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A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber, which is confined by the core.

For step index fiber, light entering the fiber will be guided if it falls within the acceptance cone of the fiber, that is if it makes an angle with the fiber axis that is less than the acceptance angle,^[1]

\theta <\arcsin \left({\sqrt {n_{0}^{2}-n_{\mathrm {c} }^{2}}}\right)

,

where

θ is the angle the ray makes with the fiber axis, before entering the fiber,

n₀ is the refractive index along the central axis (core) of the fiber, and

n_c is the refractive index of the cladding.

The quantity $\sin \theta$ is the numerical aperture of the fiber. The quantity $2\theta$ is sometimes called the total acceptance angle of the fiber.

This result can be derived from Snell's law by considering the critical angle. Light that enters the core with an angle below the acceptance angle strikes the core-cladding boundary at an angle above the critical angle, and experiences total internal reflection. This repeats on every bounce within the fiber core, and so the light is confined to the core. The confinement of light by the fiber can also be described in terms of bound modes or guided modes. This treatment is necessary when considering single-mode fiber, since the ray model does not accurately describe the propagation of light in this type of fiber.

References

Federal Standard 1037C

^ DeVeau, Russell L. (2000). Fiber Optic Lighting: A Guide for Specifiers. The Fairmont Press, Inc. ISBN 0-88173-325-3. Retrieved 14 October 2016.

This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.

[1] DeVeau, Russell L. (2000). Fiber Optic Lighting: A Guide for Specifiers. The Fairmont Press, Inc. ISBN 0-88173-325-3. Retrieved 14 October 2016.

[1]

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-'''Guided ray''' is a [[ray]] of light in an [[optical fiber]] that is confined primarily to the [[core]].
+A '''guided ray''' (also '''bound ray''' or '''trapped ray''') is a [[Ray (optics)|ray]] of light in a [[multi-mode optical fiber]], which is confined by the [[Fiber_optics#Principle_of_operation|core]].
+For [[Step-index profile|step index fiber]], light entering the fiber will be guided if it falls within the '''acceptance cone''' of the fiber, that is if it makes an angle with the fiber axis that is less than the '''acceptance angle''',<ref>{{cite book |url=https://books.google.com/books?id=-2Z2OMC3j-wC&q=half+acceptance+angle&pg=PA55 |publisher=The Fairmont Press, Inc. |title=Fiber Optic Lighting: A Guide for Specifiers |access-date=14 October 2016 |first= Russell L. |last=DeVeau |date=2000 |isbn=0-88173-325-3}}</ref>
-A guided ray satisfies the relation given by:
-:<math>0 \le \sin \theta_r \le \sqrt{ n_r^2 - n_a^2 }</math>
+:<math>\theta < \arcsin \left( \sqrt{n_0^2 - n_\mathrm{c}^2} \right)</math> ,
-where:
+where
+:''θ'' is the angle the ray makes with the fiber axis, ''before'' entering the fiber,
+:''n''<sub>0</sub> is the [[refractive index]] along the central axis (core) of the fiber, and
+:''n''<sub>c</sub> is the refractive index of the cladding.
+The quantity <math>\sin \theta</math> is the [[numerical aperture]] of the fiber. The quantity <math>2 \theta</math> is sometimes called the ''total acceptance angle'' of the fiber.
-:&theta;<sub>''r''</sub> is the angle the ray makes with the fiber axis;
-:''r'' is the radial position, ''i.e.'', radial distance, of the ray from the fiber axis;
-:''n<sub>r</sub>'' is the [[refractive index]] at the radial distance r from the fiber axis;
-:''n<sub>a</sub>'' is the refractive index at the core radius, a, ''i.e.'', at the core-[[cladding]] [[interface]].
+This result can be derived from [[Snell's law]] by considering the [[Critical angle (optics)|critical angle]]. Light that enters the core with an angle below the acceptance angle strikes the core-cladding boundary at an angle above the critical angle, and experiences [[total internal reflection]]. This repeats on every bounce within the fiber core, and so the light is confined to the core. The confinement of light by the fiber can also be described in terms of bound modes or guided modes. This treatment is necessary when considering [[single-mode fiber]], since the ray model does not accurately describe the propagation of light in this type of fiber.
-Guided rays correspond to bound modes, ''i.e.'', guided modes, in terms of modes rather than rays. Synonyms for a guided ray are "bound ray", and "trapped ray".
-==External links==
+==See also==
+*[[Numerical aperture]]
-* [http://www.its.bldrdoc.gov/fs-1037/dir-017/_2518.htm Federal Standard 1037C]
+*[[Acceptance angle (solar concentrator)]], same construct for another use
+==References==
+:* [http://www.its.bldrdoc.gov/fs-1037/dir-017/_2518.htm Federal Standard 1037C]
+{{reflist}}
+{{FS1037C}}
 [[Category:Fiber optics]]