# Dispersion-shifted Fibers

Author: the photonics expert Dr. Rüdiger Paschotta

Definition: fibers with a non-standard zero dispersion wavelength

More general term: telecom fibers

Categories: fiber optics and waveguides, lightwave communications, light pulses

Standard telecom fibers exhibit zero chromatic dispersion in the 1.3-μm wavelength region. This was convenient for early optical fiber communications systems, which often operated around 1310 nm. However, the 1.5-μm region later became more important because the fiber losses are lower there, and erbium-doped fiber amplifiers (EDFAs) are available for this region (whereas 1.3-μm amplifiers do not reach comparable performance). In this wavelength region, however, standard single-mode fibers (now sometimes called *dispersion-unshifted fibers*) exhibit significant anomalous dispersion. For linear transmission, this can be a problem because it leads to significant dispersive pulse broadening, limiting the achievable transmission rates or distances.

Therefore, some special fiber types with substantially modified dispersion characteristics have been developed, where one utilizes modified waveguide dispersion resulting from a modified refractive index profile of the core. In particular, there are *dispersion-shifted fibers* [11] and *dispersion-flattened fibers* with much reduced dispersion slope. A review paper [9] gives a detailed history of the developments.

## Dispersion-shifted Fibers with Substantial Dispersion Slope

An ordinary step-index single-mode fiber has its zero dispersion wavelength around 1.3 μm – only slightly longer than the zero dispersion wavelength of fused silica – and substantially anomalous dispersion around 1.5 μm. The first approach was to develop fiber designs where the zero dispersion wavelength is shifted into the 1.5-μm region, i.e., close to the used signal wavelengths. Essentially, one requires increased waveguide dispersion of the normal type.

The original attempt was to simply modify the parameters of the step-index design: use a smaller core in conjunction with rather high numerical aperture such as to roughly preserve the V number. While this was successful in terms of shifting the dispersion, the propagation losses of such fibers turned out to be rather high. Initially, the reason for that was not fully clear, as the loss increase was larger than expected. It turned out that mechanical stress at the core–cladding interface (here, with a large GeO_{2} concentration difference) played an important role.

### Designing Dispersion-modified Fibers

For working out such designs, considering a number of trade-offs, you need a very flexible simulation tool. The RP Fiber Power software is ideal for such work.

Therefore, researchers started to investigate designs of graded-index fibers, i.e., with a gradual variation of the germania concentration and thus the refractive index. A common type of index profile was of the form

$$n(r) = n_{\rm c} (1 - 2 \Delta (r / a)^{\alpha})^{0.5}$$which for the most common value <$\alpha = 1$> is called triangular, although precisely speaking it is not exactly triangular due to the power of 0.5. (What is triangular is actually <$n^2(r)$>, which is the dielectric constant <$\epsilon$>, but for the typically small values of <$\Delta$>, that difference is not substantial.) Modified variants of that profile have the index peak in the center capped and/or use another index step where the triangular portion ends, for example. With such designs, it became possible to shift the zero dispersion wavelength without significantly increasing the propagation losses, and also with maintaining robust single-mode guidance.

Concerning telecom applications, the original idea was to minimize chromatic dispersion at the signal wavelengths. However, it turned out that zero chromatic dispersion is not necessarily ideal for data transmission. Particularly for the transmission of multiple channels (→ *wavelength division multiplexing*), four-wave mixing effects can be phase-matched and thus introduce significant distortions, if the dispersion is too weak. Therefore, it can be advantageous to use *non-zero dispersion-shifted fibers* [12], which are designed to have a moderate amount of group velocity dispersion (GVD) in the wavelength range of the data transmission, with the zero dispersion wavelength lying somewhat outside this region. There are different versions:

- NZD+ fibers have their zero dispersion wavelength at 1510 nm and anomalous dispersion at the typical signal wavelengths (longer than 1510 nm).
- NZD− fibers have a zero dispersion wavelength of 1580 nm, resulting in normal dispersion at the signal wavelengths.

Dispersion-shifted fibers still have a substantial positive *dispersion slope* (specified with units of ps/(nm^{2} km)), i.e., their group velocity dispersion decreases with increasing wavelength, or increases with increasing optical frequency. That implies positive third-order dispersion (TOD).

Often, the effective mode area of dispersion-shifted fibers is smaller than for an ordinary single-mode fiber. This can be detrimental, e.g. in terms of a required higher precision in the fusion splicing of fibers, increased splice losses when connecting ordinary and dispersion-shifted fibers, and increased nonlinear effects. Therefore, the effective mode area should be considered as one of the important design goals, but there are certain trade-offs.

## Case Study: Dispersion Engineering for Telecom Fibers

We explore different ways of optimizing refractive index profile for specific chromatic dispersion properties of telecom fibers, resulting in dispersion-shifted or dispersion-flattened fibers. This also involves automatic optimizations.

## Dispersion-flattened Fibers

The above-mentioned dispersion slope can be a problem, particularly in wavelength division multiplexing, where different signals experience substantially different GVD values. Even when only a single signal wavelength is used, it is inconvenient that the dispersion slope strongly restricts the usable wavelength range.

For such reasons, *dispersion-flattened* fibers with a much reduced dispersion slope, i.e., with relatively constant group velocity dispersion over some wavelength range, have been developed. In other words, they exhibit low higher-order dispersion. They can, for example, exhibit near zero dispersion or some moderate relatively constant amount of GVD in the telecom C band. Such fibers are important not only for transmission fibers, but also e.g. for adiabatic soliton compression, for signal processing using four-wave mixing and for wavelength channel translation, and for the generation of broadband frequency combs.

