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# Acceptance Angle in Fiber Optics

Definition: the maximum incidence angle of a light ray which can be used for injecting light into a fiber core or waveguide

German: Akzeptanzwinkel in der Faseroptik

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The acceptance angle of an optical fiber is defined based on a purely geometrical consideration (ray optics): it is the maximum angle of a ray (against the fiber axis) hitting the fiber core which allows the incident light to be guided by the core. The sine of that acceptable angle (assuming an incident ray in air or vacuum) is called the numerical aperture, and it is essentially determined by the refractive index contrast between core and cladding of the fiber, assuming that the incident beam comes from air or vacuum: Here, ncore and ncladding are the refractive indices of core and cladding, respectively, and n0 is the refractive index of the medium around the fiber, which is close to 1 in case of air. Figure 1: An incident light ray is first refracted and then undergoes total internal reflection at the core–cladding interface. However, that works only if the incidence angle is not too large.

## Calculating the acceptance angle of a fiber

 Core index: Cladding index: Index of input medium: Numerical aperture: calc Acceptance angle: calc

Enter input values with units, where appropriate. After you have modified some values, click a "calc" button to recalculate the field left of it.

## Further Remarks

The concept of ray optics is not fully appropriate for describing the operation details of optical fibers, because wave aspects are important – particularly for fibers with small core such as single-mode fibers, while the approximation is more appropriate for large-core multimode fibers. A real light beam (for example, a laser beam) is not well resembled by a ray, since it inevitably has both a finite beam radius and a finite beam divergence. Therefore, there is in reality not a well-defined transition between guidance and non-guidance, when a beam angle is varied. However, the acceptance angle gives at least some estimate concerning how large an incidence angle may be for efficiently launching light.

Note that the term acceptance angle also plays a role in nonlinear optics – see the article on critical phase matching.

## Questions and Comments from Users

2020-07-04

If a fiber is immersed in water, how does that change its acceptance angle?

The acceptance angle is substantially reduced, as you can calculate with the formula given above.

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