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 ($r > a$):

$$n(r) \;=\; \begin{cases} n_1 & r < a \\ n_2 & r > a \end{cases}$$

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.

Fiber type	Core diameter	$\Delta n = n_1 - n_2$	NA	Use
SMF-28 (G.652)	8.2 μm	0.005	0.14	Standard single-mode telecom
Step-index multimode (50/125)	50 μm	0.013	0.20	Legacy local-area network
Step-index multimode (62.5/125)	62.5 μm	0.013	0.275	Legacy LAN (OM1)
Large-mode-area fiber	10 – 30 μm	0.001 – 0.005	0.06 – 0.10	High-power fiber lasers
Polarization-maintaining (PANDA, bow-tie)	4 – 9 μm	0.005	0.12 – 0.16	PM applications
Visible-wavelength fiber (S630-HP)	3.5 μm	0.005	0.13	633 nm HeNe systems
HI-1060	6.0 μm	0.005	0.14	1060 nm fiber lasers

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

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

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:

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

For OM1 fiber (62.5/125, $V \approx 30$ at 850 nm), $M \approx 450$ guided mode groups.

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 $c/n_1$
• The highest-order mode propagates at angle $\sim \theta_c$ from the axis, traveling a longer geometric path
• Path-length difference $\Delta L = L \cdot (n_1 - n_2)/n_2$
• 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: a silica tube has the core layer deposited inside by modified chemical vapor deposition (MCVD), outside vapor deposition (OVD), or vapor axial deposition (VAD); typical core dopant is germanium for index raising
2. Preform collapse: the tube is collapsed into a solid rod by sintering
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 ($\Delta n / n_1 = 0.58$) 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.