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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.