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Part
I
Introductory Concepts
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Source: Photonics Essentials

Introductory Concepts

Chapter
1
Introduction
Photons have been around ever since the Big Bang, which is a long
time. Photons, by definition, are always on the move: 3 × 1010
cm/sec
in air. Some of the important milestones in the history of the human
civilization are those at which we have improved our ability to control
the movement of photons. A few notable examples are the control of
fire, the design of lenses, the conception of Maxwell’s equations, the
invention of photography, broadcast radio, and the laser.
Photonics is the study of how photons and electronics interact, how
electrical current can be used to create photons as in a semiconductor
laser diode, and how photons can create an electrical current, as in a
solar cell. The field of photonics is in its infancy. Great discoveries re-
main to be made in using photonics to improve our lives.
The list of applications in photonics is long. Some of the rapidly
growing areas are:
Ecology:
Solar cell energy generation
Air quality and pollution monitoring
Imaging:
Camcorders
Satellite weather pictures
Digital cameras
Night vision
Military surveillance
3

Information displays:
Computer terminals
Traffic signals
Operating displays in automobiles and appliances
Information storage:
CD-ROM
DVD
Life Sciences:
Identification of molecules and proteins
Lighting
Medicine:
Minimally invasive diagnostics
Photodynamic chemotherapy
Telecommunications:
Lasers
Photodetectors
Light modulators
Telecommunications is an application of considerable activity and
economic importance because of the transformation of the world-wide
communications network from one that used to support only voice
traffic to one that now supports media transmitted through the Inter-
net, including voice, data, music, and video. Of course, in the digital
world these different media are all transmitted by ones and zeros.
However, if a picture can be said to be worth more than a thousand
words, a transmitted picture counts for about a million words. The
growth of the internet and its capacity to transmit both images and
sound has been made possible only because of the vast improvements
in speed and capacity of fiber optic telecommunications. At the heart
of this revolution are the semiconductor laser, fast light modulators,
photodiodes, and communications-grade optical fiber.
From this text you can learn what makes these key devices work
and how they perform. Laboratory measurements are emphasized for
an important reason: there are many different kinds of photonic de-
vices, but only a few basic characterization measurements. When you
learn these laboratory techniques, you can measure and understand
almost any kind of device. The experiments are based on components
that you can find easily in any electronics store. This means that the
laboratory fees should be reasonable, and that you can quickly find a
replacement device when you need one.
This course is an excellent preparation for subsequent work in the
4 Introductory Concepts
Introduction

physics of semiconductor devices, the design of biomedical instru-
mentation, optical fiber telecommunications, sensors, and micro
opto-electro mechanical systems (MOEMS). You may also want to
consider a summer internship as a test and measurement engineer
with one of the growing number of start-up companies in the opto-
electronics industry.
The largest market for photonic devices today is the telecommuni-
cations industry. Historically, this industry has been growing at
about 5% per year. The development of the optical fiber and the inter-
net have changed all that (see Fig. 1-1).
An optical fiber is generally a thin strand of glass that is used to
carry a beam of light. Once the light is introduced in the fiber, by us-
ing a lens, for example, it can only escape by propagating to the other
end of the fiber. The light beam is prevented from leaking out of the
sidewalls by an effect called total internal reflection. Thus, the fiber
acts as a guide for photons. When engineers showed that sending
high-speed communications by light waves was far superior to send-
ing communications by electricity, growth rates in the industry
Introduction 5
Figure 1.1. The growth of telecommunications systems got a big jolt with the deployment
of optical fibers in 1980, creating the first optical fiber telecommunications networks. There
was another big jolt in 1990 when optical amplifiers were rediscovered and adapted to op-
tical fiber telecommunications. This implemented multiple wavelength transmission (wave-
length-division multiplexing) and made it possible for the Internet to grow.
1880 1900 1920 1940 1960 1980 2000 2020 2040
Year
1014
1012
1010
108
106
104
102
100
10–2
Relative
Information
Capacity
(bit/s)
Single channel
(ETDM)
OPTICAL
FIBER
SYSTEMS
Multi-channel
(WDM)
Communication
Satellites
Advanced
coaxial and
microwave systems
{
Early coaxial cable links
Carrier Telephony first used 12 voice
channels on one wire pair
Telephone lines first constructed
{
Introduction

changed dramatically, as can be seen in Fig. 1.1. This is the definition
of a disruptive technology.
An important side effect of this growth is that the composition of
the telecommunications industry is changing rapidly. Old-line compa-
nies, like Alcatel, Lucent, and Philips, that were masters at handling
slow growth and predictable schedules for deployment of new technol-
ogy are being pushed to the sidelines. For example, Alcatel has re-
cently announced that it intends to own no factories by 2010. These
are being replaced in the photonic devices industry sector by a very
large number of smaller companies, many of which have been in busi-
ness for only a few years. Not all of these companies will succeed.
Making a career in the photonics industry is both exciting and punc-
tuated occasionally by moments of instability provoked by the reorga-
nization of this industry resulting from the implementation of new
technologies, take-overs, and creation of new start-up companies. For-
tunately, there is a strong and steady growth rate, much greater than
5%, that is underlying this effervescence. To succeed, you need to
keep a close watch on both the technology and the opportunities.
Introduction

Chapter
2
Electrons and Photons
2.1 Introduction
You will discover by measurement that all p-n diodes are sensitive to
light, even if they are intended for some other application. A photodi-
ode is a simple and inexpensive component that you will use to meas-
ure the particle behavior of light. This is a fundamental quantum-
mechanical property of matter, and is the effect for which Albert Ein-
stein was awarded the Nobel Prize in physics in 1921.
Photonic devices are used to convert photons to electrons and vice-
versa. Photons and electrons are two of the basic quantum-mechani-
cal particles. Like all quantum-mechanical particles, electrons and
photons also behave like waves.
In this chapter, you will learn about the wave-like and particle-like
aspects of the behavior of electrons and photons. Each electron that
carries current in a semiconductor is spread out over many thousands
of atoms; that is, it is delocalized. Trying to specify its position or its
velocity is a hopeless task. Furthermore, the semiconductor is full of
many absolutely identical electrons. They are all moving around at a
frenetic pace. Clearly, a different approach is needed.
An important new idea in this chapter is to introduce a “road map”
for electrons in a semiconductor. It tells you what states the electrons
are allowed to occupy, just as a road map tells you where the roads
are located that cars may travel on. The road map for electrons does
not tell you where the electrons are or how fast they are moving, just
as a roadmap for cars does not tell you where the cars are or how fast
they are moving. This road map is called a band structure.
Position and velocity are not very useful ideas for describing either
7

electrons or photons. However, two fundamental physical laws always
apply: conservation of energy and conservation of momentum. The be-
havior of electrons and photons can be tracked by their respective en-
ergies and momenta. The band structure is a particularly useful tool
for this task.
2.2 The Fundamental Relationships
There are two simple principles that support almost all the science of
photonic devices. One is the Boltzmann relationship and the other is
Planck’s equation relating the energy of a photon to the frequency of
the light wave associated with the photon.
Ludwig Boltzmann
Boltzmann studied gases and the motion of molecules in gases. In a
dense gas, Boltzmann said, the velocities of the molecules are statisti-
cally distributed about the average velocity v0 = 0. Since the Law of
Large Numbers in statistics says that all distributions tend toward a
Gaussian or normal distribution, Boltzmann started from this point,
too.
The probability of finding a particular velocity v1 is given by a
Gaussian distribution:
Pr(v = v1) = A · e (2.1)
where v
苶0
苶 means the average velocity = 0, and 具v
苶2
苶典 means the average
of the square of the velocity. Even though v
苶0
苶 = 0, 具v
苶2
苶典 is definitely not
equal to zero. This is the “spread” of the distribution.
Remember that:
Ekinetic = 1
–
2mv2
Pr(v = v1) = A · e
1
–
2 m具
苶v
苶2
苶典
苶 = spread in the energy = E
苶
Pr(v = v1) = A · e–(E/E
苶)
(2.2)
From Brownian motion studies more than a century earlier, as well
as mechanical equivalent of heat studies, energy is proportional to
temperature. That is, E
苶 = constant · T and
Pr(v = v1) = Pr(E = E1) = A · e–(E/constant · T)
– 1
–
2
m(v1
2)
ᎏ
1
–
2
m具v
苶2
苶典
–(v1 – v
苶0
苶)2
ᎏ
具v2典

