OPTICAL PROPERTIES
Learning Objectives
After studying optical properties, you should be able to do the following:
Compute the energy of a photon given its Frequency and the value of Planck’s constant.
Briefly describe the electronic polarization the results from electromagnetic radiation–
atomic Interactions, and cite two consequences of electronic polarization.
Briefly explain why metallic materials are opaque to visible light.
Define index of refraction.
Describe the mechanism of photon absorption for
(a) high-purity insulators and semiconductors and
(b) Insulators and semiconductors that contain electrically active defects.
For inherently transparent dielectric materials, note three sources of internal scattering
that can lead to translucency and opacity.
Briefly describe the construction and operation of ruby and semiconductor lasers
Introduction and basic concepts of optical properties
Introduction
Optical property refers to a material’s response to exposure to electromagnetic radiation and, in
particular, to visible light.
And also it refers to the behavior of light when it interacts with different materials. These
properties are determined by the composition and structure of the material. Understanding
optical properties is crucial in fields such as optics, photonics, material science, and engineering,
as it allows for the design and development of devices and systems that utilize or manipulate
light.
The behavior of light when it interacts with different materials can be described and explained
based on their optical properties. Different materials have different refractive indices, which
determine how much they bend light. Materials with a higher refractive index will cause light to
bend more.
The composition and structure of a material also determine its absorption and transmission
properties. For example, transparent materials allow light to pass through with minimal
absorption, while opaque materials absorb most of the incident light.
Understanding the introduction and basic concepts of optical properties is crucial for various
applications in optics, photonics, material science, and engineering.
It involves understanding the principles of reflection, refraction, absorption, transmission, and
scattering of light, as well as the behavior of light when it interacts with different materials. By
applying this knowledge, researchers can design and develop devices and systems that utilize or
manipulate light to solve real-world problems.
Basic concepts
Electromagnetic Radiation
Electromagnetic radiation refers to the energy that is propagated through space in the form of
electromagnetic waves. It consists of electric and magnetic fields oscillating perpendicular to
each other and to the direction of wave propagation. Electromagnetic radiation includes a wide
range of wavelengths and frequencies, known as the electromagnetic spectrum.
Electromagnetic radiation is considered to be wavelike, consisting of electric and magnetic field
components that are perpendicular to each other and also to the direction of propagation.
Light, heat (or radiant energy), radar, radio waves, and x-rays are all forms of electromagnetic
radiation. Each is characterized primarily by a specific range of wavelengths and also according
to the technique by which it is generated. The electromagnetic spectrum of radiation spans the
wide range from 𝛾-rays (emitted by radioactive materials) having wavelengths on the order of
10−12 m (10−3 nm) through x-rays, ultraviolet, visible, infrared, and finally radio waves with
wavelengths as long as 105 m. This spectrum is shown on a logarithmic scale.
Figure 1: The spectrum of electromagnetic radiation, including wavelength ranges for the various
colors in the visible spectrum.
Visible light lies within a very narrow region of the spectrum, with wavelengths ranging between
about 0.4 μm (4 × 10−7 m) and 0.7 μm. The perceived color is determined by wavelength; for
example, radiation having a wavelength of approximately 0.4 μm appears violet, whereas green
and red occur at about 0.5 and 0.65 μm, respectively. The spectral ranges for several colors are
included in Figure 1.
White light is simply a mixture of all colors. The ensuing discussion is concerned primarily with
this visible radiation, by definition the only radiation to which the eye is sensitive. All
electromagnetic radiation traverses a vacuum at the same velocity, that of light—namely, 3 × 108
m/s (186,000 miles/s). This velocity, c, is related to the electric permittivity of a vacuum 𝜀0 and
the magnetic permeability of a vacuum 𝜇0 through Thus, there is an association between the
electromagnetic constant c and these electrical and magnetic constants.
Furthermore, the frequency 𝜈 and the wavelength λ of the electromagnetic radiation are a
function of velocity according to
Frequency is expressed in terms of hertz (Hz), and 1 Hz = 1 cycle per second. Ranges of
frequency for the various forms of electromagnetic radiation are also included in the spectrum.
