Open Access
Add to BibSonomyAbstract
Mode area scaling of optical fiber is highly desirable for high power fiber laser applications. It is well known that incorporation of additional smaller cores in the cladding can be used to resonantly out-couple higher-order modes from a main core to suppress higher-order-mode propagation in the main core. Using a novel design with multiple coupled smaller cores in the cladding, we have successfully demonstrated a single-mode photonic bandgap fiber with record effective mode area of ~2650µm2. Detailed numeric studies have been conducted for multiple cladding designs. For the optimal designs, the simulated minimum higher-order-mode losses are well over two orders of magnitudes higher than that of fundamental mode when expressed in dBs. To our knowledge, this is the best higher-order-mode suppression ever found in fibers with this large effective mode areas. We have also experimentally validated one of the designs. M2<1.08 across the transmission band was demonstrated.
© 2015 Optical Society of America
1. Introduction
In the course of developing high-power fiber lasers, mode area scaling is a key to mitigate nonlinear effects as a result of high optical intensity, such as stimulated Brillouin scattering (SBS), stimulated Raman scatting (SRS), Self-phase modulation (SPM) and four-wave mixing (FWM) [1,2]. In many applications, diffraction-limited beam is highly desired. We now know that mode instability can lead to poor mode quality at higher powers even in fibers with some higher-order-mode suppression [3–7]. To ensure single-mode output at high powers, very strong higher-order-mode suppression is also required along with the need for large effective mode areas.
In the recent decade, numerous approaches have been proposed, which led to a significant progress in mode area scaling of optical fibers. One notable area is in photonic crystal fibers (PCF) [3–5, 8, 9]. The short straight PCF rods used in the demonstrations have prevented their use in multi-kilowatts fiber lasers due to limited heat dissipation. The air holes in the cladding have also prevented them from being used in robust monolithic fiber lasers. The lack of strong higher-order-mode suppression has also led to mode instability issues [3–5]. To overcome some of the drawbacks, we have studied all-glass and coil-able leakage channel fibers (LCF) [10–13]. In the light of recent works in mode instabilities [6,7], much stronger higher-order-mode suppression is necessary to ensure single-mode operation at high powers.
Recently there have been significant interests in all-solid bandgap fibers (AS-PBF) [14–18]. The unique combination of an open cladding and a dispersive anti-resonant cladding which enhances the mode dependence enables some of the strongest higher-order-mode suppressions. In a recent work, we have demonstrated the existence of a robust single-mode regime near the short-wavelength edge of the bandgap in an ytterbium-doped 50µm-core all-solid photonic bandgap fiber [18]. Our efforts in further mode area scaling of all-solid photonic bandgap fibers using similar designs have failed to find a design with sufficient higher-order-mode suppression for 100µm-core fibers. This led us to look for significant improvement in the designs.
It is well known that additional cores in the cladding which are in resonance for coupling with the higher-order modes in the main core can be used to suppress the higher-order modes in the main core [19,20]. This has even been recently used in hollow-core photonic bangap fibers for suppressing higher-order modes [21,22]. Recently, it has been suggested that multiple-coupled cores in the cladding can lead to much improved higher-order-mode suppression [23]. The key improvement is the use of multiple coupled small cores in the claddings which both enhances the coupling with higher-order modes in the main core and broadens the coupling resonance. The higher-order-mode in the main core is coupling to multiple coupled cores in the cladding simultaneously in the new design instead of just few isolated cores in the cladding in previous works. Narrow coupling resonance in the previous approaches [19,20] has always made them somewhat impractical. Such multiple coupled cores can be easily incorporated in the existing fabrication process of photonic bandgap fibers. The new proposal is, therefore, significant in providing a far more practical design. Recently, robust single-mode operation with mode field diameter of 44µm in a straight fiber was demonstrated using this approach in an all-solid photonic bandgap fiber [24].
In this work, we theoretically and experimentally investigated the multiple-cladding-resonance (MCR) designs in all-solid photonic bandgap fibers for further mode area scaling as well as for coiled operations. We have demonstrated robust single-mode operation with record effective mode area of ~2650 µm2, i.e. a mode field diameter of 58µm, in straight fibers. This represents a significant improvement over previous demonstrations of robust single-mode operation in all-solid photonic bandgap fibers. Our simulation also indicates well over two orders of magnitude suppression of higher-order modes in coiled operations. This is the strongest higher-order-mode suppression at this large effective mode area to our knowledge.
