## Semi-guiding high-aspect-ratio core (SHARC) fiber providing single-mode operation and an ultra-large core area in a compact coilable package |

Optics Express, Vol. 19, Issue 15, pp. 14746-14762 (2011)

http://dx.doi.org/10.1364/OE.19.014746

Acrobat PDF (1165 KB)

### Abstract

A new class of optical fiber is presented that departs from the circular-core symmetry common to conventional fibers. By using a high-aspect-ratio (~30:1) rectangular core, the mode area can be significantly expanded well beyond 10,000 μm^{2}. Moreover, by also specifying a very small refractive-index step at the narrow core edges, the core becomes “semi-guiding,” i.e. it guides in the narrow dimension and is effectively un-guiding in the wide mm-scale dimension. The mode dependence of the resulting Fresnel leakage loss in the wide dimension strongly favors the fundamental mode, promoting single-mode operation. Since the modal loss ratios are independent of mode area, this core structure offers nearly unlimited scalability. The implications of using such a fiber in fiber laser and amplifier systems are also discussed.

© 2011 OSA

## 1. Introduction

1. 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]

2. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. **66**(3), 216–220 (1976). [CrossRef]

3. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B **27**(11), B63–B92 (2010). [CrossRef]

6. 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]

7. 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]

8. J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, F. Röser, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “High-power rod-type photonic crystal fiber laser,” Opt. Express **13**(4), 1055–1058 (2005). [CrossRef] [PubMed]

9. 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]

9. 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]

^{2}.

## 2. Semi-Guiding High-Aspect-Ratio Fiber

^{2}or more (conventional LMA fibers have core areas ~400 μm

^{2}), while retaining a thin, mechanically flexible narrow dimension. Second, the aspect ratio of the core will typically range from 30:1 to 100:1 or more, depending on the output power requirement; such aspect ratios are significantly greater than those of currently available rectangular-core fibers [10].

^{2}, which is equivalent to a circular core having a diameter of ~200 μm. In this example, stimulated Brillouin scattering (SBS) suppression occurs by virtue of the large core area and low intensity, which lead to an SBS threshold power in excess of 3 kW. Hence, in order to deliver multi-kW-level optical powers, SHARC fibers do not require additional SBS suppression techniques such as multi-GHz signal modulation [11

11. G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett. **35**(10), 1542–1544 (2010). [CrossRef] [PubMed]

12. C. M. Zeringue, I. Dajani, and G. T. Moore, “Suppression of stimulated Brillouin scattering in optical fibers through phase-modulation: a time dependent model,” Proc. SPIE **7914**, 791409, 791409-9 (2011). [CrossRef]

## 3. SHARC Fiber Analytic Calculations

*s*and

*f*can then be represented by M

_{s,f}(x,y,z,t) = E

_{s,f}(x,y)exp(−iωt + iβ

_{s,f}z), where the transverse mode pattern can be factorized as E

_{s,f}(x,y) ≅ X

_{s}(x)Y

_{f}(y). The parameter β

_{s,f}= k

_{0}(n

_{co}− δn

_{f}− δn

_{s}) is the propagation coefficient of the mode, where k

_{0}= (2π/λ) is the wavenumber, and δn

_{s}and δn

_{f}quantify how the effective refractive indexes in the slow- and fast-axis directions, respectively, differ from the core and fast axis cladding material indexes n

_{co}and n

_{cl}that are shown in Fig. 1. Specifically, the planar (1-D) waveguide mode Y

_{f}(y) formed by the fast-axis claddings has an effective index n

_{eff}= n

_{co}− δn

_{f}, and n

_{eff}lies in the range n

_{cl}< n

_{eff}< n

_{co}. The slow-axis correction δn

_{s}is defined in a manner analogous to δn

_{f}; it is nominally small compared to δn

_{f}, and it is induced by the planar waveguide mode solution X

_{s}(x) along the wide slow-axis dimension. The accuracy of this simplified approach was validated by comparing the analytic modes to a numerical calculation of the modes using a finite difference method for a representative SHARC core geometry. A normalized overlap integral of the analytic and numerically calculated modes yielded a value larger than 99.99%, which fully justifies the mode factorization approach presented in this section.

