216
5 Optical Power Coupling
and α = 2.0 is 0.185 mW = −7.33 dBm. (c) How do these numbers compare
to the values for similar sized step-index fibers described in Example 5.2?
These analyses assumed perfect coupling conditions between the source and the
fiber. This can be achieved only if the refractive index of the medium separating
the source and the fiber end matches the index n 1 of the fiber core. If the refractive
index n of this medium is different from n 1 , then for perpendicular fiber end faces
the power coupled into the fiber reduces by the factor
R =
n 1 − n
n 1 + n
2
(5.10)
where R is the Fresnel reflection or the reflectivity at the fiber-core end face (see
Sect. 2.11). The ratio r = (n 1 − n)/(n 1 + n), which is known as the reflection
coefficient, relates the amplitude of the reflected wave to the amplitude of the incident
wave.
Example 5.3 A GaAs optical source with a refractive index of 3.6 is coupled to a
silica fiber that has a refractive index of 1.48. What is the power loss between the
source and the fiber?
Solution If the fiber end and the source are in close physical contact, then, from
Eq. (5.10), the Fresnel reflection at the interface is
R =
n 1 − n
n 1 + n
2
=
3.60 − 1.48
3.60 + 1.48
2
= 0.174
This value of R corresponds to a reflection of 17.4% of the emitted optical power
back into the source. Given that
P coupled = (1 − R)P emitted
the power loss L power in decibels is found from:
L power = −10log
P coupled
P emitted
= −10log(1 − R)
= −10log(0.826) = 0.83 dB
An index-matching material between the source and the fiber end can reduce this
loss number.
Example 5.4 An InGaAsP light source that has a refractive index of 3.540 is coupled
to a step-index fiber that has a core refractive index of 1.480. Assume that the source
size is smaller than the fiber core and that there is a small gap between the source and
the fiber. (a) If the gap is filled with a gel that has a refractive index of 1.520, what is
5 Optical Power Coupling
and α = 2.0 is 0.185 mW = −7.33 dBm. (c) How do these numbers compare
to the values for similar sized step-index fibers described in Example 5.2?
These analyses assumed perfect coupling conditions between the source and the
fiber. This can be achieved only if the refractive index of the medium separating
the source and the fiber end matches the index n 1 of the fiber core. If the refractive
index n of this medium is different from n 1 , then for perpendicular fiber end faces
the power coupled into the fiber reduces by the factor
R =
n 1 − n
n 1 + n
2
(5.10)
where R is the Fresnel reflection or the reflectivity at the fiber-core end face (see
Sect. 2.11). The ratio r = (n 1 − n)/(n 1 + n), which is known as the reflection
coefficient, relates the amplitude of the reflected wave to the amplitude of the incident
wave.
Example 5.3 A GaAs optical source with a refractive index of 3.6 is coupled to a
silica fiber that has a refractive index of 1.48. What is the power loss between the
source and the fiber?
Solution If the fiber end and the source are in close physical contact, then, from
Eq. (5.10), the Fresnel reflection at the interface is
R =
n 1 − n
n 1 + n
2
=
3.60 − 1.48
3.60 + 1.48
2
= 0.174
This value of R corresponds to a reflection of 17.4% of the emitted optical power
back into the source. Given that
P coupled = (1 − R)P emitted
the power loss L power in decibels is found from:
L power = −10log
P coupled
P emitted
= −10log(1 − R)
= −10log(0.826) = 0.83 dB
An index-matching material between the source and the fiber end can reduce this
loss number.
Example 5.4 An InGaAsP light source that has a refractive index of 3.540 is coupled
to a step-index fiber that has a core refractive index of 1.480. Assume that the source
size is smaller than the fiber core and that there is a small gap between the source and
the fiber. (a) If the gap is filled with a gel that has a refractive index of 1.520, what is