Fiber optic
Light trapped inside glass by geometry alone. When a ray hits the core-cladding boundary at a shallow enough angle, it reflects completely — no light escapes. Steepen the angle past critical, and the fiber goes dark.
n₁ sin θ₁ = n₂ sin θ₂ → θc = arcsin(n₂/n₁) → total internal reflection
Snell’s law and total internal reflection
When light passes from a denser medium (higher refractive index n₁) to a less dense one (lower n₂), it bends away from the normal according to Snell’s law: n₁ sin θ₁ = n₂ sin θ₂. If the incidence angle θ₁ is large enough that sin θ₂ would exceed 1, refraction becomes impossible. Above this critical angle θc = arcsin(n₂/n₁), 100% of the light reflects back into the denser medium. This is total internal reflection — the physical principle that makes optical fibers possible.
Numerical aperture and acceptance cone
Not every ray entering a fiber will be guided. The fiber accepts light only within a cone of half-angle determined by the numerical aperture: NA = √(n₁² − n₂²). Rays entering within this cone hit the core-cladding interface at angles exceeding the critical angle and are guided by total internal reflection. Rays outside the cone strike the boundary too steeply and refract out into the cladding — they are lost.
The evanescent field
Even under total internal reflection, the electromagnetic field does not abruptly vanish at the boundary. A ghostly evanescent wave penetrates a fraction of a wavelength into the cladding, decaying exponentially with distance. This evanescent field carries no net energy away from the core (as long as the cladding is thick enough), but it plays crucial roles in fiber couplers, sensors, and near-field optics. If you bring another core close enough to intercept the evanescent field, energy can tunnel across — this is the basis of evanescent wave coupling.
Modes in an optical fiber
A thick fiber with a large core supports many different ray paths (angles), each called a mode. The lowest-order mode travels nearly straight down the axis, while higher-order modes bounce at steeper angles and travel a longer path. Because different modes arrive at different times, they cause modal dispersion — a short pulse of light spreads out as it propagates, limiting bandwidth. Single-mode fibers solve this by shrinking the core until only one mode propagates, but they require precision laser sources and alignment. Multi-mode fibers are cheaper and easier to work with over short distances.
Bending losses
When a fiber is bent, the incidence angle at the outer wall of the bend changes. For gentle bends, rays that were safely above the critical angle remain so, and loss is negligible. But if the bend radius is too tight, some rays strike the boundary below the critical angle and escape. This bending loss increases exponentially as the bend radius decreases. In practice, each fiber has a minimum bend radius below which light leaks out unacceptably. This is why fiber optic cables must be handled carefully — kinking a fiber can kill the signal.