Fiber Numerical Aperture Calculator

Formula Used

1) Numerical aperture from refractive indices
NA = √(n₁² − n₂²)

2) Numerical aperture from acceptance half-angle
NA = n₀ sin(θ_a)

3) Relative index difference
Δ = (n₁ − n₂) / n₁
n₂ = n₁(1 − Δ)

4) V number
V = (2πa / λ) × NA

5) Output power after attenuation
P_out = P_in × 10^−(αL/10)

Here, n₁ is core index, n₂ is cladding index, n₀ is surrounding medium index, a is core radius, λ is wavelength, α is attenuation, and L is fiber length.

How to Use This Calculator

Select the calculation mode that matches your available data.
Enter the external medium index. Air is usually 1.000.
Provide core and cladding indices, or use angle or delta mode.
Add wavelength and core radius to evaluate V number and mode behavior.
Add attenuation, power, and length to estimate output power loss.
Click Calculate Fiber NA to show the result block above the form.
Use the CSV and PDF buttons to export the result summary.

Example Data Table

Case	n1	n2	n0	Wavelength (nm)	Core Radius (µm)	NA	Half-Angle (deg)
Silica multimode example	1.480	1.460	1.000	850	25	0.2425	14.03
Higher contrast design	1.500	1.470	1.000	850	31.25	0.2985	17.37
Low contrast fiber	1.460	1.455	1.000	1310	4.5	0.1207	6.93
Wide launch cone example	1.490	1.400	1.000	650	50	0.5100	30.66

These examples are provided for learning, comparison, and quick testing of the page layout and export tools.

Frequently Asked Questions

1) What does numerical aperture represent?

Numerical aperture measures the light-gathering ability of a fiber. A larger value means the fiber can accept rays over a wider entrance cone and is usually easier to couple with light sources.

2) Why must the core index be larger than the cladding index?

Total internal reflection happens only when light travels from a higher-index core toward a lower-index cladding. If the cladding index equals or exceeds the core index, guided propagation will not occur as expected.

3) Is the acceptance angle measured from the axis or the surface?

In fiber optics, the acceptance half-angle is measured from the fiber axis. The full acceptance cone is simply twice that half-angle.

4) Why does the surrounding medium matter?

The surrounding medium changes the launch condition because the relation becomes NA = n0 sin(θa). Air, water, and immersion fluids can give different acceptance angles for the same fiber.

5) What is the V number used for?

The V number helps classify whether the fiber operates in a single-mode or multimode regime. It also supports quick estimates of the number of guided modes.

6) Does a higher numerical aperture always mean better performance?

Not always. Higher NA improves coupling tolerance, but it can also increase modal dispersion in multimode fibers. The best value depends on your source, distance, bandwidth target, and system design.

7) Why does the calculator estimate output power?

NA alone does not describe transmission loss. Adding attenuation and length gives a practical view of how much launched optical power may remain after the fiber span.

8) Why are there CSV and PDF exports?

They help save results for reports, lab notes, classroom exercises, and design comparisons. CSV is useful for spreadsheets, while PDF is convenient for printable summaries.