Encyclopedia … combined with a great Buyer's Guide!

Sponsors:     and others

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

How to cite the article; suggest additional literature


URL: https://www.rp-photonics.com/acceptance_angle_in_fiber_optics.html

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:

acceptance angle of fiber

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.

acceptance angle of a fiber
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.

For larger incidence angles, there is no total internal reflection, and much of the incident light will not be reflected at the core–cladding boundary. It will thus get into the cladding and will then usually experience strong propagation losses particularly at the outer part of the cladding.

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

For a strongly multimode waveguide, the acceptance angle can be used to estimate the maximum input angle of a laser beam for which a high launch efficiency of the waveguide can be achieved. For single-mode fibers, however, this rule does not hold, as explained in the following.

The concept of ray optics (geometrical 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; the launch efficiency varies gradually. Only in the limit of a highly multimode waveguide, such estimates based on geometrical optics become reasonably accurate.

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


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.


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.


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.


Why is the acceptance angle not dependent on the diameter? Isn't there any diffraction effects? Or doesn't the divergence angle of the Gaussian beam come into play?

Answer from the author:

The acceptance angle is based on purely geometric reasoning (geometrical optics). Diffraction is not considered in that context. Within wave optics, where diffraction can be considered, there is no precisely defined acceptance angle.


Does the acceptance angle depend on the wavelength of light?

Answer from the author:

Only weakly through the refractive index.

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here; we would otherwise delete it soon. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him e.g. via e-mail.

Your question or comment:

Spam check:

  (Please enter the sum of thirteen and three in the form of digits!)

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.

See also: numerical aperture, fibers, waveguides, total internal reflection, fiber optics
and other articles in the category fiber optics and waveguides


Share this with your friends and colleagues, e.g. via social media:

These sharing buttons are implemented in a privacy-friendly way!