Optical fiber, NA, single vs multimode

Optical fiber

An optical fiber is a thin strand of glass or plastic that carries light signals by total internal reflection. It has a core (index n₁) surrounded by a cladding (index n₂ < n₁).

Acceptance angle and numerical aperture

• Acceptance angle θ₀: the largest angle to the fiber axis at which a ray from air can enter the core and be guided. The cone of half-angle θ₀ is the acceptance cone.
• Numerical aperture: NA = n₀ sin θ₀ = √(n₁² − n₂²) = n₁ √(2Δ), with Δ = (n₁ − n₂)/n₁. It measures the light-collecting ability of the fiber.

   rays outside cone are lost
      \   |  /  
       \ θ0 /      ---------- cladding n2
 air    \|/  -------core n1--------> guided
 n0=1   /|\  ---------------------
       / | \

Derivation in brief: a ray with θ₁ inside the core hits the cladding boundary at 90° − θ₁. At the critical angle sin φ_c = n₂/n₁, and Snell's law at the entrance gives sin θ₀ = √(n₁² − n₂²).

Single-mode and multimode fibers