v.2019.AUG C. Optical Properties of Materials Contents Objectives • light (9.1) • What happens when light shines • refractive index, n (9.2) on a material? • dispersion, n(l) (9.3) • colors of materials – vg, Ng, zero dispersion (9.4) • principles • Why are some materials – Snell (9.6): direction transparent and others not? – Fresnel (9.7): amplitudes, phases • Optical applications: • losses & origins – optical fibers – n-jK, er'-jer", k'-jk" (9.8) – lattice absorption (9.9) – optical amplification – VB CB absorption (9.10) – luminescence, phosphors – scattering (9.11) – nanostructures • case studies – optical fibre (9.12) – luminescence, phosphor (9.13) Reference: S.O. Kasap (3rd,4th Ed.) Chap. 9; RJD Tilley (Understanding solids, 2nd Ed) Chap. 14. Optcal Properties 2102308 1 9.1 Light (L0) • optical properties of matter describe the interaction of light with matter • types of interactions: scattering, reflection, absorption, transmission, diffraction… • properties of light: wave-particle duality – for propagation & scattering, light = EM wave – for absorption & emission, photons = particle • visible light has energy ~1.8-3.1 eV, wavelength ~400-700 nm (visible spectrum) vs. • a much wider electromagnetic spectrum (Fig./Table 14.1) (L1) • wavelength l of interest: 10 nm (X-rays) – 100 mm. Selected applications: – germicide/cosmetic: 300-400 nm (UV) – display: 400-700 nm (VIS) – optical communication: 1.3 and 1.55 mm (IR) • light is an oscillating electromagnetic (EM) field where electric component E ⊥ to magnetic component B, both of which ⊥ to propagation direction k (Fig. 9.1) (L2-L3) – simplest description: monochromatic light travelling in space in 1D (Fig. 9.2) – more complete description must be in 3D (Fig. 9.3) • light can be generated by electrons in atoms, molecules, solids (crystals) dropping from high to low energy levels/bands (L4-L5). Other courses explain the principle of light generation by semiconductor devices (2102385, SKJ), and lasers (2102589, SPY) Optcal Properties 2102308 2 (L1) Optcal Properties 2102308 3 (L2) “Light -” an electromagnetic wave Ex By Which (E, B) is more important? - Electric and magnetic fields always co-exist by virtue of Faraday’s Law: time-varying (B field E field) - Most materials (atoms in the periodic table) only respond to E, thus B is usually ignored - Optical field refers to E field light-related vocabularies: - monochromatic: single or very narrow monochromatic plane wave: range of l (red laser yes, the sun no) time space phase - coherent: photons constituting light beam are in phase (laser yes, LED no) in 1D: Ex Eocost kzo - polarization: direction of E field, k is propagation constant or wavenumber light sources can be (*) unpolarized, (a) plane polarized, (b) elliptically E polarized, (c) circularly polarized, T f 1/T t time 2 /T z space k 2 / l l * Optcal Properties 2102308 4 (L3) - propagation monochromatic plane wave propagates in space at velocity v 1D (far from source) for any given plane, the phase t kz plane wave o is a constant which moves dz at “planes” every dt phase velocity: dz v lf dt k f 1/T 2 /T k 2 / l 3D (close to source) spherical wave Er,t Eocost k r o Optcal Properties 2102308 5 (L4) - generation GAS SOLID H semiconductors 2 direct indirect InP Si Optcal Properties 2102308 6 H2, He W C (L5) - generation by hot bodies (incandescence) • heated elements/molecules: () electrons excited to E2 and relaxed to E1 (Fig. 14.4), releasing photons • output spectrum depends solely on temperature T described by Planck’s law of blackbody radiation Optcal Properties 2102308 7 (I0) Light-Matter Interaction RAT - incident light is mostly Reflected, Absorbed, Transmitted (refracted, non-normal incidence), and partly scatterd (Fig. 14.13) (I1). Other types of interactions: diffraction, fluorescent… - conservation of energy: (ignoring scattering and secondary effects) Io IT I A IR - optical materials/systems often designed to maximize or minimize R, A or T (l) – see pix (I1) - interaction of light with - metals (I2): reflection, mostly - non-metals: absorption, luminescence (I3) - results of light-matter interactions: - colours: (I4) CdS, Hope, (I5) ruby - opacity: internal reflection by microstructure determines opacity (I5) - refractive index: light slowed down, bent (refracted) (I6) Optcal Properties 2102308 8 (I1) Light-Matter Interaction “interaction” overview of applications surface condition Reflection Absorption (rough) A (smooth) T R Cloaking Transmission Optcal Properties 2102308 9 Light interaction with metals RAT (I2) Absorption Reflection re-emitted photon from material surface Energy of electron unfilled states I R “conducting” electron E filled states • Metals have fine succession of energy states. • Metals appear reflective (shiny) because • Near-surface electrons absorb visible light. • Reflectivity = IR/Io is ~ 0.90-0.95. (reflected light same frequency as incident) Colors Pd Au Color of metals dictated by interfacial property (metal/insulator interface) called Transmission (none) “surface plasmon resonance (SPR)” since IA + IR ~ 1 IT ~ 