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Fiber Numerical Aperture, Acceptance Angle and V-Number Calculator

Numerical aperture sets how much light a fiber can accept, and the V-number tells you whether it guides one mode or many. This calculator works both out from the refractive indices, core size and wavelength of a step-index fiber.

Your numbers

Core refractive index

Cladding refractive index

Must be lower than the core index.

Core diameter

Use the physical core diameter, not the mode field diameter.

Operating wavelength

1,310 nm

Outside medium index

1.00 for air.

Your results

Numerical aperture

0.1161

V-number

2.2837

Relative index difference

0.3128

Delta in percent.

NA / outside index

0.1161

Acceptance half-angle

6.6688

Degrees, from a series approximation of asin(NA/n0); accurate for NA below about 0.5.

Cutoff wavelength

1,243.9265

Nanometres. Single-mode operation requires wavelengths above this value (theoretical step-index cutoff).

Approximate guided modes

Step-index estimate; a graded-index core carries about half as many.

Step-index model. Real fibers use graded-index or complex profiles, and the cabled cutoff wavelength is lower than the fiber cutoff. Use measured values per ITU-T G.650.1 for specification.

Save results:

V-number vs wavelength (single-mode below 2.405)

Sweeps Operating wavelength from 800 to 1700, holding your other inputs fixed.

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How to use the calculator

Enter the core and cladding refractive indices, the core diameter and the wavelength you plan to run. The tool returns the numerical aperture, the acceptance half-angle in air, the relative index difference, the V-number, the theoretical cutoff wavelength and an estimate of how many modes the core supports. The wavelength slider and chart show how the V-number falls as wavelength increases, with the single-mode threshold at 2.405.

Formulas

Numerical aperture is NA = sqrt(n1 squared minus n2 squared). The acceptance half-angle is asin(NA / n0). The V-number is V = 2 x pi x a x NA / lambda, where a is the core radius. A step-index fiber is single-mode when V is below 2.405, so the cutoff wavelength is lambda_c = 2 x pi x a x NA / 2.405. The mode count is approximately V squared over 2 for a step-index core and V squared over 4 for a parabolic graded-index core.

Worked example

A core of 1.4682 with cladding of 1.4636 gives NA = 0.116 and a relative index difference of 0.31 percent. With an 8.2 micron core at 1310 nm, V = 2.28, so the fiber is single-mode and the theoretical cutoff is near 1244 nm. At 850 nm the same fiber has V = 3.5 and would guide a few modes, which is why single-mode fiber is not used with 850 nm VCSEL optics. A 50 micron OM4 core with NA 0.2 has V of about 37 at 850 nm.

Common mistakes

Do not confuse core diameter with mode field diameter, which is larger and is what splice and bend loss depend on. Specified cabled cutoff wavelength is measured on a cable and is lower than the fiber cutoff, so a fiber that fails at the fiber level may still be compliant with G.652 in cable form. Also, the series used for the acceptance angle should not be trusted for large NA values above about 0.5.

Frequently Asked Questions

What is the NA of standard single-mode fiber?

About 0.12 to 0.14. This corresponds to a relative index difference of roughly 0.3 to 0.4 percent between core and cladding, with a core diameter near 8 to 9 microns.

What does V below 2.405 mean?

It is the single-mode condition for a step-index fiber, where only the fundamental LP01 mode is guided. Above 2.405 higher-order modes appear and the fiber supports more than one mode.

Is the cutoff wavelength the same as the cabled cutoff?

No. Fiber cutoff is higher than cabled cutoff because bends and cabling strip the higher-order mode. G.652 specifies a maximum cabled cutoff of 1260 nm.

Does a larger NA mean a better fiber?

Not necessarily. A larger NA collects more light and tolerates bends better but increases modal dispersion in multimode fiber and reduces the cutoff wavelength margin in single-mode fiber.

Netray can help structure engineering data like fiber specifications so it is available alongside items and suppliers in your ERP.

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