So, what is this constant? Boltzmann’s constant, of course!
Pr(E = E1) = A · e–(E/kBT)
kBT ⬵ 0.026 eV @ 295 K = room temp (2.3)
If the total number of gas molecules in the bottle is NT, the number
of molecules having energy E1 is given by the total number of mole-
cules times the probability that a molecule has energy E1:
n(E1) = NTPr(E = E1) = NT · e–(E1/kBT)
(2.4)
The number of molecules at energy E2 relative to those at energy E1
is readily expressed:
= e–(E2–E1)/kBT
(2.5)
The Boltzmann relation given in Eq. 2.5 is a fundamental tool that
you use to determine how photonic devices operate. The Boltzmann
relation can be applied to electrons as well as to molecules, provided
that these electrons is are equilibrium. With suitable and simple mod-
ifications, it is possible to use this relationship under nonequilibrium
conditions. The current–voltage expression for a p-n diode is exactly
that adjustment. We will use this tool over and over throughout this
book. Its importance cannot be overestimated.
n(E2)
ᎏ
n(E1)
Electrons and Photons 9
Figure 2.1. A schematic picture of a collection of atoms in a gas. The arrows give the
magnitude and direction of the velocity of each atom. If the gas is contained in a bottle on
your lab bench, then the average velocity of the atoms relative to you is 0. However, the
average of the square of the velocity is a positive number.

2.3 Properties of Photons
a. According to Maxwell, light is an electromagnetic wave.
b. According to Michelson and Morley, light always travels at a con-
stant speed, c.
c. speed of light = c = wavelength × frequency = ␭f ~ 3 × 1010
cm/sec
d. visible light:
400 nm < ␭ < 700 nm (400 nm = blue, 700 nm = red)
near infrared:
700 nm < ␭ < 2000 nm
There are many important applications in the visible and near-
infrared regions of the spectrum, including the wavelengths that opti-
mize optical fiber communications. The most important properties of
optical fibers for communications are attenuation of the signal by ab-
sorption and distortion of the signal (noise).
High-performance optical fibers are made from glass. Attenuation
is caused by fluctuations in the density of the glass on the atomic
scale and from residual concentrations of water molecules. The water
molecules absorb light near specific wavelengths. In between these
wavelengths, windows of lower attenuation are formed at ␭ = 1300
nm and ␭ 1500 nm. A good picture of this situation is shown in Fig.
2.2 for state of the art optical fibers. The properties of several types of
fibers, all of which are made by chemical vapor deposition, are shown.
The properties of optical fibers are covered in more detail in Chapter
9.
Another important application for infrared wavelengths is night vi-
sion binoculars. These instruments are composed of detectors that im-
age the infrared heat radiation from objects and convert this signal to
a visible image so that the wearer can see in the dark.
Light beams behave like waves, and the wave properties of light are
easy to observe:
앫 diffraction effects
앫 dispersion effects; for example, a rainbow
앫 interference effects
앫 wavelength
앫 frequency
Light beams also display effects associated with particles. These ef-
fects are not as apparent in everyday experience. In the laboratory,
you will observe this behavior often.

Let us look at Planck’s study of incandescent radiation.
Observation: when things get hot, they begin to glow. As they get
hotter, (1) they glow more brightly and (2) the color of the glow
changes. We can measure the color of the glow by the frequency of the
light. So there seems to be a relationship between temperature and
frequency (color).
Exercise 2.1
If you have an electric heating appliance, you can try the following ex-
periment. After turning off the room lights, turn on the appliance and
watch it as it heats up. Record your observations.
Note: Some people have sensitivity to infrared wavelengths beyond
the range of normal vision. According to Edwin Land, inventor of the
Polaroid camera, who studied this effect, the “color” associated with
Figure 2.2. Optical fibers are made of glass and can be very transparent if the glass is
pure. At 1500 nm, the loss is about 0.2 dB per kilometer. This means that a kilometer of
optical fiber is about as transparent as an ordinary windowpane. Fibers are drawn like taffy
from a preform. The properties of preforms made in three different ways are shown: vapor
axial deposition, outside vapor deposition, and inside vapor deposition. The large loss
peak at 1400 nm is the result of absorption by the first harmonic of residual OH molecules
in the glass. Please see Chapter 9 for more details. (Adapted from D. Keck et al., Proc.
SPIE, by permission.

this sensitivity is yellow. It appears just before the dark red glow of
the heating element appears in the visible range as it warms up. In
my classes, this effect is seen by about one out of thirty students. Sen-
sitivity does not appear to depend on age or sex.
Planck’s proposition was that temperature is proportional to fre-
quency. But Boltzmann already knew that temperature is proportion-
al to energy. Therefore, we conclude that color is proportional to ener-
gy. As the energy goes up, how does the frequency change?
Remembering that ␭f = c, as the energy gets larger, does the wave-
length increase or decrease? As the energy gets larger, does the fre-
quency increase or decrease?
So, of the two things that characterize light, ␭ and f, which one is
proportional to the energy? As the energy goes up, the wavelength
gets shorter or smaller. However, the frequency has to increase be-
cause ␭f = c. Thus, energy is proportional to frequency:
E = hf (2.6)
h, of course, is Planck’s constant.
Energy in a monochromatic beam of red light equal to n · h · f(red
light), where n is the amplitude, or the number of vibrations, each one
of which carries hf of energy:
energy = 冱
f
hf · nf over all frequencies
where nf is the number of photons distributed according to Bose–Ein-
stein statistics:
nf = const · 冢冣 (2.7)
When hf > kBT, such as in the case of an incandescent body like a
stove element, nf is distributed to a good approximation by Boltz-
mann’s law.
Some important results obtained so far are:
1. Boltzmann’s law. For a group of electrons at equilbrium,
= e–(E2–E1)/kBT
2. Energy is proportional to frequency: E = hf, where h is Planck’s
constant, equal to 6.63 × 10–34
joule-sec.
n(E2)
ᎏ
n(E1)
1
ᎏᎏ
ehf/kBT
– 1

Exercise 2.2
Take ␭ = 1000 nm = 1 ␮m = 10–4
cm. For a tungsten light bulb, this is
the wavelength of peak intensity. What is the energy associated with
this wavelength?
Procedure:
␭f = c, or f = c/␭
f ⬵
f = 3 · 1014
/sec . . whew!!!
E = 6.6 · 10–34
× 3 · 10–14
= 1.98 · 10–19
joules
This sounds small, which it is according our everyday scale. Howev-
er, it is very close to the energy that an electron would have if it were
accelerated through a potential of one volt:
1 eV = 1.6 · 10–19
coul × 1 V = 1.6 · 10–19
joule
In photonics, the typical energies that you work with involve electrons
in a potential of 1 or 2 V. So we use the energy of an electron acceler-
ated through a potential of 1 V as a handy unit—the electron volt
(eV).
The energy of a photon with a wavelength of 1000 nm (or 1 ␮m) is
E = = 1.24 eV (2.8)
It is easy to show that reverse is true. That is, a photon with an en-
ergy of 1 eV has a wavelength of 1.24 ␮m (= 1240 nm). If a photon
with a wavelength of 1 ␮m has an energy of 1.24 eV, what is the ener-
gy of a photon having a wavelength of 0.5 ␮m (= 500 nm)? Answer: E
= 2.48 eV.
What is the energy of red photons (␭ = 612 nm)? Answer: E = 2.0 eV.
Exercise 2.3
Prove that the energy of any photon is given by
E = eV (2.9)
Prove that the wavelength of any photon is given by
␭ = ␮m (2.20)
1.24 eV
ᎏ
E
1.24 ␮m
ᎏᎏ
␭
1.98 · 10–19
ᎏᎏ
1.6 · 10–19
3 · 1010
cm/sec
ᎏᎏ
10–4
cm

