Attenuation
The attenuation or transmission loss of optical fibers has proved to be one of the most
important
factors
in
bringing
about
their
wide
acceptance
in
telecommunications.Aschannel attenuation largely determined the maximum
transmission distance prior to signalrestoration, optical fiber communications became
especially attractive when the transmissionlosses of fibers were reduced below those of
the competing metallic conductors (lessthan 5 dB km−1).
Attenuation in an optical fiber is caused by absorption, scattering, and bending
losses.Attenuation is the loss of optical power as light travels along the fiber. Signal
attenuation is defined as the ratio of optical input power (P i) to the optical output power
(Po). Optical input power is the power injected into the fiber from an optical source.
Optical output power is the power received at the fiber end or optical detector. The
following equation defines signal attenuation as a unit of length:
Signal attenuation is a log relationship. Length (L) is expressed in kilometers. Therefore,
the unit of attenuation is decibels/kilometer (dB/km). As previously stated, attenuation is
caused by absorption, scattering, and bending losses. Each mechanism of loss is
influenced by fiber-material properties and fiber structure. However, loss is also present
at fiber connections.
This logarithmic unit has the advantage that the operations of multiplication and division
reduce to addition and subtraction, while powers and roots reduce to multiplication and
division. However, addition and subtraction require a conversion to numerical values
which may be obtained using the relationship:
In optical fiber communications the attenuation is usually expressed in decibels per unit
length (i.e. dB km−1) following:
Where αdB is the signal attenuation per unit length in decibels which is also referred to
as the fiber loss parameter and L is the fiber length.
Example 3.1
When the mean optical power launched into an 8 km length of fiber is 120 μW, the
mean optical power at the fiber output is 3 μW.
Determine:
(a) The overall signal attenuation or loss in decibels through the fiber assuming there
are no connectors or splices;
(b) The signal attenuation per kilometer for the fiber.
(c) The overall signal attenuation for a 10 km optical link using the same fiber with
splices at 1 km intervals, each giving an attenuation of 1 dB;
(d) The numerical input/output power ratio in (c).
Solution: (a) Using Eq. (3.1), the overall signal attenuation in decibels through the fiber
is:
(b) The signal attenuation per kilometer for the fiber may be simply obtained by dividing the
result in (a) by the fiber length which corresponds to it using Eq. (3.3) where:
(c) As αdB = 2 dB km−1, the loss incurred along 10 km of the fiber is given by:
However, the link also has nine splices (at 1 km intervals) each with an attenuation of 1
dB. Therefore, the loss due to the splices is 9 dB. Hence, the overall signal attenuation
for the link is:
(d) To obtain a numerical value for the input/output power ratio, Eq. (3.2) may be used where:
Problems
1. The mean optical power launched into an optical fiber link is 1.5 mW and the
fiber has an attenuation of 0.5 dB km−1. Determine the maximum possible link
length without repeaters (assuming lossless connectors) when the minimum
mean optical power level required at the detector is 2 μW.
Answer: 57.5 km
2. The numerical input/output mean optical power ratio in a 1 km, length of optical
fiber is found to be 2.5. Calculate the received mean optical power when a mean
optical power of 1 mW is launched into a 5 km length of the fiber (assuming no
joints or connectors).
Answer: 10.0 μW
3. A 15 km optical fiber link uses fiber with a loss of 1.5 dB km−1. The fiber is
jointed every kilometer with connectors which give an attenuation of 0.8 dB each.
Determine the minimum mean optical power which must be launched into the
fiber in order to maintain a mean optical power level of 0.3 μW at the detector.
Answer: 703 μW