2. Basic theory
Additional smaller cores can be easily created in the cladding of photonic bandgap fibers by missing several nodes. The smaller cores share the same cladding as the main core. If the cladding cores are well isolated, the resonant conditions between the fundamental mode in the cladding cores and various higher-order modes of the main core can be easily calculated. Using step-index fiber analogue, the propagation constant of modes in the main core can be written as
where k is the vacuum wavenumber; nb is the refractive index of the background glass; ρm is the main core radius; and main core parameter Um is as normally defined for optical fibers [25]. It needs to be noted that the refractive index of all the cores is the same as that of the background glass nb in this case. Similarly, the propagation constant of modes in the cladding cores can be written asThe cladding core parameter Uc is defined similarly as Um. The resonant condition for maximum coupling of a mode in the main core and a mode in the cladding core is βm = βc. Using the relations obtained thus far in Eq. (1) and Eq. (2), the resonant condition can be written as
Since the refractive index of core and cladding are the same for both main and cladding cores. The resonant condition can be rewritten using the normalized frequency, i.e. V value, Vm and Vc for the main and cladding cores respectively.This can be easily calculated for the fundamental mode of the cores in the cladding and various higher-order modes in the main core (see Fig. 1).
Fig. 1 Required core diameter ratio (ρc/ρm) for maximum resonant coupling between the fundamental mode of the cladding core and one of the higher-order modes of the main core versus normalized frequency (V value) of the main core.
The horizontal axis is the V value of the main core. For weakly coupled cladding cores, Fig. 1 provides a reasonable approximations for a straight fiber. In the multimode regime with V>10, for coupling with LP11 and LP21 modes in the main core, ρc/ρm≈0.6 and 0.44 respectively. As it turned out, this approximation works reasonably well for cladding cores of a photonic bandgap fibers.
3. FEM simulations
Based on the approximation in Fig. 1 as guidance, three cladding designs were numerically studied using a FEM mode solver. The cross-sections of all designs are shown in Fig. 2. For all the designs, a 7-cell core is adopted. Instead of the periodically arranged high-index inclusions surrounding the core, several cladding structures are used to form the cladding. The smaller cores in the cladding are formed by purposefully taking out a certain number of nodes such that a cladding defect core is created. The first design shown in the left side of Fig. 1 is referred to the “mixed-cell” since it has two and three nodes removed to create the cladding cores. The second and third design shown in the middle and right side of the Fig. 2 are accordingly referred to “three-cell” and “two-cell” respectively. The core diameter ratio ρc/ρm≈0.65 and 0.53 for the 3- and 2-cell cores respectively, close to the 0.6 required in Fig. 1 for coupling with LP11 mode in the main core. It is worth noting that the effective mode index of the cladding core will increase or decrease in a coiled fiber depending on its relative location to the center of the coil. The condition required in Eq. (4) is, therefore, only an approximation in this case.
Fig. 2 Cross-section of PBFs studied. From left to right are: mixed-cell, three-cell and two-cell AS-PBF.
The nodes in the cladding were made of germanium-doped silica with a graded index profile similar to the one used in our previous Yb-doped PBF [17,18]. The pitch, that is the distance between two adjacent cladding nodes, is 25μm, which yields a 100μm core diameter. The ratio between the diameter of the cladding nodes and pitch is fixed, at 0.24.
A commercially available COMSOL Finite Element Method (FEM) mode solver is used for the simulation. A perfectly matched layer is implemented to obtain the mode loss. The fiber is simulated under 50cm bending radius. This provides a coil diameter which is acceptable for multi-kw high-power fiber lasers and minimizes mode compression due to coiling. The wavelength is scanned from 900nm to 1100nm. Given the symmetry of the cladding arrangement, propagation loss under different bending orientations has been studied. The arrow in the inset of Fig. 3 indicates the direction where the center of the coil is. The loss curves with respect to the wavelength are plotted in Fig. 3.
For the mixed-cell PBF (Fig. 3(a)) and three-cell PBF (Fig. 3(c)), each has three possible different bending orientations: one horizontal and two vertical. Meanwhile two-cell PBF only has two fundamentally different ways to coil. The first three dominant modes, namely LP01 and LP11 (LP11A and LP11B) with two orthogonal orientations are presented. The inset in Fig. 3(a) shows the generic mode pattern for LP01, LP11A and LP11B. It can be clearly seen that when fiber is bent horizontally, all three designs demonstrate significant differential mode loss within the third bandgap at wavelength ranging from 1000nm to 1030nm, which indicates a possible window for single-mode operation. The lowest fundamental mode loss can be as low as ~0.01dB/m.
