Optical Properties of materials

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1 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 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. 1

2 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. 2

3 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. 3

4 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 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 4

5 Optical Reflectance: The reflectivity or reflectance R represents the fraction of the incident light that is reflected at the interface, where I 0 and I R 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 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 (MgF 2 ). In metals, the reflectivity is typically on the order of 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 5

6 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 τ i 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. 6

7 Transmission: transmitted through the material. Fraction of light beam that is not reflected or absorbed is 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 7

8 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 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. 8

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.

9 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 n 1 must be slightly higher than that of the cladding n 2 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 θ c = n 2 /n 1 Fig 3: Total Internal Reflection These conditions are illustrated in Figure 3. When light ray travels from core of refractive index n 1 to cladding of refractive index n 2, 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 θ c (Fig. 3b). When angle of incidence is further increased, the ray is reflected 9

10 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 θ 1 and θ 2 are the angles of incidence and refraction respectively and n 1, n 2 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 n o into core of refractive index n 1. 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. 10

$Figure 4. Acceptance angle From Figure, in triangle ABC, θ = 90- θ' or θ' = 90-θ From Snell s law, If θ' is less than critical angle θ c, the ray will be lost by refraction.$

11 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 θ c, the ray will be lost by refraction. Therefore limiting value for containing the beam inside the core, by total internal reflection, is θ c. Let α i be the maximum possible angle of incidence at the fiber end face at A for which θ' is equal to θ c. If for a ray α i exceeds α i (max), then θ' will be less than θ c and hence at B the ray will be refracted. Hence the above equation can be written as We know that, Cos Therefore, 11

12 Or This maximum angle is called as the acceptance angle or the acceptance cone halfangle. 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. 12

13 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, GeO 2 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. 13

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.

14 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 (α B ), α B = C exp(-r/r c ) where C is a constant, R is the radius of curvature of the fiber bend and R c is given by R c = 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. 14

15 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 (P out /P in ) db P out is the power emerging out of the fiber P in 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 (P out /P in ) 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. 15

16 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 and respectively. 16

17 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. 17

Lecture 7 Notes: 07 / 11. Reflection and refraction

$Lecture 7 Notes: 07 / 11. Reflection and refraction$ Lecture 7 Notes: 07 / 11 Reflection and refraction When an electromagnetic wave, such as light, encounters the surface of a medium, some of it is reflected off the surface, while some crosses the boundary