Review questions for HW 1

1. What is figure of merit for communication systems?

Date rate times distance or bandwidth times distance

2. What are the advantages of optical communication?

Wide bandwidth, compact fiber, immunity from EM interference.

3. Why a transparent optical network is better than an opaque optical network?

Transparent (all-optical) network avoids bottlenecks from E/O and O/E conversions as well as the limitation of 40GHz from electronic switching.

4. Name 2 multiplexing schemes used in optical network.

TDM and WDM

5. Name 3 approaches to increase network capacity.

1. increase number of cables or fibers.
2. increase bandwidth of a channel.
3. carry more channels per cable or fiber.

6. A multiplexing system has 2 channels with data rate of 10Gb/s and 5 channels with data rate of 5Gb/s. What is the minimal data rate for the system?

2 times10G + 5 times 5G = 45Gb/s

7. A system has a total bandwidth of 100GHz. Each channel requires 500MHz. How many channels can be supported by the system ideally?

# of Channels = 100G/0.5G = 200

8. A plane wave with $\omega=10^{14}$ rad/s propagates in air along x axis. Its H field in in y directions. Find i) its wave number and ii) polarization direction.

i) k = $\omega$ / c = $\frac {10^{14}} {3 \times 10^8} = 10^6/3$ (rad/m)
ii) z

9. A plane propagates in air and has electric field e = 5 $\cos ( 10^{11} t - k y ) \hat z$ (V/m). Find i) k, ii) amplitude of its magnetic field, iii) its average Poynting vector.

i) k = $\frac {10^{11}} {3 \times 10^8} = 10^3/3$ (rad/m)
ii) $H_o= E_o/ \eta$ = 5/377 = 0.01326 (A/m)
iii) $\vec S_{ave} = \hat y 0.5 |E_o|^2/ \eta = \hat y 0.5 5^2 / 377 = \hat y 0.03316(W/m^2)$

10. A laser emitting photons at wavelength of 1.5 micron. Find its photon energy in eV.

E(ev) = 1.24 / 1.5 = 0.8267 (eV)

11. If the laser in question 10 has linewidth of 1nm, find its bandwidth in Hz.

bandwidth = $\nu \frac {\Delta \lambda} \lambda = c \frac {\Delta \lambda} {\lambda^2} = \frac {3 \times 10^8 \times 10^{-9}} {(1.5 \times 10^{-6})^2} = 1.333 \times 10^{14}$ (Hz)

12. If the laser in question 10 has power of 1mW, how many photons are generated per sec?

# photons/sec = $P_{op}/E(J) = 10^{-3}/(q 0.8267)=7.56 \times 10^{15}$ (1/s)

13. If it takes 8 electrons to generate 1 photons, how much current is required to sustain the power in question 12?

I = q (# electrons/sec) = $q 8 \times 10^{-3}/(q 0.8267)$ = 9.677(mA)