---
title: "B-Integral calculator — AperiOptic"
description: "Accumulated nonlinear phase shift in transparent media. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/b-integral"
---

# B-Integral calculator

Accumulated nonlinear phase shift in transparent media.

Category: [Nonlinear Optics](https://aperioptic.com/calculators)

Formula: `B = (2π/λ)·n₂·I·L`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| λ | `lam` | nm | 800 |
| n₂ | `n2` | 10⁻¹⁶cm²/W | 3 |
| Intensity | `I` | GW/cm² | 10 |
| Length | `L` | mm | 5 |

## Result with the default inputs

- B: 0.1178 rad
- Risk SPM (B>3): ✓ low

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/b-integral?lam=800`](https://aperioptic.com/calculators/b-integral?lam=800). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Self-phase modulation](https://en.wikipedia.org/wiki/Self-phase_modulation)

[All optics calculators](https://aperioptic.com/calculators)

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The interactive page: https://aperioptic.com/calculators/b-integral (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt