5.1 Source-to-Fiber Power Coupling
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the power loss in decibels from the source into the fiber? (b) What is the power loss
if no gel is used to fill the small gap?
Solution (a) Here we need to consider the reflectivity at two interfaces. First, using
Eq. (5.10) the reflectivity R sg at the source-to-gel interface is
R sg =
n source − n gel
n source + n gel
2
=
3.540 − 1.520
3.540 + 1.520
2
= 0.159
Similarly, using Eq. (5.10) the reflectivity R gf at the gel-to-fiber interface is
R g f =
n f iber − n gel
n f iber + n gel
2
=
1.480 − 1.520
1.480 + 1.520
2
= 1.777 × 10
−4
The transmission T through the matching gel then is the product of two individual
transmissions:
T =
1 − R sg
×
1 − R g f
= (1 − 0.159) ×
1 − 1.777 × 10
−4
= 0.841
The power lost (as a ratio) is
L power = 1 − T = 0.159 (i.e., 15.9% of the power is lost)
The power loss in decibels is
L power (dB) = −10 log(1 − R) = −10 log 0.841 = 0.752 dB
(b) Similarly, the transmission T through the air gap is the product of two individual
transmissions:
T =
1 −
n source − n air
n source + n air
2
×
1 −
n f iber − n air
n f iber + n air
2
= (1 − 0.313) × (1 − 0.037) = 0.662
The power lost (as a ratio) is
L power = 1 − T = 0.338 (i.e., 33.8% of the power is lost)