Page 62 - Optical Communications Essentials

Optical Fibers

52 Chapter Four

where the parameter ∆ is called the core-cladding index difference or simply the index
difference. It is defined through the equation n 2 n 1 (1 ∆). Typical values of ∆ range
from 1 to 3 percent for multimode fibers and from 0.2 to 1.0 percent for single-mode
fibers. Thus, since ∆ is much less than 1, the approximation on the right-hand side of
the above equation is valid.
Since the numerical aperture is related to the maximum acceptance angle, it is used
commonly to describe the light acceptance or gathering capability of a multimode fiber
and to calculate the source-to-fiber optical power coupling efficiencies.

Example A multimode step-index fiber has a core index n 1 1.480 and an index dif-
ference ∆ 0.01. The numerical aperture for this fiber is NA 1.480 002. 0.21.

4.4. Single-Mode Fibers

An important parameter for single-mode fibers is the cutoff wavelength. This is
designated by λ cutoff and specifies the smallest wavelength for which all fiber
modes except the fundamental mode are cut off; that is, the fiber transmits
light in a single mode only for those wavelengths that are greater than λ cutoff .
The fiber can support more than one mode if the wavelength of the light is less
than the cutoff. Thus if a fiber is single-mode at 1310nm, it is also single-mode
at 1550nm, but not necessarily at 850nm.
When a fiber is fabricated for single-mode use, the cutoff wavelength usually
is chosen to be much less than the desired operating wavelength. For example,
a fiber for single-mode use at 1310nm may have a cutoff wavelength of
1275nm.

Cutoff Wavelength For a fiber to start supporting only a single mode at a wave-
length λ cutoff , the following condition (derived from solutions to Maxwell’s equations
for a circular waveguide) needs to be satisfied:
2πa
λ cutoff n 1 n 2 1/2
2
2
2.405
where a is the radius of the fiber core, n 1 is the core index, and n 2 is the cladding index.
Example Suppose we have a fiber with a 4.2 µm, n 1 1.480, and n 2
n 1 (1 0.0034) 1.475. Its cutoff wavelength then is

2(4.2 m)  2 2 1/2
cutoff  (1.480) (1.475)   1334nm
2 405
.

4.5. Optical Fiber Attenuation
Light traveling in a fiber loses power over distance, mainly because of absorption
and scattering mechanisms in the fiber. The fiber loss is referred to as signal
attenuation or simply attenuation. Attenuation is an important property of an
optical fiber because, together with signal distortion mechanisms, it determines

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