72
2 Optical Fiber Structures and Light Guiding Principles
Fig. 2.23 A comparison of the numerical apertures for fibers having various core index profiles
by α = 2.0. In this case, M g = V
2 /4, which is half the number of modes supported
by a step-index fiber (for which α = ∞) that has the same V value.
Example 2.16 Consider a 50 μm diameter graded-index fiber that has a parabolic
refractive index profile (α = 2). If the fiber has a numerical aperture NA = 0.22,
what is the total number of guided modes at a wavelength of 1310 nm?
Solution First, from Eq. (2.27)
V =
2πa
λ
N A =
2π × 25 μm
1.31 μm
0.22 = 26.4
Then from Eq. (2.42) the total number of modes for α = 2 is
M g =
α
α + 2
V
2
2
=
V
2
4
= 174
2.6.3 Cutoff Condition in GI Fibers
Similar to step-index fibers, in order to eliminate intermodal dispersion graded-index
fibers can be designed as single-mode fibers in which only the fundamental mode is
allowed to propagate at the desired operational wavelength. An empirical expression
2 Optical Fiber Structures and Light Guiding Principles
Fig. 2.23 A comparison of the numerical apertures for fibers having various core index profiles
by α = 2.0. In this case, M g = V
2 /4, which is half the number of modes supported
by a step-index fiber (for which α = ∞) that has the same V value.
Example 2.16 Consider a 50 μm diameter graded-index fiber that has a parabolic
refractive index profile (α = 2). If the fiber has a numerical aperture NA = 0.22,
what is the total number of guided modes at a wavelength of 1310 nm?
Solution First, from Eq. (2.27)
V =
2πa
λ
N A =
2π × 25 μm
1.31 μm
0.22 = 26.4
Then from Eq. (2.42) the total number of modes for α = 2 is
M g =
α
α + 2
V
2
2
=
V
2
4
= 174
2.6.3 Cutoff Condition in GI Fibers
Similar to step-index fibers, in order to eliminate intermodal dispersion graded-index
fibers can be designed as single-mode fibers in which only the fundamental mode is
allowed to propagate at the desired operational wavelength. An empirical expression