Multimode fiber

Multimode fiber (MMF) is an optical fiber whose core guides many transverse modes at once. The communication grades have a core 50 µm or 62.5 µm in diameter inside the same 125 µm cladding as single-mode fiber, written 50/125 and 62.5/125, with numerical apertures of about 0.20 and 0.275. A 50 µm core guides about 340 modes at 850 nm. The large core accepts light from low-cost 850 nm VCSELs with loose alignment, and the price is modal dispersion: the modes arrive at slightly different times, which limits data links to a few hundred meters at current lane rates. The comparison with the small-core alternative is set out in single-mode vs multimode fiber.

Number of modes

The mode count follows from the V number, $V = 2\pi a\,\mathrm{NA}/\lambda$, for core radius $a$. Counting both polarizations, a large core guides about

$$M_\mathrm{SI} \approx \frac{V^2}{2}, \qquad M_\mathrm{GI} \approx \frac{V^2}{4}$$

modes for a step-index and a parabolic graded-index profile. For a 50 µm core with NA 0.20 at 850 nm, $V = 37.0$, which gives about 680 modes for a step-index core and 340 for the graded-index cores used in practice. At 1300 nm the same core has $V = 24.2$ and about 150 modes in the graded-index profile. A 62.5 µm core with NA 0.275 has $V = 63.5$ at 850 nm and about 1,000 modes.

Large step-index multimode fibers, with cores from 100 µm to beyond 1 mm and NA up to about 0.22 in all-silica designs, carry high laser power, illumination and spectroscopic light, where collecting light matters more than bandwidth.

Modal dispersion

Each mode has its own group delay, so a pulse that excites many modes arrives spread in time (modal dispersion). In a step-index core the spread per unit length is about

$$\frac{\Delta T}{L} \approx \frac{n_1 \Delta}{c}$$

where $\Delta = (n_1 - n_2)/n_1$ is the relative index difference. With $n_1 = 1.47$ and $\Delta = 1\%$, which corresponds to NA ≈ 0.21, the spread is 49 ns per kilometer, or 4.9 ns over 100 m: too much for gigabit signals.

A graded-index core lowers the index toward the cladding, so that rays on longer paths travel through faster glass. For an optimum, near-parabolic profile the spread falls to about

$$\frac{\Delta T}{L} \approx \frac{n_1 \Delta^2}{8c}$$

smaller than the step-index value by the factor $\Delta/8$. With the same $n_1$ and $\Delta$ this is 61 ps/km, 800 times less. The result is sensitive to the exact profile, and the optimum shifts with wavelength.

Bandwidth-distance product

Because the delay spread grows in proportion to length, the usable bandwidth falls as $1/L$, and multimode fiber is rated by a bandwidth-distance product in MHz·km at a stated wavelength. On the estimates above the step-index core is limited to megahertz over a kilometer and the ideal graded-index core to gigahertz. Manufactured fibers fall short of the ideal profile and are graded by their measured bandwidth under defined launch conditions; the multimode grades and their figures are tabulated in Types of Optical Fiber. The bandwidth a link sees also depends on which modes the source excites.

Differential mode delay

Differential mode delay (DMD) is the measured form of the profile error. A short single-mode probe pulse is launched at a series of radial offsets across the core, and the arrival time of the output pulse is recorded for each offset. In a well-graded fiber the pulses from all offsets arrive together; a profile error shows up as early or late pulses at those radii. Laser-optimized fibers are specified by DMD masks, because a VCSEL excites a restricted set of modes and the link bandwidth is set by the delays among those modes.

Launch conditions and mode conditioning

Loss and bandwidth measurements on multimode fiber depend on how the power is spread among the modes at the input. An overfilled launch puts power into lossy high-order modes that leak out over the first meters, so test standards specify a controlled launch, often by the encircled flux of the output, reached with a mode scrambler or mandrel wrap. A single-mode laser launched at the center of a graded-index core excites mainly the low-order modes, where the profile is hardest to control, so single-mode transceivers run over legacy multimode cable use a mode-conditioning patch cord that offsets the launch from the axis.

Light sources and reach

Multimode links run mostly at 850 nm with VCSELs, which couple into a 50 µm core with several micrometers of tolerance. Attenuation at 850 nm is a few dB/km, mostly Rayleigh scattering, but over a few hundred meters bandwidth matters more than loss. Reach therefore shrinks as the rate per lane rises, from hundreds of meters at 10 Gb/s per lane to around 100 m at higher rates, and longer links in the same building usually move to single-mode fiber.

Common questions

How many modes does multimode fiber carry?

About $V^2/4$ for a graded-index core: roughly 340 for a 50 µm core with NA 0.20 at 850 nm and about 1,000 for a 62.5 µm core. A step-index core of the same size and NA guides about twice as many.

Why is multimode fiber limited in distance?

Its modes travel at slightly different speeds, so pulses spread in time in proportion to length. Graded-index cores reduce the spread by a factor of several hundred compared with a step-index core, but the residual spread still limits high-rate links to a few hundred meters.

References: B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019). G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010). R. Olshansky and D. B. Keck, "Pulse broadening in graded-index optical fibers," Applied Optics 15, 483 (1976). D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell System Technical Journal 52, 1563 (1973).