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Home/Optics & Light/Fiber: Numerical Aperture

Fiber: Numerical Aperture

Optical fibers guide light using the principle of total internal reflection, which occurs when light travels from a higher-refractive-index core into a lower-index cladding. This simulator visualizes the core concept of Numerical Aperture (NA), a single figure that quantifies the light-gathering ability and acceptance cone of an optical fiber. The NA is derived from the refractive indices of the core (n_core) and cladding (n_clad) using the equation NA = √(n_core² – n_clad²). A key learning outcome is the relationship between NA and the acceptance angle (θ_acceptance), the maximum external angle at which light can enter the fiber and still be guided. This is given by θ_acceptance = arcsin(NA), assuming the external medium is air (n_air ≈ 1). The model simplifies real fibers by assuming a perfect step-index profile, a perfectly smooth core-cladding interface, and ignores material absorption and scattering losses. By interactively adjusting n_core and n_clad, students can observe how the NA and the depicted acceptance cone change, directly linking material properties to system performance. The simulator also provides a qualitative cue for bend loss, illustrating that a high NA fiber (with a large difference between n_core and n_clad) can typically tolerate tighter bends before light leaks out, a critical consideration in fiber optic cable installation and design.

Who it's for: Undergraduate students in physics, electrical engineering, or photonics courses studying wave optics, fiber optic communications, or optical engineering principles.

Key terms

  • Numerical Aperture
  • Refractive Index
  • Total Internal Reflection
  • Acceptance Angle
  • Core and Cladding
  • Step-Index Fiber
  • Bend Loss
  • Optical Fiber

Indices

1.48
1.46
0.35

NA = √(n_core² − n_clad²) in air; sin θ_accept,max ≈ NA. Tighter bends leak power (macro-bending + mode coupling — only sketched here).

Shortcuts

  • •Compare NA to θ_accept for your index pair
  • •Bend slider only skews the drawing — see bend-loss sim for leakage

Measured values

NA0.2425
θ_accept (≈)14.03°

How it works

Step-index multimode intuition: larger NA accepts faster off-axis rays but increases dispersion. Single-mode fibers use smaller cores and NA.

Frequently asked questions

Why can't the acceptance angle be 90 degrees? Doesn't that mean all light would be accepted?
An acceptance angle of 90 degrees would require a Numerical Aperture (NA) of 1, which in turn requires n_clad = 0—a physical impossibility. The maximum theoretical NA for an air-clad fiber (n_clad=1) is √(n_core² - 1), which is still less than 1 for any real glass. In practice, NA values for communication fibers are typically between 0.1 and 0.5, creating a relatively narrow acceptance cone. This ensures light rays propagate at shallow angles, minimizing dispersion and signal distortion.
How does bend loss relate to the Numerical Aperture?
Bend loss occurs when a fiber is curved too tightly, causing guided light rays to strike the core-cladding boundary at an angle less than the critical angle, allowing them to refract out. A higher NA fiber has a larger difference between n_core and n_clad, resulting in a larger critical angle. This means the guided rays are more tightly confined, allowing the fiber to be bent more sharply before these rays escape. Low-NA fibers, used for long-distance communication, are much more susceptible to bend-induced signal loss.
Does the simulator show what happens to light that enters outside the acceptance angle?
While the primary visualization focuses on the acceptance cone, the underlying principle is that any light ray entering from air at an angle greater than θ_acceptance will refract into the core but will then strike the core-cladding boundary at an angle less than the critical angle for total internal reflection. This light will partially refract into the cladding and be lost over a short distance, representing radiation loss. The model simplifies this by showing only the cone of rays that will be successfully guided.
In real fibers, is the cladding always made of a different material than the core?
Yes. The cladding is always composed of a material (often a slightly different type of glass or polymer) with a deliberately lower refractive index than the core. This index difference is what enables total internal reflection. Sometimes this is achieved by doping the core material to increase its index. The cladding also serves a mechanical protective role and prevents surface contaminants from interfering with the light guidance at the core boundary.