One should note that at 1030nm the FM tends to have a small loss peak, which can be attributed to the resonance effect with the cladding, as it can be clearly seen in the inset of Fig. 3(a). The differential loss is much worse when bending vertically. For example, for the three cell PBF shown in the Fig. 3(c), the LP11A mode has almost the same loss as LP01 mode does. At longer wavelengths, it can even have less loss than LP01 mode. The loss of all LP modes tend to increase significantly outside the bandgap when the wavelength is below 1000nm or beyond 1050nm. The mode can be severely distorted in the high loss regime.
Table 1. summarized the FM loss, minimum HOM loss and loss ratios at the wavelength that has the minimum FM loss for the horizontally coiled fibers. Note that the corresponding HOM loss is picked between LP11A and LP11B, whichever has the lower loss. From the table, it can be seen that the three-cell PBF has the highest loss ratio at 1040nm but the bandwidth for low FM loss is rather narrow in this case. The two-cell PBF has the second highest loss ratio, yet the LP11 mode loss drops down dramatically once the wavelength is longer than 1000nm. It is worth noting that, as for the mixed-cell fiber design under horizontal bending, both LP11A and LP11B mode loss are above 10dB/m while the fundamental mode loss is kept at or below 0.2dB/m around 1000nm. In addition, the bandwidth for such high differential loss is broader compared to the three-cell and two-cell designs. As the wavelength move toward 1020nm, the LP01 continues to drop below 0.1dB/m, even though the LP11A mode loss simultaneously decreases, the loss ratio between the LP11 to LP01 still reaches as high as 192 (see Table 1.).
Table 1. Summary of loss ratio for three types of fiber design
Ideally, the bending orientation should be controlled to be horizontal for best HOM suppression. However, in practical cases, the bending direction may be arbitrary, meaning a fiber can have a combination of all the possible bending orientations throughout its length. In this case, total HOM loss will be an average loss of all the orientations. Since FM loss remains largely independent of the orientations, it is still sufficient to realize single transverse-mode operation over a few meters of fiber although with a lesser HOM suppression.
4. Experiments
To validate the simulation, the mixed-cell design was fabricated through standard stack-and-draw process. The dimension of the fiber is illustrated in Table 2. and the cross-section of the actual fiber is shown in Fig. 4. One can notice that there is a slight difference between actual dimension and numeric simulation, which can be attributed to parameter control during the fabrication. The germanium nodes in the cladding have the same refractive index profile as the one used in the simulation. The center core is made of silica. The outer shape of the fiber is rounded hexagon, which also helps increase the differential mode loss [11].
Table 2. Dimensions of Fabricated hetero-structured PBF
Fig. 4 Simulated loss of LP01 (blue) and LP11 modes (Orange and Green) in (a) mixed-cell design, (b) two-cell design and (c) three-cell design. The insets show the layout of different cladding arrangement. The arrow in the inset indicates the coil center. Insets also show the mode patterns of LP01 and LP11.
Transmission, mode pattern and beam quality of the mixed-cell PBF have been fully characterized. In all measurements, the fiber is bent at diameter of 1m, conforming to the bending radius set in the numeric simulation. It is also worth mentioning that the bending direction was not controlled during the measurement. The transmission of a 4m PBF is shown in Fig. 5 in a linear scale. The scanning wavelength ranges from 998nm to 1041nm. The highest transmission peak is observed at the vicinity of 1015nm. Knowing the dimension difference, this is well correspondent to the computational results, which has low attenuation around 1020nm under all three bending configuration.
The simulated effective mode area (EMA) of the fiber versus bending diameter is shown in Fig. 6. At bending diameter of 1m, the EMA is ~1842µm2, marked by the orange diamond in Fig. 6.
Fig. 6 Estimated effective mode area (EMA) of the fabricate PBF. The coil diameter is in log scale. The insets are mode patterns under different coil diameters. At 1m bending diameter, the EMA is estimated to be ~1842µm2, shown as the orange diamond in the chart. The dash line indicates the EMA of a straight fiber.
At large core diameters as in the fabricated fibers in this work, the effective mode indexes of the fundamental and higher-order modes are very close, leading to small intermodal delays. This causes significant difficulty in using the well-known quantitative mode characterization techniques such as S2 and C2 techniques [26, 27]. Much wide wavelength scan range is required for the S2 method. In case of the C2 method, broadband source with coherent length less than few tens of femtosecond is required, in addition to the necessary dispersion compensation. Recently we have demonstrated the first quantitative mode characterization in a 100µm-core fiber using a matched white-light interferometry where dispersion is completely compensated [28]. The fabricated fiber in this work, however, has very narrow transmission band, which makes any quantitative mode characterization impossible.
