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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21866–21873
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Large mode area fibers with asymmetric bend compensation

John M. Fini  »View Author Affiliations


Optics Express, Vol. 19, Issue 22, pp. 21866-21873 (2011)
http://dx.doi.org/10.1364/OE.19.021866


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Abstract

Fibers with asymmetrical bend compensation offer to completely remove the tradeoff between mode area and single-modedness, with potentially huge impact on high-power amplification. These fibers would be difficult to fabricate, but are the only fundamental-mode strategy that can remove the bend-distortion limitations on mode-area scaling. Here, we show that even imperfect fibers can achieve essentially complete HOM suppression for areas of 2000 square microns or larger. Ultimate performance limits due to finite cladding size and fabrication imperfections are calculated.

© 2011 OSA

1. Introduction

The rapidly increasing power obtainable from fiber amplifiers and lasers has been enabled in large part by large mode area (LMA) gain fibers [1

1. M. O'Connor, V. Gapontsev, V. Fomin, M. Abramov, and A. Ferin, “Power Scaling of SM Fiber Lasers toward 10kW,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThA3.

]. While available powers are now sufficient for fiber lasers to displace some competing technologies, further power scaling is needed for some applications. Limitations intrinsic to conventional fibers must overcome to achieve even higher power output in a pure fundamental mode [2

2. J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-13240. [CrossRef] [PubMed]

].

There is one strategy for avoiding bend distortion completely: if the fabricated profile is pre-compensated for the bend-induced index perturbation, then light will ideally see the desired profile [6

6. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006). [CrossRef] [PubMed]

]. This asymmetric bend-compensated (ABC) strategy, in the limit of ideal fabrication, would completely remove the tradeoff between mode area, macrobending loss, and single-modedness. The strategy is difficult to implement—it requires fabrication of an asymmetric fiber and deployment of the fiber in a fixed bend orientation. However in contrast to other advanced strategies for fundamental-mode area scaling [9

9. O. Schmidt, J. Rothhardt, T. Eidam, F. Röser, J. Limpert, A. Tünnermann, K. P. Hansen, C. Jakobsen, and J. Broeng, “Single-polarization ultra-large-mode-area Yb-doped photonic crystal fiber,” Opt. Express 16(6), 3918–3923 (2008). [CrossRef] [PubMed]

11

11. H.-W. Chen, T. Sosnowski, C.-H. Liu, L. J. Chen, J. R. Birge, A. Galvanauskas, F. X. Kärtner, and G. Chang, “Chirally-coupled-core Yb-fiber laser delivering 80-fs pulses with diffraction-limited beam quality warranted by a high-dispersion mirror based compressor,” Opt. Express 18(24), 24699–24705 (2010). [CrossRef] [PubMed]

], it removes the key obstacle of bend distortion, allowing much greater scaling of mode area in a compact, coiled device. This approach is thus an alternative to amplification in very pure higher-order modes, which is naturally immune to bend distortion [12

12. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31(12), 1797–1799 (2006). [CrossRef] [PubMed]

14

14. J. W. Nicholson, J. M. Fini, A. M. DeSantolo, E. Monberg, F. DiMarcello, J. Fleming, C. Headley, D. J. DiGiovanni, S. Ghalmi, and S. Ramachandran, “A higher-order-mode erbium-doped-fiber amplifier,” Opt. Express 18(17), 17651–17657 (2010). [CrossRef] [PubMed]

] and can also achieve very large mode area. However, ABC does not require an output mode conversion in applications where a Gaussian-like output is desired. We recently confirmed numerically [15

15. J. M. Fini, “Large Mode Area Fiber Design With Asymmetric Bend Compensation,” in CLEO:2011- Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JWA30.

] that the ABC strategy scales to very large areas, but the specific designs studied there had only modest suppression of higher-order modes.

