2.3 Optical Fiber Configurations and Modes
53
Fig. 2.16 Ray optics
representation of skew rays
traveling in a step-index
optical fiber core
Core
center
Helical ray path
in the core
Ray path projected
on the fiber end face
Core
boundary
track as it travels along the fiber. Meridional rays can be divided into two general
classes: bound rays that are trapped in the core and propagate along the fiber axis
according to the laws of geometrical optics, and unbound rays that are refracted out
of the fiber core.
Skew rays are not confined to a single plane, but instead tend to follow a helicaltype path along the fiber as shown in Fig. 2.16. These rays are more difficult to track
as they travel along the fiber because they do not lie in a single plane. Although skew
rays constitute a major portion of the total number of guided rays, their analysis is not
necessary to obtain a general picture of rays propagating in a fiber. The examination
of meridional rays will suffice for this purpose. However, a detailed inclusion of
skew rays will change such expressions as the light-acceptance ability of the fiber
and power losses of light traveling along a waveguide.
A greater power loss arises when skew rays are included in the analyses because
many of the skew rays that geometric optics predicts to be trapped in the fiber are
actually leaky rays [6, 12, 13]. These leaky rays are only partially confined to the
core of the circular optical fiber and attenuate as the light travels along the optical
waveguide. This partial reflection of leaky rays cannot be described by pure ray
theory alone. Instead, the analysis of radiation loss arising from these types of rays
must be described by mode theory.
The meridional ray is shown in Fig. 2.17 for a step-index fiber. The light ray enters
the fiber core from a medium of refractive index n at an angle θ 0 with respect to the
fiber axis and strikes the core-cladding interface at a normal angle ϕ. If it strikes this
interface at such an angle that it is totally internally reflected, then the meridional
ray follows a zigzag path along the fiber core, passing through the axis of the guide
after each reflection.
From Snell’s law, the minimum or critical angle ϕ c that supports total internal
reflection for the meridional ray is given by
sin φ c =
n 2
n 1
(2.21)
Rays striking the core-to-cladding interface at angles less than ϕ c will refract out
of the core and be lost in the cladding, as the dashed line shows. By applying Snell’s
law to the air–fiber face boundary, the condition of Eq. (2.21) can be related to the
53
Fig. 2.16 Ray optics
representation of skew rays
traveling in a step-index
optical fiber core
Core
center
Helical ray path
in the core
Ray path projected
on the fiber end face
Core
boundary
track as it travels along the fiber. Meridional rays can be divided into two general
classes: bound rays that are trapped in the core and propagate along the fiber axis
according to the laws of geometrical optics, and unbound rays that are refracted out
of the fiber core.
Skew rays are not confined to a single plane, but instead tend to follow a helicaltype path along the fiber as shown in Fig. 2.16. These rays are more difficult to track
as they travel along the fiber because they do not lie in a single plane. Although skew
rays constitute a major portion of the total number of guided rays, their analysis is not
necessary to obtain a general picture of rays propagating in a fiber. The examination
of meridional rays will suffice for this purpose. However, a detailed inclusion of
skew rays will change such expressions as the light-acceptance ability of the fiber
and power losses of light traveling along a waveguide.
A greater power loss arises when skew rays are included in the analyses because
many of the skew rays that geometric optics predicts to be trapped in the fiber are
actually leaky rays [6, 12, 13]. These leaky rays are only partially confined to the
core of the circular optical fiber and attenuate as the light travels along the optical
waveguide. This partial reflection of leaky rays cannot be described by pure ray
theory alone. Instead, the analysis of radiation loss arising from these types of rays
must be described by mode theory.
The meridional ray is shown in Fig. 2.17 for a step-index fiber. The light ray enters
the fiber core from a medium of refractive index n at an angle θ 0 with respect to the
fiber axis and strikes the core-cladding interface at a normal angle ϕ. If it strikes this
interface at such an angle that it is totally internally reflected, then the meridional
ray follows a zigzag path along the fiber core, passing through the axis of the guide
after each reflection.
From Snell’s law, the minimum or critical angle ϕ c that supports total internal
reflection for the meridional ray is given by
sin φ c =
n 2
n 1
(2.21)
Rays striking the core-to-cladding interface at angles less than ϕ c will refract out
of the core and be lost in the cladding, as the dashed line shows. By applying Snell’s
law to the air–fiber face boundary, the condition of Eq. (2.21) can be related to the