Abstract

Hole-assisted fibers have been proposed for a number of applications, including low-bend-loss access transmission. Suppression of higher-order modes is essential in these designs, and is explained here as the result of index-matched coupling between core and cladding modes. This physical principle is shown to explain previous empirically optimized designs, and enables intuitive generalizations. The improved tradeoff between bend loss and suppression of higher-order modes in these designs is discussed. Novel solid and microstructure fiber designs with suppressed higher-order modes illustrate these principles.

© 2005 Optical Society of America

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References

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ECOC 2003 (2)

T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya. Bend-insensitive single-mode holey fibre with SMF compatibility for optical wiring applications. In European Conference on Optical Communications, page We2.7.3 (2003).

J. M. Fini. �??Bloch theory describing cladding modes of microstructure optical fiber,�?? In European Conference on Optical Communications, We4.P.37, (2003).

Electron. Lett. (1)

T. A. Birks, P. J. Roberts, et al. �??Full 2d photonic bandgaps in silica/air structures,�?? Electron. Lett. 31, 1941 (1995).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

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

Opt. Express (5)

Opt. Lett. (3)

Optical Fiber Communications 2004 (3)

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russel. �??Low loss (1.7db/km) hollow core photonic bandgap fiber,�?? In Optical Fiber Communications Conference (OFC), PDP24 (2004).

F. Gerome, J. L. Auguste, and J. M. Blondy. �??Very high negative chromatic dispersion in a dual concentric core photonic crystal fiber,�?? In Optical Fiber Communications Conference (OFC), WA2 (2004).

A. D. Yablon and Ryan Bise. �??Low-loss high-strength microstructure fiber fusion splices using grin fiber lenses,�?? In Optical Fiber Communications Conference (OFC), MF14 (2004).

Photon. Technol. Lett. (3)

J. K. Chandalia, B. J. Eggleton, R. S.Windeler, S. G. Kosinski, X. Liu, and C. Xu. �??Adiabatic coupling in tapered air-silica microstructured optical fiber,�?? Photon. Technol. Lett. 13, 52 (2001).
[CrossRef]

K. Nakajima, K. Hogari, et al. �??Hole assisted fiber design for small bending and splice losses,�?? Photon. Technol. Lett. 15, 1737 (2003)
[CrossRef]

M. Yan, P. Shum, and C. Lu. �??Hole-assisted multiring fiber with low dispersion around 1550 nm,�?? Photon. Technol. Lett. 16, 123 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

S. A. Diddams, D. J. Jones, et al. �??Direct link between microwave and optical frequencies with a 300THz femtosecond laser comb,�?? Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

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Figures (16)

Fig. 1.
Fig. 1.

A simple step-index fiber design can achieve reduced macrobending losses by using higher index contrast (left). However, if contrast is too large (right), higher-order modes are guided in the core, leading to problems with microbend coupling.

Fig. 2.
Fig. 2.

Cladding features can be designed to give index-matching between cladding modes and unwanted core modes. The fiber index profile is shown schematically with two high-index, waveguiding regions (core and cladding). The modes of the individual waveguides are represented by red curves (with effective index indicated by dashed lines). Index-matching leads to large mixing of energy between the unwanted modes and the cladding. At the same time, signal modes are not index-matched and have essentially no energy in the cladding region.

Fig. 3.
Fig. 3.

Index matching of unwanted and cladding modes typically occurs over a narrow wavelength range. If the mode indices are plotted as a function of wavelength, the signal operating wavelength should be near the intersection of index curves for the unwanted and cladding modes.

Fig. 4.
Fig. 4.

A two-ring hole-assisted fiber was proposed by Hasegawa, et. al., to achieve low bending loss. It consists of a central doped core surrounded by two hexagonal rings of air holes. Unequal hole spacings, L 1 and L 2, are used for the two rings in order to suppress the higher-order modes of the core.

Fig. 5.
Fig. 5.

The effective index model is a useful approximation, where a periodic cladding is replaced by a single, wavelength-dependent average index. The appropriate index can be calculated using Bloch analysis (for example, see [18, 14]).

Fig. 6.
Fig. 6.

A high-index ring emerges when an effective-index approximation is used for the hole-assisted fiber with two hole spacings. The standard average-index concept can be generalized by averaging the index in a “unit-cell” about each hole, corresponding to the spacing in that cladding region.

Fig. 7.
Fig. 7.

Numerical analysis of the hole-assisted fiber with regular-lattice cladding (left) shows core and cladding modes. Intensity plots are given for three modes indicated by black circles on the effective index vs. wavelength plot. Dashed lines and shading are used to highlight the doped-core index, the index of the undoped silica substrate, and the average cladding index obtained from Bloch analysis of the inner holes (dashed line at the bottom of the unshaded region). Core modes, both fundamental and higher-order, have power primarily in the core and effective index above the average-cladding index. The lower red lines represent cladding or “ring” modes, with power mostly outside the core. The ring mode index crosses above the average cladding index as the geometry is adjusted from L 2=L 1 (left) to L 2=1.05L 1 (right).