_{s}(x)exp(−ik

_{0}δn

_{s}z), with the goal of investigating the mode characteristics of weakly confined modes that have essentially no total internal reflection (TIR) at the edges of a very wide multimode planar stripe. For the narrow planar waveguide along the fast axis, which has TIR index-guiding walls, the mode structure, Y

_{f}(y)exp(−ik

_{0}δn

_{f}z), is well known [16]. To simplify these analytical calculations, the fast-axis planar waveguide is assumed to be single-mode, although the basic propagation properties and the resulting mode discrimination also arise in the case of a multi-mode fast-axis waveguide, as is discussed below in connection with Section 4. As such, the modes of the two-dimensional SHARC structure are spatially differentiated by the slow-axis mode profiles alone, and thus only need a single mode order, the parameter

*s*, for mathematical representation.

_{cl}< n

_{eff}< n

_{co}. Since the slow-axis cladding index n

_{scl}is nominally the same as, or very close to, the core index, the effective fast-axis mode index n

_{eff}is generally less than that of the slow-axis mode, n

_{eff}< n

_{scl}. This result has two consequences. First, the difference between n

_{eff}and n

_{co}will allow Fresnel reflections at the fast-axis claddings that largely contain the mode power in the fast-axis dimension. Second, the slow-axis dimension will never exhibit TIR guiding, and the modes will leak out of the core region. This leakage is precisely the mechanism that leads to mode filtering that discriminates against the higher-order modes. Specifically, due to the absence of TIR guiding in the slow-axis direction, all modes of the SHARC fiber experience loss, and as such are termed

*leaky modes*[17

17. J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photon. **1**(1), 58–106 (2009). [CrossRef]

_{co}is equal to the slow-axis cladding index n

_{scl}, the slow axis interface between the regions appears to be “optically open,” as if the core modes can freely propagate into the slow-axis claddings. However, partial reflections at the borders cannot be eliminated. Recall that the light-propagation environment is very different on opposite sides of the slow-axis edge: in the fast axis direction, light is TIR guided in the slow-axis core, but freely diffracting in the slow-axis cladding. The propagation characteristics inside and outside the core are distinct even when n

_{co}= n

_{scl}. As a consequence, the effective index of the fast-axis mode is lower than that of the slow-axis cladding and therefore will result in an effective Fresnel reflection. One may be inclined to think that the slow-axis interface can be truly eliminated by matching the slow-axis cladding index to the effective index of the fast-axis mode. However, the fast-axis mode is represented by the combination of a core index and cladding index, as the oscillatory and evanescent portions of the mode reside in each respective region. As such, it is impossible to match the slow-axis cladding to both core and fast-axis cladding simultaneously. Therefore, there is always a Fresnel reflection at the interface, as will be evident in later simulations.

_{0}inside the core and by the complex refractive index n

_{1}in the surrounding cladding:The index n

_{0}is, in fact, n

_{eff}, the effective index of the fast-axis planar waveguide mode. The cladding index n

_{1}has a real part, n

_{scl}, given by the material index of the slow-axis claddings, and an imaginary part, κ, phenomenologically added to emulate radiation leaking from the core, as depicted in Fig. 3. There is no

*a priori*information with which to quantify the effective loss parameter κ, so it is kept as a variable of the problem to be determined by matching either to experimental data, if available, or to results of a more accurate model. However, strong radiative losses would represent an impractical waveguide, so the additional condition κ << 1 is imposed.