Frequency=1/time
Sometimes it is more convenient to view electromagnetic radiation from a quantummechanical
perspective, in which the radiation, rather than consisting of waves, is composed of groups or
packets of energy called photons. The energy E of a photon is said to be quantized, or can only
have specific values, defined by the relationship
Where h is a universal constant called Planck’s constant, which has a value of 6.63 × 10−34 J·s.
Thus, photon energy is proportional to the frequency of the radiation, or inversely proportional to
the wavelength.
When describing optical phenomena involving the interactions between radiation and matter, an
explanation is often facilitated if light is treated in terms of photons. On other occasions, a wave
treatment is preferred; both approaches are used in this discussion, as appropriate.
Electromagnetic radiation can be emitted or absorbed by charged particles when they undergo
acceleration or deceleration. It can also be generated by the vibrations and rotations of atoms and
molecules. The energy carried by electromagnetic radiation can be transferred to matter, causing
various effects such as heating, chemical reactions, and ionization.
The understanding and manipulation of electromagnetic radiation have led to numerous
technological advancements and applications in various fields. For example, radio waves are
used for communication and broadcasting, microwaves are used in cooking and
telecommunications, visible light is essential for vision and photography, x-rays are used for
medical imaging, and gamma rays have applications in nuclear medicine and radiation therapy.
Overall, electromagnetic radiation plays a fundamental role in our daily lives and has
revolutionized many aspects of science, technology, and communication.
Light interactions with solids
Light interactions with solids refer to the ways in which light interacts with solid materials.
These interactions can result in various optical properties, including absorption, reflection,
transmission, and scattering. When light interacts with a solid, it can be absorbed by the material,
reflected off its surface, pass through without being absorbed or reflected, or be redirected in
different directions due to scattering. The specific interactions depend on factors such as the
energy levels of electrons in the material, the material's composition and crystal structure, and its
surface characteristics. Understanding these interactions is essential in fields such as optics,
photonics, and materials science for designing and manipulating materials for specific
applications.
When light proceeds from one medium into another (e.g., from air into a solid substance),
several things happen. Some of the light radiation may be transmitted through the medium, some
will be absorbed, and some will be reflected at the interface between the two media. The
intensity I0 of the beam incident to the surface of the solid medium must equal the sum of the
intensities of the transmitted, absorbed, and reflected beams, denoted as IT, IA, and IR,
respectively.
Radiation intensity, expressed in watts per square meter, corresponds to the energy being
transmitted per unit of time across a unit area that is perpendicular to the direction of
propagation.
An alternate of the above equation is
T+A+R=1
where T, A, and R represent, respectively, the transmissivity (IT/I0), absorptivity (IA/I0), and
reflectivity (IR/I0), or the fractions of incident light that are transmitted, absorbed, and reflected
by a material; their sum must equal unity because all the incident light is transmitted, absorbed,
or reflected.
Transparent: Materials that are capable of transmitting light with relatively little absorption and
reflection one can see through them.
Translucent: materials are those through which light is transmitted diffusely; that is, light is
scattered within the interior to the degree that objects are not clearly distinguishable when
viewed through a specimen of the material.
Opaque: Materials that are impervious to the transmission of visible light
Bulk metals are opaque throughout the entire visible spectrum that is, all light radiation is either
absorbed or reflected. However, electrically insulating materials can be made to be transparent.
Furthermore, some semiconducting materials are transparent, whereas others are opaque.
Atomic and electronic interactions
The optical phenomena that occur within solid materials involve interactions between the
electromagnetic radiation and atoms, ions, and/or electrons. Two of the most important of these
interactions are electronic polarization and electron energy transitions .
Electronic Polarization
One component of an electromagnetic wave is simply a rapidly fluctuating electric field (Figure
2). For the visible range of frequencies, this electric field interacts with the electron cloud
surrounding each atom within its path in such a way as to induce electronic polarization or to
shift the electron cloud relative to the nucleus of the atom with each change in direction of
electric field component.