This paper explores the limits on performance of the ABC approach, and the ways in which a real fiber inevitably deviates from an ideal structure. We find that extremely large areas and robust single-modedness can be achieved by assembling a preform of reasonable granularity and size. We also show that there is a tradeoff between mode area and the index control needed. In particular, we find that remarkably robust single modedness—essentially complete (~100dB) suppression of higher-order modes (HOMs)—can be achieved with very large fiber area (Aeff~2000µm2 or larger) in the desirable regime of coiled fiber amplifiers (Rbend = 15cm, 5m length), with challenging but achievable fabrication requirements. This is in stark contrast with other design strategies, where single-moded operation at much smaller areas requires careful management of fiber layout and input launch. The ultimate limits of area determined by fabrication precision are discussed.

2. Bend distortion

Bends play a crucial role in large mode area fiber design—not only because of loss. Figure 1
Fig. 1 Scaling fiber designs to very large core area gives diminishing increases in mode area for a coiled configuration (bend radii 15cm and 48cm are shown). Mode images are shown for 15cm bend radius.
shows that for conventional designs (SIF with contrast ncore-nclad = 0.0008), as one increases the core size, the mode area eventually sees minimal increase. For realistic bend radii, mode area is in practice limited to about 1000µm2. This bend impact on mode area has been experimentally confirmed [8

8. J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headley, “Demonstration of bend-induced nonlinearities in large-mode-area fibers,” Opt. Lett. 32(17), 2562–2564 (2007). [CrossRef] [PubMed]

].

Bend distortion also has a crucial impact on gain competition by pushing the fundamental mode out of the center of the core. As mode area becomes larger, loss-suppression of HOMs becomes nearly impossible, and gain-suppression of higher-order modes by tailoring the dopant profile [16

16. J. M. Oh, C. Headley, M. J. Andrejco, A. D. Yablon, and D. J. DiGiovanni, Increased Amplifier Efficiency by Matching the Area of the Doped Fiber Region with the Fundamental Fiber Mode,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OThC6.

] is increasingly important. However, gain tailoring fails drastically if the dopant profile design fails to take bend distortion into consideration, and eventually becomes impossible for highly distorted modes [17

17. J. M. Fini, “Design of large-mode-area amplifier fibers resistant to bend-induced distortion,” J. Opt. Soc. Am. B 24(8), 1669–1676 (2007). [CrossRef]

].

Parabolic designs help significantly—in part because the fabricated gradient cancels the bend-induced gradient at the center of the displaced mode [6

6. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006). [CrossRef] [PubMed]

]. Mode displacement and area reduction are mitigated, but still ultimately limit scalability in parabolic fibers. Holes are useful for controlling HOM suppression, but are certainly no guarantee of single-modedness [5

5. J. Bromage, J. M. Fini, C. Dorrer, and J. D. Zuegel, “Characterization and optimization of Yb-doped photonic-crystal fiber rod amplifiers using spatially resolved spectral interferometry,” Appl. Opt. 50(14), 2001–2007 (2011). [CrossRef] [PubMed]

]. Leakage-channel type fibers experience bend distortion similar to others [10

10. L. Dong, H. A. Mckay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending Effective Area of Fundamental Mode in Optical Fibers,” J. Lightwave Technol. 27, 1565–1570 (2009).

], and so fail to provide gain suppression.

3. Bend-compensated designs

The ABC strategy is illustrated conceptually in Fig. 2 (a-b)
Fig. 2 The asymmetrical bend compensated (ABC) fiber design strategy incorporates a material index gradient that cancels the bend perturbation.
. The fabricated profile has a gradient that cancels the bend induced perturbation, so that the equivalent index determining the mode shape is a perfect step-index profile (or whatever other profile we design), at least within the region of the compensation. Figure 2 (c-d) illustrates how we might implement this as a finite number of constant-index cells.

In the ideal limit, it is clear that a fabricated ABC profile can result in whatever equivalent index profile we want. That is, in the limit of fine-grained cells, a large bend-compensated cladding, precise index control, and a known bend, we simply fabricate,nfab(x,y)=ntarget(x,y)dnbendntarget(x,y)(1γx/Rbend).

Here, γ is 1 according to the geometrical conformal mapping [18

18. D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21(23), 4208–4213 (1982). [CrossRef] [PubMed]

], and may include a stress correction. The x-axis is defined to point towards the outside of the bend. The bend perturbation can only be subtracted if the orientation is known, and so the fiber must be wound so that the gradient faces in the desired direction over the fiber length during use. This is challenging, but is clearly achievable in high-performance amplifier and laser applications where careful fiber layout is the norm.

