Optical Fibre

Fibre optics carries a signal by turning it from an electrical impulse into light, sending that light down a hair-thin strand of glass, and turning it back into an electrical signal at the far end. The strand doing the work is the optical fibre itself: a cylindrical waveguide of transparent glass or plastic that guides light along its length by total internal reflection.

Structure of an optical fibre

Every optical fibre is built from three coaxial layers, wrapped one around the next.

• Core. The innermost region, and the only one that actually carries light. Its refractive index n₁ is always greater than the cladding's n₂. Core diameter runs from 8.5 µm to 62.5 µm.
• Cladding. The layer wrapped around the core, with a refractive index n₂ that is always less than n₁. That step down in index is what confines light to the core in the first place. Cladding diameter is close to 125 µm.
• Sheath. The outermost layer, also called the protective buffer coating. It does no optical work at all — it just shields the core and cladding from abrasion and moisture. Sheath diameter runs from 250 µm to 900 µm.

Working of an optical fibre

The fibre works on total internal reflection. When light travelling through a denser medium meets the boundary with a rarer medium at an angle beyond the critical angle, none of it refracts through — all of it reflects back into the denser medium instead. Because the core's refractive index is higher than the cladding's, that condition is met readily at the core–cladding interface.

A ray entering the fibre at a suitable angle travels through the core and meets the core–cladding interface beyond the critical angle, so it reflects back into the core rather than escaping into the cladding. It crosses the core, meets the opposite interface at the same steep angle, and reflects again. The ray repeats this the entire length of the fibre — bouncing wall to wall in a zig-zag path, undergoing total internal reflection at every crossing — until it emerges from the far end with barely any of its intensity lost. That is how a signal travels long distances through glass with so little attenuation.

Not every ray that enters the fibre survives the trip, though. Only rays that meet the core–cladding interface beyond the critical angle undergo total internal reflection; anything shallower leaks straight through the cladding and is lost within the first few bounces. Whether a ray clears that threshold depends entirely on the angle at which it entered — which is exactly what the acceptance angle measures.

Acceptance angle and acceptance cone

The acceptance angle, θ₀, is the largest angle of incidence at which a ray can be launched into the fibre and still continue to propagate down its length.

θ₀ = sin⁻¹(√(n₁² − n₂²) / n₀)

Rotate that limiting ray a full turn about the fibre's axis and it sweeps out the acceptance cone: every ray landing within a full angle of 2θ₀ is accepted and guided by the fibre, and everything outside it is lost.

Acceptance cone = 2θ₀

Numerical aperture

The sine of the acceptance angle has its own name: the numerical aperture, N.A. It folds the two refractive indices into one number that says how wide a cone of light the fibre will accept.

N.A. = sin θ₀ = √(n₁² − n₂²) / n₀

Turned around, it gives the acceptance angle directly once N.A. is known:

θ₀ = sin⁻¹(N.A.)

Advantages of optical fibre

None of this would matter much if optical fibre weren't also a dramatically better way to move information than copper wire. Eleven reasons it replaced copper on almost every long-distance line:

• Wider bandwidth, more capacity. A metallic cable with 900 pairs of wires carries about 10,000 calls; a single 1 mm optical fibre carries 50,000.
• Smaller, lighter, still strong. A fibre's cross-section is only a few microns across, so it is far smaller and lighter than copper — a copper cable weighs about 1100 kg/km against roughly 6 kg/km for fibre — while staying flexible and strong.
• Not hazardous. No electric current flows through a fibre, so there is no risk of short-circuit or sparking.
• Low cost. Fibres are drawn from silica (SiO₂), one of the most abundant materials on Earth.
• Immune to EMI and RFI. Information travels as photons, which carry no charge, so electromagnetic and radio-frequency interference cannot touch a fibre signal.
• No cross-talk. Light guided inside a fibre cannot leak out, and light from outside cannot get in, so neighbouring fibres do not bleed into one another.
• Low transmission loss. A fibre loses only about 4 dB/km, which lets repeaters sit much further apart — roughly every 2 km on copper against 100 km or more on fibre.
• High temperature tolerance. Fibres keep working at temperatures up to 800 °C.
• Safe in explosive environments. With no current and no sparking, fibre can run through them without risk.
• Corrosion resistant. Water and most chemicals barely affect a fibre.
• No grounding needed.