Dispersion-flattened fibers often have a W-shaped profile of the refractive index, although profiles with a graded index and multiple steps have also been developed. Typically, there is a ring with increased refractive index around the actual core region, which serves to substantially modify mainly the GVD at longer wavelengths and also influences the stability of guiding the fundamental mode. Such designs are not easy to work out in detail, since various trade-offs need to be considered, e.g. concerning aspects like dispersion, effective mode area, sufficiently robust guiding and fabrication tolerances. Typically, the fabrication tolerances must be fairly strict, requiring high precision in fiber fabrication.

## Common Trade-offs

Unfortunately, the optimization of chromatic dispersion can have various side effects, which are sometimes negative for applications. Some examples:

- The effective mode area is often substantially smaller than for standard single-mode fibers. This has mainly two effects:
- Simple splicing of fibers with different mode areas leads to substantial power losses. One may require a mode field adapter to minimize that.
- Nonlinear effects like self-phase modulation and four-wave mixing get stronger for smaller mode areas.
- One should therefore take the mode area as another design goal – for example as one factor for a figure-of-merit function to be optimized –, but this can introduce additional trade-offs.

- Polarization mode dispersion is often stronger in dispersion-shifted fibers because they have a relatively high numerical aperture, which causes an increased sensitivity to a slight ellipticity of the fiber core.

Also, the fabrication cost is typically higher than for standard single-mode fibers. That is particularly the case for dispersion-flattened fibers due to the substantially tighter fabrication tolerances.

The decision for the use of a certain type of dispersion-shifted fiber, or rather some standard single-mode fiber, should be based on complex reasoning, taking into account many factors, including some basic aspects of fundamental system design.

## Dispersion Compensation

An alternative solution can be to use dispersion-unshifted (i.e., standard) fiber with larger dispersion at 1.5 μm, combined with some kind of dispersion compensation. Note, however, that in many cases it is not that only the *total* chromatic dispersion of a fiber span is what matters. For example, if substantial signal distortions due to four-wave mixing occur in some initial length of fiber, that problem may remain even if FWM is suppressed in a later piece of the fiber. On the other hand, dispersion compensation can be effective where the problem is only dispersive broadening of pulses or signals.

## More to Learn

Encyclopedia articles:

## Suppliers

The **RP Photonics Buyer's Guide** contains seven suppliers for dispersion-shifted fibers. Among them:

### Cycle

Effective dispersion compensation is a key requirement for many applications involving ultrafast lasers and broadband optical signals. Cycle can offer a variety of dispersion compensating fibers to satisfy the needs of your application. Our products include:

- single-mode dispersion compensating fibers (SM-DCF) and
- polarization-maintaining dispersion compensating fibers (PM-DCF)

with different connector types and customized lengths. Please contact us for more information.

### Bibliography

[1] | R. B. Dyott and J. R. Stem, “Group delay in glass fibre waveguide”, Proc. Conf. Trunk Telecommun. Guided Waves, IEE Conf. publ. no. 71 (London, England), 176 (1970) |

[2] | W. A. Gambling, H. Matsumura and C. M. Ragdale, “Mode dispersion, material dispersion and profile dispersion in graded-index single-mode fibers”, Microwaves, Opt., Acoust. 3, 239 (1979) |

[3] | W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Zero total dispersion in graded-index single mode fibres”, Electron. Lett. 15, 474 (1979) |

[4] | L. G. Cohen et al., “Tailoring zero chromatic dispersion into the 1.5 μm–1.6 μm low-loss spectral region of single-mode fibres”, Electron. Lett. 15 (12), 334 (1979); https://doi.org/10.1049/el:19790237 |

[5] | U. C. Paek, G. E. Peterson and A. Camevale, “Dispersionless single-mode lightguides with α index profiles”, Bell Syst. Tech. J. 60, 583 (1981) |

[6] | K. I. White, “Design parameters for dispersion-shifted triangular-profile single-mode fibers”, Electron. Lett. 18, 725 (1982)- M. A. Saifi et al., “Triangular-profile single-mode fiber”, Opt. Lett. 7 (1), 43 (1982); https://doi.org/10.1364/OL.7.000043 |

[7] | B. J. Ainslie et al., “Monomode fibre with ultra-low loss and minimum dispersion at 1.55 μm”, Electron. Lett. 18, 842 (1982); https://doi.org/10.1049/el:19820573 |

[8] | V. A. Bhagavatula and M. S. Spitz, “Dispersion-shifted segmented-core single-mode fibers”, Opt. Lett. 9 (5), 186 (1984); https://doi.org/10.1364/OL.9.000186 |

[9] | B. J. Ainsley and C. R. Day, “A review of single-mode fibers with modified dispersion characteristics”, J. Lightwave Technol. LT-4 (8), 967 (1984) |

[10] | M. Wandel and P. Kristensen, “Fiber designs for high figure of merit and high slope dispersion compensating fibers”, J. Opt. Fiber Commun. Rep. 3, 25–60 (2005); https://doi.org/10.1049/el:19820573 |

[11] | ITU standard G.653 (07/10), “Characteristics of a dispersion-shifted single-mode optical fibre and cable”, International Telecommunication Union (2007) |

[12] | ITU standard G.655 (11/09), “Characteristics of a non-zero dispersion-shifted single-mode optical fibre and cable”, International Telecommunication Union (2011) |

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