [PubMed]

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

Jørgensen, M. M.

Kirchhof, J.

Lægsgaard, J.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 3997–4008 (2013).
[CrossRef]

M. M. Jørgensen, S. R. Petersen, M. Laurila, J. Lægsgaard, and T. T. Alkeskjold, “Optimizing single mode robustness of the distributed modal filtering rod fiber amplifier,” Opt. Express20(7), 7263–7273 (2012).
[CrossRef] [PubMed]

Laurila, M.

Leich, M.

Leveille, R.

P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).

Li, Y.

M.-Y. Chen, Y. Li, J. Zhou, and Y.-K. Zhang, “Design of asymmetric large-mode area optical fiber with low bending loss,” J. of Lightwave Technol.31(3), 476–481 (2013).
[CrossRef]

Liem, A.

Limpert, J.

F. Jansen, F. Stutzki, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “High-power thermally guiding index-antiguiding-core fibers,” Opt. Lett.38(4), 510–512 (2013).
[CrossRef] [PubMed]

J. Limpert, F. Stutzki, F. Jansen, H. J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science & Applications1, e8, (2012).
[CrossRef]

F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26mJ, 130W Q-switched fiber laser system with near-diffraction-limited beam quality,” Opt. Lett.37(6), 1073–1075 (2012).
[CrossRef] [PubMed]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express19(14), 13218–13224 (2011).
[CrossRef] [PubMed]

F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “Non-hexagonal large-pitch fibers for enhanced mode discrimination,” Opt. Express19(13), 12081–12086 (2011).
[CrossRef] [PubMed]

F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Avoided crossings in photonic crystal fibers,” Opt. Express19(14), 13578–13589 (2011).
[CrossRef] [PubMed]

J. Limpert, “Large-pitch fibers: pushing very large mode areas to highest powers,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper T2A.1 (2012).
[CrossRef]

Majid, I.

P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).

McIsaac, P.

P. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides,” IEEE Trans. Microwave Theory Tech.23(5), 421–433 (1975).
[CrossRef]

Moulton, P. F.

P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).

Otto, H.

Otto, H. J.

J. Limpert, F. Stutzki, F. Jansen, H. J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science & Applications1, e8, (2012).
[CrossRef]

Otto, H.-J.

Petersen, S. R.

Rines, G.

P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).

Roy, P.

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

Salin, F.

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

Schmidt, O.

Schreiber, T.

Schuster, K.

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

Schwuchow, A.

Shevandin, V. S.

V. V Demidov, K. V Dukelskii, and V. S. Shevandin, “Novel bend-resistant design of single-mode microstructured fibers,” Conference on Lasers and Electro-Optics, paper CE.P35 (2011).

P. M. Agruzov, K. V Dukelskii, and V. S. Shevandin, “Three types of microstructured large core fibers : development and investigation,” Conference on Lasers and Electro-Optics, paper CE.P.28 (2009).

Shuisheng, J.

Shuqin, L.

Steel, M.

Stutzki, F.

Tankala, K.

P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).

Tünnermann, A.

Unger, S.

Wirth, C.

Zhang, Y.-K.

M.-Y. Chen, Y. Li, J. Zhou, and Y.-K. Zhang, “Design of asymmetric large-mode area optical fiber with low bending loss,” J. of Lightwave Technol.31(3), 476–481 (2013).
[CrossRef]

Zhi, W.

Zhou, J.

M.-Y. Chen, Y. Li, J. Zhou, and Y.-K. Zhang, “Design of asymmetric large-mode area optical fiber with low bending loss,” J. of Lightwave Technol.31(3), 476–481 (2013).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides,” IEEE Trans. Microwave Theory Tech.23(5), 421–433 (1975).
[CrossRef]

J. of Lightwave Technol. (1)

M.-Y. Chen, Y. Li, J. Zhou, and Y.-K. Zhang, “Design of asymmetric large-mode area optical fiber with low bending loss,” J. of Lightwave Technol.31(3), 476–481 (2013).
[CrossRef]

J. Opt. Soc. Am. B (1)

Light: Science & Applications (1)

J. Limpert, F. Stutzki, F. Jansen, H. J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Science & Applications1, e8, (2012).
[CrossRef]

Opt. Express (8)

F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Avoided crossings in photonic crystal fibers,” Opt. Express19(14), 13578–13589 (2011).
[CrossRef] [PubMed]

