Modal dispersion

Modal dispersion (sometimes called intermodal dispersion or inter-modal dispersion) is the broadening of optical pulses in multimode fiber caused by different guided modes propagating at different group velocities. A pulse launched into all modes of a multimode fiber arrives at the output spread out in time, limiting the maximum data rate the fiber can support.

Physical origin in step-index multimode fiber. In step-index multimode fiber, light propagates through a series of total-internal reflections at the core-cladding boundary. Light traveling closer to the fiber axis (low-order modes) takes a nearly straight path; light traveling at angles close to the critical angle (high-order modes) follows a zigzag path that is geometrically longer. Path-length difference produces arrival-time difference at the output.

For step-index fiber with relative index $\Delta = (n_1 - n_2)/n_1$:

$$\frac{\Delta\tau}{L} \;\approx\; \frac{n_1 \Delta}{c} \;=\; \frac{\text{NA}^2}{2 n_1 c}.$$

For SI 50/125 multimode fiber ($n_1 = 1.50$, $\Delta = 0.013$): $\Delta\tau/L \approx 65$ ns/km.

Graded-index reduction. A parabolic refractive-index profile (see graded-index fiber) reduces modal dispersion by compensating geometric-path differences with refractive-index velocity differences. The remaining modal dispersion in optimally-designed graded-index fiber is:

$$\frac{\Delta\tau}{L} \;\approx\; \frac{n_1 \Delta^2}{8c},$$

approximately 100× smaller than step-index. For graded-index 50/125 fiber: $\sim 0.06$ ns/km.

Bandwidth-distance product. Modal dispersion limits the effective bandwidth of the fiber. For a Gaussian-modulated pulse, the 3-dB bandwidth is:

$$\text{BW} \;\approx\; \frac{0.187}{\Delta\tau},$$

giving the bandwidth-distance product (BLP):

Fiber type	Modal dispersion	BLP
Step-index multimode 50/125	60 ns/km	5 MHz·km
Step-index multimode 62.5/125	80 ns/km	4 MHz·km
Graded-index OM1 (62.5/125)	1 – 2 ns/km	200 MHz·km at 850 nm
Graded-index OM3 (50/125)	0.1 ns/km	2000 MHz·km at 850 nm
Graded-index OM4 (50/125)	0.04 ns/km	4700 MHz·km at 850 nm
Single-mode fiber (SMF-28)	none (only LP01)	$> 10$ THz·km (limited by chromatic dispersion)

Differential mode delay (DMD). A more granular characterization of modal dispersion: for a known launch pattern, measure the arrival time of each individual modal group at the fiber output. Modern OM4 specifications include strict DMD masks specifying maximum allowed delay variation across the mode groups. Compliance with the DMD mask is essential for 10G/40G/100G short-reach operation.

Effective modal bandwidth (EMB). An updated metric for laser-launched multimode fiber (replaces the older "overfilled launch" bandwidth specification). EMB is calculated by:

1. Measuring DMD with a controlled tunable-launch source
2. Computing the effective bandwidth using a defined VCSEL spot-encircled-flux template
3. Reporting the result for 850 nm and 953 nm (for OM5 specifically)

EMB is the parameter that determines actual reach of 10G/40G/100G/400G short-reach Ethernet over OM3/OM4/OM5.

Launch conditions. Modal dispersion is sensitive to which modes are excited at the input. Different launch conditions produce different modal distributions and hence different observed dispersion:

• Overfilled launch (OFL): all modes excited equally; produces the worst-case modal dispersion
• Restricted modal launch (RML): low-order modes only; reduces effective modal dispersion
• Laser-optimized launch: encircled-flux launch matching VCSEL spot; intermediate

This is why short-reach datacom standards (10G-SR, 40G-SR4) specify launch condition along with fiber type.

Equalizing modal dispersion electronically. Modern 10G+ short-reach receivers include decision-feedback equalization (DFE) and feedforward equalization (FFE) that compensate for residual modal dispersion in OM3/OM4/OM5 fiber. This electronic equalization extends the reach of multimode fiber beyond what passive bandwidth alone supports — for example, 100G-SR4 specifies 70 m reach over OM3 but uses equalizer-enabled receivers to reach this.

Why modal dispersion does not affect single-mode fiber. Single-mode fiber supports only the fundamental LP01 mode, so by definition there is no inter-modal differential delay. Pulse broadening in single-mode fiber comes from chromatic dispersion and polarization-mode dispersion.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 9; Olshansky & Keck, Pulse broadening in graded-index optical fibers, Appl. Opt. 1976 (the foundational paper on graded-index optimization); TIA-455-204 for DMD measurement; IEC 60793-1-49 for EMB measurement.