In the limit of perfect index control, there is no need for simulations, and the familiar tradeoffs between area, bend loss, and multi-modedness vanish: as is well-known [19

19. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer 1983).

], a SIF can be rigorously single-modeded for arbitrarily large area. Further, there can be no macrobend loss if the equivalent index of the entire cladding is below the mode index. If light sees a perfect SIF (equivalent) profile, then only secondary considerations (e.g., microbending) limit mode area. Clearly a real fabricated ABC fiber will have finite size, finite granularity, and imperfect control of the index of each cell. Below, we explore the impact of these on fiber performance.

4. Cladding size and suppression of higher-order modes

Several ABC designs were constructed and simulated with cell spacing L, core diameter Dcore = 5L (“19-cell” core), and cladding size either 12L (Dclad = 2.4Dcore) or 18L (Dclad = 3.6Dcore, as in Fig. 2c), assuming a fairly large but practical coil size, Rbend = 15cm. In the illustrative design of Fig. 2c with L = 10, the bend-compensating gradient corresponds to steps along the x-axis of around nsilγx/Rbend, or around 8×10−5 as shown in Fig. 3
Fig. 3 The fabricated refractive index (left) and equivalent index of the coiled fiber (bend radius 15cm) illustrates how a desired step-index profile (dashed red) can be approximated with a structure that is reasonable to fabricate.
. A small core contrast (for the approximate SIF profile, red dashed) of 9×10−5 is needed to maximize leakage of HOMs while providing an acceptable calculated bend loss for the fundamental mode, 0.1dB/m. The simulations confirm that very large area (Aeff=2160µm2) is compatible with large suppression of HOMs (HOM Loss ~140 times the fundamental loss).

The advantages of the ABC strategy are better understood by comparing the performance tradeoffs for different fiber types. Several ABC fibers are compared to traditional designs in Fig. 4a
Fig. 4 The basic performance tradeoff for single-moded LMA fiber can be plotted (a) as HOM suppression vs mode area (for fixed bend loss 0.1dB/m). Ideal conventional designs are limited in area by a strict tradeoff, but this tradeoff is essentially removed for ABC fibers (in the limit of ideal fabrication). The core contrast and effective area are plotted (b) vs. core radius for the SIF family.
. The three-way tradeoff between bend loss, HOM suppression, and effective area is summarized there by locking all fiber designs to a calculated bend loss of 0.1dB/m at Rbend = 15cm and plotting relative HOM suppression (HOM loss/fundamental loss) vs. Aeff. For example, the family of step-index fibers has two degrees of freedom (core size and contrast). For each core size the contrast is selected to satisfy the 0.1dB/m bend loss requirement, so that only one degree of freedom remains. These core contrast values are plotted in Fig. 4b as a function of core radius, along with effective area. Thus, the SIF (red) and parabolic (blue) designs reduce to simple curves in Fig. 4a. The mode areas are calculated at the bend radius 15cm—that is, in the actual configuration of the fiber during operation. These are more relevant than the straight-fiber areas often quoted in design papers, and can easily be smaller by a factor of 2 or more. The lowest-loss of the HOMs is used in the calculation.

These curves confirm the point illustrated by Fig. 1, that SIF designs cannot be scaled significantly above 1000µm2 for typical coiling requirements, because of a tradeoff with HOM suppression. We note that this curve applies to ideal SIF fibers. The actual contrast values are quite small, and these ideal fibers would be challenging to make with conventional fabrication. Typically, fibers with higher contrast have been used, requiring tighter bends to strip higher-order modes, further degrading the bend distortion and single-modedness. Parabolic fibers show a significantly improved tradeoff, but are still limited in area if bend-loss suppression of HOMs is required.

The simulated ABC designs (black and green circles) illustrate a qualitatively different type of behavior, confirming that the strategy essentially removes the tradeoff with area. As the core size is increased by scaling L (and the contrast adjusted to meet the loss requirement), mode area increases with little impact on the HOM suppression ratio. The HOM suppression is essentially determined by the relative size of the cladding (Dclad/Dcore) alone.

