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Optical Properties of materials
Optical reflectance and absorption
Introduction to Optical reflectance and optical absorption
(Board Teaching and PPT)
Light interaction with materials: Optical property of a material is
defined as its interaction with electro-magnetic radiation in the visible.
Electromagnetic spectrum of radiation spans the wide range from γ-rays with
wavelength as 10-12 m, through x-rays, ultraviolet, visible, infrared, and finally
radio waves with wavelengths as long as 105 m. Visible light is one form of
electromagnetic radiation with wavelengths ranging from 0.39 to 0.77 μm. Light can
be considered as having waves and consisting of particles called photons.
Interaction of photons with the electronic or crystal structure of a material
leads to a number of phenomena. The photons may give their energy to the material
(absorption); photons give their energy, but photons of identical energy are
immediately emitted by the material (reflection); photons may not interact with the
material structure (transmission); or during transmission photons are changes in
velocity (refraction). At any instance of light interaction with a material, the total
intensity of the incident light striking a surface is equal to sum of the absorbed,
reflected, and transmitted intensities i.e.
Light interacts with matter in many different ways. Metals are shiny, but water is
transparent. Stained glass and gemstones transmit some colours, but absorb others.
Other materials such as milk appear white because they scatter the incoming light in
all directions.
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The wide-ranging optical properties observed in solid state materials can
be classified into a small number of general phenomena. The simplest group,
namely reflection, propagation and transmission. This shows when a light beam
incident on an optical medium, some of the light is
reflected from the front surface, while the rest enters the medium and propagates
through it. If any of this light reaches the back surface, it can be reflected
again, or it can be transmitted through to the other side. The amount of light
transmitted is therefore related to the reflectivity at the front and back surfaces
and also to the way the light propagates through the medium.
Optical materials:
Materials are classified on the basis of their interaction with visible light
into three categories. Materials that are capable of transmitting light with relatively
little absorption and reflection are called transparent materials i.e. we can see
through them. Translucent materials are those through which light is transmitted
diffusely i.e. objects are not clearly distinguishable when viewed through. Those
materials that are impervious to the transmission of visible light are termed as
opaque materials. These materials absorb all the energy from the light photons.
Atomic and electronic interactions:
The optical phenomenon that occurs when light interacts with solid
(absorption, reflection, transmission) involve interactions between electromagnetic
radiation and atoms, ions and electrons. The two important such interactions are
electronic polarization and electron energy transitions.
The electronic polarization is the consequence of interaction of
electromagnetic radiation of visible frequency range with electron cloud surrounding
each atom, that lies in the path of propagation of the electromagnetic wave.
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The two consequences of this polarization are: 1. some of the radiation
energy may absorbed. 2. Light waves are retarded in velocity as they pass through
the medium. The second consequence is manifested as refraction.
The absorption and emission of electromagnetic radiation involve electron
transition from one energy level to another.
Verify
1. Define reflectivity, transmittivity and absorptivity.
2. Classify the materials based on their interaction with light.
3. Explain the interaction of electromagnetic radiation with atoms.
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Optical properties of metal and non-metals (Board Teaching and PPT)
Optical properties of metals:
Metals consist partially filled high-energy conduction bands. When
photons are directed at metals, their energy is used to excite electrons into
unoccupied states. Thus metals are opaque to the visible light. Metals are, however,
transparent to high end frequencies i.e. x-rays and γ-rays. Absorption of takes place
in very thin outer layer. Thus, metallic films thinner than 0.1 μm can transmit the
light. The absorbed radiation is emitted from the metallic surface in the form of
visible light of the same wavelength as reflected light. The reflectivity of metals is
about 0.95.
Optical properties of non-metals: Non-metallic materials consist of various energy
band structures. Thus, all four optical phenomena are important.
Fig.1 Propagation of light from one medium to another medium
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Optical Reflectance:
The reflectivity or reflectance R represents the fraction of the incident light
that is reflected at the interface,
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 and are the indices of refraction of the two media. If the incident light is not
normal to the interface, R will depend on the angle of incidence. When light is
transmitted from a vacuum or air into a solid s, then
Thus, the higher the index of refraction of the solid, the greater is 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 also 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). In metals, the
reflectivity is typically on the order of 0.90-0.95. The high reflectivity of metals is
one reason that they are opaque. High reflectivity is desired in many applications
including mirrors, coatings on glasses, etc.