0; therefore, all metals are opaque (except thin foil < 100 nm, transmit visible light) Optcal Properties 2102308 10 Light interaction with non-metals (I3) (insulators, semiconductors) RAT Absorption (conditional): if hn > Egap Reflection: depends on n, ex. - R ≈ 4% for glass (insulator, n ~ 1.4) - R ≈ 30 % for Si (semicond, n ~ 3.5) - for details, see Fresnel (9.7) Energy range of visible light: Luminescence incident photon (re-emitted light) energy hn • If EG < 1.8 eV, full absorption; color is black ([email protected], [email protected] eV) • If EG > 3.1 eV, no absorption; colorless ([email protected], glass@9 eV), transparent (!), see (I5) • If EG in between or has impurity level, partial absorption; material has a color. Optcal Properties 2102308 11 (I4) Light-Matter Interaction: Results LDR • Colour determined by sum of frequencies of - transmitted light, scattered light - re-emitted light from electron transitions CdS • Ex. 1 (Semiconductor): Cadmium Sulfide (CdS) - Egap = 2.4 eV, - absorbs higher energy visible light (blue, violet), - Red/yellow/orange is transmitted, gives color. (2.48 eV) Diamond • Ex. 2 (Insulator) The Hope Diamond = C (+ % B) - Egap = 5.6 eV - luminesce after UV exposure (l<220nm) (1.88 eV) - phosphorescence (re-emission occurs with delay time > 1 s) Origin of color: Boron (0-8 ppm depends on position, av. 0.36 ppm) http://nhminsci.blogspot.com/2012/05/hope-diamond-blue-by-day-red-by-night_22.html Optcal Properties 2102308 12 (I5) Light-Matter Interaction: Results • Ex. 3 (Insulator) Ruby Ruby = Sapphire (Al2O3) + Cr2O3 Ruby (laser) - Egap > 3.1eV - pure sapphire is colorless (mineral) - adding Cr2O3 : (0.5-2) at. % • alters the band gap • blue light is absorbed Opacity/Transparency (EG>3.1eV) • yellow is absorbed Transparency of insulators • red is transmitted dictated by microstructure: • Result: Ruby is deep red. single-crystal poly-crystal (dense) poly-crystal (porous) Intrinsically transparent dielectrics can be made translucent/opaque by “interior” reflection/refraction/scattering. Optcal Properties 2102308 13 (I6) Light-Matter Interaction: Results • Transmitted light distorts electron clouds. no transmitted + light • Result 1: Light is slower in a material vs vacuum. Index of refraction (n) = speed of light in a vacuum speed of light in a material - Adding large, heavy ions (e.g. lead, Pb) Material n can decrease the speed of light. Lead glass ~ 2 Si O Pb Silica glass 1.46 Si O • Result 2: Intensity of transmitted light decreases Soda-lime glass 1.51 Si O Na Ca with distance traveled (thick pieces less transparent) Quartz 1.55 Si O -- see later in Losses (9.8) Plexiglas 1.49 C O H Polypropylene 1.49 C O H • Result 3: Light can be “bent” Diamond 2.41 C or “refracted”, see later Snell (9.6) Refraction (qi ≠ 0): a change in propagation direction of a wave when it changes a medium Optcal Properties 2102308 14 Optcal Properties 2102308 15 9.2 Refractive Index (n) (R0) • refractive index (n) measures how much light slows down in a material, with respect to vacuum. Speed of light in i) vacuum = c, ii) material = phase velocity v (), ∴ n • materials slow down light due to light-matter interaction: atoms/molecules/grains in optical/dielectric materials are polarized by the electric field component of light E (Reminder: polarization mechanisms), Fig. A (R1) • propagation of light (E) in a material is effectively delayed (phase lag) wrt. vacuum • (from ) material permittivity er stronger dipoles (drag ) delays • atoms/molecules in medium are polarized at the same frequency as E, hence the frequency of light does not change, but other wave propagation & parameters do change, Table A (R1). Typical wavefronts in films, Fig. B (R1) • n is not a constant, but can change with incident direction, especially in some 1 c c crystals (birefringent) which show v e re omr mo e r mr e r optical anisotropy (9.14) (R2,R3) c n e • n is not a constant, but can change with v r optical materials are incident wavelength, thus n(l), see non-magnetic (mr ≅ 1) example (R4), for details next section 9.3 Dispersion Optcal Properties 2102308 16 Dielectric properties of materials (R1) - complex relative permittivity as a function of frequency - contribution of various polarization mechanisms Interfacial and space charge Fig. A Orientational, e' r Dipolar n e r Ionic Electronic n(l) e r ( f ) er'' er' = 1 ƒ 10•2 1 102 104 106 108 1010 1012 1014 1016 Radio Infrared Ultraviolet light Table A: Wave propagation parameters Fig. B Wave travelling into optical films vacuum medium f f c = lof v = lf lo l lo/n ko k = nko c l f l 2 / l k n o o v lf l 2 / lo ko - Estimate n in Film 1, Film 2 - Film 1 is lossy, 2 lossless Optcal Properties 2102308 17 Optical anisotropy (9.14) (R2) - most non-crystalline materials (glasses, liquids) and all cubic crystals are optically isotropic (they “look” the same in all directions) - crystals are different: n of crystals depend on direction of electric field in the propagating light beam - Optically anisotropic crystals are called bi-refringent because incident light beam may be doubly refracted (Figs.