Numerical Aperture Calculator

Core Refractive Index (n_core)

Index

Cladding Refractive Index (n_clad)

Index

Numerical Aperture (NA)

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Enter values above

Acceptance Angle (θ_a)

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Max angle for light coupling (in Air)

How it works?

The Numerical Aperture (NA) is a dimensionless number that characterizes the range of angles over which an optical system can accept or emit light. In optical fibers, it quantifies the "light-gathering ability" of the fiber based on the refractive index difference between the core and the cladding.

$$ \text{NA} = \sqrt{n_{\text{core}}^2 - n_{\text{clad}}^2} $$

$$ \text{Also: } \text{NA} = \sin(\theta_{max}) $$

Where:

NA is the Numerical Aperture.
$ n_{\text{core}} $ is the refractive index of the fiber core.
$ n_{\text{clad}} $ is the refractive index of the cladding.
$\theta_{max}$ is the maximum acceptance angle (half-angle).

For light to be guided via Total Internal Reflection (TIR), the core index ($n_{core}$) must be strictly greater than the cladding index ($n_{clad}$). A higher NA means the fiber can accept light from a wider cone of angles, but it also typically results in higher modal dispersion in multi-mode fibers.

Why calculate Numerical Aperture?

Why this matters

Light Collection: Determines how much light a fiber or lens can physically capture.
Resolution Limit: A higher NA lens can resolve finer details (diffraction limit).
Coupling Efficiency: Critical for matching a laser source to a fiber to avoid signal loss.
Depth of Field: High NA means a tighter focus but a shallower depth of field.

The "Acceptance Cone" of Optics

The Numerical Aperture (NA) is essentially the measure of an optical component's "mouth." It defines the cone of angles within which light can enter or exit the system. For an optical fiber, it is derived from the refractive index contrast between the core and the cladding.

In simpler terms: A high NA means the fiber or lens is "wide open" and can accept light from steep angles. A low NA means it is "narrow" and highly selective, only accepting light that comes in nearly straight.

Critical Applications

1. Fiber Optic Splicing

When joining two fibers, their NAs must match. If you splice a low-NA fiber into a high-NA fiber, you lose light because the second fiber cannot "capture" all the angles coming from the first.

2. Microscopy Resolution

In microscopes, resolution is defined by λ / (2 · NA). To see smaller bacteria or cell structures, you don't just need magnification; you need a higher NA objective lens.

3. Laser Power Density

High NA lenses focus light to a smaller spot size. This is crucial for laser cutting and surgery, where you need maximum intensity (irradiance) at the focus point.

4. Sensor Sensitivity

Fiber optic sensors often use high-NA fibers to capture more scattered light (fluorescence or Raman signal) from the sample, improving signal-to-noise ratio.

The NA Trade-off

High NA (> 0.5): Captures more light and focuses tighter, but has a very short working distance and depth of focus.

Low NA (< 0.2): Captures less light but maintains a long, collimated beam over greater distances (ideal for telecom).

Deep Dive Article Numerical Aperture: The Physics of Light Collection Understand acceptance angles, see the math behind the derivation, and learn why NA is the limit of optical resolution.

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