Fiber Optics: How Total Internal Reflection Guides Light

simulator intermediate ~10 min
Loading simulation...
NA = 0.242, critical angle 80.6°

With core index 1.48 and cladding index 1.46, the fiber has NA 0.242 and a critical angle of 80.6°. Light entering within 14° of the fiber axis will propagate via total internal reflection.

Formula

θ_c = arcsin(n₂ / n₁)
NA = √(n₁² − n₂²)
θ_acceptance = arcsin(NA)

Light Trapped in Glass

Optical fibers guide light through a simple but elegant mechanism: total internal reflection. When a light ray inside the glass core strikes the core-cladding boundary at an angle steeper than the critical angle, it bounces back completely rather than passing through. This critical angle depends on the ratio of refractive indices — and it's the reason light can travel hundreds of kilometers through a hair-thin glass strand with remarkably low loss.

Numerical Aperture and Acceptance Cone

The numerical aperture of a fiber determines which rays can successfully enter and propagate. NA equals the square root of (n₁² − n₂²), and it defines the maximum acceptance half-angle via θ = arcsin(NA). Rays entering at steeper angles refract out through the cladding and are lost. This simple geometry governs how efficiently light couples from a source into the fiber.

Single-Mode vs Multi-Mode

When the core is large enough (typically > 50 µm), many different ray paths — modes — can propagate simultaneously. Each mode travels a slightly different effective distance, causing pulse spreading called modal dispersion. Shrinking the core to about 8 µm forces only the fundamental mode to propagate, eliminating modal dispersion and enabling data rates of terabits per second over hundreds of kilometers.

Real-World Fiber Networks

The global internet backbone runs on single-mode silica fibers operating at 1550 nm, where attenuation drops to just 0.2 dB/km. Wavelength-division multiplexing packs hundreds of independent channels into a single fiber, each carrying 100+ Gbps. Submarine cables spanning ocean floors carry over 99% of intercontinental data traffic — a testament to the power of total internal reflection at scale.

FAQ

How does total internal reflection work in fiber optics?

When light travels from a denser medium (core, n₁) to a less dense medium (cladding, n₂) at an angle exceeding the critical angle, it reflects completely back into the core. This critical angle equals arcsin(n₂/n₁). By bouncing between the core-cladding boundary, light propagates along the fiber with minimal loss.

What is numerical aperture in fiber optics?

Numerical aperture (NA) describes the cone of light a fiber can accept. It equals √(n₁² − n₂²), where n₁ and n₂ are the core and cladding refractive indices. Higher NA means the fiber accepts light from wider angles but also supports more propagation modes.

What is the difference between single-mode and multi-mode fiber?

Single-mode fiber has a tiny core (~8–10 µm) that permits only one light mode, eliminating modal dispersion. Multi-mode fiber has a larger core (50–200 µm) carrying many modes, which is cheaper but suffers from pulse spreading over long distances.

Why do optical fibers lose signal over distance?

Signal attenuation comes from Rayleigh scattering (intrinsic to the glass), absorption by impurities (especially OH ions), and bending losses. Modern single-mode fibers achieve as low as 0.2 dB/km at 1550 nm, allowing signals to travel 80+ km without amplification.

Sources

Embed

<iframe src="https://homo-deus.com/lab/optics-instruments/fiber-optics/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub