V number calculator

Normalized Frequency (V)
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Enter parameters above
Cut-off Wavelength (λc)
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Single-mode limit (V = 2.405)

How it works?

The V-Number (or normalized frequency) is a dimensionless parameter that determines the number of modes a step-index fiber can support. It relates the fiber's physical geometry and refractive indices to the wavelength of light.

$$V = \frac{2 \pi a}{\lambda} \sqrt{n_{core}^2 - n_{clad}^2}$$


$$\text{Or using NA: } V = \frac{2 \pi a}{\lambda} \times \text{NA}$$

Where:

  • V is the normalized frequency (V-Number).
  • a is the core radius of the fiber (half the core diameter).
  • \(\lambda\) is the vacuum wavelength of the light.
  • \(n_{core}\) is the refractive index of the fiber core.
  • \(n_{clad}\) is the refractive index of the cladding.
  • NA is the Numerical Aperture.

The critical cutoff value is 2.405. If the calculated V-Number is less than 2.405, the fiber supports only a single mode (Single-Mode Operation). If V > 2.405, the fiber becomes Multi-Mode, supporting multiple propagation paths.

Why calculate the V-Number?

Key Takeaways
  • Single-Mode Limit: Determines the exact wavelength where a fiber stops being single-mode.
  • Mode Count: Estimates how many optical modes can travel through a multi-mode fiber.
  • Bend Sensitivity: Low V-numbers (< 1.5) indicate weak guidance and high susceptibility to bending loss.
  • Design Control: Essential for tailoring core size and NA during fiber fabrication.

The "Normalized Frequency" of Fiber Optics

The V-Number (V) is arguably the most critical parameter in fiber optics because it acts as a gatekeeper. It tells you, with a single number, how light behaves inside the core. It combines the three main variables of a fiber: core radius ($a$), numerical aperture ($NA$), and wavelength ($\lambda$).

The magic number is 2.405. If your calculated V is below this threshold, physics dictates that only the fundamental mode ($LP_{01}$) can propagate. Above this number, higher-order modes enter the equation, introducing modal dispersion and signal distortion.

Critical Applications

1. Cutoff Wavelength Calculation

The "cutoff" is simply the wavelength where V = 2.405. Operating below this wavelength risks multi-mode noise; operating too far above it risks high bend loss.

2. Multi-Mode Capacity

For large-core fibers (where V >> 2.405), the number of modes can be approximated as $M \approx V^2 / 2$. This is vital for calculating data capacity in MM fibers.

3. Evanescent Field Power

As V decreases (e.g., V < 1.5), the mode spreads significantly into the cladding. This is used in fiber sensors to detect changes in the external environment.

4. Dispersion Engineering

The V-number determines the waveguide dispersion component. By tuning V (changing core size), engineers can shift the zero-dispersion wavelength.

The Single-Mode Rule

For standard step-index fibers:

V < 2.405: Single-Mode Operation (Purest signal, no modal dispersion).
V > 2.405: Multi-Mode Operation (Higher power handling, but signal spreads over time).

Want to learn more?

Deep Dive Article V-Number in Optical Fibers: The Complete Guide

Learn the derivation, see real-world examples, and understand how V-number dictates fiber cut-off wavelength.

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