acceptance angle in fiber optics (original) (raw)

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

Category: article belongs to category fiber optics and waveguides fiber optics and waveguides

Related: The Numerical Aperture of a Fiber: a Strict Limit for the Acceptance Angle?numerical aperturefiberswaveguidestotal internal reflectionfiber optics

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DOI: 10.61835/wg6 Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Definition of Acceptance Angle

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 since total internal reflection can occur at the core–cladding boundary. For larger incidence angles, there are significant power losses at each reflection point.

All accepted directions together form a cone of acceptance.

Geometric Calculation of a Fiber's Acceptance Angle

The acceptance angle is usually calculated in the simplest possible situation, assuming a step-index fiber and an incident ray hitting the center of the fiber's input end. Further, one ignores the curvature of the core–cladding interface, applying the well-known equation for total internal reflection for a plane interface between two materials with different refractive indices. The medium from which the incident ray comes is not necessarily air or vacuum; one can more generally assume a homogeneous medium with some refractive index ($n_0$).

The simple calculation leads to the following formula for the acceptance angle: {\theta _{{\rm{acc}}}} = \arcsin \left( {\frac{1}{n_0} \sqrt {n_{\rm{co}}^2 - {n_{\rm{cl}}}^{\rm{2}}} } \right)$$

Here, ($n_\textrm{co}$) and ($n_\textrm{cl}$) are the refractive indices of core and cladding.

The term ($\sqrt {n_{\rm{co}}^2 - {n_{\rm{cl}}}^{\rm{2}}}$) is called the numerical aperture, and it is essentially determined by the refractive index contrast between core and cladding of the fiber.

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.

Considering Wave Optics

Geometric rays are generally a poor approximation for light beams when the dimensions get small, as they typically do for optical waveguides. In general, one needs to consider wave optics. 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.

Nevertheless, for a strongly multimode waveguide, the acceptance angle as calculated above 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 provides at most a very rough estimate.

In reality, there is 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. See the case study below.

Acceptance Angle in Nonlinear Optics

Note that the term acceptance angle also plays a role in nonlinear optics — see the article on critical phase matching. Here, that term has a quite different meaning.

Frequently Asked Questions

What is the acceptance angle of an optical fiber?

It is the maximum angle to the fiber axis at which light can enter the fiber and be guided by its core. This concept from ray optics assumes that the light is trapped by total internal reflection at the core–cladding boundary.

What is the cone of acceptance?

The cone of acceptance contains all directions from which incident light can be guided by an optical fiber. It is a three-dimensional cone defined by the acceptance angle.

How is the acceptance angle of a fiber calculated?

The acceptance angle is calculated from the fiber's numerical aperture (NA) and the refractive index of the input medium (($n_0$)). The NA itself, ($\sqrt {n_{\rm{co}}^2 - {n_{\rm{cl}}}^{\rm{2}}}$), depends on the refractive indices of the core and cladding.

Is the acceptance angle concept accurate for all types of fibers?

No; as a concept from geometrical optics, it is a good approximation only for highly multimode fibers. For accurately describing light launching into single-mode fibers, one must use wave optics.

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