This is what we might expect based on a simple analogy: to understand the impact of the finite extent of the compensated inner cladding region, think of Fig. 3(b) as approximating a 3-layer “w-fiber” with high-index outer cladding starting at 85microns. For example, we can compare the relative tunneling losses of the HOM and fundamental for an unbent w-fiber with outer cladding index equal to the core index (the precise outer index should not matter much), and with Dclad/Dcore similar to the ABC fiber. This simple 1d calculation has been included as a guideline in Fig. 4a (dashed black and green lines), and is quit a useful rough estimate of the more correct (and much more complicated) 2D calculations (black and green circles). Intuitively, the selectivity of the HOM suppression increases with the size of the cladding, since there is more cladding that the fundamental needs to tunnel through to escape.

ABC fibers can thus remove a fundamental limitation on area that constrains other strategies. They can achieve mode areas in the 2000-3000µm2 range with a level of single modedness—and thus beam quality—analogous to conventional fibers with 600-700µm2. In the Aeff~1000µm2 regime, SIF and parabolic designs are not only very difficult to make with conventional fabrication methods, they fail to provide robust HOM suppression even when fabrication is perfect. For example, a 5m long SIF with Aeff~1000µm2 and <0.5dB total bend loss can achieve at most a meager 2-3dB of HOM bend-loss suppression. A parabolic fiber can approach a respectable 10-15dB of suppression, although actual performance will inevitably be worse than these idealized calculations. In any case, these are well short of total suppression, and confirm the actual experiences of real-world users: good beam quality is achievable in hero experiments, but relies heavily on very careful management of input launch, fiber layout, and handling.

The calculations for ABC fibers are in stark contrast. With >100 times relative suppression (and 0.5dB total bend loss), they show “complete” >50dB suppression of HOMs for areas Aeff>2000µm2 (or even Aeff>3000µm2). The mode in Fig. 5 has an excellent shape and no displacement, and so a gain-doped region (e.g., dashed) can be tailored for high gain overlap and high gain selectivity. The ultimate limit of area scaling will be determined by the precision of index control in each cell, as discussed below.

5. Sensitivity to fabrication

The impact of fabrication imperfection on performance was tested by taking each of the three Dclad=3.6Dcore target designs of Fig. 5 and adding a random perturbation to the index of each element. Figure 6
Fig. 6 Fabrication sensitivity is shown by repeating the performance tradeoff of Fig. 5 for three fiber designs along with four perturbed versions of each (green dots).
summarizes the impact in terms of the main performance tradeoff. Independent Gaussian random perturbations (with standard deviation 5×10−5) were added to each cell in half of the structure y>=0. For simplicity, symmetric perturbations were assumed for the cells with y<0. Four randomly perturbed structures were generated for each target design, and for each the bend radius was adjusted slightly so that the fundamental loss met the target (0.1dB/m). As one would expect, fabrication sensitivity increases as core size increases: at large area the core contrast becomes very small, and is easily overwhelmed by the random variation in index. The smaller-area fibers, however, are reasonably robust: Performance was relatively unchanged for the Aeff~1310µm2 fiber. Two of the perturbed Aeff~2160µm2 fibers performed essentially as-designed. The performance for the other two, although very degraded, is still much better than the ideal performance (assuming perfect fabrication) of competing technologies, including leakage channel fibers. For the largest Aeff~3280µm2 design, the perturbed profiles significant degrade mode shape, making one of the fibers unusable (dashed), but three of the four perturbed fibers show excellent performance. Intensity profiles for the Aeff~2160µm2 fibers are shown in Fig. 7
Fig. 7 Fundamental mode intensity is shown for the four perturbed versions of the 2160µm2-area fiber.
. They show distortion, but maintain large area and reasonably small displacement, allowing effective gain overlap.

7. Conclusion

References and links

1.

M. O'Connor, V. Gapontsev, V. Fomin, M. Abramov, and A. Ferin, “Power Scaling of SM Fiber Lasers toward 10kW,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThA3.

2.

J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-13240. [CrossRef] [PubMed]

3.

