Transcript wlq5
Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London Rainbows 2 Rainbows i r x r r r r i r i 3 Rainbows i r x r r r r i r i 4 Rainbows i r x r r r r i r i 5 Rainbows 6 Rainbows 7 Rainbows 8 Sinusoidal waves z • simple harmonic motion yx, t r sin t kz • circular motion r, where t kz r cost kz, r sin t kz 9 Sinusoidal waves y t t0 x yx, t y0 sin t kx at t t0 , yx, t0 y0 sin kx t0 y0 sin 2 ~ x t0 2 y0 sin x t0 • wavenumber • spectroscopists’ wavenumber • wavelength k 2 1 ~ 10 Sinusoidal waves y x x0 t yx, t y0 sin t kx at x x0, yx0 , t y0 sin t kx0 • angular frequency y0 sin 2 t kx0 • frequency 2 y0 sin t kx0 • period 2 1 11 Suggested textbooks Hecht Optics Pedrotti & Pedrotti Introduction to Optics Smith, King & Wilkins Optics and Photonics 12 Birefringence • asymmetry in crystal structure causes two different refractive indices • opposite polarizations follow different paths through crystal • birefringence, double refraction 13 Optical polarization • light is a transverse wave: E perpendicular to k • for any wavevector, there are two field components • any wave may be written as a superposition of the two polarizations 14 Linear dichroism • conductivity of wire grid depends upon field polarization • electric fields perpendicular to the wires are transmitted • fields parallel to the wires are absorbed WIRE GRID POLARIZER 15 Malus’ law • amplitude transmission cos • intensity transmission cos 2 WIRE GRID POLARIZER 16 Linear dichroism • crystals may similarly show absorption which depends upon linear polarization • absorption also depends upon wavelength • polarization therefore determines crystal colour • pleochroism, dichroism, trichroism TOURMALINE 17 Polarization in nature • the European cuttlefish also has polarization-sensitive vision CUTTLEFISH (sepia officinalis) • … and can change its colour and polarization! MAN’S VIEW CUTTLEFISH VIEW (red = horizontal polarization) 18 Characterizing the optical polarization • wavevector insufficient to define electromagnetic wave • we must additionally define the polarization vector a ax , a y • e.g. linear polarization at angle i a cos, esin sin k x z y 19 Categories of optical polarization • linear (plane) polarization • non-equal components in phase • circular polarization • equal components 90° out of phase • elliptical polarization • all other cases 20 Polarization notation • circular polarization • right- or left-handed rotation when looking towards source • traces out opposite (right- or left-) handed thread RCP plane of incidence perpendicular parallel • linear (plane) polarization • parallel or perpendicular to plane of incidence • plane of incidence contains wavevector and normal to surface 21 Circular dichroism • absorption may also depend upon circular polarization • the scarab beetle has polarizationsensitive vision, which it uses for navigation • the beetle’s own colour depends upon the circular polarization SCARAB BEETLE LEFT CIRCULAR RIGHT CIRCULAR POLARIZED LIGHT POLARIZED LIGHT 22 Optical activity (circular birefringence) • optical activity is birefringence for circular polarizations • an asymmetry between right and left allows opposing circular polarizations to have differing refractive indices • optical activity rotates the polarization plane of linearly polarized light • may be observed in vapours, liquids and solids CH3 CH2 CH3 CH3 CH3 H l-limonene (orange) H CH2 r-limonene (lemon) CHIRAL MOLECULES 23 Birefringence • asymmetry in crystal structure causes polarization dependent refractive index • ray splits into orthogonally polarized components, which follow different paths through crystal • note that polarization axes are not related to plane of incidence 24 Optical polarization • light is a transverse wave: E perpendicular to k • for any wavevector, there are two field components • any wave may be written as a superposition of the two polarizations 25 Electromagnetic waves • light is a transverse wave: E perpendicular to k x Ex z By Ex • Faraday • Ampère y B . d S t E B.ds 0 J 0 t .dS E B.ds 0 0 t .dS E.ds x y z By 26 Dielectrics • atomic electrons move in response to electric field • resulting atomic dipole radiates field which adds to original • Faraday • Ampère z B.dS t EE B . d s J .dS 0 0 r .dS t t E.ds 27 Birefringence • asymmetry in crystal structure causes polarization dependent refractive index • ray splits into orthogonally polarized components, which follow different paths through crystal • note that polarization axes are not related to plane of incidence 28 Linear polarizers (analyzers) • birefringence results in different angles of refraction and total internal reflection • many different designs, offering different geometries and acceptance angles o-ray e-ray 38.5º e-ray o-ray s-ray • a similar function results from multiple reflection p-ray 29 Waveplates (retarders) • at normal incidence, a birefringent material retards one polarization relative to the other • linearly polarized light becomes elliptically polarized 2 0 e l WAVEPLATE 30 Compensators • a variable waveplate uses two wedges to provide a variable thickness of birefringent crystal adjust • a further crystal, oriented with the fast and slow axes interchanged, allows the retardation to be adjusted around zero variable • with a single, fixed first section, this is a ‘single order’ (or ‘zero order’) waveplate for small constant retardation SOLEIL COMPENSATOR fixed 31