Optical absorptance:
When a light beam in impinged on a material surface, portion of the
incident beam that is not reflected by the material is either absorbed or transmitted
through the material. The presence of lattice defects in a solid can give rise to
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optical absorption. Absorption is the process by which incident radiant flux is
converted to another form of energy, usually heat. Absorptance is the fraction of
incident flux that is absorbed. The absorptance a of an element is defined by,
Similarly, the spectral absorptance α(λ) is the ratio of spectral power absorbed to the
incident spectral power .
An absorption coefficient α’ (cm
-1 or km
-1) is often used in the expression
where τi is internal transmittance and t is path length (cm or km).
Beer-Lambert’s law: The fraction of beam that is absorbed is related to the
thickness of the materials and the manner in which the photons interact with the
material’s structure.
Absorption occurs by two mechanisms: Rayleigh scattering and Compton scattering
Rayleigh scattering: where photon interacts with the electrons, it is deflected
without any change in its energy. This is significant for high atomic number atoms
and low photon energies. Ex.: Bluecolor in the sunlight gets scattered more than
other colors in the visible spectrum and thus making sky look blue.
Tyndall effect is where scattering occurs from particles much larger than the
wavelength of light. Ex.: Clouds look white.
Compton scattering – interacting photon knocks out an electron losing some of its
energy during the process. This is also significant for high atomic number atoms and
low photon energies.
Photoelectric effect occurs when photon energy is consumed to release an electron
from atom nucleus. This effect arises from the fact that the potential energy barrier
for electrons is finite at the surface of the metal. Ex.: Solar cells.
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Transmission: Fraction of light beam that is not reflected or absorbed is
transmitted through the material.
Verify
1. What is an optical property
2. Explain Reflection.
3. Define Transmission
4. Define optical reflectance
5. Explain optical absorptance
Optical Fiber
Introduction
The development in the fields of communication and information technology
demand very easy and rapid transmission of data over long distances. Fiber optics
technology is increasingly replacing wire transmission lines in communication
systems and is expected to be as common as electrical wiring even in our vehicles
and houses very shortly. Optical fiber lines offer several important advantages over
wire lines. Optical fibers are the light equivalent of microwave guides with the
advantage of very high bandwidth and hence very high information carrying
capacity. Through at the beginning, fiber optic communication systems were more
expensive than equivalent wire or radio-systems, now the situation has changed very
much. Fiber optic systems have become competitive with other systems in price and
eventually started replacing them.
5.2 Principles of optical fiber
In 1870, Tyndall demonstrated that light could be guided within a water-jet based on
the phenomenon of total internal reflection. But it was not until the mid 1960s that
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the idea of communication system based on the propagation of light within the water
jet like wave circular wave-guides called optical fibers was considered seriously.
The light launched at one end of the fiber has to travel through the entire
length and reach the other end without much loss. Initially only single circular
dielectric rods were considered as waveguides but the light launched through its one
end penetrated into the air surrounding the rod thereby causing the losses to be very
high. Moreover they had to be made very thin to accommodate a single
electromagnetic mode. These major problems were overcome with the development
of cladded dielectric waveguides in 1954. Optical fiber is a very thin and flexible
medium having a cylindrical shape consisting of three sections:
i) The core,
ii) The cladding and
iii) The outer jacket.
Fig 2: Structure of an optical Fiber
The structure of the optical fiber is given in the Figure 2. The fiber has a core
surrounded with a cladding with refractive index slightly less than that of the core to
satisfy the condition for total internal reflection. To give mechanical protection to the
fiber, a protective skin called outer jacket is also used.
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The light launched inside the core through its one end propagates to the other
end due to total internal reflection at the core and cladding interface. This is the
principle of optical fiber. Total internal reflection at the fiber wall can occur only if
the following two conditions are met.
1. The refractive index of the core material n1 must be slightly higher than that of
the cladding n2 surrounding it.