M. E. Fermann, “Single-mode excitation of multimode fibers with ultrashort pulses,” Opt. Lett. 23(1), 52–54 (1998). [CrossRef] [PubMed]

4.

J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25(7), 442–444 (2000). [CrossRef] [PubMed]

5.

J. Bromage, J. M. Fini, C. Dorrer, and J. D. Zuegel, “Characterization and optimization of Yb-doped photonic-crystal fiber rod amplifiers using spatially resolved spectral interferometry,” Appl. Opt. 50(14), 2001–2007 (2011). [CrossRef] [PubMed]

6.

J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006). [CrossRef] [PubMed]

7.

R. L. Farrow, D. A. V. Kliner, G. R. Hadley, and A. V. Smith, “Peak-power limits on fiber amplifiers imposed by self-focusing,” Opt. Lett. 31(23), 3423–3425 (2006). [CrossRef] [PubMed]

8.

J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headley, “Demonstration of bend-induced nonlinearities in large-mode-area fibers,” Opt. Lett. 32(17), 2562–2564 (2007). [CrossRef] [PubMed]

9.

O. Schmidt, J. Rothhardt, T. Eidam, F. Röser, J. Limpert, A. Tünnermann, K. P. Hansen, C. Jakobsen, and J. Broeng, “Single-polarization ultra-large-mode-area Yb-doped photonic crystal fiber,” Opt. Express 16(6), 3918–3923 (2008). [CrossRef] [PubMed]

10.

L. Dong, H. A. Mckay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending Effective Area of Fundamental Mode in Optical Fibers,” J. Lightwave Technol. 27, 1565–1570 (2009).

11.

H.-W. Chen, T. Sosnowski, C.-H. Liu, L. J. Chen, J. R. Birge, A. Galvanauskas, F. X. Kärtner, and G. Chang, “Chirally-coupled-core Yb-fiber laser delivering 80-fs pulses with diffraction-limited beam quality warranted by a high-dispersion mirror based compressor,” Opt. Express 18(24), 24699–24705 (2010). [CrossRef] [PubMed]

12.

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31(12), 1797–1799 (2006). [CrossRef] [PubMed]

13.

J. M. Fini and S. Ramachandran, “Natural bend-distortion immunity of higher-order-mode large-mode-area fibers,” Opt. Lett. 32(7), 748–750 (2007). [CrossRef] [PubMed]

14.

J. W. Nicholson, J. M. Fini, A. M. DeSantolo, E. Monberg, F. DiMarcello, J. Fleming, C. Headley, D. J. DiGiovanni, S. Ghalmi, and S. Ramachandran, “A higher-order-mode erbium-doped-fiber amplifier,” Opt. Express 18(17), 17651–17657 (2010). [CrossRef] [PubMed]

15.

J. M. Fini, “Large Mode Area Fiber Design With Asymmetric Bend Compensation,” in CLEO:2011- Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JWA30.

16.

J. M. Oh, C. Headley, M. J. Andrejco, A. D. Yablon, and D. J. DiGiovanni, Increased Amplifier Efficiency by Matching the Area of the Doped Fiber Region with the Fundamental Fiber Mode,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OThC6.

17.

J. M. Fini, “Design of large-mode-area amplifier fibers resistant to bend-induced distortion,” J. Opt. Soc. Am. B 24(8), 1669–1676 (2007). [CrossRef]

18.

D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21(23), 4208–4213 (1982). [CrossRef] [PubMed]

19.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer 1983).

20.

L. Dong, X. Peng, and J. Li, “Leakage channel optical fibers with large effective area,” J. Opt. Soc. Am. B 24(8), 1689–1697 (2007). [CrossRef]

21.

