The Science and Engineering
of Materials, 4th ed
Donald R. Askeland – Pradeep P. Phulé
Chapter 20 – Photonic Materials
1
Objectives of Chapter 20
 To present a summary of fundamental
principles that have guided applications of
optical materials.
 To explore two avenues by which we can
use the optical properties of materials:
emission of photons from materials and
interaction of photons with materials.
2
Chapter Outline
 20.1 The Electromagnetic Spectrum
 20.2 Refraction, Reflection,
Absorption, and Transmission
 20.3 Selective Absorption,
Transmission, or Reflection
 20.4 Examples and Use of Emission
Phenomena
 20.5 Fiber Optic Communication
System
3
Section 20.1
The Electromagnetic Spectrum
 Light is energy, or radiation, in the form of waves or
particles called photons that can be emitted from a
material.
 The important characteristics of the photons—their
energy E, wavelength λ, and frequency ν—are related by
the equation
4
Figure 20.1 The electromagnetic spectrum of radiation; the bandgaps
and cutoff frequencies for some optical materials are also shown.
(Source: From Optoelectronics: An Introduction to Materials and Devices,
by J. Singh. Copyright © 1996 The McGraw-Hill Companies. Reprinted by
permission of The McGraw-Hill Companies.)
5
Figure 20.1 The electromagnetic spectrum of radiation; the bandgaps
and cutoff frequencies for some optical materials are also shown.
(Source: From Optoelectronics: An Introduction to Materials and
Devices, by J. Singh. Copyright © 1996 The McGraw-Hill Companies.
Reprinted by permission of The McGraw-Hill Companies.)
6
Section 20.2
Refraction, Reflection, Absorption,
and Transmission
 Index of refraction - Relates the change in velocity and
direction of radiation as it passes through a transparent
medium (also known as refractive index).
 Dispersion - Frequency dependence of the refractive
index.
 Reflectivity - The percentage of incident radiation that is
reflected.
 Linear absorption coefficient - Describes the ability of a
material to absorb radiation.
 Photoconduction - Production of a voltage due to the
stimulation of electrons into the conduction band by light
radiation.
7
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Figure 20.2 (a) Interaction of photons with a material. In
addition to reflection, absorption, and transmission, the bream
changes direction, or is refracted. The change in direction is
given by the index of refraction n. (b) The absorption index (k)
as a function of wavelength.
8
9
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Figure 20.3 (a) When a ray of light enters from material 1
into material 2, if the refractive index of material 1 (n1) is
greater than that of material 2 (n2), then the ray bends away
from the normal and toward the boundary surface. [1, 9] (b)
Diagram a light beam in glass fiber for Example 20.1.
10
Example 20.1
Design of a Fiber Optic System
Optical fibers are commonly made from high-purity silicate
glasses. They consist of a core that has refractive index (~ 1.48)
that is higher than a region called cladding (refractive index ~
1.46). This is why even a simple glass fiber in air (refractive index
1.0) can serve as an optical fiber. In designing a fiber optic
transmission system, we plan to introduce a beam of photons from
a laser into a glass fiber whose index of refraction of is 1.5. Design
a system to introduce the beam with a minimum of leakage of the
beam from the fiber.
Figure 20.3 (b) Diagram a
light beam in glass fiber
for Example 20.1.
11
Example 20.1 SOLUTION
To prevent leakage of the beam, we need the total internal
reflection and thus the angle θt must be at least 90o.
Suppose that the photons enter at a 60o angle to the axis
of the fiber. From Figure 20.3(b), we find that θi = 90 - 60
= 30o. If we let the glass be Material 1 and if the glass
fiber is in air (n = 1.0), then
Because θt is less than 90o, photons escape from the fiber.
To prevent transmission, we must introduce the photons at
a shallower angle, giving θt = 90o.
12
Example 20.1 SOLUTION (Continued)
If the angle between the beam and the axis of the fiber is
90 - 41.8 = 48.2 or less, the beam is reflected.
If the fiber were immersed in water (n = 1.333), then:
In water, the photons would have to be introduced at an
angle of less than 90 – 62.7 = 27.3 in order to prevent
transmission.
