Homework Chapter 1: Introduction

1.1. Calculate the carrier frequency for optical communication systems operating at

0.88, 1.3, and 1.55 m. What is the photon energy (in eV) in each case?

1.2. 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 W at the receiving end?

b. What is the required input power if the fiber has a loss of 2.5 dB/km?

1.3. A 1.55 m digital communication system operating at 1 Gb/s receives an average

power of 40 dBm at the detector. Assuming that 1 and 0 bits are equally likely to occur,

calculate the number of photons received within each 1 bit.

1.4. Sketch the variation of optical power with time for a digital NRZ bit stream

010111101110 by assuming a bit rate of 2.5 Gb/s. What is the duration of the shortest and

widest optical pulse?

Homework Chapter 2 Fiber

2.1. Light traveling in air strikes a glass plate at an angle 1 =33o, where 1 measured

between the incoming ray and the glass surface. Upon striking the glass, part of the beam

is reflected and part is refracted. If the refracted and reflected beams make an angle of

900 with each other, what is the refractive index of the glass? What is the critical angle

for this glass?

2.2. Find the core radius necessary for single-mode operation at 820 nm of a step-index

fiber with n1=1.48 and n2=1.478. What is the numerical aperture and maximum

acceptance angle of this fiber?

2.3. A manufacturer wishes to make a silica-core, step-index fiber with V=75 and a

numerical aperture NA=0.3 to be used at 820 nm. If n1=1.458, what should the core size

and cladding index be?

2.4. Determine the normalized frequency at 0.82 m for a step-index fiber having a 25m

core radius, n1=1.48, and n2=1.46. How many modes propagate in this fiber at 0.82m?

How many modes propagate at a wavelength of 1.3m? What percentage of the optical

power flows in the cladding in each case?

Homework Chapter 3: Sources

3.1

A laser diode has a maximum average output of 1mW (0dBm). The laser is to be

amplitude-modulated with a signal x(t) that has a dc component of 0.2 and a periodic

component of +2.56 and -2.56. If the current-input to optical-output relationship is

P(t)=i(t)/10, find the values of I0 and m if the modulating current is i(t)=Io[1+mx(t)].

3.2. A GaAs laser emitting at 800 nm has a 400-m-long cavity with a refractive index

n=3.6. If the gain dg exceeds the total loss , throughout the range 750nm

4.2. An InGaAs pin photodiode has the following parameters at a wavelength of 1300 nm,

ID=4nm, =0.65, RL=1000, and the surface leakage current is negligible. The incident

optical power is 300 nW(-35dBm), and the receiver bandwidth is 20 MHz. Find the

various noise trems of the receiver.

4.3. A digital fiber optic link operating at 850 nm requires a maximum BER of 10-9

a. Find the quantum limit in terms of the quantum efficiency of the detector and

energy of the incident photon.

b. Find the minimum incident optical fiber P0 that must fall on the photodetector to

achieve a 10-9

BER at a data rate of 10Mb/s for a simple binary-level signaling

scheme( the detector quantum efficiency =1)

4.4. Suppose an avalanche photodiode has the following parameters: IL=1nA, ID=1nA,

=0.85, F =M1/2, RL=103, and B=1kHz. Consider a sinusoidal varying 850-nm signal,

which has a modulation index m=0.85 and an average power level P0=-50dBm, to fall on

the detector at room temperature. At what value of M does the maximum signal-to-noise

ratio occur?