Calculate the numerical aperture (NA) that tells you how much light an optical fiber can gather. Change the core and cladding refractive indices, the core diameter and the wavelength to see the acceptance angle, V-number and mode count update in real time, and feel where the single-mode / multimode boundary lies.
Parameters
Core refractive index n₁
Refractive index of the central core glass (higher than the cladding)
Cladding refractive index n₂
Refractive index of the cladding around the core (lower than the core)
Core diameter d
µm
Diameter of the core through which light travels
Wavelength λ
nm
Wavelength of the transmitted light (850/1310/1550 nm are typical)
Results
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Numerical aperture NA
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Acceptance half-angle (°)
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Index difference Δ (%)
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V-number
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Mode count (approx.)
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Fiber type
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Optical fiber section — total internal reflection & acceptance cone
Rays entering shallower than the acceptance angle travel down the core by total internal reflection. A too-steep ray (red) leaks into the cladding and is lost.
Numerical aperture NA and V-number V. n₁: core index, n₂: cladding index, d: core diameter, λ: wavelength. The fiber is single-mode for V below 2.405 and multimode above it.
Acceptance half-angle θ_a and relative index difference Δ. θ_a is the half-angle of the cone accepted at the input face; Δ measures the index gap between core and cladding.
$$M\approx\frac{V^{2}}{2}\quad(V\geq 2.405)$$
Approximate number of guided modes M of a multimode fiber. A larger V supports more modes and produces more modal dispersion.
What is the Optical Fiber Numerical Aperture?
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An optical fiber is a strand of glass as thin as a hair, right? How does light travel kilometres inside it without leaking out?
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The mechanism is surprisingly simple. A fiber is a two-layer structure: a glass "core" of slightly higher refractive index, wrapped in a "cladding" of slightly lower index. When light travelling inside the core strikes the core-cladding boundary at a shallow enough angle, "total internal reflection" happens — the light is reflected perfectly, with no loss at all — so it zig-zags down a mirror tunnel and stays trapped for kilometres.
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So is every ray I shine into the end face trapped inside?
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No — and that is the key point. A ray entering at too steep an angle strikes the boundary too steeply as well, fails to reflect, and escapes into the cladding, where it is lost. In other words there is an upper limit on the input angle that can be captured. The half-angle of that cone is called the "acceptance angle", and the single number that captures the width of the cone — the light-gathering power — is the "numerical aperture (NA)". Move the core and cladding indices on the left: the bigger their difference, the bigger the NA and the wider the acceptance cone.
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I see. So a bigger NA lets in more light — that's just better, right?
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It isn't that simple. A larger NA does make it easier to scoop up light from a divergent source like an LED, which is a real win for coupling. But there is a price. The bigger the NA, the bigger another number, the "V-number", becomes — and that increases the number of "modes", the distinct light paths the fiber supports. Move the core diameter on the chart below and watch V climb steeply.
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What goes wrong when there are more modes?
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If there are several paths, each has a slightly different length. So even when you send in one pulse — one packet of light signal — the fast modes arrive ahead of the slow ones, and the pulse spreads out at the exit. This is "modal dispersion", the great enemy that limits the speed and reach of a link. Once V drops below 2.405 the fiber has just one light path — a "single-mode fiber". With one path there is no modal dispersion, which is why long-distance, high-capacity backbones use single-mode fiber.
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Then is multimode fiber, with its many paths, of no use?
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Far from it. Multimode fiber has a large core (50 or 62.5 microns), so launching light, splicing connectors and aligning axes are all much easier. For short runs inside a data centre or a building, the distance is short, so modal dispersion barely matters, and the easy, cheap installation wins. So "single-mode for long haul, multimode for short haul" — choosing by application while watching NA and V — is the starting point of every fiber-optic design.
Frequently Asked Questions
The numerical aperture is NA = √(n₁² − n₂²), where n₁ is the core refractive index and n₂ is the cladding refractive index. The NA is a dimensionless number that measures the width of the light cone the fiber accepts at its input face — its light-gathering power — and it grows with the index difference between core and cladding. The acceptance half-angle is θ = arcsin(NA); only light arriving from air at a shallower angle than this is captured and guided inside the core.
The V-number is the dimensionless quantity V = (π·d/λ)·NA, where d is the core diameter and λ the wavelength. It combines the numerical aperture, the core size and the wavelength into a single value, and it determines how many modes — distinct light paths — the fiber can support. If V is below 2.405 the fiber carries only one mode and is single-mode; at or above 2.405 it is multimode. The mode count of a multimode fiber can be estimated roughly as V²/2.
A single-mode fiber has V below 2.405 and carries just one light path, so it has no modal dispersion and is used for long-distance, high-capacity links. Its core is small (about 9 µm), which makes coupling and splicing harder. A multimode fiber has V at or above 2.405 and carries many modes; its core is large (50 to 62.5 µm), which makes coupling to a source and alignment far easier, but because the modes travel slightly different path lengths a pulse spreads out, limiting bandwidth and reach.