S. Jetschke, S. Unger, A. Schwuchow, M. Leich, and J. Kirchhof, “Efficient Yb laser fibers with low photodark-ening by optimization of the core composition,” Opt. Express16(20), 15540–15545 (2008).
[CrossRef] [PubMed]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express19(14), 13218–13224 (2011).
[CrossRef] [PubMed]

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 3997–4008 (2013).
[CrossRef]

F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “Non-hexagonal large-pitch fibers for enhanced mode discrimination,” Opt. Express19(13), 12081–12086 (2011).
[CrossRef] [PubMed]

M. M. Jørgensen, S. R. Petersen, M. Laurila, J. Lægsgaard, and T. T. Alkeskjold, “Optimizing single mode robustness of the distributed modal filtering rod fiber amplifier,” Opt. Express20(7), 7263–7273 (2012).
[CrossRef] [PubMed]

R. Guobin, W. Zhi, L. Shuqin, and J. Shuisheng, “Mode classification and degeneracy in photonic crystal fibers,” Opt. Express11(11), 1310–1321 (2003).
[CrossRef] [PubMed]

M. Steel, “Reflection symmetry and mode transversality in microstructured fibers,” Opt. Express12(8), 1497–509 (2004).
[CrossRef] [PubMed]

Opt. Lett. (2)

Proc. of SPIE 7580 (1)

P. F. Moulton, T. Ehrenreich, R. Leveille, I. Majid, K. Tankala, and G. Rines, “1-kW, all-glass Tm : fiber laser,” Proc. of SPIE 7580, paper 7580112 (2010).

Proc. Solid State and Diode Laser Technology Review (1)

D. Gapontsev, “6kW CW single mode ytterbium fiber laser in all-fiber format,” Proc. Solid State and Diode Laser Technology Review (2008).

Other (4)

J. Limpert, “Large-pitch fibers: pushing very large mode areas to highest powers,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper T2A.1 (2012).
[CrossRef]

P. M. Agruzov, K. V Dukelskii, and V. S. Shevandin, “Three types of microstructured large core fibers : development and investigation,” Conference on Lasers and Electro-Optics, paper CE.P.28 (2009).

V. V Demidov, K. V Dukelskii, and V. S. Shevandin, “Novel bend-resistant design of single-mode microstructured fibers,” Conference on Lasers and Electro-Optics, paper CE.P35 (2011).

R. Dauliat, D. A. Gaponov, A. Benoit, F. Salin, K. Schuster, S. Jetschke, S. Grimm, and P. Roy, “Ytterbium doped all solid large pitch fiber made from powder sintering and vitrification,” International Conference on Fibre Optics and Photonics - OSA Technical Digest, paper TPo.7 (2012).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

(a) 2D refractive index repartition of the air/silica LPF described in [2]. The gain region is in red, the pure silica in blue and the air holes in yellow. (b) Overlap factor of the fundamental mode (solid lines) and modal discrimination (dashed lines) computed for the air/silica LPF. Calculations have been done for three air-clad diameters: 170 μm (black), 180 μm (red), and 190 μm (blue) and various ratio d/Λ. Insets: computed intensity distributions corresponding to the fundamental mode coupling (top), and the most disturbing HOM (bottom).

Fig. 2
Fig. 2

Spectral evolution of the modal discrimination for the whole 50 μm all-solid structures proposed: (a) LPF structures (air/silica LPF and structures n°2 and 4), (b) Vortex (n°3), hexagonal symmetry free (n°5) and aperiodic quasi-pentagonal (n°6) fibers. The latter two fibers feature two different refractive index contrasts.

Tables (2)

Tables Icon

Table 1 On the left side, the structures are numbered and named. The middle column depicts the distribution of the fiber refractive index, based on which the actively (passively) doped region is in red (clear blue) and pure silica in dark blue. On the right side, a representation of the modal confinement for the first 300 guided modes is shown for different core diameters: 50 μm (in black), 60 μm (in red) and 70 μm (in blue). The intensity distributions of the FM and the most disturbing HOM are depicted in the inset.

Tables Icon

Table 2 Similar to Table 1 with three structures based on symmetry reduction.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

O F = A d | E | 2 dS A p | E | 2 dS
Δ O F = O F F M O F H O M

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