graded-index fibers (original) (raw)

Definition: optical fibers with a continuously varying refractive index in the radial dimension

Alternative term: gradient index fibers

Categories: fiber optics and waveguides, lightwave communications

• fiber optics
  • fibers
    * passive fibers
    * active fibers
    * step-index fibers
    * graded-index fibers
    * polarization-maintaining fibers
    * photonic crystal fibers
    * photonic bandgap fibers
    * hollow-core fibers
    * multi-core fibers
    * nanofibers
    * single-mode fibers
    * single-polarization fibers
    * few-mode fibers
    * multimode fibers
    * large-core fibers
    * large mode area fibers
    * tapered fibers
    * mid-infrared fibers
    * dispersion-engineered fibers
    * telecom fibers
    * silica fibers
    * fluoride fibers
    * single-crystal fibers
    * plastic optical fibers
    * specialty fibers
    * (more topics)

Related: Telecom Fiber With Parabolic Index ProfileDispersion Engineering for Telecom Fibersfiberstelecom fibersoptical fiber communicationsmultimode fibersintermodal dispersionmodal bandwidthdispersion-shifted fibers

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Contents

What are Graded-index Fibers?

Many fibers are so-called step-index fibers, where the refractive index is a function of the radial position, i.e., it is constant in some regions and exhibits steps (sharp changes) at certain locations. However, there are also so-called graded-index fibers (or gradient index fibers), where the refractive index varies smoothly in the radial direction. That can be achieved with fiber fabrication techniques where the chemical composition of the glass preform varies continuously. For silica fibers, it is common to vary the concentration of germania, but one may in addition use spatially variable fluorine doping, which reduces the refractive index.

Graded-index fiber designs are used both for single-mode fibers and multimode fibers. The design goals are typically quite different between those cases, and are discussed in the following sections.

Graded-index Multimode Fibers

A typical design of a graded-index multimode fiber contains a parabolic profile from the fiber axis out to a certain radial position; outside that area, there can either be a constant refractive index (the cladding index) or first a depressed index region (trench). Figure 1 shows a simple design without such an index trench.

Figure 1: Refractive index profile of a graded-index fiber, which is parabolic in the core region. The effective refractive indices of the guided modes (shown as gray lines) for a wavelength of 1.55 μm are approximately equally spaced. For this model, set up with the RP Fiber Power software, a parabolic profile for the GeO2 concentration in a germanosilicate fiber has been assumed, which leads to an approximately parabolic index profile.

The fiber cladding is assumed to consist of pure silica (→ silica fibers).

Precisely speaking, what is meant to be parabolic is the square of the refractive index, i.e., the dielectric constant, rather than the refractive index itself. This detail, however, is quantitatively not that important in most cases, since the refractive index contrast is typically quite small.

A remarkable feature of such parabolic index designs is that the effective refractive indices of the guided modes are equally spaced (only not precisely for the highest-order modes, “seeing” the outer region which deviates from the parabolic shape). Figure 2 shows the effective indices versus mode area.

Interesting, the effective index essentially depends on the principal mode number ($2 m + l$). Therefore, many points in the diagram are located at a very similar vertical position as others. In Fig. 1, many horizontal lines nearly coincide.

Figure 2: Effective indices of the fiber versus effective mode area, with the colors of the points depending on the mode index ($l$).

As shown in Figure 3, the group indices are approximately the same for all modes — except for the highest-order modes. This shows that the intermodal dispersion, which can be characterized by the differential mode delay, is quite small — much smaller than for a step-index fiber.

Figure 3: Effective indices of the fiber versus effective mode area, with the colors of the points depending on the mode index ($l$).

Of course, one can further tailor the refractive index profile, slightly deviating from a parabolic shape, to further optimize mode properties. In particular, one may generalize the parabolic profile by using a different exponent; the higher that exponent, the closer the profile would be to a step-index profile. An optimized profile exponent, deviating slightly from 2 (the value for parabolic profile), can be determined for fibers with high index contrast; the optimum value depends on the so-called profile dispersion parameter, describing the relation between group index and refractive index for the chosen material composition. For example, the results of Figure 3, obtained for a parabolic profile, can be significantly enhanced further with a modified profile exponent of ≈1.85.

Simulations on Graded-index Fibers

When developing or using graded-index fibers, many questions may arise which can be answered only with numerical simulations. For example, how should the index profile be to achieve certain performance, and how critical is exact conformance to a nominal profile. For this kind of work, you need a very flexible simulation tool like the RP Fiber Power software.

In an intuitive picture, one may consider hypothetical rays propagating along the fiber. Such rays would perform sinusoidal oscillations around the fiber axis; the index gradient always “bends” them back towards the axis. The strongly reduced intermodal dispersion is sometimes “explained” with the higher velocity of light away from the fiber core, which compensates the longer geometrical path length of the strongly oscillating ray, thus effectively leading to an effective path length per meter fiber which is the same for all rays. This picture is rather crude, however; for example, it suggests that phase delays acquired by the rays are strongly related to time delays, which is actually not true. In fact, the strongly mode-dependent effective indices (see Figure 2) show that the phase delays acquired by different modes are quite different, while the time delays are indeed quite similar according to Figure 3.

Figure 4 shows a simulation (with numerical beam propagation) where a Gaussian input beam has been somewhat displaced against the center of the fiber core. In the fiber, the intensity profile oscillates without fully reaching the edges of the core region. The observed oscillation is somewhat similar as in the ray picture mentioned above, but the perfect periodicity is destroyed by the cut-off parabolic shape. Also note that the transverse size of the oscillating intensity peak varies substantially along the fiber.

