06/08/2018 Before this lecture there were two lectures: 1. Introduction about this course. 2. Qualitative description about the various polarizations. Retarders • In retarders, one polarization gets ‘retarded’, or delayed, with respect to the other one. There is a final phase difference between the 2 components of the polarization. Therefore, the polarization is changed. • Most retarders are based on birefringent materials (quartz, mica, polymers) that have different indices of refraction depending on the polarization of the incoming light. 3 Phase shift of half wavelength Quarter Wave plate Circular polarization (IV) 7 How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Wire grid polarizer Polaroid How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Birefringence How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Polarized Reflecting Light • When an unpolarized light wave reflects off a non-metallic surface, it can be completely polarized, partially polarized or unpolarized depending on the angle of incidence. A completely polarized wave occurs for an angle called Brewster’s angle (named after Sir David Brewster) Snell's law Incident Reflected ray ray p n 90o 1 n2 r n1sin P = n2sin r n1sin P = n2sin r = n2sin (90-P) = n2cos P tan P = n2/n1 P = Brewster’s angel Reflection • When an unpolarized wave reflects off a nonmetallic surface, the reflected wave is partially plane polarized parallel to the surface. The amount of polarization depends upon the angle (more later). The reflected ray contains more vibrations parallel to the reflecting surface while the transmitted beam contains more vibrations at right angles to these. Applications • Knowing that reflected light or glare from surfaces is at least partially plane polarized, one can use Polaroid sunglasses. The polarization axes of the lenses are vertical as the glare usually comes from reflection off horizontal surfaces. Polarized Lens on a Camera Reduce Reflections How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Polarization by Scattering • When a light wave passes through a gas, it will be absorbed and then re-radiated in a variety of directions. This process is called scattering. y Gas molecule z O Unpolarized x sunlight Light scattered at right angles is plane-polarized Polarization by Scatterings 3D Movie Projection and Viewing • Modern 3D movies are projected using different polarizations instead of different colors. • Without glasses, the images look like this: 3D Movie Projection and Viewing • The two overlapping images are actually projected through a polarizing filter, alternating in rapid succession • The glasses separate the polarized light and each eye sees something different, creating the illusion of depth • The system actually uses circularly polarized light, so the glasses won’t work like your polarized sunglasses 08/08/2018 08/08/2018 • Concept of polarizer and analyzer Mathematics of Polarization, Malus’s Law Orientations of Polarizers Example 1 • Two polarizers are After the first polarizer: orientated with their 1 I I axes at an angle of 1o2 o 35.0 , what proportion After the second polarizer: of the original light 2 remains? First polarizer I21 I cos reduce the intensity 1 2 o II2 o cos 35.0 half of original intensity. 2 II2 0.336 o Birefringence Refractive Index in Isotropic and Anisotropic Crystal Optic Axis Beam propagation in anisotropic crystals Optic axis of a crystal is the direction in which a ray of transmitted light suffers no birefringence (double refraction). Light propagates along that axis with a speed independent of its polarization However, if the light beam is not parallel to the optical axis, then, when passing through the crystal the beam is split into two rays: the ordinary and extraordinary, to be mutually perpendicular polarized. A crystal which has only one optic axis is called uniaxial crystal. A crystal which has only two optic axis is called biaxial crystal. Calcite experiment and double refraction O E Fig 6-8 Bloss, Optical Crystallography, MSA Fig 6-7 Bloss, Optical Crystallography, MSA How light behaves depends on crystal structure (there is a reason you took mineralogy!) Isotropic Isometric – All crystallographic axes are equal Uniaxial Hexagonal, trigonal, tetragonal – All axes c are equal but c is unique Biaxial Orthorhombic, monoclinic, triclinic – All axes are unequal Let’s use all of this information to help us identify minerals Thin layer of balsam cement with n = 1.55 Other Crystallographic systems: Orthorhombic, monoclinic, and triclinic have two optic axes and are biaxial. For example, Mica KH2Al3(SiO4)3 has three different