Since photons always travel at the speed of light, it is natural to
think about the flow of energy or power in a light beam. Power is
measured in watts:
Watts = power that comes out of the light bulb = energy/sec
Watts = number of photons of frequency f/sec
× energy, summed over all f
Power = 冱
f
nf · Ef
So the total power is made up of the sum of all these little packets of
E = hf
It is sometimes more convenient in many applications to use angu-
lar frequency ␻ instead of regular frequency:
␻ = 2␲f
To make everything work out right you have to divide Planck’s con-
stant by 2␲:
h/2␲ 씮 ß
E = ß␻
In photonics, you will use ␭ and E almost always. Rarely will you
calculate f. The most important reason for this is experimental in ori-
gin. There are no instruments that measure frequency of photons di-
rectly.
2.4 Properties of Electrons
Electrons are the ONICS of photONICS. Electrons can interact with
photons one at a time (mostly) through the medium of a semiconduc-
tor crystal. When a semiconductor absorbs a photon, the energy of the
photon can be transferred to an electron as potential energy. When
the electron loses potential energy, the semiconductor can account for
the energy difference by emitting a photon.
Exercise 2.4
A photon with energy 1.5 eV strikes GaAs. The energy is absorbed by
breaking one bond, promoting one electron from a bonding state (va-
lence band) to an antibonding state (conduction band), and leaving a
vacant state (hole) in the valence band. Some time later, the electron
recombines with the hole, completing the bond and releasing a photon
of 1.42 eV, the bonding energy of GaAs at room temperature.

An electron can be characterized by its mass, charge and magnetic
moment, all of which are fixed in magnitude. It is also characterized
by its energy and momentum, which are variable. Although the elec-
tron does not have a well-defined size, it behaves in many respects as
a particle. For example, we could write down expressions for the mo-
mentum and energy of a baseball:
momentum = mv = p
kinetic energy = mv2
= = (2.21)
The same thing is true for electrons. Photons, of course, don’t have
any mass. So this equation does not work for photons.
A graph of the energy of a free electron as a function of its momen-
tum, just like that of a baseball, is a parabola (see Fig. 2.3). Remem-
ber that a 1 eV photon has ␭ =1240 nm.
On the other hand, we know from Maxwell’s equations that photons
do have a momentum that is equal to
p = = (2.22)
But, since c = f␭,
p = = ßk, where k = (2.23)
So, photons don’t have mass, but they have momentum.
2␲
ᎏ
␭
h
ᎏ
␭
hf
ᎏ
c
E
ᎏ
c
p2
ᎏ
2m
(mv)2
ᎏ
2m
1
ᎏ
2
Figure 2.3. The kinetic energy of a particle with mass, like that of an electron, is propor-
tional to the square of its momentum.
+ MOMENTUM –
ENERGY

Electrons have momentum, but can they have a wavelength? Well if
your name were Prince Louis-Victor, Duke de Broglie, and the year
was 1924, maybe such an idea would not seem so strange. If this were
the case, then the energy of an electron would be
E = ·
Using this equation, you could actually calculate the wavelength if
you knew the electron energy. Suppose your electron has an energy of
1 eV. This is the energy of an electron that falls through a potential of
1 V.
1 eV = 1.6 × 10–19
joules
␭ = = = 12 Å
In 1929, de Broglie received the Nobel prize for this revolutionary
idea. His reasoning was different from the simple analysis above, and
involved little math, not to mention Maxwell’s equations. His insight
was based on an analogy with his everyday experience and is present-
ed later on in Section 2.6. Nearly ten years later, in 1937, the Nobel
prize was awarded to Clint Davisson for his observation of electron
diffraction, a property of electrons that can be described only by its
fundamental wave-like nature. His lab partner, Lester Germer, got
left out of the prize list, a mystery to this day.
The work of Davisson and Germer led directly to the invention of
the electron microscope, a widely used instrument in all branches of
materials physics and engineering.
For a 1 eV photon, ␭ = 12,400 Å
For a 1 eV electron, ␭= 12 Å
At 1 eV energy (only), = 1000
This ratio depends on the electron energy. But 1 eV is characteristic of
electrons in solids. What does this mean?
Relative to the electron, the photon has mostly energy, but not very
much momentum. We can see this on the diagram of energy and mo-
mentum (Fig. 2.4).
Except for the uninteresting case in which E = 0, the energy mo-
mentum curves for free electrons and photons do not intersect. That
is: there is no point on the curves where the energy and momentum of
an electron are equal to the energy and momentum of a photon. This
␭photon
ᎏ
␭electron
6.6 × 10–34
joule-sec
ᎏᎏᎏᎏᎏ
兹2
苶 ·
苶 9
苶 ×
苶 1
苶0
苶–3
苶1
苶k
苶g
苶 ·
苶 1
苶.6
苶 ×
苶 1
苶0
苶–1
苶9
苶jo
苶u
苶le
苶s
苶
h
ᎏ
兹2
苶m
苶E
苶
h2
ᎏ
␭2
1
ᎏ
2m

means that a free electron and a photon cannot interact with each
other. However, in a solid material the situation is different. Elec-
trons and photons can interact because the host material can supply
the momentum that is missing in the case of a free electron and a pho-
ton. This is discussed in more detail in Section 2.7.
Imagine a vapor of single atoms of the same element. Before atomic
bonding occurs, the constituent atoms are “free” to wander around.
They are in an antibonding state. We could take silicon as an exam-
ple. When two such free silicon atoms meet, they may bond together.
They will do so because the bonding state is at a lower energy than
what existed previously. The valence electrons have thus fallen into
some kind of potential well, and to do so they gave up some of their
energy. This energy that separates the bonding state from the higher
energy antibonding state is called the bonding energy. In silicon, this
energy difference is about 1 eV.
If a photon comes along, or if the thermal energy is large enough,
one of those bonds might happen to break and now there would be an
electron that is promoted from the bonding state to the antibonding
state. Of course, if all the bonds were broken the silicon would melt.
But what does the situation look like for us? At room temperature in
perfect silicon are there any broken bonds? How could you estimate
this?
Figure 2.4. The energy of a photon is linearly proportional to its momentum. When plotted
on the same graph as that for an electron, the energy–momentum relationship for a photon
looks like a vertical line.
electron
photon
Energy
+ MOMENTUM –

