Step-index fiber

A step-index fiber has a refractive-index profile $n(r)$ that takes one value $n_1$ inside the core ($r<a$) and another value $n_2<n_1$ in the cladding ($r>a$):

$$n(r)=\{\begin{array}{ll}{n}_1& r<a\\ n_2& r>a\end{array}$$

The transition between core and cladding is abrupt: a single "step" in the index profile. This contrasts with graded-index fiber, where the index varies smoothly across the core.

Standard parameters.

The index step follows from the NA, $\mathrm{\Delta }n=n_1-n_2\approx {\text{NA}}^2\mathrm{/}(2n_1)$: about 0.007 for an NA of 0.14 and 0.017 for 0.22. The 50 and 62.5 µm multimode fibers of datacom links are graded-index, not step-index. Datasheet NAs of single-mode fibers are measured from the far field and overstate the index step: for SMF-28 the index difference of about 0.36%, or 0.005, corresponds to an NA of 0.123, as the V number entry works through.

Mode structure. Step-index fibers support a discrete set of guided modes determined by the V-number:

$$V=\frac{2\pi a}{\lambda }\sqrt{n_1^2-n_2^2}\mathrm{.}$$

For $V<2.405$, only the fundamental LP01 mode propagates: the fiber is single-mode. For $V>2.405$, the LP11 mode also propagates; higher V values support additional modes (LP21, LP02, LP31, ...).

The number of guided modes in a multimode step-index fiber is approximately:

$$M\approx \frac{V^2}{2}\mathrm{.}$$

For a step-index core of 62.5 μm diameter with NA 0.275 at 850 nm, $V\approx 64$ and $M\approx 2000$ guided modes (a graded-index core of the same size and NA, such as OM1, supports about half as many, $M\approx V^2\mathrm{/}4$).

Why step-index dominates single-mode applications. Single-mode operation requires $V<2.405$, which uniquely determines the relationship between core size, NA, and operating wavelength. The step-index profile is the simplest manufacturing geometry that satisfies this: a uniformly doped core surrounded by uniformly doped cladding. There is no compelling reason to add complexity for single-mode operation.

Why step-index is suboptimal for multimode applications. For multimode operation, modal dispersion limits the bandwidth-distance product. In step-index multimode fiber:

• The fundamental mode propagates at speed $c\mathrm{/}{n}_1$
• The highest-order mode propagates at angle $\sim {\theta }_c$ from the axis, traveling a longer geometric path
• Path-length difference $\mathrm{\Delta }L=L\cdot (n_1-n_2)\mathrm{/}{n}_2$
• Pulse spreading per kilometer: $\sim 50$ ns/km for typical multimode step-index fiber

This severely limits bandwidth-distance product to roughly 10 – 100 MHz·km. Graded-index fiber largely eliminates modal dispersion by engineering all modes to have nearly equal effective group velocities, raising the bandwidth-distance product to 500 – 5000 MHz·km.

Manufacturing. Step-index single-mode fiber is fabricated by:

1. Preform fabrication: in modified chemical vapor deposition (MCVD) the core layers are deposited inside a rotating silica tube; in outside vapor deposition (OVD) and vapor axial deposition (VAD) glass soot is deposited on the outside of a rotating rod or on the end of a seed rod, building a porous preform; the typical core dopant is germanium for index raising
2. Preform collapse or consolidation: the MCVD tube is collapsed into a solid rod by heating, and OVD and VAD soot preforms are sintered into clear glass
3. Drawing: the rod is heated to 2000+ °C and pulled into a fiber on a drawing tower; outer diameter is monitored and feedback-controlled to maintain 125 μm
4. Coating: dual-layer acrylate UV coating provides mechanical protection

Production drawing speeds: 1 – 30 m/s, producing several thousand km of fiber from a single preform.

Step-index waveguide on chip. Silicon photonic waveguides are step-index by construction: silicon ($n=3.48$) core surrounded by silica ($n=1.45$) cladding. The very large index contrast ($\mathrm{\Delta }n\mathrm{/}{n}_1=0.58$) enables sub-wavelength mode confinement and tight waveguide bends (5 μm radius vs 30 mm radius for fiber). The corresponding penalty is high polarization sensitivity and significant sidewall-roughness scattering loss.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 9 (optical fibers); Snyder & Love, Optical Waveguide Theory (Chapman & Hall, 1983), Ch. 12 for the rigorous modal analysis; ITU-T G.652 for the standard SMF specification.