2. At the core-cladding interface the angle of incidence θ (between the ray and the
normal to the interface) must be greater than critical angle defined as
Sin θc = n2/n1
Fig 3: Total Internal Reflection
These conditions are illustrated in Figure 3. When light ray travels from core of
refractive index n1 to cladding of refractive index n2, refraction occurs. Since it travels
from denser to rarer medium the angle of refraction is greater than the angle of
incidence (Fig.3a). With the increase in angle of incidence the angle of refraction also
increases and for a particular angle of incidence the refracted ray just grazes the
interface between the core and cladding. This angle of incidence is known as critical
angle θc (Fig. 3b). When angle of incidence is further increased, the ray is reflected
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back into the core at the interface obeying the law of reflection. This phenomenon is
called as total internal reflection (Fig 3c).
Snell’s Law:
It is also known as the Snell–Descartes law or the law of refraction. Snell's law states
that the ratio of the sin’s of the angles of incidence and refraction is equivalent to the
ratio phase velocities in the two media, or equivalent to the reciprocal of the ratio of
the refractive indices.
Where θ1 and θ2 are the angles of incidence and refraction respectively and n1, n2 are
higher refractive index of medium and lower refractive index of medium.
Acceptance angle:
When we launch the light beam into a fiber at its one end using a focusing lens, the
entire light may not pass through the core and propagate. Only the rays, which make
the angle of incidence greater than critical angle at the core-cladding interface, undergo
total internal reflection and propagate through core. The other rays are refracted to the
cladding and are the lost. Hence it is very essential to know up to what angle we have
to launch the beam at its end to enable the entire light to pass through the core. This
maximum angle of launch is called acceptance angle.
Figure 3 shows the longitudinal cross section of the launch end of a fiber with a
ray entering it. The light is launched from a medium of refractive index no into core of
refractive index n1. The ray enters with an angle of incidence i to the fiber end face
(i.e., the incident ray makes an angle i with the fiber axis which is nothing but the
normal to the end face at its center). This particular ray enters the core at its axis point
A and proceeds after refraction at an angle θ from the axis. It then undergoes a total
internal reflection at B on core wall at an internal incidence angle θ'. Let us now find
up to what value of i at A, total internal reflection at B possible.
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Figure 4. Acceptance angle
From Figure, in triangle ABC, θ = 90- θ' or θ' = 90-θ
From Snell’s law,
If θ' is less than critical angle θc, the ray will be lost by refraction. Therefore limiting
value for containing the beam inside the core, by total internal reflection, is θc. Let αi
be the maximum possible angle of incidence at the fiber end face at A for which θ' is
equal to θc. If for a ray αi exceeds αi(max), then θ' will be less than θc and hence at B
the ray will be refracted.
Hence the above equation can be written as
We know that, Cos
Therefore,
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Or
This maximum angle is called as the acceptance angle or the acceptance cone half-
angle. Rotating the acceptance angle about the fiber axis describes the acceptance
cone of the fiber. Light launched at the fiber end within this acceptance cone alone
will be accepted and propagated to the other end of the fiber by total internal
reflection. Larger acceptance angles make launching easier.
Attenuation or Losses in Optical Fibers:
The power of light at the output end is found to be always less than the power
launched at the input end. The attenuation is found to be a function of fiber material,
wavelength of light and length of fiber. Losses intrinsic to fibers result in attenuation
decrease of light transmittance. These losses are three types.
Scattering Losses:
The glass in optical fiber is an amorphous solid that is formed by allowing the glass
to cool from its molten state at high temperature until it freezes. While it is still
plastic, the glass is drawn in the form of a very thin fiber under proper tension.
During this process, sub microscopic variations in the density of the glass are frozen
into the glass. Dopants added to the silica modify the refractive index also cause
fluctuation in refractive index. These inhomogeneity’s act as reflecting and
refracting facets to scatter a small portion of the light passing through the glass,
contributing for the losses. If the scale of these fluctuations is of the order of λ/10 or
less, each irregularity acts as a point source scattering center. This type of scattering
is known as Rayleigh scattering. The losses induced because of scattering vary
inversely with the fourth power of the light wavelength used.
