2.9 Optical Fiber Cables
85
and a heavy outer armor jacket. Cables that run under the ocean have further layers
of armoring and contain copper wires to provide electrical power for submersed
optical amplifiers or regenerators.
2.10 Summary
This chapter examines the structure of optical fibers and presents two mechanisms
that show how light propagates along these fibers. In its simplest form an optical
fiber is a coaxial cylindrical arrangement of two homogeneous dielectric (glass or
plastic) materials. This fiber type consists of a central core of uniform refractive
index n 1 surrounded by a cladding region of refractive index n 2 that is less than n 1 .
This configuration is referred to as a step-index fiber because the cross-sectional
refractive-index profile has a step function at the interface between the core and the
cladding.
In a graded-index fiber the refractive-index profile varies as a function of the radial
coordinate r in the core but is constant in the cladding. This index profile n(r) often
is represented as a r
α power law where α defines the shape of the core index profile.
A commonly used value of the power law exponent is α = 2. This special case is
referred to as a parabolic graded-index profile. A graded-index profile reduces signal
dispersion in multimode fibers and thus provides a wider bandwidth than offered by
a step-index fiber.
A photonic crystal fiber (PCF) or a microstructured fiber differs from a conventional fiber in that the cladding and, in some cases, the core regions of a PCF
contain air holes, which run along the entire length of the fiber. Whereas the material
properties of the core and cladding define the light transmission characteristics of
conventional fibers, the structural arrangement of holes in a PCF creates an internal
microstructure, which offers extra dimensions in controlling the optical properties
of light, such as the dispersion, nonlinear effects, and birefringence effects in optical
fibers.
A general picture of light propagation in a conventional fiber can be obtained by
considering a ray-tracing (or geometrical optics) model in a slab waveguide. The
slab consists of a central region of refractive index n 1 , which is sandwiched between
two material layers having a lower refractive index n 2 . Light rays propagate along
the slab waveguide by undergoing total internal reflection at the material boundaries.
Although the ray model is adequate for an intuitive picture of how light travels
along a fiber, a more comprehensive description of light propagation, signal dispersion, and power loss in a cylindrical optical fiber waveguide requires a wave theory
approach. In this approach, electromagnetic fields (at optical frequencies) traveling
in the fiber can be expressed as superpositions of elementary field configurations
called the modes of the fiber. A mode of monochromatic light of radian frequency ω
traveling in the axial (positive z) direction in a fiber can be described by the factor
exp[j(ωt – βz)], where β is the propagation constant of the mode. For guided (bound)
modes β can assume only a finite number of possible solutions. These solutions are
85
and a heavy outer armor jacket. Cables that run under the ocean have further layers
of armoring and contain copper wires to provide electrical power for submersed
optical amplifiers or regenerators.
2.10 Summary
This chapter examines the structure of optical fibers and presents two mechanisms
that show how light propagates along these fibers. In its simplest form an optical
fiber is a coaxial cylindrical arrangement of two homogeneous dielectric (glass or
plastic) materials. This fiber type consists of a central core of uniform refractive
index n 1 surrounded by a cladding region of refractive index n 2 that is less than n 1 .
This configuration is referred to as a step-index fiber because the cross-sectional
refractive-index profile has a step function at the interface between the core and the
cladding.
In a graded-index fiber the refractive-index profile varies as a function of the radial
coordinate r in the core but is constant in the cladding. This index profile n(r) often
is represented as a r
α power law where α defines the shape of the core index profile.
A commonly used value of the power law exponent is α = 2. This special case is
referred to as a parabolic graded-index profile. A graded-index profile reduces signal
dispersion in multimode fibers and thus provides a wider bandwidth than offered by
a step-index fiber.
A photonic crystal fiber (PCF) or a microstructured fiber differs from a conventional fiber in that the cladding and, in some cases, the core regions of a PCF
contain air holes, which run along the entire length of the fiber. Whereas the material
properties of the core and cladding define the light transmission characteristics of
conventional fibers, the structural arrangement of holes in a PCF creates an internal
microstructure, which offers extra dimensions in controlling the optical properties
of light, such as the dispersion, nonlinear effects, and birefringence effects in optical
fibers.
A general picture of light propagation in a conventional fiber can be obtained by
considering a ray-tracing (or geometrical optics) model in a slab waveguide. The
slab consists of a central region of refractive index n 1 , which is sandwiched between
two material layers having a lower refractive index n 2 . Light rays propagate along
the slab waveguide by undergoing total internal reflection at the material boundaries.
Although the ray model is adequate for an intuitive picture of how light travels
along a fiber, a more comprehensive description of light propagation, signal dispersion, and power loss in a cylindrical optical fiber waveguide requires a wave theory
approach. In this approach, electromagnetic fields (at optical frequencies) traveling
in the fiber can be expressed as superpositions of elementary field configurations
called the modes of the fiber. A mode of monochromatic light of radian frequency ω
traveling in the axial (positive z) direction in a fiber can be described by the factor
exp[j(ωt – βz)], where β is the propagation constant of the mode. For guided (bound)
modes β can assume only a finite number of possible solutions. These solutions are