indices n. Birefringent devices – Separation of the o- and e- rays. • Optic axis of a uniaxial crystal is the high- order symmetry axis Extent of Birefringence 09/08/2018 Index Ellipsoid and classification of Crystal ne n0 n0 n0 = n0 > ne For Uniaxial crystal Wave surfaces of Ordinary and Extraordinary rays Dependence of refractive index of extraordinary ray: The refractive index of ‘e’ ray depends on the direction of propagation relative to optic axis. Where is angle between propagation vector and Optic axis The index of refraction varies from o n(θ) = no for θ = 0 0 n(θ) = ne for θ = 90 Wave surfaces of Ordinary and Extraordinary rays Huygen’s Explanation of Double Refraction • Spherical wavelet associated with ordinary waves • Ellipsoidal wavelet associated with extraordinary waves. Dependence of incident angle and propagation properties of light a) When optic axis is inclined to some angle to the incident light. b) When optic axis is perpendicular to incident light. c) When optic axis is parallel to incident light direction. Huygen’s wavefront theory Every point on a wave-front may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wave-front is the tangential surface to all of these secondary wavelets. Effect of Incident Angle END 12/08/2018 Total Internal Reflection Total Internal Reflection Fiber Optics Total Internal Reflection Total Internal Reflection Prisms Polarising Prism: Nicol Prism The so-called “Nicol prism”. It is made of two pieces of calcite with a gap between, filled with “Canada Balsam” (a transparent glue). Due to the different refractive indices of the ordinary and the extraordinary waves, the ordinary undergoes a total internal reflection and is removed from the prism, while the extraordinary gets through. The Nicol Prism is an extremely efficient polarizer, but very expensive. Therefore, it is used only in apparatus in which high precision is crucial. Nicol Prism Glan–Thompson polarizing prism Glan–Foucault polarizing prism Glan–Taylor polarizing prism A ray of light makes a transition from a sample of benzene to water. What is the minimum angle the light must make with respect the normal in order for the light to be completely reflected back into the sample of benzene? The index of refraction for water is 1.33 and for benzene is 1.50. Correct answer: 62.5 degree Consider an optical fiber having a core index of 1.46 and a cladding index of 1.45. What is the critical angle for this core-cladding interface? Correct answer: 83.3 degree END 16/08/2018 Einstein Coefficients, absorption, spontaneous emission and Stimulated Emission 16/08/2018 • Population Inversion in two level and three level systems 20/08/2018 Absorption E1 E2 Spontaneous Emission Stimulated Emission Stimulated vs Spontaneous Emission Stimulated emission requires the presence of a photon. An “incoming” photon stimulates a molecule in an excited state to decay to the ground state by emitting a photon. The stimulated photons travel in the same direction as the incoming photon. Spontaneous emission does not require the presence of a photon. Instead a molecule in the excited state can relax to the ground state by spontaneously emitting a photon. Spontaneously emitted photons are emitted in all directions. For stimualted emission to be the dominant process, the excited state population must be larger than the lower state population. In other words, for a medium to produce laser light, there must be a “population inversion” where Nupper > Nlower How can a population inversion be created when the population in the ground state is always greater that the population in the excited state? What kinds of materials will “allow” for an inversion of population in its electronic states? How can a population inversion be created? By excitation of the lasing atoms or molecules - this is called PUMPING. If the pump source is very intense, the number of atoms or molecules excited can be large. However, once excited, the atoms and molecules must say in the excited state long enough to create an excited population > ground state population Two-Level System Em, Nm Em, Nm En, Nn En, Nn Even with very a intense pump source, the best one can achieve with a two-level system is excited state population = ground state population Example of a 3 level system E3 Rapid decay E2 LASING E1 Three-Level System The first laser, the ruby laser, was a three-level system upper lasing state lower lasing state 2 4 Laser light due to transition from E state to A2 state Example of a 4 level system E4 Rapid decay E3 LASING E2 Rapid decay E1 • 1→4 transition is pumped. • Rapid decay from 4 →3. • A population