Optical Fiber Numerical Aperture Calculator
Calculate the numerical aperture and acceptance angle of an optical fiber from core and cladding refractive indices.
Also calculates the V-number.
Numerical Aperture (NA)
The numerical aperture (NA) of an optical fiber defines the maximum acceptance angle of light that can propagate by total internal reflection:
NA = √(n_core² − n_clad²) = sin(θ_max)
The V-number (or normalized frequency) determines how many modes can propagate: V = (2πr/λ) × NA
Where:
- NA = Numerical aperture
- n_core = Refractive index of the fiber core
- n_clad = Refractive index of the cladding
- θ_max = Half-angle of the acceptance cone (in air)
- r = Core radius
- λ = Wavelength of light
V-number interpretation:
- V < 2.405: Single-mode fiber (one light path only — best for long-distance communications)
- V > 2.405: Multi-mode fiber (many light paths — simpler but more dispersion)
Typical fiber parameters:
| Fiber type | n_core | n_clad | NA | θ_max |
|---|---|---|---|---|
| Single-mode (SMF-28) | 1.4677 | 1.4625 | 0.12 | 6.9° |
| Multi-mode (50μm) | 1.480 | 1.460 | 0.24 | 13.9° |
| Plastic optical fiber | 1.490 | 1.400 | 0.51 | 30.7° |
Why NA matters:
- Higher NA = wider acceptance cone = easier to couple light in
- But higher NA also means more modes and more dispersion (pulse spreading)
- Single-mode fiber has low NA but negligible dispersion — used for trans-oceanic cables
- Multi-mode fiber has higher NA — used for short-distance data centers and buildings