ForHosting KIT · Developer Utilities

Single-mode fiber cutoff wavelength calculator

This single-mode fiber cutoff wavelength calculator finds the wavelength above which an ideal weakly guiding step-index optical fiber supports only its fundamental guided mode.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Enter the core radius in metres and the dimensionless numerical aperture. The calculator uses the normalized-frequency boundary Vc = 2.405, evaluates the corresponding cutoff wavelength, and reports it in metres, micrometres, and nanometres. It is useful for fiber selection, classroom exercises, specification checks, and quick design estimates where a deterministic result is more helpful than a full numerical mode solver.

Connect cutoff wavelength to the fiber V-number

A step-index fiber confines light because its core refractive index is slightly greater than its cladding refractive index. The normalized frequency, commonly called the V-number, combines the three quantities that control its guided-mode behavior: core radius a, numerical aperture NA, and vacuum wavelength lambda. Its definition is V = 2 pi a NA divided by lambda. As wavelength increases, V decreases. The fundamental LP01 mode has no lower cutoff, but the next mode group begins at approximately V = 2.405 under the weak-guidance approximation. Setting the fiber V-number equal to that boundary and rearranging gives lambda_c = 2 pi a NA divided by 2.405. For wavelengths greater than lambda_c, V is less than 2.405, so only the fundamental guided spatial mode remains in this ideal model. At wavelengths below lambda_c, the model permits higher-order modes, although whether they are appreciably excited also depends on launch conditions, bends, fiber length, and imperfections. This calculator focuses on the conventional design boundary, not on the measured attenuation of every individual mode.

Enter radius and numerical aperture without unit mistakes

Supply the core radius, not the core diameter, in metres. A specification that lists an 8.2 micrometre core diameter therefore corresponds to a radius of 4.1 micrometres, or 4.1e-6 metres. Accidentally entering the diameter doubles the calculated cutoff wavelength. Numerical aperture is dimensionless and is normally given directly by the fiber data sheet; enter 0.14 as 0.14, not as 14 percent or 14. The solver accepts only finite positive values and limits numerical aperture to one, preventing outputs based on a zero radius, negative geometry, or an implausible NA outside this contract. The response repeats the cleaned inputs and returns the same cutoff in metres, micrometres, and nanometres, making it easy to compare the answer with telecom windows or component data sheets. The calculation uses a fixed cutoff V-number of 2.405 and twelve-significant-digit normalization for reproducible JSON. It performs no unit guessing: convert micrometres, millimetres, or other radius units to metres before calling the capability. Keeping that conversion explicit makes automated spreadsheets, test fixtures, and API integrations easier to audit.

Interpret the boundary and know the model limits

Treat the reported value as the conventional theoretical cutoff for a circular, weakly guiding step-index fiber. Operation above the result means the normalized frequency is below 2.405 and the ideal guide supports only the fundamental spatial mode. Operation exactly at the boundary is a mathematical threshold, so practical designs normally include margin rather than choosing a source wavelength equal to the rounded cutoff. Real manufacturers may publish a measured cable cutoff wavelength or fiber cutoff wavelength obtained under standardized bend and length conditions; those values can differ from this simple estimate because higher-order modes may leak away, bends modify confinement, refractive-index profiles are not perfectly abrupt, and production tolerances change radius and NA. The formula is also not a substitute for a vector mode solver for high-index-contrast waveguides, noncircular cores, photonic-crystal fibers, graded-index fibers, or few-mode devices. Use it for first-pass design, education, and sanity checking, then compare critical deployments with the manufacturer specification and the relevant measurement standard. The browser calculation is free, while each successful automated API item uses the published base price of $0.002.

What you can do with it

Check a telecom fiber design

Estimate whether a proposed core radius and numerical aperture place the cutoff below the intended operating wavelength.

Verify a data-sheet value

Compare the simple V-number prediction with a manufacturer's specified cutoff and investigate large discrepancies.

Build optics exercises

Generate reproducible answers for lessons about normalized frequency, mode cutoff, and single-mode operation.

FAQ

What equation does the calculator use?

It sets V = 2 pi a NA / lambda equal to the conventional LP11 cutoff Vc = 2.405 and solves lambda_c = 2 pi a NA / 2.405.

Should I enter core radius or diameter?

Enter core radius in metres. Divide a stated core diameter by two, then convert that radius to metres.

Is the fiber single-mode above or below the result?

In the ideal weakly guiding step-index model, wavelengths above the cutoff support only the fundamental guided spatial mode; wavelengths below it can support higher-order modes.

Why can a manufacturer's cutoff specification differ?

Measured cutoff depends on fiber length, bends, launch conditions, index-profile details, and test definitions. This calculator gives the ideal V-number estimate.

How much does an API calculation cost?

A successful API item uses the published base price of $0.002. The browser calculator is free to run.

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/optics/single-mode-cutoff-wavelength

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/optics/single-mode-cutoff-wavelength \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"core_radius_m":0.0000041,"numerical_aperture":0.14}'

const res = await fetch("https://api.kit.forhosting.com/optics/single-mode-cutoff-wavelength", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "core_radius_m": 0.0000041,
    "numerical_aperture": 0.14
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/optics/single-mode-cutoff-wavelength",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "core_radius_m": 0.0000041,
    "numerical_aperture": 0.14
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/single-mode-cutoff-wavelength", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"core_radius_m":0.0000041,"numerical_aperture":0.14}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"core_radius_m":0.0000041,"numerical_aperture":0.14}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/single-mode-cutoff-wavelength", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "core_radius_m": 0.0000041,
  "numerical_aperture": 0.14
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "optics.single_mode_cutoff_wavelength",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Read the full KIT documentation →