Not necessarily. A larger numerical aperture widens the acceptance cone, making it easier to collect light from a divergent source such as an LED. But a larger NA also raises the V-number, and in a multimode fiber that means more modes and stronger modal dispersion, which reduces bandwidth. For long-distance, high-speed links a small-NA single-mode fiber is used, while for short links where easy coupling matters most a large-NA multimode fiber is preferred. The choice depends on the application.
Real-World Applications
Long-haul communication backbones: Intercontinental submarine cables and city-to-city backbone links use single-mode fiber with a small numerical aperture (roughly 0.12 to 0.14). With a core of about 9 µm and V kept at or below 2.405, the fiber is restricted to a single mode and modal dispersion is eliminated. The low-loss 1310 nm and 1550 nm bands are chosen for the wavelength, and the choice of NA and wavelength directly governs the achievable transmission distance.
Data centres and premises cabling: Short links between servers and between floors are dominated by 50 µm multimode fiber (OM3/OM4/OM5). The larger NA and wider core make coupling to inexpensive VCSEL sources and aligning connectors easy, lowering installation cost. Over a few hundred metres modal dispersion has little effect, so the ease of handling multimode fiber wins.
Sensors, instrumentation and industrial use: In fiber-optic sensors and the illumination or image guides of endoscopes, performance is set by how much light can be collected. For pairing with divergent sources such as LEDs and lamps, high-NA fiber with a wide acceptance cone (NA 0.2 to 0.5) is chosen. Computing the acceptance angle is the starting point for estimating the coupling efficiency between source and fiber.
Optical component design and coupling efficiency: When connecting a laser diode or LED to a fiber, the radiation angle of the source is compared with the acceptance angle of the fiber to estimate what fraction of the light couples in. Light radiated wider than the acceptance angle cannot be captured and becomes loss. NA and acceptance-angle estimates like this tool are used routinely as a pre-study for lens-system design and fiber selection.
Common Misconceptions and Pitfalls
A common misconception is that "the numerical aperture is set by the thickness of the fiber". The numerical aperture NA = √(n₁² − n₂²) depends only on the core and cladding refractive indices and has nothing to do with the core diameter. Core diameter enters through the V-number instead: only when NA, core diameter and wavelength come together in V = (π·d/λ)·NA is the mode count fixed. "Thicker fiber = higher NA" is false. Treat NA and core diameter as separate design parameters.
Next, the assumption that "whether a fiber is single-mode or multimode is decided by the fiber alone". The same fiber changes its mode count with the wavelength used, because V changes. Since V = (π·d/λ)·NA is inversely proportional to λ, launching a shorter wavelength than the design value raises V, and a fiber that is single-mode by design can behave as multimode. Every fiber has a "cutoff wavelength"; below it, single-mode operation is not guaranteed. Always consider the wavelength together with the fiber specification.
Finally, the over-simplification that "raising the numerical aperture improves light gathering and therefore performance". A high NA does make light easier to collect, but for communication a higher NA backfires. Raising NA raises V, and in a multimode fiber the mode count rises, modal dispersion worsens and the bandwidth — the speed that can be transmitted — drops. Ease of light gathering (coupling efficiency) and bandwidth are in a trade-off. Decide what the application must prioritise first, then choose the NA, core diameter and wavelength.
How to Use
Enter the core refractive index (typically 1.48–1.49 for silica glass) in the coreIndexNum field.
Set the cladding refractive index (usually 1.46–1.48) to establish the index difference Δ that confines light.
Specify operating wavelength in nanometers (1310 nm or 1550 nm for telecommunications).
The simulator calculates NA, acceptance angle, V-number, and predicted modal count automatically.
Worked Example
For a step-index multimode fiber with core index n₁=1.485, cladding index n₂=1.465, core diameter 50 μm, and 1550 nm wavelength: NA = √(1.485² − 1.465²) ≈ 0.20, acceptance half-angle ≈ 11.5°, index difference Δ ≈ 1.36%, V-number ≈ 101, supporting approximately 2000 modes. This configuration is typical for short-reach data center links where modal dispersion is acceptable over 300 m distances.
Practical Notes
Single-mode fibers (V < 2.405) minimize dispersion for long-haul telecommunication cables; multimode fibers (V > 2.405) accept more light but suffer mode coupling loss in extended runs.
Higher NA increases light-gathering capacity but amplifies chromatic and modal dispersion; submarine cables use NA ≈ 0.08–0.10 for bandwidth optimization.
Acceptance angle directly determines coupling efficiency with laser diodes or LEDs; a 50/125 μm graded-index fiber (NA ≈ 0.20) couples 4–6 times more light than standard single-mode (NA ≈ 0.13).