Exercise 2.5
For each broken bond in a perfect crystal of silicon, an electron is pro-
moted from the valence band to the conduction band. Using Boltz-
mann statistics you can write:
= e–⌬E/kT
At room temperature, we will approximate kT by 0.025 eV,
= e–1/0.025
= e–40
nantibonding ⬇ e–40
· 1024
= ?? (2.24)
This is an interesting number. Take the log of both sides:
log10(nantibonding) ⬇ 24 – 40log10(e) = 24 – (40)(0.4) = 24 – 16 = 8
nantibonding ⬇ 108
bonds/cm3
This back of the envelope estimate shows that on the average a
semiconductor whose band gap (= antibonding – bonding energies) = 1
eV will have about 108
broken bonds per cm3
. A more detailed calcula-
tion for silicon based on the same principles gives ~1010
cm–3
broken
bonds at room temperature.
When the bond is broken, the electron is promoted from the valence
band, or bonding orbitals to the conduction band or antibonding or-
bitals. Another name of the conduction band is simply the set of unoc-
cupied levels that are closest in energy to the valence band levels.
When the bonds are not broken, they act like springs that hold the
atoms in the crystal at the right distance from each other. These
springs vibrate as a way of storing the thermal energy of the crystal.
The vibrational energy of each atom = 1
–
2 kT for each degree of freedom,
or 3
–
2 kT. So the average vibrational energy at room temperature is
about 40 meV. These vibrations have a frequency and a wavelength
that are related by the speed of sound:
vs = f␭
The speed of sound in solid materials is about 105
cm/sec = 103
m/sec.
Exercise 2.6
What is the ratio of vs to the speed of light?
nantibonding
ᎏᎏᎏ
ᎏ
⬇ 1024
atoms/cm3
nantibonding
ᎏᎏ
nbonding

vs /c ~ 105
/1010
~ 10–5
So for the same frequency f (= same energy),
= ____________?
What is the frequency of a 40 meV vibration?
f = = = 9 × 1012
= 1013
Hz (2.27)
What is the wavelength ?
␭= vs/f = 105
/1013
= 10–8
cm
Well, this is only a few times larger than the lattice parameter of Si.
Does this make sense?
The lower limit on the wavelength is the interatomic distance
which is about 0.12 × 10–8
cm in silicon. So lattice vibrations have a
wavelength that is an integral multiple of the lattice parameter.
These vibrational quanta are called phonons. They are important be-
cause they allow the semiconductor to reach equilibrium.
To summarize our story so far:
Wavelength of a 1 eV electron = 12 Å
Wavelength of a 1 eV photon = 1240 nm
= 1000 × ␭electron (only true around 1 eV!)
So, what is the wavelength of a 1 eV phonon? The answer is, a 1 eV
phonon does not exist. It cannot exist because its wavelength would
be much smaller than the separation between atoms, and the phonon
represents vibrations of atoms. However, the wavelength of a 40 m eV
phonon is about the same as that for the 1 eV electron.
Since momentum = h/␭, at room temperature, the momentum of a
typical phonon is similar to the momentum of 1 eV electron.
As electrons move around in the semiconductor, they need to con-
serve energy and momentum. In this never ending struggle, the
phonon acts as a source of momentum that contributes very little en-
ergy, whereas the photon can contribute energy with very little mo-
mentum. As the electron interacts with light, the electric field, etc.,
both phonons and photons interact with the electron so that both en-
ergy and momentum are conserved.
(40 × 10–3
)(1.6 × 10–19
)
ᎏᎏᎏ
6.6 × 10–34
E
ᎏ
h
␭s
ᎏ
␭␾

2.5 Some History
The proposition of de Broglie (pronounced duh Broy-yuh) was ab-
solutely revolutionary, but not at all obvious at the time. The princi-
pal result of his idea was to open the way for the development of
Schrödinger’s wave equation and the first quantitative description of
the behavior of electrons and atoms. de Broglie had the advantage
that he was a student. He knew a little bit, but not too much. This fea-
ture was key, in my opinion, because it allowed him to see the forest
in spite of the trees. Later in life, when he knew more, he was much
less productive, and because of his celebrity, his views took on an im-
portance unsupported by their content alone.
de Broglie defended his thesis in late November of 1924. The cover
page is shown in Fig. 2.5. The thesis is short, about 100 pages in all.
Almost all of the chapters are concerned with the effect of special rela-
tivity on the properties of various fundamental particles such as the
energy and phase of a propagating light beam.
In Chapter 3 of the thesis, there is an abrupt change of subject, and
de Broglie addresses hypothesis proposed by Bohr to explain the exis-
tence of discrete atomic energy levels. Seven years earlier, Neils Bohr
proposed that the electrons in atoms traveled in stable orbits, thus al-
lowing atoms to have long lifetimes, an experimental truth we all rec-
ognize. The condition originally proposed by Bohr was
m0␻R2
= n (2.28)
where m is the mass of the electron, ␻ the angular frequency of rota-
tion around the atom, and R the radius of its orbit. For a circular or-
bit, ␻ = v/R, and Bohr’s condition becomes
m0vR = n (2.29)
This has the simple interpretation that the angular momentum of the
electron (= mvR) is quantized in units of
ß =
However, in 1924 there was no idea about why this quantization oc-
curred, or what properties of the electron assured this behavior.
On page 44 of his thesis (Fig. 2.6), de Broglie offered an interpreta-
tion that was consistent with his everyday experience: the Bohr condi-
tion was similar to the behavior of waves of water in a closed circular
tank. Stable states occur when there are standing waves. The condi-
h
ᎏ
2␲
h
ᎏ
2␲
h
ᎏ
2␲

Figure 2.5. Cover page for the doctoral thesis of Louis de Broglie. Each doctoral candi-
date had to write on two subjects: one chosen by the candidate, and one assigned. The ti-
tle of his chosen subject is: “Research on the Theory of Quanta.”

tion for the existence of a standing wave is that the length of the cir-
cuit be an integral number of wavelengths of the standing wave.
There are only certain fixed lengths of the tank that can support
standing waves. The possible tank lengths are given by the relation L
= n␭. The argument of de Broglie contains no equations.
If we substitute the resonance condition of de Broglie into Eq. 2.29
(remember that R = 1/2␲) we get:
m0v冢冣= n
m0v(n␭) = nh
m0v = (2.30)
Equation 2.30 says that the electron has a wavelength that is in-
versely proportional to its momentum. This simple equation does not
appear in de Broglie’s thesis, nor does the extension of this result to
free electrons or other particles like photons. However, de Broglie let
h
ᎏ
␭
h
ᎏ
2␲
l
ᎏ
2␲
Figure 2.6. The proposition by de Broglie in his thesis that the stable orbits of electrons in
atoms are like waves of water in a closed circular tank. Translation of the boxed portion:
“The propagation (of the electron) is therefore analogous to that of a wave of liquid in a
tank that forms a closed path. In order to have a stable condition for the wave, it is physi-
cally evident that the length of the tank must be in resonance with the wave. In other
words, the portions of the wave that are located a full length l of the tank behind preceding
portion of the wave must be in phase with the preceding portion. The condition for reso-
nance is l = n␭.”

the cat out the bag so to speak, for which he was awarded the Nobel
Prize in 1929. He claimed credit in his thesis for “the first plausible
physical explanation for the condition of stable orbits as proposed by
Bohr and Sommerfeld.”
I find that the most interesting part of de Broglie’s reasoning to be
the notion that because quantization exists, there must be an associ-
ated wave behavior.
2.6 Changing Places: How Electrons Behave
in Solids
The energy momentum relationship for an electron is the same as the
energy momentum relationship for a baseball. But, because the elec-
tron has a wavelength, we can represent its behavior by a wavefunc-
tion:
⌿(k, x) = A sin(kx)
A semiconductor crystal is a periodic arrangement of atoms. The peri-
odicity applies to all the physical properties of the crystal. This means
that the allowed values for energy and momentum have to be period-
ic, too:
A sin(kx) = A sin[k(x + a)], where a = the period of the crystal lattice
= A sin kx cos ka – A cos kx sin ka
This is true if
ka = 2␲
or
k =
At these special k values, everything looks the same. Since every-
thing looks the same, we just keep the central zone that has the
unique information between k = –␲/a and k = ␲/a. This is called the
Brillouin zone. Brillouin was a classmate of de Broglie.
The diagram in Fig. 2.7 has its characteristic shape because of the
periodicity, or to use a more general term, the symmetry of the crys-
tal. There are two essential components of the energy–momentum re-
lationship in crystals of real materials: symmetry and chemistry. The
component added by chemistry is the potential added by the atoms
that make up the crystal. Si atoms have a different potential from Ge
atoms, and the energy–momentum relationship for Si is slightly dif-
ferent from that for Ge.
2␲
ᎏ
a

