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Fibre types and numerical aperture

Short answer

Optical fibres have a high-index core and lower-index cladding guiding light by total internal reflection. Step-index multimode (50-200 µm core) uses many zig-zag paths for short links; single-mode (8-10 µm core) has one straight path for long haul; graded-index multimode has a parabolic profile with curved rays to reduce dispersion and is used in LANs. Numerical aperture NA = sin θa = √(n1² − n2²) defines light-gathering ability.

Explain the construction and propagation mechanism and application of different types of optical fibers. Define numerical aperture.

An optical fibre has a high-index core (n1) surrounded by a lower-index cladding (n2) and a protective plastic buffer/jacket. Light is guided by total internal reflection at the core–cladding boundary for rays entering within the acceptance angle. Fibres are of three main types.

1. Step-index multimode fibre

  • Core 50–200 µm, cladding 125–400 µm; index changes in one step from n1 to n2.
  • Many modes travel in zig-zag paths of different lengths, causing large modal dispersion and low bandwidth.
  • Easy coupling with LEDs; cheap.
  • Applications: short links, sensors, illumination, plastic fibre in cars.

2. Step-index single-mode fibre

  • Core 8–10 µm, cladding 125 µm, small Δ; only one mode propagates almost along the axis.
  • No modal dispersion; highest bandwidth and lowest loss (~0.2 dB/km at 1550 nm). Needs laser sources.
  • Applications: long-haul backbones, submarine cables, FTTH.

3. Graded-index multimode fibre

  • Core index is maximum at the axis and decreases (nearly parabolically) towards the cladding; core 50/62.5 µm.
  • Rays follow curved (sinusoidal) paths. Outer rays travel further but faster, so modal dispersion is greatly reduced.
  • Applications: LANs, data centres, campus networks.
 Step MM         Single mode      Graded MM
 n1 |~~~~~|      n1 |~|           n1   /~~\
 n2_|     |_     n2_| |_          n2 _/    \_
   zig-zag         straight         curved

Numerical aperture

Numerical aperture (NA) is the light-gathering ability of a fibre, equal to the sine of the acceptance angle (for launching from air):

NA = n0 sin θa = √(n1² − n2²) ≈ n1 √(2Δ)

For example, n1 = 1.48 and n2 = 1.46 give NA = 0.24 and θa = 14°.

✓ Answer checked by Claude Opus 5.5 (high effort)

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