L. Dong, J. Li, and X. Peng, “Bend-resistant fundamental mode operation in ytterbium-doped leakage channel fibers with effective areas up to 3160 µm 2,” Opt. Express 14(24), 11512–11519 (2006). [CrossRef] [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(140.3510) Lasers and laser optics : Lasers, fiber

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 14, 2011
Revised Manuscript: October 4, 2011
Manuscript Accepted: October 4, 2011
Published: October 20, 2011

Citation
John M. Fini, "Large mode area fibers with asymmetric bend compensation," Opt. Express 19, 21866-21873 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-21866


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References

  1. M. O'Connor, V. Gapontsev, V. Fomin, M. Abramov, and A. Ferin, “Power Scaling of SM Fiber Lasers toward 10kW,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThA3.
  2. J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express16(17), 13240–13266 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-13240 . [CrossRef] [PubMed]
  3. M. E. Fermann, “Single-mode excitation of multimode fibers with ultrashort pulses,” Opt. Lett.23(1), 52–54 (1998). [CrossRef] [PubMed]
  4. J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett.25(7), 442–444 (2000). [CrossRef] [PubMed]
  5. J. Bromage, J. M. Fini, C. Dorrer, and J. D. Zuegel, “Characterization and optimization of Yb-doped photonic-crystal fiber rod amplifiers using spatially resolved spectral interferometry,” Appl. Opt.50(14), 2001–2007 (2011). [CrossRef] [PubMed]
  6. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express14(1), 69–81 (2006). [CrossRef] [PubMed]
  7. R. L. Farrow, D. A. V. Kliner, G. R. Hadley, and A. V. Smith, “Peak-power limits on fiber amplifiers imposed by self-focusing,” Opt. Lett.31(23), 3423–3425 (2006). [CrossRef] [PubMed]
  8. J. W. Nicholson, J. M. Fini, A. D. Yablon, P. S. Westbrook, K. Feder, and C. Headley, “Demonstration of bend-induced nonlinearities in large-mode-area fibers,” Opt. Lett.32(17), 2562–2564 (2007). [CrossRef] [PubMed]
  9. O. Schmidt, J. Rothhardt, T. Eidam, F. Röser, J. Limpert, A. Tünnermann, K. P. Hansen, C. Jakobsen, and J. Broeng, “Single-polarization ultra-large-mode-area Yb-doped photonic crystal fiber,” Opt. Express16(6), 3918–3923 (2008). [CrossRef] [PubMed]
  10. L. Dong, H. A. Mckay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending Effective Area of Fundamental Mode in Optical Fibers,” J. Lightwave Technol.27, 1565–1570 (2009).
  11. H.-W. Chen, T. Sosnowski, C.-H. Liu, L. J. Chen, J. R. Birge, A. Galvanauskas, F. X. Kärtner, and G. Chang, “Chirally-coupled-core Yb-fiber laser delivering 80-fs pulses with diffraction-limited beam quality warranted by a high-dispersion mirror based compressor,” Opt. Express18(24), 24699–24705 (2010). [CrossRef] [PubMed]
  12. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett.31(12), 1797–1799 (2006). [CrossRef] [PubMed]
  13. J. M. Fini and S. Ramachandran, “Natural bend-distortion immunity of higher-order-mode large-mode-area fibers,” Opt. Lett.32(7), 748–750 (2007). [CrossRef] [PubMed]
  14. J. W. Nicholson, J. M. Fini, A. M. DeSantolo, E. Monberg, F. DiMarcello, J. Fleming, C. Headley, D. J. DiGiovanni, S. Ghalmi, and S. Ramachandran, “A higher-order-mode erbium-doped-fiber amplifier,” Opt. Express18(17), 17651–17657 (2010). [CrossRef] [PubMed]
  15. J. M. Fini, “Large Mode Area Fiber Design With Asymmetric Bend Compensation,” in CLEO:2011- Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JWA30.
  16. J. M. Oh, C. Headley, M. J. Andrejco, A. D. Yablon, and D. J. DiGiovanni, Increased Amplifier Efficiency by Matching the Area of the Doped Fiber Region with the Fundamental Fiber Mode,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006), paper OThC6.
  17. J. M. Fini, “Design of large-mode-area amplifier fibers resistant to bend-induced distortion,” J. Opt. Soc. Am. B24(8), 1669–1676 (2007). [CrossRef]
  18. D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt.21(23), 4208–4213 (1982). [CrossRef] [PubMed]
  19. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer 1983).
  20. L. Dong, X. Peng, and J. Li, “Leakage channel optical fibers with large effective area,” J. Opt. Soc. Am. B24(8), 1689–1697 (2007). [CrossRef]
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