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 $\mathrm{\Delta }=(n_1-n_2)\mathrm{/}{n}_1$:

$$\frac{\mathrm{\Delta }\tau }{L}\approx \frac{n_1\mathrm{\Delta }}{c}=\frac{{\text{NA}}^2}{2n_{1}c}\mathrm{.}$$

For SI 50/125 multimode fiber ($n_1=1.50$, $\mathrm{\Delta }=0.013$): $\mathrm{\Delta }\tau \mathrm{/}L\approx 65$ 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:

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

a factor of $8\mathrm{/}\mathrm{\Delta }$ smaller than step-index, several hundred times for typical $\mathrm{\Delta }\approx 0.01$. For a graded-index fiber with $\mathrm{\Delta }=0.01$ this is about 0.06 ns/km.

Bandwidth-distance product. Modal dispersion limits the effective bandwidth of the fiber. For a Gaussian impulse response of rms width ${\sigma }_{\tau }$, the 3-dB optical bandwidth is:

$$\text{BW}\approx \frac{0.187}{{\sigma }_{\tau }},$$

and for the roughly rectangular spread of an overfilled step-index fiber, ${\sigma }_{\tau }=\mathrm{\Delta }\tau \mathrm{/}\sqrt{12}$, so $\text{BW}\approx 0.65\mathrm{/}\mathrm{\Delta }\tau$. That gives the bandwidth-distance product (BLP):

The step-index rows convert the delay spreads above with $\text{BW}\approx 0.65\mathrm{/}\mathrm{\Delta }\tau$. Measured step-index bandwidths are often higher, because mode coupling and the higher loss of high-order modes narrow the spread over long lengths. The graded-index rows give the specified minimum bandwidths and the rms delay spread that $0.187\mathrm{/}{\sigma }_{\tau }$ associates with them.

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. Many short-reach receivers, particularly at PAM4 lane rates, 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, 10GBASE-LRM uses electronic dispersion compensation to reach 220 m over legacy OM1/OM2 fiber, and 100GBASE-SR4 relies on RS-FEC to reach 70 m over OM3.

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 (IEC 60793-1-41) for bandwidth measurement; IEC 60793-1-49 for DMD measurement and the effective modal bandwidth calculated from it.