Two consequences of this polarization are as follows:
(1) Some of the radiation energy may be absorbed, and
(2) Light waves are decreased in velocity as they pass through the medium.
Figure 2: An electromagnetic wave showing electric field ℰ and magnetic field H components
and the wavelength λ.
Electron Transitions
The absorption and emission of electromagnetic radiation may involve electron transitions from
one energy state to another. For the sake of this discussion, consider an isolated atom, the
electron energy diagram for which is represented in Figure 3. An electron may be excited from
an occupied state at energy E2 to a vacant and higher-lying one, denoted E4, by the absorption of
a photon of energy. The change in energy experienced by the electron, ΔE, depends on the
radiation frequency as follows:
Where, again, h is Planck’s constant. At this point, it is important to understand several concepts:
First, because the energy states for the atom are discrete, only specific ΔEs exist between the
energy levels; thus, only photons of frequencies corresponding to the possible ΔEs for the atom
can be absorbed by electron transitions. Furthermore, all of a photon’s energy is absorbed in each
excitation event.
Figure 3: For an isolated atom, a schematic illustration of photon absorption by the excitation of
an electron from one energy state to another. The energy of the photon (hν42) must be exactly
equal to the difference in energy between the two states (E4 − E2).
A second important concept is that a stimulated electron cannot remain in an excited state
indefinitely; after a short time, it falls or decays back into its ground state, or unexcited level,
with reemission of electromagnetic radiation.
The optical characteristics of solid materials that relate to absorption and emission of
electromagnetic radiation are explained in terms of the electron band structure of the material
and the principles relating to electron transitions.
Optical Properties of Metals
The optical properties of metals refer to how they interact with light. Metals have unique optical
properties due to the behavior of their electrons. When light interacts with a metal, it can be
absorbed, reflected, or transmitted.
One important optical property of metals is their high reflectivity. Due to the presence of free
electrons in metals, incident light can induce oscillations in these electrons, known as plasmons.
These plasmons can then re-emit the light, resulting in high reflectivity. This is why metals like
gold and silver appear shiny.
Metals also exhibit a phenomenon called metallic luster, which is the ability to reflect light
uniformly in all directions. This gives metals their characteristic metallic appearance.
Another optical property of metals is their ability to absorb light at specific wavelengths. This
absorption is related to the energy levels of the electrons in the metal. When light of a certain
energy matches the energy difference between two electron states, it can be absorbed, leading to
the metal appearing colored. For example, copper appears reddish-brown due to its absorption of
certain wavelengths of light.
In addition to absorption and reflection, metals can also transmit light to some extent. However,
this transmission is usually limited, especially in thick metal samples.
Overall, the optical properties of metals are determined by the behavior of their electrons and
play a crucial role in various applications, such as in optics, electronics, and solar energy
conversion.
Metals are opaque because the incident radiation having frequencies within the visible range
excites electrons into unoccupied energy states above the Fermi energy, as demonstrated in
Figure 4a; as a consequence, the incident radiation is absorbed. Total absorption is within a very
thin outer layer, usually less than 0.1 μm; thus only metallic films thinner than 0.1 μm are
capable of transmitting visible light.
Most of the absorbed radiation is reemitted from the surface in the form of visible light of the
same wavelength, which appears as reflected light; an electron transition accompanying
reradiation is shown in Figure 4b. The reflectivity for most metals is between 0.90 and 0.95;
some small fraction of the energy from electron decay processes is dissipated as heat.
Because metals are opaque and highly reflective, the perceived color is determined by the
wavelength distribution of the radiation that is reflected and not absorbed. A bright silvery
appearance when exposed to white light indicates that the metal is highly reflective over the
entire range of the visible spectrum. In other words, for the reflected beam, the composition of
these reemitted photons, in terms of frequency and number, is approximately the same as for the
incident beam. Aluminum and silver are two metals that exhibit this reflective behavior. Copper
and gold appear red-orange and yellow, respectively, because some of the energy associated with
light photons having short wavelengths is not reemitted as visible light.