The diagram of energy and momentum is a picture that shows
which states are allowed to be occupied by electrons. You need extra
information to know which states actually are occupied. In Fig. 2.8,
we show an analogous diagram for cars: a road map. On this road
map we see some lines indicating roads. These lines tell you what
places (or states) can be occupied by automobiles under normal or
equilibrium conditions. However, you need more information in order
to know which states are actually occupied by automobiles. The road
map does not tell you much about the velocity of the cars, either. In
Fig. 2.8a, we see that the shape of the road map with nice straight
lines gives us some information about the terrain of the region: it is
probably rather flat. In Fig. 2.8b, we show another road map. Here
the lines are not so simple, indicating that there are rises and falls in
the terrain of this region. These changes in terrain are changes in po-
tential. They play the same role in a road map as chemistry plays in
the energy–momentum relationship for electrons.
This energy–momentum map is called the band structure. It tells
you what are the allowed (or stable) states of energy and momentum
for electrons in the outermost band (or valence band) of the semicon-
ductor. It is analogous to a road map that tells you the streets and
highways (allowed or stable states for an electron) that your car can
have when it is freed from the garage. Just like the road map, the
band structure does not tell you where the electron is. Rather, the
band structure tells you what the possible states are, and about the
properties that an electron would have if it occupied a particular
state. For example, from a road map you can tell the difference be-
tween a residential street and a superhighway. In addition to the lo-
Figure 2.7. Diagram of electron energy as a function of electron momentum for an elec-
tron in a periodic environment. Each period of the structure reflects the same electron be-
havior, just like a mirror.

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NOTRE-DAME mould; the courses of hewn stone gaped
widely at the joints, and grass grew upon the platform where no foot
ever trod; the structure cast a horrid shadow against the sky,
particularly at night, when the moon shone feebly upon those white
skulls, or when the breeze stirred chains and skeletons, and made
them rattle in the darkness. The presence of this gibbet was enough
to give the entire neighbourhood an evil name. The stone base of
the odious structure was hollow. It had been made into a vast vault,
closed by an antique grating of battered iron, into which were cast
not only the human remains taken from the chains at Montfaucon,
but the bodies of all the unfortunates executed upon the other
permanent gallows throughout Paris. In this deep charnel-house,
where so many mortal remains and so many crimes rotted together,
many of the great ones of the earth, many innocent beings, have
laid their bones, from Enguerrand de Marigni, who was the first
victim of Montfaucon, and who was an upright man, down to
Admiral de Coligni, who was the last, and who was likewise a good
man. As for the mysterious disappearance of Quasimodo, all that we
have been able to discover is this : — Some two years or eighteen
months after the events which close this story, when search was
made in the vault at Montfaucon for the body of Olivier le Daim, who
had been hanged two days previous, and to whom Charles VIII. had
accorded permission to be buried at Saint-Laurent in better
company, among all those hideous carcasses two skeletons were
found locked in a close embrace. One of the two, which was that of
a woman, still had about it some fragments of a gown, of stuff once
white, and about its neck was a necklace of grains of adrezarach,
with a little silk bag, adorned with green glass beads, which was
open and empty. These articles were doubtless of so little value that
the hangman had not cared to remove them. The other skeleton,
which held this in so close an embrace, was that of a man. It was
noticed that his spine was curved, his head close between his

shoulder-blades, and one leg shorter than the other. Moreover, his
neck was not

accurate
NOTRE-DAME 249 broken, and it was evident that he had
not been hanged. The man to whom these bones belonged must
therefore have come hither himself and died here. When an attempt
was made to loose him from the skeleton which he clasped, he
crumbled into dust.

accurate
NOTE ADDED TO THE LAST EDITION IT was through error
that this edition was announced beforehand as enlarged by several
new chapters. They should have been spoken of as unpublished; for
if by " new " we understand " recently made," the chapters added to
this edition are not new. They were written at the same time as the
rest of the work ; they date from the same epoch, and came from
the same idea ; they have always been part of the manuscript of "
Notre-Dame de Paris." Furthermore, the author does not understand
how any one can add new developments to a work of this class.
That cannot be done at will. A romance, in his opinion, is born, in a
way in a certain sense necessary, with all its chapters ; a drama is
born with all its scenes. Dp not believe that there is anything
arbitrary of which this whole is composed, — this mysterious
microcosm that you call a drama or a romance. Grafting and
soldering act unfortunately upon works of this nature, which should
spring into being at a single leap and remain such as they are. Once
the thing is done, do not revise or retouch it. Once the book is
published, and its sex — virile or not — recognized and proclaimed,
once the child has uttered its first cry, it is born; here it is; it is made
thus; neither father nor mother can alter it; it belongs to the air and
the sun; let it live or die as it is. Is your book immature? So much
the worse. Never add chapters to an immature book. Is it
incomplete? You should have completed it when you brought it forth.
Is your tree gnarled? 250

accurate
NOTE TO THE LAST EDITION 251 Do not attempt to
straighten it. Is your romance sickly; is your romance to be short-
lived? You cannot give to it the breath which it lacks. Is your drama
born limping? Believe me, you cannot give it a wooden leg. The
author, then, attaches a particular value to this, that the public
should know that the chapters added here have not been made
expressly for this reprint. That they were not published in earlier
editions of the book was for a very simple reason. At the time when
" Notre-Dame de Paris " was printed for the first time, the package
which contained these three chapters was lost. It was necessary to
re-write or omit them. The author concluded that the only two
chapters which would have been important by their scope were
those chapters on art and history whose loss would detract nothing
from the drama and the romance; that the public would be none the
wiser concerning their disappearance; and that he alone, the author,
would be in the secret of this gap. He decided to go on without them
; and besides — to make a clean breast of it,— his indolence
recoiled before the task of re-writing the three lost chapters. He
would have found it Jess work to write a new romance. To-day the
chapters are found, and he seizes the first occasion to replace them
where they belong. Here, then, is his entire work, as he dreamed it,
as he wrote it, good or bad, lasting or fleeting, but such as he
wished it. Without doubt these recovered chapters will have little
value in the eyes of persons, in other respects very judicious, who
have sought in " Notre-Dame de Paris " only the drama, only the
romance; but there are perhaps other readers who have not found it
unprofitable to study the aesthetic and philosophic thought hidden in
this book, who would have been glad, in reading " Notre-Dame de
Paris," to detect under the romance something besides romance,
and to have followed, if we may be allowed somewhat ambitious
expressions, the system of the historian and the object of the artist
through the creation, such as it is, of the poet.

accurate
252 NOTE TO THE LAST EDITION It is to such especially
that the added chapters of this edition will complete " Notre-Dame
de Paris," admitting that " Notre-Dame de Paris " is worth being
completed. The author expresses and develops in one of these
chapters the actual decline of architecture, and, according to him,
the to-day almost inevitable death of this art king, — an opinion
unfortunately very firmly rooted in him, and thoroughly reflected
upon. But he feels the need of saying here that he eagerly desires
that the future may prove him to have been in error. He knows that
art under all its forms may hope everything from the new
generations whose genius, still in the bud, can be heard springing
forth in our studios. The seed is in the ground; the harvest will
certainly be fine. He fears only, and in the second volume of this
edition one can see why, that the sap has been entirely withdrawn
from the old soil of architecture which during so many ages has
been the best garden for art. However, there is to-day so much life
in our artistic youth, so much power, and, as it were, predestination,
that in our architectural schools in particular, at the present time, the
professors, who are detestable, make not merely unwittingly, but
even in spite of themselves, scholars who are excellent, — the
reverse of that potter of whom Horace speaks, who would have
made amphorae and produced only saucepans. Currit rota, urceus
exit. But, at all events, whatever may be the future of architecture,
in whatever way our young architects determine some day the
question of their art, while waiting for new monuments, let us keep
the ancient ones. Let us, if possible, inspire the nation with the love
of national architecture. That, the author declares, is one of the
principle objects of this book; that, one of the principal objects of his
life. " Notre-Dame de Paris " has perhaps opened some true
perspectives in the art of the Middle Ages, in that marvellous art not
as yet understood by some, and, what is worse, misunderstood by
others. But the author is far from considering as accomplished the
task which he voluntarily assumed,

