OPTICAL PROPERTIES K L University Department of Physics

SESSION 15

Contents Introduction Optical Reflectance Optical Absorbance Optical Refraction Optical Scattering Exciton binding energy Raman effect in crystals

Introduction Optical property: Classical concept- electromagnetic radiation - wavenature - electric and magnetic field components - perpendicular to each other and also to the direction of propagation. Ex: Light, heat (or radiant energy), radio waves and x-rays are all forms of electromagnetic radiation.

The electric field component of the wave should interact with electrons electrostatically

The spectrum of electromagnetic radiation, including wavelength ranges for the various colors in the visible spectrum.

The speed of light c, in vacuum, Quantum-mechanical perspective - radiation, rather than consisting of waves - packets of energy - Photons. The energy of a single photon is

Light Interactions with Solids Incident light is reflected, absorbed, scattered, and/or transmitted: solid Air Incident: I0 Absorbed: IA Transmitted: IT Scattered: IS Reflected: IR

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); During transmission photons are changes in velocity (refraction).

Absorption Reflection Transmission Where T = Transmissivity = IT/I0 A = Absorptivity = IA/I0 R = Reflectivity = IR/I0

Classification of Optical Materials 1.Transparent Materials 2.Translucent Materials 3.Opaque Materials

Materials that are capable of transmitting light with relatively little absorption and reflection are TRANSPARENT. 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. Materials that are resistant to the transmission of visible light are termed OPAQUE.

single-crystal material (sapphire), which is transparent; a polycrystalline and fully dense (nonporous) material, which is translucent; and a polycrystalline material that contains approximately 5% porosity, which is opaque

The interaction of EM radiation with solid materials: At Atomic Level. Electronic Polarization – Two Consequences A. Some of light is absorbed B.The velocity of light is reduced in the medium - Leads to the concept of “Refraction” or “Refractive index” Electronic Transitions The Absorption or Emission of EM Radiation may involve electron transition from one energy state to another energy state

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 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. Electron Transitions For an electron transition, change in energy equals the product of Planck’s constant and the frequency of radiation absorbed (or emitted) E = hν

Optical Properties Refraction Reflection Absorption Transmission

Optical Properties - Metals Absorption 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, transparent to high end frequencies i.e. x-rays and γ-rays.

Reflectivity = IR /I0 is between 0.90 and 0.95. Reflection Reflectivity = IR /I0 is between 0.90 and 0.95. Metals are opaque and highly reflective. Color of reflected light depends on wavelength distribution. 18

Metal surfaces appear shiny. Most of absorbed light is reflected at the same wavelength Small fraction of light may be absorbed. Example: The metals copper and gold –red-orange and yellow Al and Silver – reflective nature.

A bright silvery appearance when exposed to white light indicates that the metal is highly reflective over the entire range of the visible spectrum 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.

Optical Properties – Non-Metals Non-metallic materials are transparent to visible light. In addition to reflection and absorption, refraction and transmission is to be considered. Refraction

Refraction Light is transmitted into the interior of transparent materials experiences a decrease in velocity as a result bent at the interface n = index of refraction + no transmitted light electron cloud distorts

-Light can be “bent” as it passes through a transparent prism

Material Refractive Index Typical glasses 1.5 – 1.7 Plastics 1.3 – 1.6 PbO (Litharge) 2.67 Diamond 2.41

Reflection The reflectivity R represents the fraction of the incident light that is reflected at the interface, If the light is normal (or perpendicular) to the interface, then. When light is transmitted from a vacuum or air into a solid s, then

26 Example: For Diamond n = 2.41 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).

High reflectivity is desired in many applications including mirrors, coatings on glasses, etc. 9/19/2018

Absorption 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.

These excitations with the accompanying absorption can take place only if the photon energy is greater than that of the band gap Eg - that is, if E2 photon E1

Maximum possible band gap energy for absorption of visible light by valence band-to- conduction band electron transitions

Minimum possible band gap energy for absorption of visible light by valence band- to-conduction band electron transitions.

Of visible spectra absorbed by the materials 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. Band gap energies 1.8 – 3.1 ev Of visible spectra absorbed by the materials

33 The amount of light absorbed by a material is calculated using Beer’s Law  = absorption coefficient, mm-1  = sample thickness, cm = Non reflected incident light intensity = transmitted light intensity Rearranging and taking the natural log of both sides of the equation leads to

Transmission For an incident beam of intensity Io, that impinges on front surface of specimen of thickness l and absorption coeff. , the transmitted intensity at the back face IT is R - Reflectance

Computations of Minimum Wavelength Absorbed 36 Computations of Minimum Wavelength Absorbed (a) What is the minimum wavelength absorbed by Ge, for which Eg = 0.67 eV? Solution: (b) Redoing this computation for Si which has a band gap of 1.1 eV Note: the presence of donor and/or acceptor states allows for light absorption at other wavelengths.