To verify the robustness of single-mode operation, a tunable laser light was launched into a 4m PBF bending at 1m diameter. The fiber was initially aligned such that light could be directly launched into the center core while the tunable laser scanned the wavelength from 1010nm to 1030nm at the increment of 5nm. The near field mode pattern was captured using a CCD camera at the other end of the PBF. Then the fiber was moved off the optimal launching condition by 12µm, 24µm and 36µm sequentially in attempt to excite HOM. After each offset, the tunable laser would repeat the same wavelength scan.
Figure 7 shows the near field mode image under different launching conditions at various wavelengths. At the optimal launching condition, the fundamental mode was well guided from 1010nm to 1015nm and start to degrade slightly at 1030nm. The HOM was constantly absent across the wavelength spectrum as the launching condition was gradually deteriorated from the optimal launching position. This measurement effectively demonstrated the single-mode operation for this PBF.
Fig. 7 Near filed mode pattern of the mixed-cell PBF at various wavelengths. Δ is the distance of the launch offset.
The beam quality was further verified by employing M2 technique. Three wavelengths from the tunable laser, namely 1013nm, 1018nm and 1024nm were selected for this measurement. The fiber length and coil diameter are the same as the ones in the tests mentioned above. A CCD camera is deployed to trace the propagation of the output beam. The results are shown in Fig. 8. It can be seen that for all the three wavelengths, the measured M2 values along the horizontal and vertical direction are equal or less than 1.08. The beam profiles captured also indicate a good single-mode operation. This further confirms that robust single-mode operation is supported in the large core while HOM is highly suppressed by the outer cladding defects due to coupling.
Fig. 8 Beam quality measurement at wavelength of 1013nm, 1018nm and 1024nm. Both x-axis (blue) and y-axis (green) were measured with selected mode profiles along the curve.
5. Conclusion
In summary, we have demonstrated robust single-mode operation in a MCR-PBF with a record mode area of ~2650μm2. Three types cladding layouts have been theoretically studied. Comparing among different bending orientations, horizontal bending performs much better in terms of differential mode loss than that vertical bending does. With controlled bending configuration, a very high loss ratio between LP11 and LP01 can be realized. Mixed-cell design was fabricated and demonstrated to be robustly single-mode at coil diameter of 1m. The M2 was measured to be less than 1.08 across the bandgap. This work further pushes mode area scaling limit in single-mode all-solid photonic bandgap fibers. The MCR mechanism can be potentially adopted to realize rare-earth doped single-mode fiber lasers with 100µm core diameter.
Acknowledgment
This material is based upon work supported in part by the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF-10-1-0423 through a Joint Technology Office MRI program.
References and links
1. A. Tünnermann, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: an ultrafast performance evolution,” Appl. Opt. 49(25), F71–F78 (2010). [CrossRef] [PubMed]
2. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [Invited],” J. Opt. Soc. Am. B 27(11), B63–B92 (2010). [CrossRef]
3. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010). [CrossRef] [PubMed]
4. F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011). [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. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011). [CrossRef] [PubMed]
7. L. Dong, “Stimulated thermal Rayleigh scattering in optical fibers,” Opt. Express 21(3), 2642–2656 (2013). [CrossRef] [PubMed]
8. J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11(7), 818–823 (2003). [CrossRef] [PubMed]
9. J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14(7), 2715–2720 (2006). [CrossRef] [PubMed]
