# Fiber Numerical Aperture, Acceptance Angle and V-Number Calculator

> Source: https://netray.co/tools/fiber-optic-numerical-aperture-v-number-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Compute NA, acceptance angle, relative index difference, V-number, cutoff wavelength and mode count for a step-index fiber.

## Category

engineering-plm

## Industry

Fiber Optics

## Audience

- Photonics engineer
- Fiber optic engineer
- Component design engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Core refractive index

**Key:** n1

**Type:** number

**Default:** 1.4682

**Min:** 1

**Step:** 0.0001

#### Cladding refractive index

**Key:** n2

**Type:** number

**Default:** 1.4636

**Min:** 1

**Step:** 0.0001

**Help:** Must be lower than the core index.

#### Core diameter

**Key:** dia

**Type:** number

**Default:** 8.2

**Min:** 0.1

**Step:** 0.1

**Unit:** um

**Help:** Use the physical core diameter, not the mode field diameter.

#### Operating wavelength

**Key:** wl

**Type:** slider

**Default:** 1310

**Min:** 800

**Max:** 1700

**Step:** 10

**Unit:** nm

#### Outside medium index

**Key:** n0

**Type:** number

**Default:** 1

**Min:** 1

**Step:** 0.01

**Help:** 1.00 for air.

**Outputs:**

#### Numerical aperture

**Key:** na

**Expr:** sqrt(max(0, n1 * n1 - n2 * n2))

**Format:** decimal

**Primary:** true

#### Relative index difference

**Key:** delta

**Expr:** (n1 * n1 - n2 * n2) / (2 * n1 * n1) * 100

**Format:** decimal

**Description:** Delta in percent.

#### NA / outside index

**Key:** x

**Expr:** min(1, na / n0)

**Format:** decimal

#### Acceptance half-angle

**Key:** angle

**Expr:** (x + x * x * x / 6 + 3 * pow(x, 5) / 40 + 15 * pow(x, 7) / 336) * 180 / pi

**Format:** decimal

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

#### V-number

**Key:** v

**Expr:** 2 * pi * (dia / 2) * na / (wl / 1000)

**Format:** decimal

**Primary:** true

#### Cutoff wavelength

**Key:** cutoff

**Expr:** 2 * pi * (dia / 2) * na / 2.405 * 1000

**Format:** decimal

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

#### Approximate guided modes

**Key:** modes

**Expr:** if(lt(v, 2.405), 1, v * v / 2)

**Format:** integer

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

**Chart:**

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

**Type:** line

**X:** wl

**From:** 800

**To:** 1700

**Steps:** 30

**Series:**

- v

**Disclaimer:** 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.

## Content

**Intro:** 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.

**Sections:**

#### How to use the calculator

**Body:** 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

**Body:** 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

**Body:** 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

**Body:** 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.

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

**Faq:**

#### What is the NA of standard single-mode fiber?

**Answer:** 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?

**Answer:** 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?

**Answer:** 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?

**Answer:** 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.

## Search terms

numerical aperture calculator, v number fiber calculator, fiber cutoff wavelength calculator, acceptance angle fiber, single mode condition, step index fiber calculator, core cladding refractive index, fiber mode count

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