Multimode Fibers

Multimode fibers are optical fibers which support multiple transverse guided modes for a given optical frequency and polarization. In most cases, that number of guided modes is large, e.g. several hundreds or even more.

Compared with standard single-mode fibers, multimode fibers usually have significantly larger core areas, but also often a higher numerical aperture of e.g. 0.2–0.3. The latter leads to robust guidance, even under conditions of tight bending, but also to higher propagation losses without bending, as irregularities at the core–cladding interface can scatter light more effectively. The refractive index profile is usually rectangular (→ step-index fibers), but sometimes parabolic (see below).

A basic specification of a multimode fiber contains the core diameter and the outer diameter of a multimode fiber. Common types for fiber-optic communications (see below) are 50/125 μm and 62.5/125 μm fibers, having a core diameter of 50 μm or 62.5 μm, respectively, and a standard cladding diameter of 125 μm. Such fibers support hundreds of guided modes. There are also large-core fibers with even substantially larger core diameters of hundreds of micrometers, and correspondingly more modes.

In most cases, a multimode fiber has a simple step-index profile, i.e., nominally a constant refractive index within the fiber core. Some are graded-index fibers with a continuous variation of refractive index. Multi-step designs are possible but not common.

Multimode Fibers for Common Applications

Multimode Fibers for Transporting Laser Light

Multimode fibers are used for transporting light from a laser source to the place where it is needed, particularly when the light source has a poor beam quality and/or the high optical power requires a large area of the fiber core. For example, light from stationary high-power lasers of various types can be sent to laser material processing stations for cutting or welding, where e.g. a robot moves a laser head mounted at the end of a fiber cable.

Also, fiber-coupled high-power diode bars and diode stacks use multimode fibers, as their beam quality is far from diffraction-limited. Fiber coupling is useful because it allows one e.g. to separate the pump diodes and their cooling arrangement from the laser head of a diode-pumped solid-state laser. However, fiber-coupled laser diodes are more expensive, and depending on the beam shapers used, there can be some significant loss of radiance.

For such applications, the number of guided modes of the fiber should often not be larger than necessary for efficient launching, since otherwise the laser radiation might be distributed over a large than necessary number of modes, and the beam quality and brightness would be reduced.

In practice, a simple step-index refractive profile is normally used. The numerical aperture is often held constant at some standard value such as 0.22, and the core diameter is chosen according to the beam quality of the light source. Common values for the core diameter are 50, 100, 200, 400, 600 and 800 μm.

Multimode Fibers for Optical Communications

For short-distance optical fiber communications, multimode fibers are often preferred over single-mode fibers because they can accept light from simpler light sources (e.g. light-emitting diodes = LEDs), and their alignment (e.g. in fiber connectors) is less critical. However, the possible data rates and/or transmission distances achievable with such fibers are limited by the phenomenon of intermodal dispersion: the group velocity depends on the propagation mode, so that ultrashort pulses propagating in a multimode fiber may be split into several pulses with different arrival times, possibly smearing out any transmitted signal. This effect can be greatly reduced by making multimode fibers with a parabolic refractive index profile (graded-index fibers, Figure 4), so that a substantially larger bandwidth–distance product can be achieved. Unavoidable imperfections still set limits. There are ISO standards like OM1, OM2, OM3, OM4 and OM5, which quantify the residual level of intermodal dispersion, limiting the transmission bandwidth (or the bandwidth–distance product). Highest performance is achieved e.g. with OM4 50/125-μm laser-optimized fibers, having a very precisely controlled refractive index profile. The data transmitter then often contains an 850-nm VCSEL.

See the article on graded-index fibers for more details.

For long-haul data transmission, single-mode fibers are preferable, as they do not exhibit any intermodal dispersion, whereas the system cost is substantially higher.

The International Telecommunications Union (ITU) has developed a number of standards for various types of fibers as used for optical fiber communications. The standards for multimode fibers are:

Active Multimode Fibers

Multimode fiber designs with a substantial number of modes are not common for active (amplifying) fibers because of the poor output beam quality. However, active fibers for high-power fiber amplifiers are often designed such that they have a few guided modes (→ few-mode fibers), because that way it is easier to achieve a large effective mode area (→ large mode area fibers) and still sufficiently robust guiding. It is often possible to obtain a nearly diffraction-limited output by launching the input signal light into the fundamental mode and by minimizing mode mixing.

Materials and Fabrication

Various materials can be used for multimode fibers. The most common multimode glass fibers are silica fibers, where a pure silica core is surrounded by a region which is doped with some index-lowering agent (e.g. fluorine). Alternatively or in addition, the core can have some additional doping, e.g. with germania, to increase the refractive index. Particularly for large-core fibers, the plasma outside deposition (POD) method allows the efficient fabrication of fluorine-doped “depressed index claddings” around a pure silica core.

There are also other glasses, e.g. fluoride and chalcogenide glasses for guiding light with longer wavelengths, and polymers (polymer optical fiber, POF). Such materials require adapted fabrication techniques.

Another possibility is to use photonic crystal fibers (PCF), which can be made from different glasses and can have, e.g., an air cladding to achieve a very high numerical aperture.

The Mode Structure of Multimode Fibers

Modes of fibers can be described as LP modes, assuming that the refractive index contrast is small (which is nearly always the case for all-glass fibers). Each of those (for a given wavelength) is specified with two indices l and m. The lowest order (fundamental) mode is LP₀₁. While the l index determines the number of oscillations in the azimuthal direction, the m index is the number of zero crossings in the radial direction plus 1. Each such mode has a characteristics intensity profile:

These are all modes guided by the core; in addition, there can be many cladding modes.