accurate
NOTE TO THE LAST EDITION 253 he has already pleaded,
upon more than one occasion, for our ancient architecture; he has
already denounced loudly many of the profanations, many of the
destructions, many of the impious alterations. He will never cease to
do so. He has pledged himself to return often to this subject. He will
re* turn to it. He will be as indefatigable in defending our historic
buildings as our iconoclasts of the schools and the academies are in
attacking them; for it is a sad thing to see into what hands the
architecture of the Middle Ages has fallen, and in what way the
bungling plasterers of the present day treat the ruins of that great
art. It is even a shame for us, intelligent men who see it done, and
who content ourselves in crying out against it. And I am not
speaking here only of what goes on in the provinces, but of what is
done in Paris, at our gates, under our windows, in the great city, —
this city of letters, of the press, of free speech, and of thought. We
cannot resist signalizing as they deserve, — to end this note, — a
few acts of vandalism which are every day projected, debated,
begun, continued, and carried out peaceably under our very eyes,
under the eyes of the artistic public of Paris, in face of criticism that
is disconcerted by so much audacity. They have just pulled down the
archbishop's palace, — a building in poor taste, and the evil is not
great; but at one blow with the archbishop's palace they have
demolished the bishop's, a rare ruin of the fourteenth century, which
the demolishing architect could not distinguish from the rest. He has
rooted up the wheat with the tares; it is all the same to him. They
are talking of tearing down the admirable Chapelle de Vincennes, to
make from its stones some sort of a fortification, I know not what, of
which Daumesnil has no need whatever. While they repair at great
expense the Bourbon Palace, — that hovel, — they allow the
magnificent windows of the Sainte-Chapelle to fall in before the
force of the equinoctial gales. There has been for some days past a
scaffolding around the tower of Saint- Jacques dc la Boucherie, and

one of these days the pickaxe will be applied to it. There has been
found a mason to build a

accurate
254 NOTE TO THE LAST EDITION small white house
between the venerable towers of the Palace of Justice ; another has
been found to maim Saint Germain des Pres, the feudal abbey with
the three bell-towers. There will be found, no doubt, another to lay
low Saint-Germain 1'Auxerrois. All these masons pretend to be
architects, are paid by the prefecture, or from the royal treasury, and
wear green coats. All the evil that bad taste can inflict upon good
taste they have done. At the moment we are writing, — deplorable
sight ! — one of them has possession of the Tuileries, another has
made a deep gash directly across the beautiful face of Philibert
Delorme; and it certainly is not one of the least scandals of our time
to see with what effrontery the clumsy architecture of this
gentleman has sprawled across one of the most delicate fa9ades of
the Renaissance. PARIS, October 20, 1832. THE END.

accurate
THE LAST DAYS OF A CONDEMNED FROM THE FRENCH OF
M. VICTOR HUGO WITH OBSERVATIONS ON CAPITAL PUNISHMENT,
BY SIR P. HESKETH FLEETWOOD, BART., M.P.

accurate
DEDICATION TO THE QUEEN'S MOST GRACIOUS MAJESTY
MADAM, — The personal favour which jour Majesty has been so
graciously pleased to confer on me, in allowing the present
dedication, — thus implying a confidence in the proba.ble nature of
the work, — will not, I trust, be found to have been misused by me,
should your Majesty hereafter honour the volume by perusal. In thus
being the medium through which the pleadings of a class of society,
so far removed from the sympathy of mankind, approach the throne
of your Majesty, may I be permitted to take this opportunity of
expressing what is responded to by every feeling heart in your
Majesty's dominions, — a respectful appreciation of the mildness and
clemency which have pervaded the administration of the laws during
the present merciful reign. With sincere prayers for the happiness of
your Majesty, I have the honour to be, MADAM, Your Majesty's Most
humble and faithful Servant and subject, P. HESKETH FLEETWOOD.
Ii oss ALL HALL, Lancashire.

accurate
PREFACE "To be, or not to be — that is the question." THAT
is indeed the question we are about to consider, — BEING or DEATH;
a short sentence, but of unequalled importance. Yet how little does
the demise of a fellow-man dwell on the human mind, unless the
ties of kindred, or any peculiarity of circumstance by which the event
may happen to bi; encircled, impart to it adventitious interest. A
newspaper paragraph entitled " Awful and sudden death " may for a
moment arrest our attention ; but it is the *; awful and sudden," not
the actual transit, which attracts the fancy. Perchance, also, it may
be printed in rather a larger type than the adjoining paragraph, or
we may expect to find some exciting detail of the facts of the case;
but the awful Reality, the earthly ending of the being, immortal
though it is to be, elicits little sympathy, and the wearied eye turns
to some other news. The dying speech of the malefactor arrests our
attention; the cfead speaker of it is unregarded as a lump of clay.
Who that amidst the excitement of a crowded court of justice has
turned his thoughts within himself, and divesting the scene of all the
panoply of pomp which surrounds him, has reflected on the moral
effect to be the result of the sentence of death if executed, but has
felt his sympathy rather awakened in favour of the culprit, and
confessed to himself how inefficient the gibbet is when viewed
(according to its intended purpose) as tlie roadside guidepost, by
which other earthly travellers, who might be disposed to stray,
should be warned of a pathway to be avoided. 5

accurate
6 PREFACE Alas! the body on the gibbet is but like the
scarecrow in the field of grain, — little heeded by its brethren in
plumage, scarcely noticed by aught save the vacant gape of curiosity
; it dangles for a time, and is remembered no more ! But let us take
a more serious view of the question, — one which commands our
deepest respect and our gravest veneration. Let us consider the
question of the assumed right to take human life on the warranty, or,
as is sometimes said, on the express command of Scripture. It has
been often urged that it is expressly commanded in the Old
Testament that " he who sheddeth man's blood, by man shall his
blood be shed ; " and, consequently, that the punishment of death
for murder is sanctioned by the high and holy God who inhabiteth
eternity. How cautious should we be, to ascertain that no fallacy
exists in this our opinion ! I grant that, according to our translation,
the above isolated text, if taken alone, may be so construed; but
what are the acts of the Creator recorded as following upon this
text? What was his first judgment on the first of murderers, Cain?
Not only did he not inflict death, but by a special providence
protected him from its infliction by his fellow-man. Behold again the
case of David, guilty of at least imagining the death of Uriah. Was
David struck dead for the crime? Whatever an isolated chapter
(much less, then, a single verse) may amount to of itself, if we take
the context of the same part of Genesis and behold the first
murderer even especially guarded, by God's mark, from the effect of
" every man's hand being against him ; " and again if we search the
New Testament, where we find no passage, under the new
dispensation, that can be construed to call for the infliction of death
for murder, — from these results I submit that the question must be
left solely to mundane argument, to stand or fall by its own efficacy
as a preventive of murder, and that the isolated phrase of Scripture
should not be construed into a command as to what ought to be
done, but rather as the probable result of human revenge, a feeling
at variance with