13
Example 20.2
Light Transmission in Polyethylene
Suppose a beam of photons in a vacuum strikes a sheet of
polyethylene at an angle of 10o to the normal of the surface of
the polymer. Calculate the index of refraction of polyethylene
and find the angle between the incident beam and the beam as
it passes through the polymer.
Example 20.2 SOLUTION
The index of refraction is related to the high-frequency
dielectric constant. For this material the high-frequency
dielectric constant k= 2.3:
The angle θt is:
14
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license.
Figure 20.4 The linear absorption coefficient relative to
wavelength for several metals. Note the sudden decrease
in the absorption coefficient for wavelengths greater than
the absorption edge.
15
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Figure 20.5 Fractions of the original beam that are
reflected, absorbed, and transmitted.
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Figure 20.6
Relationships between
absorption and the
energy gap: (a) metals,
(b) Dielectrics and
intrinsic semiconductors,
and (c) extrinsic
semiconductors.
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Figure 20.7 (a)
Photoconduction in
semiconductors involves
the absorption of a
stimulus by exciting
electrons from the valence
band to the conduction
band. Rather than
dropping back to the
valence band to cause
emission, the excited
electrons carry a charge
through an electrical
circuit. (b) A solar cell
takes advantage of this
effect.
19
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Figure 20.8 Elements of a photonic system for transmitting information
involves a laser or LED to generate photons from an electrical signal,
optical fibers to transmit the beam of photons efficiently, and an LED
receiver to convert the photons back into an electrical signal.
20
Example 20.3
Determining Critical Energy Gaps
Determine the critical energy gaps that provide complete
transmission and complete absorption of photons in the visible
spectrum.
Example 20.3 SOLUTION
The visible light spectrum varies from 4  10-5 cm to 7  10-5
cm. The minimum Eg required to assure that no photons in the
visible spectrum are absorbed is:
21
Example 20.3 SOLUTION (Continued)
The maximum Eg below which all of the photons in the
visible spectrum are absorbed is:
For materials with an intermediate Eg, a portion of the
photons in the visible spectrum will be absorbed.
22
Example 20.4
Design of a Radiation Shield
A material has a reflectivity of 0.15 and an absorption
coefficient (α) of 100 cm-1. Design a shield that will permit
only 1% of the incident radiation from being transmitted
through the material.
Example 20.4 SOLUTION
The fraction of the incident intensity that will be
transmitted is:
The material should have a thickness of 0.0428 cm in order
to transmit 1% of the incident radiation.
23
Section 20.3
Selective Absorption, Transmission,
or Reflection
 Unusual optical behavior is observed when photons are
selectively absorbed, transmitted, or reflected.
24
Example 20.5
Design of a ‘‘Stealthy’’ Aircraft
Design an aircraft that cannot be detected by radar.
Example 20.5 SOLUTION
1. We might make the aircraft from materials that are
transparent to radar. Many polymers, polymer-matrix
composites, and ceramics satisfy this requirement.
2. We might design the aircraft so that the radar signal is
reflected at severe angles from the source.
3. The internal structure of the aircraft also can be made to
absorb the radar. For example, use of a honeycomb material
in the wings may cause the radar waves to be repeatedly
reflected within the material.
4. We might make the aircraft less visible by selecting
materials that have electronic transitions of the same energy
as the radar.
25
Section 20.4
Examples and Use of
Emission Phenomena
 X-rays - Electromagnetic radiation in the wavelength
range ~ 1 to 100 Å.
 Continuous spectrum - Radiation emitted from a material
having all wavelengths longer than a critical short
wavelength limit.
 Luminescence - Conversion of radiation to visible light.
 Fluorescence - Emission of light obtained typically within
~ 10-8 seconds.
 Phosphorescence - Emission of radiation from a material
after the stimulus is removed.
26
Section 20.4 (Continued)
 Light-emitting diodes (LEDs) - Electronic p-n junction
devices that convert an electrical signal into visible light.
 Electroluminescence - Use of an applied electrical signal
to stimulate photons from a material.
 Laser - The acronym stands for light amplification by
stimulated emission of radiation. A beam of
monochromatic coherent radiation produced by the
controlled emission of photons.