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Figure 5. Rayleigh scattering losses in silica fibers
Absorption losses:
Three different mechanisms contribute to absorption losses in glass fibers. These are
the ultraviolet absorption, infrared absorption, and ion resonance absorption. In pure
fused silica, absorption of ultra violet radiation around 0.14μm results in ionization
of valence electrons into a conduction band. Thus there is loss of light due to
ionization. Also during the fabrication of fiber, to change the refractive index of the
glass to any given desired value, GeO2 is doped. This causes shift in the UV
absorption band towards longer wavelength region. Absorption of infrared photons
by atoms within the glass molecules results in increase of random mechanical
vibrations and hence heating. This infrared absorption also exhibits a main spectral
peak corresponding to silicon at 8μm, with minor peaks at 3.2, 3,8 and 4.4 μm. The
peaks are broad and tail off into the visible part of the spectrum. OH- ions are
present in the material due to trapping of minute quantities of water molecules
during manufacturing.
The presence of other impurities such as iron, copper and chromium may also
create unacceptable losses within the usable portion of the spectrum and hence extra
care has to be taken while purification of silicon to avoid them.
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Figure 6. Absorption loss effects in fused silica glass fibers
Bending Losses:
The distortion of the fiber from the ideal straight-line configuration may also results
in fiber losses. Let us consider a wave front that travels perpendicular to the
direction of propagation. In order to maintain this, the part of the mode which is in
the outside of the bend has to travel faster than that on the inside. As per the theory,
each mode extends an infinite distance into the cladding though the intensity falls
exponentially. Since the refractive index of the cladding is less than that of the core,
the part of the mode travelling in the cladding will attempt to travel faster. As per
Einstein’s theory, the energy associated with this particular part of the mode is lost
by radiation and can be expressed by an absorption coefficient (αB),
αB = C exp(-R/Rc)
where C is a constant, R is the radius of curvature of the fiber bend and Rc is given
by Rc = a/(NA)2, where a is the radius of the fiber. Since bends with radii of
curvature of the order of magnitude of the fiber radius give rise to heavy losses, it
has to be avoided.
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Figure 7. The mechanism of radiation loss in fibers at bends
Loss in decibel:
The loss in optical fiber is defined differently depending on the type of loss
described and the design of the fiber. Attenuation loss is generally measured in terms
of the decibel (dB) which is a logarithmic unit. The decibel loss of optical power in
a fiber is calculated through the formula,
Loss if optical power = -log (Pout/Pin) dB
Pout is the power emerging out of the fiber
Pin is the power launched into the fiber.
Most fiber manufacturers characterize attenuation loss by the number of decibels
loss per kilometre of fiber. This value can be calculated by
Loss/Km = -(10/L) log (Pout/Pin) dB/km
L is the length of the fiber tested
The loss per kilometre (or dB/Km) is a standard unit for describing attenuation loss
in all fiber designs.
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Applications of optical fibers
Communication - Telephone transmission method uses fibre-optic cables. Optical
fibres transmit energy in the form of light pulses. The technology is similar to that of
the coaxial cable, except that the optical fibres can handle tens of thousands of
conversations simultaneously. Intelligent transportation systems, such as smart
highways with intelligent traffic lights, automated tollbooths, and changeable message
signs, also use fiber-optic-based telemetry systems.
Medical uses - Optical fibres are well suited for medical use. They can be made in
extremely thin, flexible strands for insertion into the blood vessels, lungs, and other
hollow parts of the body. Optical fibres are used in a number of instruments that enable
doctors to view internal body parts without having to perform surgery.
Another important application for optical fiber is the biomedical industry. Fiber-optic
systems are used in most modern telemedicine devices for transmission of digital
diagnostic images.
Simple uses - The simplest application of optical fibres is the transmission of light to
locations otherwise hard to reach. Also, bundles of several thousand very thin fibres
assembled precisely side by side and optically polished at their ends, can be used to
transmit images.
Other applications for optical fiber include space, military, automotive, and the
industrial sector.
Numericals
1. A signal of 100mW is injected into a fiber. The out coming signal from the other end is
40mW. What is the loss in dB?
2. Calculate the fractional index change for a given optical fiber if the refractive indices
of the core and the cladding are 1.563 and 1.498 respectively.
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Questions
1. What is an Optical fiber? Explain the principle and structure of an optical fiber.
2. Define total internal reflection. Explain it with diagram.
3. List out the applications of optical fibers.
4. Explain the advantages of optical communication system.