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2 Optical Fiber Structures and Light Guiding Principles
An approximation to the relative spot size w 0 /a, which for a step-index fiber has
an accuracy better than 1% in the range 1.2 < V < 2.4, is given by
w 0
a
= 0.65 + 1.619V
−3/2
+ 2.879V
−6
(2.34)
The condition V = 2.405 for single-mode operation yields w 0 /a = 1.1005. As V
decreases from 2.4, the spot size increases. The spot size thus becomes progressively
larger than the core radius a and extends farther into the cladding. As a result, when
V becomes smaller the optical beam becomes less tightly bound to the core and
becomes more susceptible to optical power losses from the cladding. Manufacturers
therefore typically design their fibers with V values greater than 2.0 to prevent high
cladding losses but somewhat less than 2.4 to avoid the possibility of having more
than one mode in the fiber.
Example 2.14 A certain single-mode step-index fiber has an MFD = 11.2 μm and
V = 2.25. What is the core diameter of this fiber?
Solution From Eq. (2.32) w 0 = MFD/2 = 5.6 μm. Using Eq. (2.34) then yields
a = w 0 /
0.65 + 1.619V
−3/2
+ 2.879V
−6
=
5.6μm
0.65 + 1.619V −3/2 + 2.879V −6
=
5.6μm
1.152
= 4.86μm
Thus the core diameter is 2a = 9.72 μm.
Drill Problem 2.7 Compare the relative spot size w 0 /a for V values of 1.2,
1.8, and 2.4.
2.5.3 Origin of Birefringence
An important point to keep in mind is that in any ordinary single-mode fiber there are
actually two independent, degenerate propagation modes [32–34]. These modes are
very similar, but their polarization planes are orthogonal. These may be chosen arbitrarily as the horizontal (H) and the vertical (V) polarizations as shown in Fig. 2.22.
Either one of these two polarization modes constitutes the fundamental HE 11 mode.
In general, the electric field of the light propagating along the fiber is a linear superposition of these two polarization modes and depends on the polarization of the light
at the launching point into the fiber.
2 Optical Fiber Structures and Light Guiding Principles
An approximation to the relative spot size w 0 /a, which for a step-index fiber has
an accuracy better than 1% in the range 1.2 < V < 2.4, is given by
w 0
a
= 0.65 + 1.619V
−3/2
+ 2.879V
−6
(2.34)
The condition V = 2.405 for single-mode operation yields w 0 /a = 1.1005. As V
decreases from 2.4, the spot size increases. The spot size thus becomes progressively
larger than the core radius a and extends farther into the cladding. As a result, when
V becomes smaller the optical beam becomes less tightly bound to the core and
becomes more susceptible to optical power losses from the cladding. Manufacturers
therefore typically design their fibers with V values greater than 2.0 to prevent high
cladding losses but somewhat less than 2.4 to avoid the possibility of having more
than one mode in the fiber.
Example 2.14 A certain single-mode step-index fiber has an MFD = 11.2 μm and
V = 2.25. What is the core diameter of this fiber?
Solution From Eq. (2.32) w 0 = MFD/2 = 5.6 μm. Using Eq. (2.34) then yields
a = w 0 /
0.65 + 1.619V
−3/2
+ 2.879V
−6
=
5.6μm
0.65 + 1.619V −3/2 + 2.879V −6
=
5.6μm
1.152
= 4.86μm
Thus the core diameter is 2a = 9.72 μm.
Drill Problem 2.7 Compare the relative spot size w 0 /a for V values of 1.2,
1.8, and 2.4.
2.5.3 Origin of Birefringence
An important point to keep in mind is that in any ordinary single-mode fiber there are
actually two independent, degenerate propagation modes [32–34]. These modes are
very similar, but their polarization planes are orthogonal. These may be chosen arbitrarily as the horizontal (H) and the vertical (V) polarizations as shown in Fig. 2.22.
Either one of these two polarization modes constitutes the fundamental HE 11 mode.
In general, the electric field of the light propagating along the fiber is a linear superposition of these two polarization modes and depends on the polarization of the light
at the launching point into the fiber.