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Waves, Light & Quanta

Waves, Light & Quanta. Tim Freegarde. Web Gallery of Art; National Gallery, London. linear (plane) polarization. non-equal components in phase. Categories of optical polarization. circular polarization. equal components 90 ° out of phase. elliptical polarization. all other cases.

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Waves, Light & Quanta

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

  2. linear (plane) polarization • non-equal components in phase Categories of optical polarization • circular polarization • equal components 90° out of phase • elliptical polarization • all other cases

  3. Polarizing components LINEAR CIRCULAR POLARIZER (filter/separator) WAVEPLATE (retarder) 3

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

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

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

  7. 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 Jones vector calculus JONES MATRIX

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

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

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

  11. adjust variable fixed • 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 Compensators 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 , • for any system • intensity 12

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

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

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

  16. S Yoshioka & S Kinoshita, Forma 17 169 (2002) • irridescence of feathers (Grimaldi, 1665) Diffraction

  17. Diffraction x

  18. Diffraction 18

  19. Diffraction

  20. propagation from a point source Huygens’ wave construction Christiaan Huygens (1629-1695)

  21. reflection at a plane surface Huygens’ wave construction Christiaan Huygens (1629-1695)

  22. refraction at a plane surface Huygens’ wave construction Christiaan Huygens (1629-1695)

  23. mirages by refraction in the atmosphere Huygens’ wave construction Christiaan Huygens (1629-1695)

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

  25. M A Fresnel, La diffraction de la lumière (1818) • S D Poisson: 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). Arago’s bright spot • 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.

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