Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London

2 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

3 Polarizing components POLARIZER (filter/separator) LINEARCIRCULAR WAVEPLATE (retarder)

4 Polarization notation circular polarization right- or left-handed rotation when looking towards source linear (plane) polarization parallel or perpendicular to plane of incidence RCP plane of incidence perpendicular parallel traces out opposite (right- or left-) handed thread plane of incidence contains wavevector and normal to surface

5 Characterizing the optical polarization wavevector insufficient to define electromagnetic wave we must additionally define the polarization vector e.g. linear polarization at angle

6 Jones vector calculus if the polarization state may be represented by a Jones vector then the action of an optical element may be described by a matrix JONES MATRIX

7 Jones vector calculus JONES MATRIX transmission by horizontal polarizer retardation by waveplate projection onto rotated axes if the polarization state may be represented by a Jones vector then the action of an optical element may be described by a matrix

8 Birefringence asymmetry in crystal structure causes two different refractive indices opposite polarizations follow different paths through crystal birefringence, double refraction

9 38.5º Linear polarizers (analyzers) e -ray o -ray e -ray o -ray s -ray p -ray birefringence results in different angles of refraction and total internal reflection many different designs, offering different geometries and acceptance angles a similar function results from multiple reflection

10 Waveplates (retarders) WAVEPLATE at normal incidence, a birefringent material retards one polarization relative to the other linearly polarized light becomes elliptically polarized

11 Compensators adjust fixed variable a variable waveplate uses two wedges to provide a variable thickness of birefringent crystal a further crystal, oriented with the fast and slow axes interchanged, allows the retardation to be adjusted around zero SOLEIL COMPENSATOR with a single, fixed first section, this is a ‘single order’ (or ‘zero order’) waveplate for small constant retardation

12 Unpolarized light if no correlation between and, if, intensity for any system

13 Electromagnetic waves light is a transverse wave: perpendicular to Faraday Ampère

14 Dielectrics z atomic electrons move in response to electric field resulting atomic dipole radiates field which adds to original Faraday Ampère

Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London

16 Diffraction S Yoshioka & S Kinoshita, Forma (2002) irridescence of feathers (Grimaldi, 1665)

17 Diffraction x

18 Diffraction

19 Diffraction

20 Huygens’ wave construction propagation from a point source Christiaan Huygens ( )

21 Huygens’ wave construction reflection at a plane surface Christiaan Huygens ( )

22 Huygens’ wave construction Christiaan Huygens ( ) refraction at a plane surface

23 Huygens’ wave construction mirages by refraction in the atmosphere Christiaan Huygens ( )

24 Huygens’ wave construction Fresnel integral phasors shorter / rotate more quickly at distance to give spiral

25 Arago’s bright spot M A Fresnel, La diffraction de la lumière (1818) Let parallel light impinge on an opaque disk, the surrounding being perfectly transparent. The disk casts a shadow - of course - but the very centre of the shadow will be bright. Succinctly, there is no darkness anywhere along the central perpendicular behind an opaque disk (except immediately behind the disk). S D Poisson: F Arago: One of your commissioners, M Poisson, had deduced from the integrals reported by [Fresnel] the singular result that the centre of the shadow of an opaque circular screen must, when the rays penetrate there at incidences which are only a little more oblique, be just as illuminated as if the screen did not exist. The consequence has been submitted to the test of direct experiment, and observation has perfectly confirmed the calculation.