Figure 4: (a) Schematic representation of the mechanism of photon absorption for metallic
materials in which an electron is excited into a higher-energy unoccupied state. The change in
energy of the electron ΔE is equal to the energy of the photon. (b) Reemission of a photon of
light by the direct transition of an electron from a high to a low energy state.
Optical Properties of Nonmetals
The optical properties of non-metals refer to how they interact with light, similar to metals.
However, non-metals have different behaviors due to their electron configurations.
Non-metals generally have lower reflectivity compared to metals. Instead of inducing plasmons,
non-metals interact with light through processes such as scattering and absorption. When light
interacts with non-metals, it can be scattered in different directions, leading to a diffuse reflection
rather than a specular reflection seen in metals.
Non-metals can also absorb light at specific wavelengths, similar to metals. However, the energy
levels and electron transitions in non-metals are different, resulting in different absorption
patterns and colors. For example, chlorophyll in plants absorbs light in the red and blue regions
of the spectrum, giving plants their green color.
In terms of transmission, non-metals can transmit light to varying degrees depending on their
composition and thickness. Some non-metals, like glass or quartz, are transparent and allow light
to pass through with minimal absorption or scattering. Others, like plastics or ceramics, may be
translucent or opaque, limiting the transmission of light.
The optical properties of non-metals are important in various fields such as optics, materials
science, and biology. They are utilized in applications such as optical fibers, lenses, sensors, and
photovoltaic devices.
By virtue of their electron energy band structures, nonmetallic materials may be transparent to
visible light. Therefore, in addition to reflection and absorption, refraction and transmission
phenomena must also be considered.
Refraction
Refraction is a phenomenon that occurs when light passes from one medium to another, causing
it to change direction. This change in direction is due to a change in the speed of light as it enters
a different medium. The change in speed is caused by the difference in the optical density of the
two media. When light enters a medium with a higher optical density (such as from air to glass),
it slows down and bends towards the normal, which is an imaginary line perpendicular to the
surface of the medium. Conversely, when light enters a medium with a lower optical density
(such as from glass to air), it speeds up and bends away from the normal.
The amount of refraction depends on the angle at which the light strikes the surface of the
medium, as well as the refractive indices of the two media involved. The refractive index is a
measure of how much a medium can slow down or bend light.
Refraction plays a crucial role in various optical phenomena, such as the bending of light in
lenses, the formation of rainbows, and the apparent displacement of objects in water. It is also
essential in fields like optics, where it is used to design and optimize lenses, prisms, and other
optical devices.
Light that is transmitted into the interior of transparent materials experiences a decrease
in velocity, and, as a result, is bent at the interface; this phenomenon is termed refraction.
The index of refraction n of a material is defined as the ratio of the velocity in a vacuum
c to the velocity in the medium 𝜐, or
The magnitude of n (or the degree of bending) depends on the wavelength of the light. This
effect is graphically demonstrated by the familiar dispersion or separation of a beam of white
light into its component colors by a glass prism. Each color is deflected by a different amount as
it passes into and out of the glass, which results in the separation of the colors. Not only does the
index of refraction affect the optical path of light, but also, as explained shortly, it influences the
fraction of incident light reflected at the surface.
Figure 5: The dispersion of white light as it passes through a prism. (© Photo Disc/Getty
Images.)
Velocity of light in a medium, in terms of the medium’s electric permittivity and magnetic
permeability:
Where 𝜀 and 𝜇 are, respectively, the permittivity and permeability of the particular substance.
From the above equation we have:
Where 𝜀r and 𝜇r are the dielectric constant and the relative
magnetic permeability, respectively. Because most substances are only slightly magnetic, 𝜇r ≅ 1,
and
Thus, for transparent materials, there is a relation between the index of refraction and the
dielectric constant. Because the retardation of electromagnetic radiation in a medium results
from electronic polarization, the size of the constituent atoms or ions has considerable influence
on the magnitude of this effect—generally, the larger an atom or ion, the greater the electronic
polarization, the slower the velocity, and the greater the index of refraction.