Fig. 8.
Fig. 8.

When L 2/L 1 is chosen just right, core HOMs and cladding modes are index-matched and power mixes between the two regions (right, effective index and intensity plots). Loss is plotted (right) vs. wavelength for a few higher-order modes (the fundamental mode, in principle, has zero confinement loss). The loss peak near 1500nm wavelength can be interpreted as resonant HOM suppression due to coupling with the very leaky cladding modes.

Fig. 9.
Fig. 9.

When L 2/L 1>1.2, the core and cladding modes are again not index-matched (in the 1500nm region), and relatively little mixing is seen.

Fig. 10.
Fig. 10.

The basic tradeoff between macrobending loss and higher-order mode suppression can be summarized using a bend-loss proxy vs. HOM loss plot if there is a single wavelength of interest. Here the stars indicate the L 2=L 1 designs, with colors indicating different hole diameters. Fitting the stars, we can infer the basic tradeoff possible using only hole size as a degree of freedom (black dashed line). Colored lines show the improved performance as the additional degree of freedom L 2>L 1 is tuned.

Fig. 11.
Fig. 11.

The plot of intensity as a function of radius indicates the degree of confinement of the fundamental mode, and should correlate with resistance to macrobending losses. A bend-loss proxy is defined as the radius at which the intensity reaches a fixed threshold (for example 10-7) times its peak value (red dashed line). Light blue curves include intensity at several angles, while the dark blue curve indicates the average over azimuthal angle. Red star, circle, and triangle symbols mark the radius of intersection for three fiber geometries. As expected, the hole-assisted fibers have a more tightly confined mode than the step-index fiber with identical core but no holes (dashed black line).

Fig. 12.
Fig. 12.

For broadband applications, an effective cutoff wavelength summarizes the HOM confinement over a wavelength range into a single number. A cutoff can be extracted simply by thresholding (left), and will depend on the value of the loss threshold (probably empirical). The basic design tradeoff can then be summarized in a plot of macrobending loss vs. cutoff (right). All cutoffs that are out-of-range are plotted as 1800nm.

Fig. 13.
Fig. 13.

Solid fiber designs were constructed as crude equivalents to the L 1-L 2 family of hole-assisted fibers. Mode analysis shows that mixing of core and ring modes arises and leads to suppression of unwanted higher-order modes. Intensity plots show poorly confined higher-order modes near the index-matching wavelength. Dashed black lines and shading indicate the four material index values of the fiber (top to bottom): ñcore, n sil=1.444, n holes2, and n holes1.

Fig. 14.
Fig. 14.

The basic design tradeoff between a well-confined fundamental (low macrobending loss) and poorly-confined higher-order modes is summarized by simple numerical estimates for the solid L 1-L 2-equivalent fiber family. The presence of cladding rings (solid curves) simultaneously improves both performance metrics. Performance at a specific wavelength is summarized as HOM loss vs. bend-loss proxy (left), where desirable designs have a low proxy and high HOM loss. Broadband performance is instead summarized as bend loss proxy versus cutoff (right), with low cutoffs being desirable. Stars represent the special case L 2=L 1, where there is no high-index ring.

Fig. 15.
Fig. 15.

This hole-assisted fiber has holes fairly evenly distributed through the cladding. The effective index of the cladding is roughly .01 below that of the substrate, so that the first higher-order mode group is well within the unshaded hole-confined region, indicating low-loss confinement in the core.

Fig. 16.
Fig. 16.

A hole-assisted fiber with a missing layer of holes has a high-index ring in the effective index profile. Index matching between the cladding modes of the ring and higher-order modes of the core is achieved at around 1.55 microns, as seen in the effective index plot (left). The loss (right) near this wavelength is hundreds of times larger than the loss of the corresponding three-layer HAF with no index-matched cladding modes (shown dashed). For this fiber, the core diameter is 7.45 microns with 0.38% relative index difference. The cladding has 1 micron diameter holes, with 12-holes on a circular layer of radius 7 microns and 24 holes on a second circular layer of radius 14.7 microns. For reference, the dashed curve gives the loss of the Fig. 15, where no holes are “missing.” Blue curves are used for modes with the same “even” symmetry as the fundamental, and red curves have “odd” symmetry. The index-matched loss curves are highlighted with black.

Equations (2)

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n ( r ) = { n ˜ core ; r < L 1 2 n holes 1 ; L 1 2 < r < 3 L 1 2 n sil ; 3 L 1 2 < r < 3 L 2 2 n holes 2 ; 3 L 2 2 < r < 5 L 2 2 n sil ; r > 5 L 2 2
n ˜ core n sil = ( n core n sil ) ( 2 R core L 1 ) 2 .

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