# Guided ray

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 (half) acceptance angle.[1]

A ray of light traveling in an optical fiber must be incident at the critical angle on the internal surface,the fiber-cladding boundary, of the fiber in order to have total internal reflection. When the ray is fed into the fiber the angle of incidence relative to the axis of the fiber, should be such that after refraction, when the ray of light reaches the cladding, it does so at the critical angle. This feed in incidence angle is the (half) acceptance angle:

${\displaystyle \sin \theta \leq NA={\sqrt {n_{o}^{2}-n_{c}^{2}}}}$ ,

where

θ is the angle the ray makes with the fiber axis, before entering the fiber,
no is the refractive index along the central axis of the fiber, and
nc is the refractive index of the cladding, and
NA is the numerical aperture.

This result can be derived from Snell's law by considering the critical angle.

(Total) acceptance angle is ${\displaystyle 2\theta }$.

Rays that fall within this angular range are reflected from the core-cladding boundary by total internal reflection, and so are confined by 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 singlemode fiber, since the ray model does not accurately describe the propagation of light in this type of fiber.