70
2 Optical Fiber Structures and Light Guiding Principles
B f =
λ
L B
=
1.31 × 10
−6 m
8 × 10
−2 m
= 1.64 × 10
−5
This is characteristic of an intermediate type fiber, because birefringence can vary
from B f = 1 × 10
–3 (for a typical high birefringence fiber) to B f = 1 × 10
–8 (for a
typical low birefringence fiber).
2.5.4 Effective Refractive Index
From Maxwell’s equations it can be shown that the phase of the fundamental HE 11
mode (or equivalently, of the LP 01 mode) is determined by means of the wave
propagation constant β for that mode. For various applications, for example, when
discussing signal propagation in few-mode fibers or when analyzing fiber Bragg
gratings, it is useful to define an effective refractive index n eff . The basic definition
is that for some fiber mode the propagation constant β is a factor of n eff times the
vacuum wave number k 0 = 2π /λ, that is,
n e f f =
β
k 0
(2.37)
In a standard single-mode fiber, because the fundamental guided LP 01 mode
extends significantly beyond the core region, the effective refractive index has a
value falling between the refractive indices of the core and the cladding. In a multimode fiber, higher-order modes extend farther into the cladding, and have smaller
effective indices than lower-order modes. The exact value of the effective refractive
index depends on factors such as the specific mode being considered, the size of the
fiber, and the wavelength. It is important to note that the definition of n eff is related to
the phase change per unit length along the fiber and not on the intensity distribution
of the modes.
2.6 Graded-Index (GI) Fibers
2.6.1 Core Structure of GI Fibers
In the graded-index fiber design the core refractive index decreases continuously with
increasing radial distance r from the center of the fiber but is generally constant in the
cladding. The most commonly used construction for the refractive-index variation
in the core is the power law relationship
2 Optical Fiber Structures and Light Guiding Principles
B f =
λ
L B
=
1.31 × 10
−6 m
8 × 10
−2 m
= 1.64 × 10
−5
This is characteristic of an intermediate type fiber, because birefringence can vary
from B f = 1 × 10
–3 (for a typical high birefringence fiber) to B f = 1 × 10
–8 (for a
typical low birefringence fiber).
2.5.4 Effective Refractive Index
From Maxwell’s equations it can be shown that the phase of the fundamental HE 11
mode (or equivalently, of the LP 01 mode) is determined by means of the wave
propagation constant β for that mode. For various applications, for example, when
discussing signal propagation in few-mode fibers or when analyzing fiber Bragg
gratings, it is useful to define an effective refractive index n eff . The basic definition
is that for some fiber mode the propagation constant β is a factor of n eff times the
vacuum wave number k 0 = 2π /λ, that is,
n e f f =
β
k 0
(2.37)
In a standard single-mode fiber, because the fundamental guided LP 01 mode
extends significantly beyond the core region, the effective refractive index has a
value falling between the refractive indices of the core and the cladding. In a multimode fiber, higher-order modes extend farther into the cladding, and have smaller
effective indices than lower-order modes. The exact value of the effective refractive
index depends on factors such as the specific mode being considered, the size of the
fiber, and the wavelength. It is important to note that the definition of n eff is related to
the phase change per unit length along the fiber and not on the intensity distribution
of the modes.
2.6 Graded-Index (GI) Fibers
2.6.1 Core Structure of GI Fibers
In the graded-index fiber design the core refractive index decreases continuously with
increasing radial distance r from the center of the fiber but is generally constant in the
cladding. The most commonly used construction for the refractive-index variation
in the core is the power law relationship