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2 Optical Fiber Structures and Light Guiding Principles
important case is the analysis of single-mode or few-mode fibers, which must be dealt
with by using electromagnetic theory. Problems involving coherence or interference
phenomena must also be solved with an electromagnetic approach. In addition, a
modal analysis is necessary when knowledge of the field distribution of individual
modes is required. This arises, for example, when analyzing the excitation of an individual mode or when analyzing the coupling of power between modes at waveguide
imperfections (which is discussed in Sect. 3.1).
Another discrepancy between the ray optics approach and the modal analysis
occurs when an optical fiber is uniformly bent with a constant radius of curvature.
As shown in Chap. 3, wave optics correctly predicts that every mode of the curved
fiber experiences some radiation loss. Ray optics, on the other hand, erroneously
predicts that some ray congruences can undergo total internal reflection at the curve
and, consequently, can remain guided without loss.
2.3.3 Structure of Step-Index Fibers
To begin the discussion of light propagation in an optical waveguide first consider
the step-index fiber illustrated in Fig. 2.15. In practical step-index glass fibers the
core of radius a has a refractive index n 1 , which is typically equal to 1.48. This is
surrounded by a cladding of slightly lower index n 2 , where
n 2 = n 1 (1 − )
(2.20)
The parameter is called the core-cladding index difference or simply the index
difference. Values of n 2 are chosen such that is nominally 1–3% for multimode
fibers and from 0.2 to 1.0% for single-mode fibers. Because the core refractive index is
larger than the cladding index, electromagnetic energy at optical frequencies is made
to propagate along the fiber waveguide through internal reflection at the core-cladding
interface.
2.3.4 Ray Optics Representation
Because the core size of multimode fibers is much larger than the wavelength of the
light being transmitted (which is approximately l μm), an intuitive picture of the
propagation mechanism in an ideal multimode step-index optical waveguide is most
easily seen by a simple ray (geometrical) optics representation [6–11]. For simplicity,
this analysis shall consider only a particular ray belonging to a ray congruence that
represents a fiber mode. The two types of rays that can propagate in a fiber are
meridional rays and skew rays. Meridional rays are confined to the meridian planes
of the fiber, which are the planes that contain the axis of symmetry of the fiber (the
core axis). Because a given meridional ray lies in a single plane, its path is easy to
2 Optical Fiber Structures and Light Guiding Principles
important case is the analysis of single-mode or few-mode fibers, which must be dealt
with by using electromagnetic theory. Problems involving coherence or interference
phenomena must also be solved with an electromagnetic approach. In addition, a
modal analysis is necessary when knowledge of the field distribution of individual
modes is required. This arises, for example, when analyzing the excitation of an individual mode or when analyzing the coupling of power between modes at waveguide
imperfections (which is discussed in Sect. 3.1).
Another discrepancy between the ray optics approach and the modal analysis
occurs when an optical fiber is uniformly bent with a constant radius of curvature.
As shown in Chap. 3, wave optics correctly predicts that every mode of the curved
fiber experiences some radiation loss. Ray optics, on the other hand, erroneously
predicts that some ray congruences can undergo total internal reflection at the curve
and, consequently, can remain guided without loss.
2.3.3 Structure of Step-Index Fibers
To begin the discussion of light propagation in an optical waveguide first consider
the step-index fiber illustrated in Fig. 2.15. In practical step-index glass fibers the
core of radius a has a refractive index n 1 , which is typically equal to 1.48. This is
surrounded by a cladding of slightly lower index n 2 , where
n 2 = n 1 (1 − )
(2.20)
The parameter is called the core-cladding index difference or simply the index
difference. Values of n 2 are chosen such that is nominally 1–3% for multimode
fibers and from 0.2 to 1.0% for single-mode fibers. Because the core refractive index is
larger than the cladding index, electromagnetic energy at optical frequencies is made
to propagate along the fiber waveguide through internal reflection at the core-cladding
interface.
2.3.4 Ray Optics Representation
Because the core size of multimode fibers is much larger than the wavelength of the
light being transmitted (which is approximately l μm), an intuitive picture of the
propagation mechanism in an ideal multimode step-index optical waveguide is most
easily seen by a simple ray (geometrical) optics representation [6–11]. For simplicity,
this analysis shall consider only a particular ray belonging to a ray congruence that
represents a fiber mode. The two types of rays that can propagate in a fiber are
meridional rays and skew rays. Meridional rays are confined to the meridian planes
of the fiber, which are the planes that contain the axis of symmetry of the fiber (the
core axis). Because a given meridional ray lies in a single plane, its path is easy to