What is Step-index fiber? — Physics

Definition 2.13 University Physics — Year 1 · Chapter 2 — Geometric Optics: Rays, Reflection, Refraction

A step-index optical fiber is a cylindrical glass core of index $n_1$ sheathed in a cladding of slightly lower index $n_2$ . Light entering the core within a cone of half-angle $\theta_a$ around the axis is guided by successive total internal reflections at the core–cladding surface. The numerical aperture is $\mathrm{NA} = \sin\theta_a$ .

A step-index fiber. A ray entering within the acceptance cone of half-angle _a meets the cladding at incidence i ≥ i_c and is guided by total reflections; the axial ray takes the shortest route, the steepest guided ray the longest — a pulse spreads in time. — A step-index fiber. A ray entering within the acceptance cone of half-angle $\theta_a$ meets the cladding at incidence $i \geq i_c$ and is guided by total reflections; the axial ray takes the shortest route, the steepest guided ray the longest — a pulse spreads in time.

Examples

Example 2.15 (A telecom fiber’s numbers)

$n_1 = 1.480$ , $n_2 = 1.465$ : $\mathrm{NA} = \sqrt{2.190 - 2.146} = 0.21$ , $\theta_a = 12^\circ$ ; $i_c = 81.8^\circ$ , so guided rays stay within $8.2^\circ$ of the axis. Intermodal spread: $\Delta t/L = (1.48/c)(1.48/1.465 - 1) = 51\,\mathrm{ns}/\mathrm{km}$ . Over $2\,\mathrm{km}$ a pulse spreads by $0.1\,\text{µ}\mathrm{s}$ , which caps the bit rate near $5\,\mathrm{Mbit}/\mathrm{s}$ : the weekend problem follows this limitation to its remedy, the single-mode fiber.

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