 Thermal emission - Emission of photons from a material
due to excitation of the material by heat.
27
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Figure 20.9 When an
accelerated electron
strikes and interacts
with a material, its
energy may be reduced
in a series of steps. In
the process, several
photons of different
energies E1 to E5 are
emitted, each with a
unique wavelength.
28
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herein under license.
Figure 20.10 The continuous and characteristic spectra of radiation
emitted from a material. Low-energy stimuli produce a continuous
spectrum of low-energy, long-wavelength photons. A more intense,
higher energy spectrum is emitted when the stimulus is more powerful
until, eventually, characteristic radiation is observed.
29
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Figure 20.11 Characteristic x-rays are produced when electrons
change from one energy level to a lower energy level, as illustrated
here for copper. The energy and wavelength of the x-rays are fixed
by the energy differences between the energy levels.
30
Example 20.6
Design/Materials Selection for
an X-ray Filter
Design a filter that preferentially absorbs Kβ x-rays from the
nickel spectrum but permits Kα x-rays to pass with little
absorption. This type of filter is used in x-ray diffraction
(XRD) analysis of materials.
31
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Figure 20.12 Elements have a
selective lack of absorption of
certain wavelengths. If a filter
is selected with an absorption
edge between the Kα and Kβ
peaks of an x-ray spectrum, all
x-rays except Kα are absorbed
(for Example 20.6).
32
Example 20.6 SOLUTION
When determining a crystal structure or identifying
unknown materials using various x-ray diffraction
techniques, we prefer to use x-rays of a single
wavelength. If both Kα and Kβ characteristic peaks are
present and interact with the material, analysis becomes
much more difficult.
However, we can use the selective absorption, or
the existence of the absorption edge, to isolate the Kα
peak. Table 20-2 includes the information that we need. If
a filter material is selected; such that the absorption edge
lies between the Kα and Kβ wavelengths, then the Kβ is
almost completely absorbed, whereas the Kα is almost
completely transmitted. In nickel, Kα = 1.660 Å and Kβ =
1.500 Å. A filter with an absorption edge between these
characteristic peaks will work. Cobalt, with an absorption
edge of 1.608 Å, would be our choice. Figure 20-12 shows
how this filtering process occurs.
33
Example 20.7
Design of an X-ray Filter
Design a filter to transmit at least 95% of the energy of a
beam composed of zinc Kα x-rays, using aluminum as the
shielding material. (The aluminum has a linear absorption
coefficient of 108 cm-1.) Assume no loss to reflection.
Example 20.7 SOLUTION
The final intensity will therefore be 0.95I0.
We would like to roll the aluminum to a thickness of
0.00047 cm or less. The filter could be thicker if a material
were selected that has a lower linear absorption coefficient
for zinc Kα x-rays.
34
Example 20.8
Generation of X-rays for XRD
Suppose an electron accelerated at 5000 V strikes a copper
target. Will Kα, Kβ, or Lα x-rays be emitted from the copper
target?
Example 20.8 SOLUTION
The electron must possess enough energy to excite an electron
to a higher level, or its wavelength must be less than that
corresponding to the energy difference between the shells:
For copper, Kα is 1.542 Å, Kβ is 1.392 Å, and Lα is 13.357 Å.
Therefore, the Lα peak may be produced, but Kα and Kβ will
not.
35
Example 20.9
Energy Dispersive X-ray Analysis (EDXA)
The micrograph in Figure 20.13 was obtained using a
scanning electron microscope at a magnification of 1000. The
beam of electrons in the SEM was directed at the three
different phases, creating x-rays and producing the
characteristic peaks. From the energy spectra, determine the
probable identity of each phase. Assume each region
represents a different phase.
36
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Figure 20.13
Scanning electron
micrograph of a
multiple-phase
material. The
energy distribution
of emitted radiation
from the three
phases marked A, B,
and C is shown.
The identity of each
phase is determined
in Example 20.9.
37
Example 20.9 SOLUTION
All three phases have an energy peak of about 1.5 keV =
1500 eV, which corresponds to a wavelength of:
In a similar manner, energies and wavelengths can be
found for the other peaks. The identity of the elements in
each phase can be found, as summarized in the table.
