**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?

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Wide bandwidth, compact fiber, immunity from EM interference.
**

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

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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.

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TDM and WDM
**

5. Name 3 approaches to increase network capacity.

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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?

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

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

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# 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.

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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.

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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.

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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?

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# 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)
**

Last Modified: January 29, 2018

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