_{s}(x)exp(iβ

_{s}z) and their propagation constants β

_{s}= k(n

_{0}− δn

_{s}). The modes are known to be harmonic functions inside the core, |x|< w/2, giving either cos(q

_{s}x) for even orders (s = 0, 2, 4…) or sin(q

_{s}x) for odd orders (s = 1, 3, 5…), with exponential tails, exp[−p

_{s}(|x|−w/2)], outside the core, for |x|> w/2. The parameters q

_{s}and p

_{s}are nominally found through the boundary conditions at the interface in conjunction with standard, simple, geometric relations applying to the propagation coefficient β

_{s}. However, in the case shown in Fig. 3, the propagation coefficient will be complex since the cladding includes an effective loss. The mode loss is given by the imaginary part of the propagation coefficient, α

_{s}= 2Im(β

_{s}). The propagation coefficient is calculated from the standard equationwhere the parameter ξ = (1 + s)(π/2) – q

_{s}w/2 is an offset, in units of the argument q

_{s}x for harmonic dependence, between the border, x = w/2, and the closest zero point, X

_{s}(x) = 0, of the mode of order

*s*. The parameter ξ is found as a solution of the transcendental equationIt is worth mentioning that while Eqs. (2) and (3) have been derived for real values of refractive indexes n

_{0}and n

_{1}, the functional form is fully applicable for the complex value for n

_{1}from Eq. (1) as well. In this case, the parameters ξ and β

_{s}also become complex-valued.

_{0}

^{2}– n

_{1}

^{2})

^{1/2}>> 1. For waveguides having large V-numbers, the mode amplitudes are nearly zero at the core interface, x = ± w/2. The corresponding profiles for the three lowest-order modes are shown in Fig. 4 .

_{s}<< 1. Applying this condition, Eq. (3) can be solved explicitly using power decompositions. Taking only the lowest order terms in the small parameter 1/V, the modal loss rate becomeswhere both n

_{0}and n

_{1}given by Eq. (1).

_{scl}− n

_{co}, are plotted in Fig. 5 for the three lowest modes of a 450-μm wide channel and a wavelength of 1.06 μm. The value n

_{eff}= 1.450803 was calculated separately for λ = 1.06 μm light via a 1-D finite difference mode solver for a waveguide thickness h = 15 μm using a n

_{co}= 1.45 and n

_{cl}= 1.449, a typical index step for an LMA-type fiber. The value κ = 10

^{−4}was used for this plot, corresponding to an effective bulk absorption coefficient α

_{scl}≅ 6 cm

^{−1}in the cladding. This value of κ was chosen to match the curves calculated via beam propagation simulations (detailed in the Section 4).

_{scl}− n

_{eff}≅ 0. The fact that this peak does not occur when the core index equals the slow cladding index, as one might expect, is a result of propagation physics, which is captured by the separation of variables applicable to this rectangular geometry.

^{2}. The implication is that the loss of the fundamental mode is four times lower than that of the second mode (s = 1), and nine times lower than the third mode (s = 2). Such strong discrimination properties inherent to the SHARC fiber suggest that nearly single-mode behavior will be obtained through a highly multimode waveguide of sufficient length L, if α

_{1}L > 1. If one also applies the condition α

_{0}L = α

_{1}L/4 << 1, the transmission efficiency of the lowest mode through the waveguide is still sufficiently high for practical applications.

^{3}, and with wavelength as λ

^{2}. Such dependences are typical for many lossy waveguides [18

18. A. Reisinger, “Characteristics of optical guided modes in lossy waveguides,” Appl. Opt. **12**(5), 1015–1025 (1973). [CrossRef] [PubMed]

_{1}L > 1 but α

_{0}L << 1, which supports single-mode low-loss propagation through the fiber.

*s*experiences per unit length of propagation is approximately θ

_{s}/w. The loss is therefore proportional to the product of the two, yielding a loss that scales in proportion to θ

_{s}

^{2}/w. Since a planar waveguide mode of order

*s*has spatial features on the order of w/(1 + s), it therefore diverges approximately as θ

_{s}≈(1 + s)λ/w. Using this relation yields a loss rate that scales in proportion to θ

_{s}

^{2}/w = (1 + s)

^{2}λ

^{2}/w

^{3}, which is readily observable in Eq. (4). The final factor in Eq. (4) is usually defined by the nature of the waveguide interface, differing by the nature of the channel loss (e.g. metal, anti-guiding dielectric, etc.); the last term in Eq. (4) quantifies this factor for SHARC waveguides.

## 4. SHARC Fiber Numerical Simulations

19. H. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood Jr., “Complex propagators for evanescent waves in bidirectional beam propagation method,” J. Lightwave Technol. **18**(8), 1155–1160 (2000). [CrossRef]

*a priori*knowledge of the modes of the fiber. In this method, the paraxial wave equation is used to model the signal beam along the fiber axis, z, asOn the right hand side, the first term represents diffraction, where

20. Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. **26**(8), 1335–1339 (1990). [CrossRef]

21. J. Yamauchi, T. Ando, and H. Nakano, “Beam propagation analysis of optical fibres by alternating direction implicit method,” Electron. Lett. **27**(18), 1663–1666 (1991). [CrossRef]

22. G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. **28**(1), 363–370 (1992). [CrossRef]

23. R. Ulrich and G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. **27**(6), 337–339 (1975). [CrossRef]

24. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. **13**(4), 615–627 (1995). [CrossRef]

_{co}− n

_{scl}represents an extra degree of freedom that can be exercised in design optimization, and it allows one to match potentially contradictory requirements for fiber length and available core width to satisfy the low-loss single-mode propagation condition: α

_{1}L > 1 but α

_{0}L << 1.

_{scl}can be slightly less than the core index n

_{co}, making that interface guiding, the slow-axis cladding index can still be greater than the signal-cladding index n

_{cl}, making that small interface anti-guiding. Hence, optical power residing within the fast-axis claddings near this interface can be drawn out into the slow-axis cladding, as schematically indicated by the red arrows in Fig. 9 . This is precisely what happens to the evanescent tail of the fast-axis mode in the vicinity of the core edges.

^{−4}(100 ppm), the above discussion for Fig. 8 has several implications. First, the benefits of the SHARC structure are inherent in the geometry and can be exploited over a range of index values, rather than being limited to a singular point-design that would be nearly impossible to realize. Second, the slow-axis cladding can be made of the same exact material as the core, which makes fabrication of the total structure simpler than requiring a specific slow-axis cladding index. Finally, realistic fabrication tolerances will also allow the design objectives to be met if, in fact, a different specific slow-axis refractive index is desired.

## 5. Bend Loss in SHARC Fibers

25. D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. **66**(4), 311–320 (1976). [CrossRef]

_{b}is the bend radius that changes with propagation distance as previously described.

## 6. Discussion and Implications of the SHARC Fiber

26. O. F. S. Laboratories and N. J. Somerset, 08873, http://www.ofsoptics.com/labs/.

27. 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]

28. 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). [CrossRef] [PubMed]

29. J. R. Marciante, R. G. Roides, V. V. Shkunov, and D. A. Rockwell, “Near-diffraction-limited operation of step-index large-mode-area fiber lasers via gain filtering,” Opt. Lett. **35**(11), 1828–1830 (2010). [CrossRef] [PubMed]

## 6. Conclusions

^{2}while the natural loss filtering promotes single-mode operation in the slow-axis direction. Further, the SHARC fiber design produces Fresnel losses where the modal-loss ratios are constant with mode area, and this implies nearly unlimited scalability. We also outlined a few of the benefits that accrue from using the SHARC fiber architecture in fiber laser and amplifier systems.

## Acknowledgments

## References and links

1. | J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. |

2. | D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. |

3. | D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B |

4. | C. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, “Effectively single-mode chirally-coupled core fiber,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME2. |

5. | Z. Jiang and J. R. Marciante, “Loss measurements for optimization of large-mode-area helical-core fibers,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FWA3. |

6. | 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. |

7. | 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 |

8. | J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, F. Röser, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “High-power rod-type photonic crystal fiber laser,” Opt. Express |

9. | L. Dong, X. Peng, and J. Li, “Leakage channel optical fibers with large effective area,” J. Opt. Soc. Am. B |

10. | http://www.nlight.net/news/releases/101~nLIGHT-Introduces-New-NonCircular-Optical-Fiber-Geometries. |

11. | G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett. |

12. | C. M. Zeringue, I. Dajani, and G. T. Moore, “Suppression of stimulated Brillouin scattering in optical fibers through phase-modulation: a time dependent model,” Proc. SPIE |

