What is numerical aperture (NA) for an optical fiber?

NA measures the range of angles over which a fiber can accept or emit light. It equals the square root of (n1² − n2²), where n1 is the core index and n2 is the cladding index. A higher NA means a wider acceptance cone but more modal dispersion.

What is the acceptance angle?

The acceptance angle (also called the half-angle of the acceptance cone) is the maximum angle at which incident light can enter the fiber and still undergo total internal reflection. It equals arcsin(NA) when measured in air.

What is the V-number and why does it matter?

The V-number (normalized frequency) is V = (π × d × NA) / λ, where d is the core diameter and λ is the wavelength. When V < 2.405 the fiber supports only one mode (single-mode); above that threshold multiple modes propagate.

What are typical refractive index values for silica fiber?

Standard single-mode silica fiber has a core index around 1.468 and a cladding index around 1.463, giving an NA of roughly 0.12. Multimode graded-index fiber (50/125 µm) typically has an NA of 0.20.

Why must n2 be less than n1?

Total internal reflection — the mechanism that guides light — only occurs when light travels from a denser medium (core, n1) to a less dense medium (cladding, n2). If n2 ≥ n1 there is no guiding and no valid NA.

Fiber NA Calculator

Name: Fiber NA Calculator
Availability: InStock
Author: Nham Vu

Enter core and cladding refractive indices to calculate NA, acceptance angle, and V-number for any optical fiber.

Fiber Parameters

Core refractive index (n₁)

Silica core: typically 1.44–1.50

Cladding refractive index (n₂)

Must be less than n₁

Optional — for V-number

Core diameter (µm)

SMF-28: 8–10 µm; OM3 multimode: 50 µm

Wavelength (nm)

Common: 850 nm, 1310 nm, 1550 nm

Results

Numerical Aperture

—

Acceptance Angle

—

half-angle in air

V-Number

—

normalized frequency

Formulas Used

1 NA = √(n₁² − n₂²)

2 Acceptance angle θ_a = arcsin(NA) [in air, n=1]

3 V-number = (π × d × NA) / λ [d and λ in same units]

4 Single-mode condition: V < 2.405

Summary