Fiber V Number Calculator Form
Use direct numerical aperture or derive it from refractive indices. The calculator accepts radius or diameter, converts units, and returns V number, cutoff insight, and an estimated modal count.
Formula Used
The normalized frequency, usually called the fiber V number, measures how strongly a step-index fiber guides light. It depends on core radius, wavelength, and numerical aperture.
V = (2πa / λ) × NA
NA = √(ncore2 − ncladding2)
Single-mode step-index cutoff occurs near V = 2.405
Approximate guided modes for a step-index multimode fiber: M ≈ V2 / 2
Variable meanings
- V = normalized frequency or fiber V number
- a = fiber core radius
- λ = operating wavelength
- NA = numerical aperture
- ncore and ncladding = refractive indices
How to Use This Calculator
- Enter the wavelength and select the correct wavelength unit.
- Provide the fiber core size and choose radius or diameter.
- Select whether you want to enter NA directly or derive it from refractive indices.
- Fill the graph wavelength range to study V-number variation with wavelength.
- Click the calculate button to show the result above the form.
- Review the cutoff interpretation, estimated modes, and LP11 cutoff wavelength.
- Download the generated result summary as CSV or PDF.
Example Data Table
Example values below use a fiber with 8.2 µm core diameter and NA = 0.12. Values are rounded for readability.
| Wavelength (nm) | Core Diameter (µm) | NA | V Number | Approx. Modes | Interpretation |
|---|---|---|---|---|---|
| 850 | 8.2 | 0.12 | 3.64 | 6.62 | Above LP11 cutoff |
| 1310 | 8.2 | 0.12 | 2.36 | 2.78 | Near cutoff |
| 1550 | 8.2 | 0.12 | 1.99 | 1.98 | Single-mode region |
| 1625 | 8.2 | 0.12 | 1.90 | 1.81 | Single-mode region |
Frequently Asked Questions
1) What does the fiber V number represent?
It is the normalized frequency of a fiber. It tells you how strongly the fiber guides light and whether higher-order modes are likely to propagate.
2) Why is 2.405 important?
For an ideal step-index fiber, the LP11 mode appears around V = 2.405. Values below that are generally treated as single-mode operation.
3) Can I enter diameter instead of radius?
Yes. This calculator accepts either diameter or radius. It converts diameter to radius internally before applying the V-number formula.
4) When should I enter NA directly?
Use direct NA when the manufacturer already provides it. That avoids extra refractive-index inputs and speeds up the calculation.
5) Is the estimated mode count exact?
No. The displayed mode count is an approximation commonly used for step-index multimode fibers. Real fibers can deviate because of profile shape and bending.
6) Why does V decrease when wavelength increases?
Wavelength is in the denominator of the formula. A larger wavelength reduces normalized frequency, so the fiber supports fewer modes.
7) Does this work for graded-index fibers?
The calculator is best for step-index interpretation. Graded-index fibers use related ideas, but mode behavior and counts are not described by the same simple estimate.
8) What is the LP11 cutoff wavelength?
It is the wavelength where the normalized frequency equals 2.405 for the chosen fiber geometry and numerical aperture. Longer wavelengths trend toward single-mode behavior.