13. | P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” CLEO 2006, paper CThZ3. |

14. | D. Walton, S. Gray, J. Wang, M.-J. Li, X. Chen, A. B. Ruffin, J. Demeritt, and L. Zenteno, “High power, narrow linewidth fiber lasers,” Proc. SPIE |

15. | L. Dong, “Limits of stimulated Brillouin scattering suppression in optical fibers with transverse acoustic waveguide designs,” J. Lightwave Technol. |

16. | A. W. Snyder and J. D. Love, |

17. | J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photon. |

18. | A. Reisinger, “Characteristics of optical guided modes in lossy waveguides,” Appl. Opt. |

19. | H. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood Jr., “Complex propagators for evanescent waves in bidirectional beam propagation method,” J. Lightwave Technol. |

20. | Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. |

21. | J. Yamauchi, T. Ando, and H. Nakano, “Beam propagation analysis of optical fibres by alternating direction implicit method,” Electron. Lett. |

22. | G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. |

23. | R. Ulrich and G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. |

24. | L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. |

25. | D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. |

26. | O. F. S. Laboratories and N. J. Somerset, 08873, http://www.ofsoptics.com/labs/. |

27. | J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express |

28. | 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 |

29. | J. R. Marciante, R. G. Roides, V. V. Shkunov, and D. A. Rockwell, “Near-diffraction-limited operation of step-index large-mode-area fiber lasers via gain filtering,” Opt. Lett. |

30. | V. V. Shkunov, D. A. Rockwell, F. P. Strohkendl, J. R. Marciante, D. J. Trevor, and D. J. DiGiovanni, “Semi-guiding high aspect ratio core (SHARC) fiber laser,” |

**OCIS Codes**

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

(060.2400) Fiber optics and optical communications : Fiber properties

(060.2430) Fiber optics and optical communications : Fibers, single-mode

(130.2790) Integrated optics : Guided waves

(230.7370) Optical devices : Waveguides

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: June 13, 2011

Manuscript Accepted: July 4, 2011

Published: July 15, 2011

**Citation**

David A. Rockwell, Vladimir V. Shkunov, and John R. Marciante, "Semi-guiding high-aspect-ratio core (SHARC) fiber providing single-mode operation and an ultra-large core area in a compact coilable package," Opt. Express **19**, 14746-14762 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14746

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### References

- 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]
- D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66(3), 216–220 (1976). [CrossRef]
- D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27(11), B63–B92 (2010). [CrossRef]
- C. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, “Effectively single-mode chirally-coupled core fiber,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME2.
- Z. Jiang and J. R. Marciante, “Loss measurements for optimization of large-mode-area helical-core fibers,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FWA3.
- 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]
- 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]
- J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, F. Röser, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “High-power rod-type photonic crystal fiber laser,” Opt. Express 13(4), 1055–1058 (2005). [CrossRef] [PubMed]
- 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]
- http://www.nlight.net/news/releases/101~nLIGHT-Introduces-New-NonCircular-Optical-Fiber-Geometries .
- G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett. 35(10), 1542–1544 (2010). [CrossRef] [PubMed]
- C. M. Zeringue, I. Dajani, and G. T. Moore, “Suppression of stimulated Brillouin scattering in optical fibers through phase-modulation: a time dependent model,” Proc. SPIE 7914, 791409, 791409-9 (2011). [CrossRef]
- P. D. Dragic, C.-H. Liu, G. C. Papen, and A. Galvanauskas, “Optical fiber with an acoustic guiding layer for stimulated Brillouin scattering suppression,” CLEO 2006, paper CThZ3.
- D. Walton, S. Gray, J. Wang, M.-J. Li, X. Chen, A. B. Ruffin, J. Demeritt, and L. Zenteno, “High power, narrow linewidth fiber lasers,” Proc. SPIE 6102, 610205, 610205-8 (2006). [CrossRef]
- L. Dong, “Limits of stimulated Brillouin scattering suppression in optical fibers with transverse acoustic waveguide designs,” J. Lightwave Technol. 28, 3156 (2010).
- A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic Publishers, 1983).
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