37 Scattering of Light The radiation emanating from the oscillating electrons which travels in all direction is called the scattered radiation. Blue color in the sunlight gets scattered more than other colors in the visible spectrum and thus making sky look blue.

Applications of Optical Phenomena 38 Applications of Optical Phenomena Luminescence – Reemission of light by a material Material absorbs light at one frequency and reemits it at another (lower) frequency. Trapped (donor/acceptor) states introduced by impurities/defects

activator level Valence band Conduction band trapped states Eg Eemission

Phosphorescence:If residence time in trapped state is relatively long(>10-8s) Fluorescence:For short residence times (<10-8s) Ex: Sulphides, oxides, tungstates Based on source for electron excitation, luminescence is three types: photo-luminescence, cathode luminescence and electro-luminescence.

42 Photoluminescence Arc between electrodes excites electrons in mercury atoms in the lamp to higher energy levels. As electron falls back into their ground states, UV light is emitted (e.g., suntan lamp). Inside surface of tube lined with material that absorbs UV and reemits visible light

43 Examples Here ultra-violet radiation from low-pressure mercury arc is converted to visible light by calciumhalo-phosphate phosphor(Ca10F2P6O24). In commercial lamps, about 20% of F-ions are replaced with Cl-ions. Antimony,Sb3+,ions provide a blue emission while manganese, Mn2+, ions provide an orange-red emission band.

Cathode-luminescence Cathode-luminescence is produced by an energized cathode which generates a beam of high-energy bombarding electrons. Ex.:Applications of this include electron microscope; cathode-ray oscilloscope; color television screens.

SESSION 16

EXCITON An exciton is a bound state of an electron and hole, which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and in some liquids.

Exciton binding energy The exciton is regarded as an elementary excitation of matter that can transport matter without transporting net electric charge. Exciton binding energy An electron and a hole bound together by their attractive coulomb interaction, the energy of the bound state is less than that of separated electron hole pair.

where Eex is the exciton binding energy Valance Band Conduction Band Band Gap Exciton Potential Energy Exciton Levels The energy of the photon involved in the excitation is hν = Eg –Eex where Eex is the exciton binding energy

Ya.I. Frenkel (1894-1952) Sir N.F. Mott (1905-1996)

Mott-Wannier exciton is weakly bound, with an electron-hole separation They are bound together at larger distances, greater than lattice constant. Hoping of the exciton from one atom to another is not possible. There are known as weekly bound excitons.

A tightly-bound or Frenkel exciton They are bound together within a short distance; less than atomic radius Hoping of the exciton from one atom to another is possible. There are known as strongly bound excitons.

Raman effect

Contents Raman effect Raman scattering Stokes lines Anti-Stokes lines Necessary condition to observe Raman effect Importance of Raman effect

Raman scattering elastic Inelastic

Raman effect: Inelastic scattering of photons from matter (liquid, gas and Solid). Discovered in 1928 by C.V. Raman and K.S. Krishnan in liquids G. Landsberg and L.I. Mandelstam in crystals C.V. Raman received Noble prize in 1930 for this discovery.

Note: Rayleigh scattering is more intense than Raman scattering Elastic in nature – No exchange of energy takes place during collision. Incident and scattered photons have same energy. Raman scattering: Inelastic in nature – exchange of energy takes place during Energy may absorb or release Stokes lines Material absorbs energy and the emitted photon has a lower energy than the absorbed photon (ʋ-ʋi ) Anti-Stokes lines Material loses energy and the emitted photon has a higher energy than the absorbed photon (ʋ+ʋi ) Note: Rayleigh scattering is more intense than Raman scattering

Scattering of photons from matter

Necessary condition to observe Raman scattering Eo : Amplitude of electric field  : frequency of electric field q : displacement of atoms P : dipole-moment  : polarizability o : polarizability at equilibrium position

From above equations First term describes an oscillating dipole that radiates light of frequency ‘ʋ’ (Rayleigh scattering). The second term gives the Raman scattering with frequency ʋ+ʋi (anti-Stokes) ʋ-ʋi (Stokes) If is zero the second term vanishes. Thus, the vibration is not Raman-active

To observe Raman effect polarizability should change during vibration

Applications: It gives the compositional and structural information of different class of materials. Phase transition in materials can be identified more accurately than powder X-ray diffraction. This principle is used in optical amplifiers.