Abstract

Achieving very large mode area is a key goal in current research on microstructure and solid fibers for high power amplifiers and lasers. One particular design regime of recent interest has effective area over 1000 square microns and has effectively-single-mode operation ensured by bend losses of the higher-order modes. Simulations show that these fibers are extremely prone to bend-induced distortion and reduction in mode area. The calculated area reduction would significantly impact nonlinear impairments for bend radii relevant to any reasonable spooled package, and can be over 50 percent for bend radii tighter than 10cm. The parabolic-profile design has a natural immunity to bend-induced mode distortion and contraction, and shows superior performance in simulated fair comparisons with other fiber families, including microstructure fibers.

© 2006 Optical Society of America

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References

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Appl. Opt. (1)

CLEO (2)

W. S. Wong, X. Peng, J. M. McLaughlin, and L. Dong, "Robust single-mode propagation in optical fibers with record effective areas," in CLEO, p. CPDB10 (2005).

M.-Y. Chen, Y.-C. Chang, A. Galvanauskas, P. Mamidipudi, R. Changkakoti, and P. Gatchell, "27-mJ nanosecond pulses in M2 = 6.5 beam from a coiled highly multimode Yb-doped fiber amplifier," in CLEO, p. CTuS4 (2004).

Opt. Commun. (1)

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-35 (2003).
[CrossRef]

Opt. Express (4)

Opt. Express. (1)

M. D. Nielsen, J. R. Folkenberg, N. A. Mortensen, and A. Bjarklev, "Bandwidth comparison of photonic crystal fibers and conventional single-mode fibers," Opt. Express. 11, 430 (2004).
[CrossRef]

Opt. Lett. (3)

Photonics Technol. Lett. (1)

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, and P. S. J. Russell, "Very High Numerical Aperture Fibers," Photonics Technol. Lett. 16, 843 (2004).
[CrossRef]

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Figures (14)

Fig. 1.
Fig. 1.

Comparison of fundamental mode intensity profiles for two fibers highlights the onset of extreme bend sensitivity as core diameter is pushed beyond 30 microns. The fibers have a W-shaped index profile, with a step-index core (white dashed lines indicate R core and R out). The top two plots show intensities for a fiber with 30-micron core diameter, without and with a bend. The bottom plots are for a 50-micron diameter. Bending to a diameter of 15cm slightly perturbs the mode shape of the smaller-core fiber, but causes a very large displacement, distortion, and contraction in the larger-core fiber.

Fig. 2.
Fig. 2.

This W-shaped index profile was used for the two fibers of Fig. 1. For both fibers, the outer cladding has the same index as the core, and R out = 3R core.

Fig. 3.
Fig. 3.

The equivalent index model accounts for path-length differences induced by a bend.

Fig. 4.
Fig. 4.

The equivalent-index model gives us an intuitive picture of bend-induced distortion and area reduction. Bends lead to an index gradient across the core, which tends to push light towards the outside of the bend. The index plot includes the fiber index profile (black) and effective index of the modes (red and blue).

Fig. 5.
Fig. 5.

Effective area is plotted versus bend radius (left), showing a quite significant bend-induced effective area reduction for the larger-core fiber. Circles show bent-fiber simulation results, while the dashed guideline indicates the straight-fiber areas, for comparison. It is also interesting to look at ratio of the areas for the two fibers, A eff,50/A eff,30 (right). This plot shows that the improvement in mode area between the two fibers can become marginal for relevant bend radii (circles), even though the straight-fiber improvement is a factor of 2.3 (black dashed line). Even this mode-area increase is somewhat less than the core-area increase, (50/30)2 ≈ 2.8 (green dashed line).

Fig. 6.
Fig. 6.

Area plotted versus bend radius (left) for a microstructure fiber [9] shows a large reduction in effective area induced by bends, relative to the straight-fiber value of around 1500 square microns (dashed line). The calculated fiber geometry (right) has two different hole sizes.

Fig. 7.
Fig. 7.

In theory, a pre-corrected fiber could be made to cancel the bend-induced field distortion. This would introduce significant difficulties in fabrication and use of the fiber.

Fig. 8.
Fig. 8.

A parabolic-profile fiber would achieve the goal presented in Fig. 7, but without the difficulties associated with an asymmetric fiber design. The parabolic index function is naturally invariant (but translated) under the influence of bending, so that mode fields should be largely free of bend-induced distortion, asymmetry, and contraction. Naturally, the profile beyond the core radius does not have this invariance property.

Fig. 9.
Fig. 9.

Simulations confirm the intuitive bend-resistance for a particular example of a fiber with truncated parabolic profile (D core = 68 microns, Δn = .00112). Even for a fairly tight bend, the mode shows essentially no distortion or contraction.

Fig. 10.
Fig. 10.

The truncated parabolic index (left) with finite layers (D core = 68 microns, Δn = .00112) was used for simulations in this section. The simulated effective area (right, black line) is largely independent of the bend radius for the example parabolic fiber. For comparison, the straight parabolic fiber area is shown (black dashed line), and the results for SIF examples of Fig. 5 are repeated (dotted red and blue lines).

Fig. 11.
Fig. 11.

Plots of effective area and relative HOM suppression as a function of core size and contrast.

Fig. 12.
Fig. 12.

Fundamental loss with interpolated Delta values.

Fig. 13.
Fig. 13.

A fair comparison of the different LMA fiber families is distilled from many simulated fibers, interpolating parameters to achieve a common fundamental bend loss of 100dB/km. Good performance is defined by large area (to the right) and HOM suppression (upwards).

Fig. 14.
Fig. 14.

The same type of comparison using unbent fiber effective area values gives a completely different and misleading picture. By ignoring bend-induced effective area reduction, this comparison overstates the advantages of using holes and completely overlooks the advantage of the parabolic design.

Equations (7)

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n eq 2 x y = n 2 x y ( 1 + 2 x R bend ) ,
A eff = ( d A E 2 ) 2 dA E 4 .
n x y = n core ( n core n clad ) ( x 2 + y 2 ) R core 2
n x y + Bx = n core Δ n R core 2 ( x 2 + y 2 ) + Bx
= n core Δ n R core 2 [ ( x x d ) 2 + y 2 ] + C .
x d = B R core 2 2 Δ n .
C = x d 2 R core 2 Δn .

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