accurate
PREFACE 7 God's holy ordinance; for we read, " Vengeance
is mine, saith the Lord," — expressly and clearly withholding the
power over hurr an life from mere mortal judgment. Let me here
give a short extract from the " Morning Herald,"'— a paper which
has always so consistently and ably advocated the sacredness of
human life: — 44 On the motion of Mr. Ewart, some important
returns connected with the subject of CAPITAL PUNISHMENTS have
been made to the House of Coni i aons, and ordered to be printed.
"first Class. — A return of the number of persons sentenced to death
for MURDER in the year 1834, whose punishment was commuted, —
specifying the counties in which their crimes occurred, and stating
the number of commitments for murder in the same counties during
the same year and in the following year, together with the increase
or diminution of commitments for murder in the same counties in
the year following the commutation of the sentences; similar returns
for 1835, 1836, 1837, and :i838. "Second Class. — A return of the
number of EXECUTIONS which took place in England and Wales
during the three years ending the 31st day of December, 1836, and
also during the three years ending the 31st day of December, 1839,
together with the number of commitments in each of those periods
respectively for offences capital, on the 2d day of January, 1834.
Also, the total number of convictions for the same offences, together
with the centesimal proportions of convictions to commitmmts in
each of those periods respectively. " The facts set forth upon the
face of these returns furnish very strong evidence, indeed, to prove
the utter inutility of CAPITAL PUNISHMENTS as a means of
preventing or repressing crime. "What are the facts? "We find that in
one county (Stafford) in the year 1834 the sentence of one convict
for murder was commuted. In that year the commitments for
murder were six, and in the following year the commitments for that
crime were also six. Thus the commutation of the sentence in that
instance was followed by neither a diminution nor an increase, of
commitments for murder. " It is sufficient for the argument of the

advocates of abolition of capit d punishment to show that the
suppression of the barbarous exhibitims of the scaffold would not
necessarily cause an increase of heinojs offences; for if the amount
of crime were to remain the same under laws non-capital as under
those which are capital, to prefer the latter to the former would
evince a passion for the wanton and unavailing destruction of human
life, unspeakably disgraceful to the Government or Legislature of any
civilized country. " In Derbyshire, in the year 1835, we find a similar
result following a commutation of sentence for murder to that which
followed a similar commutation in the county of Stafford in the
preceding year; namely, the same number of commitments for
murder in the year following the

accurate
8 PREFACE commutation as in that in which it occurred, —
being two in each; thus, also, in this instance, there was neither
increase nor diminution of the crime of murder in the year following
that of the commutation, judging from the number of commitments.
" In Warwickshire, in the year 1835, the sentence of a convict for
murder was commuted, the number of commitments for the crime in
that year being five, whereas in the year following there was but one
commitment. In this instance, then, we have not only no increase of
the crime of murder, but an actual diminution amounting to four. "In
Westmoreland, in the year 1835, there was one commutation; and
the commitments in the year following showed neither an increase
nor diminution, being two in each. " In Cheshire, in the year 1836,
the sentences of two convicts for murder were commuted^ the
commitments for the crime in that year being two; the commitments
for the year following were also two, showing neither an increase
nor diminution. 44 Here we have an instance where the sentences of
all convicted were commuted, and no increase of the crime followed.
44 In Devonshire, in the year 1836, there was one commutation of
sentence for murder, the commitments being four. In the year
following there were no commitments, making a decrease of four. "
In Lancashire, in the year 1836, the sentences of four convicts for
murder were commuted, the number of commitments in the same
year being seven. In the year following the number of commitments
was one, making a decrease of six. " In the county of Norfolk, in the
year 1836, the sentences of five convicts for murder were
commuted, the number of commitments for the same year being
eight. In the following year the number of commitments for murder
were but five, giving a decrease of three. "In the counties of Norfolk,
Nottingham, and Stafford, in the year 1837, there was one
commutation of the sentence of murder for each respectively. The
result was a fall in the committals of the following year from five to
two in the first county, — giving a decrease of three; in the second
county a fall from one to none; in the third county neither an

increase nor diminution, — the number of committals having been
three in each year. 44 In the counties of Lincoln, Stafford, and
Denbigh, in the year 1838, there was respectively one commutation
of the sentence for murder. The result was that in the following year
the commitments fell from two to one in the first county, from three
to one in the second, and from one to none in the third, thus giving
respectively a decrease of onehalf, two-thirds, and of the whole. The
last is more correctly called an extinction than a decrease. 44 In
Cheshire, Middlesex, Somersetshire, and Surrey, in the year 1838,
there were, respectively, two commutations of the sentence for
murder. The result was that in the first county the commitments, as
between that year and the year following, fell from two to one; in
the second county they fell from seven to three; in the third, from
three to one; and in the fourth, from three to two; thus giving a
diminution, respectively, of one-half, four-sevenths, two-thirds, and
one-third. " In Kent, in the year 1838, the sentences of nine convicts
for murder

accurate
PREFACE 9 were commuted, the commitments for that
crime in the same year being seventeen. In the following year the
commitments foi murder were only two, showing a decrease of
fifteen. In this last case, however, we cannot in fairness press the
argument in favour of the salutary effect of discontinuing capital
punishments to the extent that the arithmetical table would show.
That year, if we recollect right, was the year of the extraordinary
outbreak headed by the madman Courtenay or Thorn. That event
swelled the commitments for murder to an unprecedented height.
The fall in the commitments from seventeen, in that year, to two in
the year following, is not a fall under equal circumstances, and it
wculd be illogical to make it an argument for more than this: that
society received no detriment because the deluded followers of the
frantic Courtenay were sent to a penal settlement, instead of being
strangled on tie scaffold. "Looking to the table of EXECUTIONS, we
find that in the three years ending the 31st of December, 1836, the
number executed was 85, while during the three years ending the
31st of December, 1839, the number was only twenty-five. The
commitments in the former period were 3,104, in th

accurate
10 PREFACE Yet we would dispute their right to have
always blood for blood; why then may we not question the right ever
to have blood shed, under Bible sanction at least? God makes no
mention of motives or comparative reasonings as to guilt ; in this His
supposed command there is no discretionary option to soften its
asserted force. By whatever means or under whatever circumstances
one man kills another, blood is shed; and if blood for blood should
hold good, then under this reasoning the slayer must die. If it be
argued, that wilful shedding of blood is meant, I point to the words
of the text ; they refer to " life for life," they give no exceptions : "
Who then, oh man! made thee a judge to tell the signs of the
times?" Once grant an exception to execution, once admit the
doctrine of reprieve, and the authority, as a command, in the Bible
ceases altogether. Those who argue in favour of executions say, "
But as an earthly punishment, we may hang ; " may, indeed ! There
are fifty things we may do that are better avoided. Why need we
hang, when other punishments will suffice and have been proved to
have succeeded in other cases? A very few years back, and the
advances we have recently made in the civilization of our laws would
have been scouted as equally Utopian, as is now considered the
attempt to abolish the punishment of death altogether. Let us reflect
too that in a case of murder, the prisoner (from a feeling which
imperceptibly affects the minds of all) is looked on with a degree of
suspicious anxiety to convict that almost watches to make out a case
against him sufficient to condemn. The very fact of his being put on
his trial for murder prejudges him in our eyes; and a slight variation
in reporting a conversation has marvellously increased many a poor
man's danger of the gallows. There is no recalling the erroneously
condemned from the grave; a wrong judgment cannot there be
reversed! Let us bear in mind, also, that the wisest judges may
sometimes decide wrongfully. They were considered by myself and
others to have erred in respect to the privileges of the House