38
Example 20.9 SOLUTION (Continued)
Thus, phase A appears to be an aluminum matrix, phase
B appears to be a silicon needle (perhaps containing some
aluminum), and phase C appears to be an Al-Si-Mn-Fe
compound. Actually, this is an aluminum-silicon alloy. The
stable phases are aluminum and silicon, with inclusions
forming when manganese and iron are present as
impurities.
39
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Figure 20.14
Luminescence occurs when
photons have a wavelength
in the visible spectrum. (a)
In metals, there is no
energy gap, so luminescence does not occur. (b)
Fluorescence occurs when
there is an energy gap. (c)
Phosphorescence occurs
when the photons are
emitted over a period of
time due to donor traps in
the energy gap.
40
Example 20.10
Design/Materials Selection for
a Television Screen
Select a phosphor material that will produce a blue image
on a television screen.
Figure 20.1 The
electromagnetic spectrum
of radiation; the bandgaps
and cutoff frequencies for
some optical materials are
also shown. (Source: From
Optoelectronics: An
Introduction to Materials
and Devices, by J. Singh.
Copyright © 1996 The
McGraw-Hill Companies.
Reprinted by permission of
The McGraw-Hill
Companies.)
41
42
Example 20.10 SOLUTION
Photons having energies that correspond to the color blue
have wavelengths of about 4.5  10-5 cm (Figure 20.1).
The energy of the emitted photons therefore is:
Typical phosphorescent materials for television screens
might include CaWO4, which produces photons with a
wavelength of 4.3  10-5 cm (blue).
43
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license.
Figure 20.15 Diagram of a light-emitting diode (LED). A
forward-bias voltage across the p-n junction produces photons.
44
Figure 20.16 The laser converts a stimulus into a beam of
coherent photons. The mirror on one side is 100%
reflecting, the mirror on the right transmits partially.
(Source: From Optical Materials: An Introduction to
Selection and Application, by S. Musikant, p. 201, Fig. 10-1.
Copyright © 1985 Marcel Dekker, Inc.)
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Figure 20.17 Creation of a laser beam from a semiconductor: (a) Electrons
are excited into the conduction band by an applied voltage. (b) Electron 1
recombines with a hole to produce a photon. The photon stimulates the
emission of photon 2 by a second recombination. (c) Photons reflected from
the mirrored end stimulate even more photons. (d) A fraction of the photons
are emitted as a laser beam, while the rest are reflected to simulate more
recombinations.
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Figure 20.18 Schematic cross-section of a GaAs laser.
Because the surrounding p- and n-type GaAlAs layers have a
higher energy gap and a lower index of refraction than GaAs,
the photons are trapped in the active GaAs layer.
47
Figure 20.19
Intensity in relation
to wavelengths of
photons emitted
thermally from a
material. As the
temperature
increases, more
photons are
emitted from the
visible spectrum.
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48
Section 20.5
Fiber Optic Communication System





Generating the Signal - In order to best transmit and process
information, the light should be coherent and monochromatic
(to minimize dispersion).
Transmitting the Beam - Optical fibers transmit the
information.
Receiving the Signal - The job of a receiver in the fiber optic
system is to convert the optical signal into an electronic
signal.
Processing the Signal - Normally, the received signal is
converted immediately into an electronic signal and then
processed using conventional silicon-based semiconductor
devices.
Photonic bandgap materials - These are structures produced
using micromachined silicon or colloidal particles, such that
there is a range of frequencies that cannot be transmitted
through the structure.
49
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Figure 20.20 Schematic of a fiber-optic based communication system.
50
Figure 20.21 Different types of
optical fibers. (a) A step index glass
fiber, in which the index or refraction is slightly different in each glass.
(b) The profile of a refractive index in
a graded refractive index (GRIN)
fiber. (c) The path of rays entering at
different angles. [1,5]
51
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Figure 20.22 Results from an x-ray fluorescence analysis
of an unknown metal sample (for Problem 20.41).
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Figure 20.23 X-ray emission spectrum (for Problem 10.42)
53
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Figure 20.24 Intensity of the initial spectrum from a copper
x-ray source before filtering (for Problem 20.43).
54