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Optical Fiber Numerical Aperture & V-Number Calculator

Optical fibers guide light through total internal reflection within a higher-index core surrounded by a lower-index cladding.

Refractive index of fiber silica core.

Refractive index of silica cladding (must be < n1).

Radius of fiber glass core (typically 4-5 µm for SMF-28).

Telecom laser wavelength (1310 nm or 1550 nm).

Calculated Result
2.000

Normalized Frequency (V-Number)

Numerical Aperture (NA)

0.1203

Acceptance Half-Angle

6.9°

Propagation Regime

Single-Mode (V < 2.405)

Guided Bound Modes

1

Calculation Breakdown

  1. NA = √(n₁² - n₂²)√(1.45² - 1.445²) = 0.1203
  2. V = (2π·a / λ) · NA2.000
  3. Mode Cutoff (V_c = 2.4048)Single-Mode Verified

What Is the Optical Fiber Numerical Aperture & V-Number Calculator?

Numerical Aperture (NA) measures the fiber light-gathering ability and cone angle.

The V-number is a dimensionless parameter combining core size, refractive index contrast, and wavelength.

How Does the Optical Fiber Numerical Aperture & V-Number Calculator Work?

Computes NA from refractive index contrast sqrt(n1^2 - n2^2).

Calculates acceptance cone half-angle theta = arcsin(NA).

Evaluates V = (2*pi*a / lambda) * NA.

Verifies single-mode operation against the Bessel function root cutoff V_c = 2.4048.

Optical Fiber Numerical Aperture & V-Number Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\text{NA} = \sqrt{n_1^2 - n_2^2}, \quad V = \frac{2\pi a}{\lambda} \text{NA}, \quad M \approx \frac{V^2}{2} \text{ (for } V \gg 2.405\text{)}

Numerical aperture light-gathering power and Maxwell electromagnetic fiber waveguide V-parameter.

How to Use the Optical Fiber Numerical Aperture & V-Number Calculator

  1. Enter core and cladding refractive indices (n1 and n2).
  2. Enter core radius in micrometers.
  3. Specify laser operating wavelength in nanometers.

Step-by-Step Example Calculation

Corning SMF-28 Telecom Fiber at 1550 nm

Input Values:

coreRefractiveIndexN1:1.45
claddingRefractiveIndexN2:1.445
coreRadiusUm:4.1
wavelengthNm:1550
Worked Steps: Standard single-mode fiber in long-haul telecommunications.

Understanding Your Result

V < 2.4048: Single-mode fiber (SMF); only fundamental LP01 mode propagates, eliminating modal dispersion.

V > 2.4048: Multi-mode fiber (MMF); supports M ~ V^2 / 2 discrete spatial propagation modes.

Factors That Affect the Result

  • Wavelength: Decreasing wavelength below cutoff increases V-number, transforming single-mode fiber into multi-mode.
  • Core radius: Larger core allows easier laser coupling but forces multi-mode operation.

When Should You Use This Calculator?

  • Fiber optic telecommunications network design and transceiver coupling.
  • Designing specialty fibers, erbium-doped fiber amplifiers (EDFA), and fiber lasers.

Assumptions & Limitations

  • Assumes step-index circular cylindrical profile under weakly guiding approximation (Delta << 1).
  • Does not model graded-index (GRIN) parabolic profiles.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard ITU-T G.652 and Snyder & Love optical waveguide formulation.

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