Figure 4: Beam propagation in a graded-index fiber, where a Gaussian input beam has been slightly offset against the center of the fiber core.

The horizontal gray lines indicate the edges of the core.

For comparison, Figure 5 shows the same for a step-index design with the same core radius and maximum refractive index. The result looks quite different; one obtains a complicated evolution of the intensity profile.

Figure 5: Same as Figure 7, but for a step-index profile.

Applications of Graded-index Multimode Fibers

The above example has been for a germanosilicate fiber, i.e., a glass fiber. Similar designs, with typical core diameters being 50 μm and 62.5 μm, are used for multimode telecom fibers in fiber-optic links with a transmission distance of a few hundred meters, for example. The fiber designs and high-precision fabrication techniques have been refined increasingly for obtaining a minimum differential mode delay, in that way maximizing the modal bandwidth and thus the transmission capacity of such links. Early standards for named OM1 and OM2; the optimization later led to OM3 and OM4 fibers, allowing for substantially higher performance.

Typically, a small differential group delay and thus a high modal bandwidth is achieved only in a relatively limited wavelength region e.g. around 850 nm; the performance is already seriously degraded for a wavelength deviation of only 30 nm, for example. However, special wideband multimode fibers have been developed which offer relatively low intermodal dispersion over a broader wavelength range (e.g. 100 nm).

In the future, further substantial increases of transmission capacity may be achieved with mode division multiplexing, which can be realized with so-called multiple input multiple output (MIMO) techniques. For certain practical reasons, it is then still important to achieve a rather small differential group delay.

Graded-index designs are also sometimes used with other types of glass fibers, e.g. for mid-infrared fibers [9].

There are also plastic optical fibers (POF) having graded index profiles. They are often used in the same way, i.e., with the goal of minimizing intermodal dispersion effects in fiber-optic links.

Graded-index fibers are not only used for telecom purposes, but also e.g. for laser power transmission (power over fiber), where one may profit from the better output beam profile. For such applications, fibers with much larger core diameters of e.g. 100, 200, 400 or even 600 μm are available. Another application is using short pieces of such fibers as mode field adapters [14]. Some graded-index fibers are used in fiber-optic sensors, some are developed as large mode area fibers [11], and there are even versions for guiding terahertz radiation [18].

Graded-index Single-mode Fibers

Originally, most single-mode fibers had a design close to that of a step-index fibers, or perhaps only a central index dip which resulted from fiber fabrication details but was not really intended. However, particularly in the context of developing dispersion-shifted fibers, it was realized that step-index designs with large index step were problematic in terms of propagation losses. Also, the greater design freedom of non-step-index designs was found to be quite helpful.

Graded-index profiles of single-mode fibers can have different forms. A triangular profile type, or a generalized ($\alpha$) profile where a parameter ($\alpha$) controls the shape, is frequently used, particularly for dispersion engineering. One may introduce additional features, such as a ring of increased or decreased index around the triangular region.

Case Studies

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.

Fabrication of Graded-index Fibers

Optical fibers are usually fabricated by drawing them from a preform. (That applies to glass fibers as well as to plastic optical fibers.) The preform then needs to be made with a graded-index profile, so that the fiber exhibits the same profile, just on a different scale.

Different processes can be used to make such preforms:

• In the case of glass preforms, the core material is usually generated with some method of chemical vapor deposition. That process needs to be controlled such that the refractive index is varied over time by changing the composition of the deposited material.
• In the case of polymers, the refractive index can be increased by doping with high-index substances having a larger molecular weight. These also tend to exhibit lower diffusion constants. That can be exploited to maintain a concentration gradient until the polymerization is complete and the gradient is “frozen in”. Alternatively, one may use a mixture of monomers with different density and refractive indices, and obtain a concentration gradient e.g. using centrifugal forces until polymerization is complete.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is a graded-index fiber?

A graded-index fiber is an optical fiber where the refractive index varies smoothly in the radial direction from the center to the cladding. This is in contrast to a step-index fiber, which has a uniform refractive index within the core and a sharp drop at the core-cladding boundary.

Why are graded-index profiles used for multimode fibers?

In multimode fibers, graded-index profiles, particularly parabolic ones, are used to minimize intermodal dispersion. This leads to nearly equal group velocities for all guided modes, which significantly increases the modal bandwidth and data transmission capacity of fiber-optic links.

How does a graded-index profile reduce intermodal dispersion?

The graded profile causes the group indices of the different modes to be approximately the same. A simplified ray model suggests that light rays on longer, oscillating paths travel faster in the lower-index regions away from the fiber axis, compensating for the greater distance. However, the precise explanation is based on the wave nature of light.

What are OM3 and OM4 fibers?

OM3 and OM4 are industry standards for laser-optimized multimode graded-index fibers. They are designed for high transmission capacity, for example in 10 Gbit/s Ethernet links, by having an index profile which is precisely tailored to minimize differential mode delay over distances of a few hundred meters.

Are graded-index profiles also used for single-mode fibers?

Yes, graded-index profiles, such as triangular or other shapes, are used in single-mode fibers. They offer greater design freedom than simple step-index profiles, which is particularly useful for dispersion engineering, e.g., for creating dispersion-shifted fibers.

How are graded-index fibers fabricated?

Graded-index fibers are made by drawing them from a glass or plastic preform. The preform is fabricated to have the desired graded-index profile, for example by using chemical vapor deposition where the composition of the deposited material is varied over time.

What are applications of graded-index fibers apart from telecommunications?

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