# 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

Category: fiber optics and waveguides

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Author: Dr. Rüdiger Paschotta

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, *n*_{core} and *n*_{cladding} are the refractive indices of core and cladding, respectively, and *n*_{0} is the refractive index of the medium around the fiber, which is close to 1 in case of air.

## 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

2021-03-13

How do you calculate the maximum acceptance angle in water and in air for the case of an uncladded fiber?

Answer from the author:

If you just mean an optically homogeneous fiber, not having core and cladding, and you can regard the surrounding air or water as your cladding. Just use the calculator above.

2021-04-07

Does the angle of exit of light from a step-index multimode fiber tell you anything about the angle of entry?

Answer from the author:

Theoretically, that angle should be preserved, but any bending of the fiber or imperfections of the fiber structure may easily spoil that relation.

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See also: numerical aperture, fibers, waveguides, total internal reflection, fiber optics

and other articles in the category fiber optics and waveguides

2020-07-04

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

Answer from the author:

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