EE 230
Optical Fiber Communications
Homework 2
1. A certain optical fiber has an attenuation of 0.6 dB/km at 1300 nm and 0.3 dB/km at
1550 nm. Suppose the following two optical signals are launched simultaneously into the
fiber: an optical power of 150 µW at 1300 nm and an optical power of 100 µW at 1550
nm. What are the power levels in µW of these two signals at (a) 8 km and (b) 20 km?
2. A continuous 12 km-long optical fiber link has a loss of 1.5 dB/km. (a) What is the
minimum optical power level that must be launched into the fiber to maintain an optical
power level of 0.3 µW at the receiving end? (b) What is the required input power if the
fiber has a loss of 2.5 dB/km?
3. A step index fiber has a V number of 6.0. (a) Estimate the fraction of the optical
power traveling in the cladding for the six lowest-order LP modes. (b) If the fiber has a
silica core whose loss is 3.0 dB/km, and silica cladding with a loss of 4.0 dB/km, find the
attenuations for each of the six lowest-order modes. (c) Do the same for the fiber if its
silica core has a loss of 5.0 dB/km and it has a polymer cladding with loss 1000 dB/km.
4. A silica fiber’s core index is 1.455 and its cladding index is 1.450, both at 1.53 µm.
Its V number is 2.3. Given the nonlinear index n2=2.6x10-11 µm2/mW, and either of the
two expressions for effective radius w0 given in lecture, how large would the guided
power have to be before the nonlinear contribution to the index of refraction was 1% of
the difference between the core and cladding indices?
5. An EDFA produces an output signal of 27 dBm from an input signal of 2 dBm at a
wavelength of 1542 nm. The pump wavelength is 980 nm. (a) Find the amplifier gain.
(b) What is the minimum pump power required?
6. Consider a long-distance transmission system containing a cascaded chain of EDFAs.
Assume each EDFA is operated in the saturation region and that the slope of the gain vs.
input power curve in this region is -0.5; that is, the gain changes by 3 dB for a 6 dB
change in input power in the opposite direction. Each link has a nominal gain of 7.1 dB,
a nominal input power of -4.1 dBm, and a nominal output power of +3.0 dBm. Suppose
there is a sudden drop of 6 dB in the signal power at some point. Find what the new
power is after each of the next four amplifier stages.
7. Following Example 13.11 on page 887 of your text, find the optimum number of
EDFAs if the total distance D is 2000 km, the loss coefficient l is 0.2 dB/km, the number
of transverse modes mt is 1, and all other parameters given in the Example remain the
same.