Fiber material dispersion calculator
Estimate how much a light pulse spreads in glass fiber: a dispersion of 17 ps/(nm·km), a 2 nm wide source and 10 km of fiber widen each pulse by 340 ps. Compare that figure with the time each bit has. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Dispersion parameter
- 17
- Spectral width
- 2
- Fiber length
- 10
- Spectral width nm
- 2
- Fiber length km
- 10
- Abs dispersion
- 17
- Pulse broadening ps
- 340
Material dispersion spreads optical pulses because different wavelengths in a source spectrum travel at slightly different group velocities inside the glass. The first-order estimate of that temporal broadening is a simple product: absolute value of the material dispersion parameter times spectral width times fiber length. This fiber material dispersion calculator takes D in picoseconds per nanometre per kilometre, Δλ in nanometres, and L in kilometres, then returns the pulse broadening in picoseconds with a stable formula string for logs and homework. Telecom link budgets, university fiber labs, and laser-diode source comparisons all need the same closed form before they open full nonlinear or waveguide simulators.
What material dispersion pulse broadening means in fiber
Inside silica and other optical glasses the refractive index depends on wavelength, so the group delay per unit length also depends on wavelength. When a source is not monochromatic, spectral components accumulate different delays and the pulse envelope stretches in time. The industry first-order model packages that effect into a dispersion parameter D, usually quoted in picoseconds of delay change per nanometre of wavelength change per kilometre of fiber.
Multiplying the absolute value of D by the source spectral width Δλ and the span length L yields the expected material-dispersion contribution to pulse broadening: Δt equals |D| times Δλ times L. Positive D is often called the normal dispersion region; negative D is the anomalous region used in many soliton and compensation discussions. For a broadening magnitude the sign cancels, which is why this calculator uses |D|.
The model ignores waveguide dispersion (which can cancel or add to material dispersion in real single-mode fiber), polarization-mode dispersion, self-phase modulation, and higher-order dispersion slopes. It is the textbook and link-budget estimate you want when D, linewidth, and length are already known from a data sheet or a homework statement, not a full GVD solver from Sellmeier coefficients.
Where teams use this estimate in practice
Optical communications courses assign endless problems that ask for material-dispersion pulse spread from a catalog D, a laser or LED spectral width, and a link length; a single trusted oracle speeds grading and lab prep. Access-network and metro planners compare that picosecond figure against bit-period budgets before they decide whether dispersion compensation, narrower sources, or shorter regenerator spacing is required. Component vendors publish D curves versus wavelength and want a transparent product of D, Δλ, and L in marketing calculators and application notes.
Instrumentation groups estimate how much a broadband ASE source will stretch after a spool of fiber when designing OTDR, sensing, or nonlinear optics benches.
What you can do with it
Telecom link pulse-budget estimates
Multiply |D|, source spectral width, and span length to get picosecond material-dispersion broadening before comparing against bit-period margins.
Fiber lab and homework answer keys
Return a deterministic Δt from textbook D, Δλ, and L so teachers, students, and auto-graders share one ground truth.
FAQ
What formula does the fiber material dispersion calculator use?
It uses the first-order material dispersion broadening Δt = |D| · Δλ · L, with D in ps/(nm·km), Δλ in nm, L in km, and Δt in picoseconds.
Why is the absolute value of D used?
D can be positive (normal) or negative (anomalous). Pulse envelope broadening from first-order dispersion depends on the magnitude |D|, so the calculator multiplies |D| by spectral width and length.
What units do I need to use?
Use D in ps/(nm·km), spectral width in nm, and fiber length in km. Convert metres to kilometres before calling if your drawings use m.
Does this include waveguide dispersion or PMD?
No. This capability returns only the material-dispersion product |D|·Δλ·L. Waveguide dispersion, polarization-mode dispersion, and nonlinear effects require separate models and inputs.
How can I reduce pulse broadening from material dispersion?
The spread grows in step with the source spectral width and the fiber length, so a narrower source or a shorter span reduces it. Planners also weigh dispersion compensation or closer regenerators when the figure is too large.
Related tools
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
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/fiber-material-dispersion \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"dispersion_parameter":17,"spectral_width":2,"fiber_length":10}'const res = await fetch("https://api.kit.forhosting.com/optics/fiber-material-dispersion", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"dispersion_parameter": 17,
"spectral_width": 2,
"fiber_length": 10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/optics/fiber-material-dispersion",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"dispersion_parameter": 17,
"spectral_width": 2,
"fiber_length": 10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/fiber-material-dispersion", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"dispersion_parameter":17,"spectral_width":2,"fiber_length":10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"dispersion_parameter":17,"spectral_width":2,"fiber_length":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/fiber-material-dispersion", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"dispersion_parameter": 17,
"spectral_width": 2,
"fiber_length": 10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "optics.fiber_material_dispersion",
"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
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. |
Technical notes
Inputs, units, outputs, and validation rules
All three must be finite. D may be positive, negative, or zero—zero simply returns zero broadening. Send three numbers: dispersion_parameter D in ps per nm per km, spectral_width Δλ in nanometres, and fiber_length L in kilometres. Spectral width and length must be strictly positive; zero or negative values fail with invalid_input because they do not define a physical first-order spread for this product formula. Common aliases such as D, D_m, dispersion, delta_lambda, spectral_width_nm, linewidth, L, length_km, and fiber_length_km are accepted so scripts written against textbook notation do not need a rename layer. On success the response echoes cleaned dispersion_parameter, spectral_width_nm, and fiber_length_km, returns abs_dispersion as |D|, returns pulse_broadening_ps as |D| times Δλ times L, includes the formula string Δt equals |D| times Δλ times L, and a unit_note that documents the picosecond result. Classic checks include standard single-mode fiber near seventeen picoseconds per nanometre-kilometre with a two-nanometre LED-like width over ten kilometres, a narrower laser diode linewidth over a longer span, and a zero-length or zero-width case as the mandatory invalid_input path. Pricing for a successful analytic call is a flat $0.002 per item; missing fields, non-numeric strings, NaN, Infinity, and non-positive Δλ or L do not charge.
Where teams use this estimate in practice
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance. Prefer this endpoint when you already have D, spectral width, and length and need a reviewable closed form—not a Sellmeier glass model, not a full chromatic-dispersion map of a transmission fiber, and not PMD or nonlinear pulse-propagation solvers, which need different inputs and belong on separate landings.
Integration use cases
Source linewidth trade-off scripts
Batch-call the API across LED versus laser spectral widths and fiber lengths to chart material-dispersion limits without spreadsheets.
Technical questions
How much does each API call cost?
$0.002 per successful request. The browser tool above runs free locally; the API draws from your prepaid KIT balance only when the task succeeds.