Case Studies

Case Study: Mode Structure of a Multimode Fiber

We explore various properties of guided modes of multimode fibers. We also test how the mode structure of such a fiber reacts to certain changes of the index profile, e.g. to smoothening of the index step.

The number of guided modes depends both on the fiber's refractive index profile and on the optical wavelength.

For any given wavelength, each mode has its own set of properties such as the following:

• the effective refractive index, which is related to the phase change per unit length (phase constant <$\beta$>)
• the group index, determining the group velocity of light
• the effective mode area
• the group velocity dispersion (GVD)
• the attenuation constant (e.g. in units of dB/km)

Case Studies

Case Study: Telecom Fiber With Parabolic Index Profile

We investigate how intermodal dispersion of a multimode fiber can be minimized with a parabolic doping profile.

Number of Guided Modes

The number of guided modes is determined by the wavelength (or optical frequency) and the refractive index profile. For step-index fibers, the relevant quantities are the core radius and the numerical aperture; the latter depends on the refractive index contrast between fiber core and cladding. In combination, these quantities determine the V number. For large <$V$> values, the number of modes is roughly <$V^2 / 2$>, when counting both polarization directions. Particularly for fibers with a relatively large core (right-hand side in Figure 1), the number of supported modes can be several thousand.

It turns out that one can generalize that equation for arbitrary index profiles:

This is shown in a case study:

Case Studies

Case Study: Number of Modes of a Highly Multimode Fiber

We seek a simple equation for estimating for the number of modes of a highly multimode fiber, which can be applied to fiber designs with arbitrary shapes of the refractive index profile. Instead of applying complicated mathematics, we build a hypothesis and subject that to multiple numerical tests.

Superpositions of Modes

In general, light launched into a multimode fiber (see below) will be a superposition of different modes. As long as the fiber's nonlinearities are not relevant (for sufficiently low optical intensities), each mode simply propagates according to its attenuation constant and phase constant, theoretically with no interaction between them. However, some amount of mode mixing may result from various influences such as irregularities of the index profile, bending effects, or nonlinear interactions. In the following, we will ignore mode mixing effects.

For a given optical frequency (i.e., considering monochromatic light), the total electric field distribution anywhere in a multimode fiber is a superposition of contributions from the different modes. The intensity profile depends not only on the optical powers in all the modes, but also on the relative phases, and there can be constructive or destructive interference of different modes at particular locations in the fiber. Both the powers and optical phases are initially determined by the launching conditions, and the relative phases (and thus the interference conditions) evolve further due to the mode-dependent propagation constants. Therefore, the complicated intensity pattern changes all the time, typically with significant changes occurring within a propagation length of usually well below 1 mm. Also, the relative phases changes with any modifications of the launching conditions, bending or stretching of the fiber, changes of the wavelength or temperature, etc. In practice, the resulting detailed interference pattern at the fiber output is thus normally not predictable.

The power distribution over the modes and their optical phases also depend on the launch conditions. Figure 4 shows an example in the form of animated graphics, where the different frames represent intensity distributions occurring at the end of a multimode fiber when the input beam position is varied. The Gaussian input beam is scanned through the horizontal line (slightly above the center of the fiber core). This model has been made with the RP Fiber Power software and is described in more detail on a separate page.

Smoother Intensity Profiles for Polychromatic Light

Complicated intensity patterns are discussed above are not observed for light with a broad optical bandwidth (e.g. for a white light source), if only the optical intensity is detected without distinguishing different spectral components. This is because the shape of the intensity pattern is different for each wavelength component, so that contributions from different wavelengths are averaged out; this results in a much smoother kind of intensity distribution. The longer the fiber and the larger the fiber core, the lower is the optical bandwidth required to achieve this averaging.

Efficiently Launching Light into a Multimode Fiber

Efficient launching means getting most of the input optical power into guided modes, as light getting into cladding modes will usually not be usable. The resulting detailed power distribution over the different modes is often not of interest.

Launching light into a multimode fiber is easy because there are larger tolerances concerning the location and propagation angle of incident light, compared with a single-mode fiber. On the other hand, the spatial coherence of the fiber output is reduced, and the output field pattern can hardly be controlled, for reasons explained above.

For efficient launching, one has to fulfill two conditions:

• The input light should essentially only hit the core, not the cladding.
• The input light should not contain significant amounts of power propagating with angles larger than arcsin NA. In other words, its beam divergence must be limited according to the fiber's NA.

In many cases, these conditions can be easily fulfilled with a laser beam. One may place the laser beam's focus at the input end of the fiber and choose the beam radius at that location somewhat below the core radius, so that the alignment will not be critical.

However, there are limitations when the laser beam has a poor beam quality, quantified with a correspondingly large M² factor. The maximum M² factor for efficient launching of a beam with a roughly super-Gaussian profile can be estimated from the following formula:

This holds if both the spatial beam profile and the angular distribution (i.e., the profile in Fourier space) are well adapted for launching, with a kind of super-Gaussian shape. For Gaussian distributions, the M² factor needs to be somewhat lower. For more details and example cases, see Ref. [9].

More to Learn

Tutorials:

• Tutorial on Passive Fiber Optics, Part 4: Multimode Fibers

Case studies:

• Case Study: Mode Structure of a Multimode Fiber
• Case Study: Telecom Fiber With Parabolic Index Profile
• Case Study: Number of Modes of a Highly Multimode Fiber

Encyclopedia articles:

• fibers
• modes
• multimode beams
• graded-index fibers
• single-mode fibers

Blog articles:

• The Photonics Spotlight 2016-09-12