Exercises

1. What are the advantages of fiber optic technology in communication systems?

2. In order to take full advantage of the huge bandwidth available on fiber, various multiplexing techniques such as WDM, TDM, and CDM can be used which allow multiple users to share the bandwidth on a single fiber. Compare and contrast these multiplexing techniques. Why is WDM currently the most promising choice for optical communication networks?

3. Figure 1.1 shows two regions, 1200-1400 nm and 1450-1650 nm, which are capable of providing up to 50 THz of bandwidth. Calculate the actual bandwidth provided by each region. (Hint: Use the identity f = v x \lambda where v = 2.0 x 10^8 m/s.)

4. What is the bandwidth of a 1 nm signal at 1500 nm? At 1350 nm? Give an approximate relation for the bandwidth of a $\Delta \lambda$ nm signal at $\lambda$ nm.

5. Consider the three solutions for upgrading the transmission capacity of a link from OC-48 to OC-192. Suppose the cost of installing additional fiber is $100 per meter, the cost of each transciever is $1000, and the cost of a WDM multiplexer/demultiplexer is $10,000. Determine the maximum length for which you would want to use the multi-fiber solution.

6. Give the advantages and disadvantages of the following wavelength crossconnects:
   (a) passive star,
   (b) passive router, and
   (c) active switch.

7. Consider the passive star of Fig. 1.4, the passive router of Fig. 1.5, and the active switch of Fig. 1.6. Which of these devices can support the following simultaneous connections? (Assume that TDM is not used, but multicasting is allowed.)
   • Wavelength \lambda_1 from input fiber 1 to output fiber 1,
     Wavelength \lambda_1 from input fiber 1 to output fiber 2,
     Wavelength \lambda_2 from input fiber 2 to output fiber 1.
   • Wavelength \lambda_2 from input fiber 1 to output fiber 2,
     Wavelength \lambda_2 from input fiber 2 to output fiber 1,
     Wavelength \lambda_3 from input fiber 3 to output fiber 1.
   • Wavelength \lambda_1 from input fiber 1 to output fiber 1,
     Wavelength \lambda_2 from input fiber 2 to output fiber 1,
     Wavelength \lambda_3 from input fiber 1 to output fiber 3.

8. The routing matrix for an N x N passive router is called an N x N Latin Square.
   • Identify which of the following 2 x 2 matrices below are Latin Squares.

     		l1	l2	l3	l4
     	L1 =	l2	l3	l4	l1
     		l4	l1	l3	l2
     		l3	l4	l2	l1

     		l1	l2	l3	l4
     	L2 =	l2	l3	l4	l1
     		l3	l4	l1	l2
     		l4	l1	l2	l3

   • How many distinct 3 x 3 Latin Squares are there?

9. Consider the active switch of Fig. 1.6.
   (a) What is the size of each switching element in the center?
   (b) Is it possible to construct a 4 x 4 switch out of 2 x 2 switches?

10. Consider the network of Fig. 1.7. Suppose we replace the passive star by a TDM switch. Compare this new architecture with the previous architecture.

11. Consider the simple wavelength-routed optical WDM network shown in Fig. 1.9. Two connections have been established: A-B on wavelength \lambda_1, and C-B on wavelength \lambda_2. Establish the connections D-B and C-D while using the minimum number of wavelengths. How would your solution change if wavelength conversion is available at each node?

12. Suppose the photonic switching fabric in Fig. 1.8 is replaced by a passive-star coupler. What is the minimum number of wavelengths required to maintain the connections shown in the figure?