The index of refraction for a typical soda–lime glass is approximately 1.5. Additions of large
barium and lead ions (as BaO and PbO) to a glass increase in significantly. For example, highly
leaded glasses containing 90 wt. % PbO have an index of refraction of approximately 2.1. For
crystalline ceramics with cubic crystal structures and for glasses, the index of refraction is
independent of crystallographic direction (i.e., it is isotropic). Noncubic crystals, however, have
an anisotropic n—that is, the index is greatest along the directions that have the highest density
of ions.
Table 1: Refractive Indices for Some Transparent Materials
Reflection
Reflection in optical properties refers to the phenomenon where light bounces off the surface of a
material. When light encounters a non-metallic surface, such as glass or plastic, a portion of the
light is reflected back into the surrounding medium. The angle at which the light is reflected
depends on the angle at which it initially strikes the surface, as determined by the laws of
reflection.
Reflection plays a crucial role in our everyday experiences with light. For example, when we
look at ourselves in a mirror, we see our reflection because light from our body is reflected off
the mirror's surface and travels back to our eyes. Similarly, when we see objects around us, we
perceive them because light from those objects is reflected off their surfaces and enters our eyes.
The reflective properties of non-metals can vary depending on factors such as the smoothness of
the surface and the angle of incidence of the incoming light. Smooth surfaces tend to produce
regular or specular reflection, where the angle of incidence equals the angle of reflection and the
reflected light forms a clear image. Rough or textured surfaces, on the other hand, can cause
diffuse reflection, where the incoming light scatters in different directions, resulting in a blurred
or scattered reflection.
Reflection is an essential concept in optics and has numerous practical applications. It is utilized
in devices such as mirrors, lenses, and reflective coatings for various purposes including image
formation, light redirection, and enhancement of visibility.
When light radiation passes from one medium into another having a different index of refraction,
some of the light is scattered at the interface between the two media, even if both are transparent.
The reflectivity R represents the fraction of the incident light that is reflected at the interface, or
Where I0 and IR are the intensities of the incident and reflected beams, respectively. If the light
is normal (or perpendicular) to the interface, then
Where n1 and n2 are the indices of refraction of the two media. If the incident light is not normal
to the interface, R depends on the angle of incidence. When light is transmitted from a vacuum
or air into a solid s, then
Because the index of refraction of air is very nearly unity. Thus, the higher the index of
refraction of the solid, the greater the reflectivity. For typical silicate glasses, the reflectivity is
approximately 0.05. Just as the index of refraction of a solid depends on the wavelength of the
incident light, so does the reflectivity vary with wavelength. Reflection losses for lenses and
other optical instruments are minimized significantly by coating the reflecting surface with very
thin layers of dielectric materials such as magnesium fluoride (MgF2).
Absorption
Absorption in optical properties refers to the process by which light is absorbed or taken in by a
material rather than being reflected or transmitted through it. When light encounters a material,
its energy can be absorbed by the atoms or molecules within the material, causing them to
become excited. This absorption of energy can result in the conversion of light energy into other
forms of energy, such as heat. The extent to which a material absorbs light depends on its optical
properties, including its composition, structure, and the wavelength of the incident light.
Different materials have different absorption spectra, which describe how they absorb light at
different wavelengths. For example, certain pigments or dyes may selectively absorb certain
colors of light, giving them their characteristic color.
Absorption can also be influenced by factors such as the thickness of the material and the angle
at which the light strikes it. Thicker materials or materials with higher concentrations of
absorbing substances tend to absorb more light. Additionally, the angle of incidence can affect
the amount of light absorbed, with some materials exhibiting different absorption properties
depending on the angle of the incident light.
