1. Loss of fiber: 0.22dB/km x 120 km = 26.4 dB = 2.23x10-3
Optical power at the receiver: 3 mW x 2.23x10-3 = 6.69 W
Signal current: 6.69x10-6W x 0.75 A/W = 5x10-6 A
Shot noise: 2eI x BW = 2 x 1.6x10-19 x 5x10-6 x 2.5x109 = 4x10-15 A2
Thermal noise: 4kT/R x BW = 4 x 0.026 eV x 900/300 x 2.5x109 / 50 =
2.50 x 10-12 A2
Thermal noise > Shot noise
S/N = (5x10-6 A)2 / 2.50 x 10-12 A2 = 10 = 10 dB
2. Optical isolator prevents reflection induced instability of lasers and amplifiers. It is
used at the output of lasers and EDFA. Inside of the optical isolator are two polarizers
at 45o with a Faraday rotator in between. The Faraday rotator rotates the polarization
by 45o. Therefore, the linearly polarized laser beam can pass the second polarizer in
the forward direction. The reflected beam gets another 45o rotation. It becomes
normal to the first polarzier. Hence, the reflection can’t pass through the first
polarizer. The efficiency of the isolator is determined by the throughput and by the
reflection rejection efficiency. The rejection efficiency is in the –30 to –50 dB range.
EDFA provides optical amplification without much added noise. It eliminates
electronic repeaters in long-haul transmission systems. It operates similar to a threelevel laser system. The pump laser excites the Er-ions. The exited electron relaxes to
the intermediate state which has a long lifetime. The energy gets converted to
stimulated emission when the signal beam arrives. Key characteristics include the
bandwidth and the gain. Typical gain is in the range of 12-25 dB.
FBG has a grating created by exposing the fiber to uv which causes the index to
increase. Either holographic exposure or phase mask can be used to form the grating
pattern. FBG can be used in a variety of applications including add-drop filter and
dispersion compensation. The key characteristics of FBG include center wavelength,
bandwidth, and side mode rejection. The filter rejection ratio is of the order of 40-50
dB.
APD is a photodetector with gain. The high electric field causes electrons and
holes to avalanche. It can provide a current gain of 10-100. The multiplication noise
is a concern. In materials with large difference in electron and hole avalanche
coefficients, the noise is minimum.
3. According to the data sheet, the dispersion coefficient at 1550 nm is  18 psec/km-nm.
The dispersion compensating fiber has a dispersion coefficient of –127 psec/km-nm.
Therefore, we need no more than 18/127 x 120 km = 17 km.
4. RIN = (PN/P)^2 / BW
PN = (-150 dB/Hz x 140 MHz)^0.5 x 80 W = 30 nW
5. I1/I2 = exp (T1-T2)/T0
Averaging two calculated values gives 57.4 oC
Averaging three calculated values yields I0 = 11.8 mA
6. NA=(1.4674^2-1.4621^2)^0.5 = 0.1246