10. L. Dong, T. Wu, H. McKay, L. Fu, J. Li, and H. G. Winful, “All-Glass Large-Core Leakage Channel Fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 47–53 (2009). [CrossRef]
11. G. Gu, F. Kong, T. W. Hawkins, P. Foy, K. Wei, B. Samson, and L. Dong, “Impact of fiber outer boundaries on leaky mode losses in leakage channel fibers,” Opt. Express 21(20), 24039–24048 (2013). [CrossRef] [PubMed]
12. L. Dong, H. A. McKay, L. Fu, M. Ohta, A. Marcinkevicius, S. Suzuki, and M. E. Fermann, “Ytterbium-doped all glass leakage channel fibers with highly fluorine-doped silica pump cladding,” Opt. Express 17(11), 8962–8969 (2009). [CrossRef] [PubMed]
13. F. Kong, G. Gu, T. W. Hawkins, J. Parsons, M. Jones, C. Dunn, M. T. Kalichevsky-Dong, K. Wei, B. Samson, and L. Dong, “Flat-top mode from a 50 µm-core Yb-doped leakage channel fiber,” Opt. Express 21(26), 32371–32376 (2013). [CrossRef] [PubMed]
14. M. Kashiwagi, K. Saitoh, K. Takenaga, S. Tanigawa, S. Matsuo, and M. Fujimaki, “Effectively single-mode all-solid photonic bandgap fiber with large effective area and low bending loss for compact high-power all-fiber lasers,” Opt. Express 20(14), 15061–15070 (2012). [CrossRef] [PubMed]
15. M. Kashiwagi, K. Saitoh, K. Takenaga, S. Tanigawa, S. Matsuo, and M. Fujimaki, “Low bending loss and effectively single-mode all-solid photonic bandgap fiber with an effective area of 650 μm2,” Opt. Lett. 37(8), 1292–1294 (2012). [CrossRef] [PubMed]
16. S. Saitoh, K. Saitoh, M. Kashiwagi, S. Matsuo, and L. Dong, “Design Optimization of Large-Mode-Area All-Solid Photonic Bandgap Fibers for High-Power Laser Applications,” J. Lightwave Technol. 32(3), 440–449 (2014). [CrossRef]
17. F. Kong, K. Saitoh, D. Mcclane, T. Hawkins, P. Foy, G. Gu, and L. Dong, “Mode area scaling with all-solid photonic bandgap fibers,” Opt. Express 20(24), 26363–26372 (2012). [CrossRef] [PubMed]
18. G. Gu, F. Kong, T. Hawkins, J. Parsons, M. Jones, C. Dunn, M. T. Kalichevsky-Dong, K. Saitoh, and L. Dong, “Ytterbium-doped large-mode-area all-solid photonic bandgap fiber lasers,” Opt. Express 22(11), 13962–13968 (2014). [CrossRef] [PubMed]
19. J. Fini, “Design of Solid and Microstructure Fibers for Suppression of Higher-Order Modes,” Opt. Express 13(9), 3477–3490 (2005). [CrossRef] [PubMed]
20. X. Ma, C. H. Liu, G. Chang, and A. Galvanauskas, “Angular-momentum coupled optical waves in chirally-coupled-core fibers,” Opt. Express 19(27), 26515–26528 (2011). [CrossRef] [PubMed]
21. J. M. Fini, J. W. Nicholson, R. S. Windeler, E. M. Monberg, L. Meng, B. Mangan, A. Desantolo, and F. V. DiMarcello, “Low-loss hollow-core fibers with improved single-modedness,” Opt. Express 21(5), 6233–6242 (2013). [CrossRef] [PubMed]
22. J. M. Fini, B. Mangan, L. Meng, E. M. Monberg, J. W. Nicholson, and R. S. Windeler, “37-cell hollow-core-fiber designs with improved single-modedness,” in CLEO: 2014 (OSA, 2014), p. SM1N.2.
23. T. Murao, K. Saitoh, and M. Koshiba, “Multiple resonant coupling mechanism for suppression of higher-order modes in all-solid photonic bandgap fibers with heterostructured cladding,” Opt. Express 19(3), 1713–1727 (2011). [CrossRef] [PubMed]
24. A. Baz, L. Bigot, G. Bouwmans, and Y. Quiquempois, “Single-Mode, Large Mode Area, Solid-Core Photonic BandGap Fiber With Hetero-Structured Cladding,” J. Lightwave Technol. 31(5), 830–835 (2013). [CrossRef]
25. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chaptman and Hall Ltd, 1983).
26. J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the Modal Content of Large-Mode-Area Fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009). [CrossRef]
27. D. N. Schimpf, R. A. Barankov, and S. Ramachandran, “Cross-correlated (C2) imaging of fiber and waveguide modes,” Opt. Express 19(14), 13008–13019 (2011). [CrossRef] [PubMed]
28. F. Kong, G. Gu, T. W. Hawkins, J. Parsons, M. Jones, C. Dunn, M. T. Kalichevsky-Dong, S. P. Palese, E. Cheung, and L. Dong, “Quantitative mode quality characterization of fibers with extremely large mode areas by matched white-light interferometry,” Opt. Express 22(12), 14657–14665 (2014). [CrossRef] [PubMed]