accurate
PREFACE 11 of Commons; why might they not commit a
similar error in the case of a prisoner? Bit enough; let errors in
judgment speak for themselves. The}r contain matter for deep
reflection and self-examination for us all. If the average number of
executions be reduced, even by one, I shall have the satisfaction of
feeling at least that I have been an humble labourer in the great
cause of mercy, which could not have a more zealous advocate,
though it may have many more powerful and successful supporters.
Happy are we if, in all we do during the course of our career, we
have not to answer for one death; for the bitter word, the cruel
neglect, the light injurious observation, may be the cause of death,
as well as the bludgeon or the steel. I would here desire to make a
few observations as to the medium through which I have introduced
to the public my opinions in favour of the abolition of Capital
Punishment, and the advantages to the cause obtained from its
appearing in the form of a translation, the reflections being those of
a foreigner who looked not to England when he penned his work. In
all this there is a beneficial distraction of ideas created, for we look,
as it were, at a foreign scene when we read the interesting paper of
the narrative, — the sentiments conveyed, the idioms transcribed,
are foreign, and the reader appropriates alone the portion he feels is
applicable to the circumstances of his own country; in fact, he
examines the context, not as he would an original treatise, but as
one who would apply the problems found advantageous in one
region to another. He cavils not at words or similes ; his criticism is
reserved for the object at which the translator aims, — no matter
even if the phraseology be too flowery, the expressions too strong.
There may be strange similes, strained amplifications; he studies but
a translation, and cares comparatively little for them. True, he may
have some curiosity awakened as to what the original author was in
feeling and ideas; but these thoughts are light and evanescent
compared with the anxiety, or more properly the curiosity, he

accurate
12 PREFACE has to ascertain what could be the translator's
ideas in thus " wasting the midnight oil " by reducing into the
phraseology of his vernacular (English) tongue, the varied thoughts,
the acute observations, the (to English ears) novel ideas of that
clever, eccentric, single-minded writer, Victor Hugo. " What was the
aim of the copyist ? " methinks I hear repeated by many; and as my
object is one of serious importance to the realities of life, and to
arrest the attention of the reader beyond the mere passing hour, I
reply: The object for which I plead is the priceless value of human
life. Well and truly may the reading public, — and happy for this my
dear native land is it that its public is a reading one, — well may this
public explain, " who is he, or what his view, who has thus dared to
scatter these additional leaves on the pathway of a nation's
thoughts? Why has he done so, what motives urged him, what end
did he seek ? " Such are the surmises that may flit across the
reader's brain, and the translator humbly hopes that the lightning
scowl, or the thunder of maledictive criticism, will be directed alone
against the oaken plank of a hundred years' growth, and that this his
nautilus bark will feel no breeze beyond the aura populi. Probably to
the English public many of the observations in this translation will be
original. Haply to the gay and frivolous the thoughts may appear
exaggerated; but, alas! with too many they will come home to the
heart. Numbers there are, who, steeped in misery before they were
steeped in crime, had as little inclination to sin as their more
fortunate fellow-men, but whose first transgressions were the
offsprings of their misery, the necessitous urgings of their poverty.
Yes, gentle reader, — for among the fair and young I hope to have
many readers; readers whose hearts yet know how to feel, — ye
would I address, and exclaim, for the startling fact is but too true,
that though, — " we who in lavish lap have rolled And every year
with new delight have told; We who recumbent on the lacquered
barge Have dropped down life's gay stream of pleasant marge; We
may extol life's calm untroubled sea,*'

accurate
PREFACE 13 well may the miserable, the guilty answer, —
"The storms of misery never burst on thee." ** You NEVER FELT
POVERTY. You never were comparatively tempted to crime." " A
noble," say they, and truly, " a noble is tried, is judged by his peers,
as being those who alone1 are considered to know, to be able to
appreciate his case. Let poverty have her peers also." " My poverty
and not my will consented" is a phrase to which too little
consideration is given when we discuss the question of crime and
punishment; for though poverty cannot be pleaded by the criminal in
justification of his offence (nor should such justification be permitted
in the legal view), Society, whose interests are represented by the
tribunal which adjudges, should be careful that any circumstances or
defects in its conformation which may have had a tendency even to
induce the criminality of the culprit, should go in mitigation of his
punishment. It would be a startling observation in the present day,
and one for which Society is not yet prepared, to hear the assertion
made that punishment for crime is more often unjust than just ; but
after much reflection on the origin of crime, humanly speaking, I am
constrained to come to this conclusion : that the criminality of
individuals is more frequently traceable to the evils incidental to an
imperfect social system than to the greater propensity towards
crime, as affecting others, that exists in the heart of one person if
compared with another. Hjid the judge or the prosecutor entered life
under the same circumstances as the prisoner, been early initiated
into the same habits, been taught to view society through the same
distorted glass, and had their feelings blunted by the same cold
blasts of adversity, who shall say what their respective positions
might have been? In the phrase " My poverty but not my will
consented," let me not be understood to speak of poverty merely in
the light of want of money; that is a very narrow view, and very
confined as to what forms the real pains of poverty

accurate
14 PREFACE Poverty is the want of means, intellectual and
moral as well as pecuniary, to feed the being who is placed on the
area of the world; with mind active as well as body, sustenance is
necessary to its existence. If the poor man cannot obtain bread, he
takes to gin to assuage cravings of the stomach. No less, if the mind
cannot obtain light to guide it in the onward path, the visual organs
become habituated to the dark and murky gloom of almost darkness
; and through these confused gleamings, no wonder if the being fall
into the pits and whirlpools which beset with danger the pathway of
man, even when blessed with the clear light of day ; how much
more, therefore, when he has not light to discern good from evil, nor
an intellectual poor-law to supply him with food, when a beggar by
the way-side of knowledge ! How strange it is that we can
incarcerate the bodies of the poor because they are poor, objecting
to let them be dependent on casual charity for bodily sustenance,
and yet cannot be equally strict in legislating for the mind. Surely if,
as members of one common society, we contend it is necessary for
the well-being of the community at large that each person should be
provided with work to enable him to procure food, and that if
persons be unable to obtain work, or purchase food, then that the
State shall provide for them, — should we not equally be provident
for the mental as well as we are for the corporeal wants of those
who hold a less fortunate position in the scale of society ; more
particularly when we reflect on the effect mind has on matter, and
that did we sufficiently provide for the former, each individual would
probably find little difficulty in procuring a supply for his bodily
wants. The poverty of the mind, if relieved, will probably be a
permanent good; whereas bodily relief is at best but temporary. How
vast, too, is the effect of knowledge, on the creation of food.
Knowledge teaches industry, knowledge and industry multiply an
hundred fold the product of labour. Comfort and security are thus
increased; idleness, and consequently crime, is diminished, — for a
man of information is

accurate
PREFACE 15 seldom idle, and one surrounded with comforts
is rarely inclined to commit crimes against society. Would not,
therefore, the effects resulting from education be the best
preventative of crime? — and, if so, heavy indeed is the
responsibility of every man who puts an impediment in the way of a
nation's enlightenment. Circumstanced as Great Britain now is,
internally speaking, with her countless millions congregated or hived
in large towns, ready to follow any leader of more daring or greater
knowledge than themselves, comparatively indifferent as to the
means for compassing any much desired end, — though actuated by
no wish to work ill to others, even when excited beyond the
unmanageableness of irrational physical force, — there is much to
be feared from the effects of any combustion which might suddenly
inflame a people thus charged to the full with every ingredient
requisite for scenes of violence, whilst at the same time, through a
strong line of prescribed demarcation, separated from the privileged
classes ; and it cannot but be mainly by the controlling power of
knowledge that we can expect to see the masses endeavouring to
be satisfied with their lot in life. Thus it is, as I have before asserted,
that the poverty of opportunity for information, and consequently
acquirement of knowledge, originates much of the present state of
crime. Oh, that I could distinctly see my way through the halo which
as yet obscures that glorious day, when ignorance shall be deplored
as much as shame! With what satisfaction would the statesman then
die and bequeath his country to the care of, not the fate of accident,
as now, but the masses of its own population. Methinks the gleam
which harbingers this bright morning, already, though faintly, begins
to tinge the horizon, under the happy auspices of our beloved Queen
; and to the credit of the liberal advisers of Her Majesty, a more
liberal arrangement of schools has been established,— though it
probably remains for ages yet unborn to develop fully the blessings
of such a system. Well worthy, aye, brighter than a diadem of a

thousand stars, is the advancement of a nation's happiness. May
such thoughts have

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