The absorption of light is an important phenomenon in various fields and applications. In
materials science, understanding absorption properties is crucial for designing materials with
specific optical characteristics, such as solar cells or photovoltaic devices that aim to efficiently
convert light into electrical energy. In spectroscopy, absorption spectra are used to identify and
analyze the composition of substances based on their unique absorption patterns. Absorption is
also relevant in photography, where it influences factors such as exposure and color rendering.
Nonmetallic materials may be opaque or transparent to visible light; if transparent, they often
appear colored. In principle, light radiation is absorbed in this group of materials by two basic
mechanisms that also influence the transmission characteristics of these nonmetals. Absorption
by electronic polarization is important only at light frequencies in the vicinity of the relaxation
frequency of the constituent atoms.
Absorption of a photon of light may occur by the promotion or excitation of an electron from the
nearly filled valence band, across the band gap, and into an empty state within the conduction
band, as demonstrated in Figure 6; a free electron in the conduction band and a hole in the
valence band are created.
Figure 6: (a) Mechanism of photon absorption for nonmetallic materials in which an electron is
excited across the band gap, leaving behind a hole in the valence band. The energy of the photon
absorbed is ΔE, which is necessarily greater than the band gap energy Eg. (b) Emission of a
photon of light by a direct electron transition across the band gap.
For a nonmetallic material, condition for absorption of a photon (of radiation) by an electron
transition in terms of radiation frequency
In terms of wave length
The minimum wavelength for visible light, λ (min), is about 0.4 μm, and because c = 3 × 108
m/s and h = 4.13 × 10−15 eV·s, the maximum band gap energy Eg (max) for which absorption
of visible light is possible is
In other words, no visible light is absorbed
by nonmetallic materials having band
gap energies greater than about 3.1 eV; these materials, if of high purity, appear transparent and
colorless.
However, the maximum wavelength for visible light, 𝜆(max), is about 0.7 μm; computation of
the minimum band gap energy Eg(min) for which there is absorption of visible light gives:
This result means that all visible light is absorbed by valence band–conduction band electron
transitions for semiconducting materials that have band gap energies less than about 1.8 eV; thus,
these materials are opaque. Only a portion of the visible spectrum is absorbed by materials
having band gap energies between 1.8 and 3.1 eV; consequently, these materials appear colored.
Every nonmetallic material becomes opaque at some wavelength, which depends on the
magnitude of its Eg. For example, diamond, having a band gap of 5.6 eV, is opaque to radiation
having wavelengths less than about 0.22 μm.
Light radiation of specific wavelengths may be emitted as a result of electron transitions
involving these levels within the band gap. For example, consider Figure 7a, which shows the
valence band–conduction band electron excitation for a material that has one such impurity level.
Again, the electromagnetic energy that is absorbed by this electron excitation must be dissipated
in some manner; several mechanisms are possible. For one, this dissipation may occur via direct
electron and hole recombination according to the reaction:
Electron + hole → energy (ΔE)
Figure 7: (a) Photon absorption via a valence band–conduction band electron excitation for a
material that has an impurity level that lies within the band gap. (b) Emission of two photons
involving electron decay first into an impurity state and finally to the ground state. (c)
Generation of both a phonon and a photon as an excited electron falls first into an impurity level
and finally back to its ground state.
One possibility, as indicated in Figure7b, is the emission of two photons; one is emitted as the
electron drops from a state in the conduction band to the impurity level, the other as it decays
back into the valence band. Alternatively, one of the transitions may involve the generation of a
phonon (Figure 7c), in which the associated energy is dissipated in the form of heat.
The intensity of the net absorbed radiation is dependent on the character of the medium and the
path length within. The intensity of transmitted or no absorbed radiation IT′ continuously
decreases with the distance x that the light traverses:
Where I′ 0 is the intensity of the non-reflected incident radiation and 𝛽, the absorption coefficient
(in mm−1), is characteristic of the particular material; 𝛽 varies with the wavelength of the
incident radiation. The distance parameter x is measured from the incident surface into the
material. Materials with large 𝛽 values are considered highly absorptive.
Transmission
