Understanding Optical Polarization and Birefringence: A Deep Dive into Waves and Light

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

2.  where Sinusoidal waves z • simple harmonic motion • circular motion

3. wavenumber • spectroscopists’ at , wavenumber • wavelength Sinusoidal waves

4. angular frequency • frequency • period Sinusoidal waves at ,

5. Birefringence • asymmetry in crystal structure causes two different refractive indices • opposite polarizations follow different paths through crystal • birefringence, double refraction 5

6. light is a transverse wave: perpendicular to Optical polarization • for any wavevector, there are two field components • any wave may be written as a superposition of the two polarizations

7. conductivity of wire grid depends upon field polarization • electric fields perpendicular to the wires are transmitted Linear dichroism • fields parallel to the wires are absorbed WIRE GRID POLARIZER

8. Malus’ law • amplitude transmission • intensity transmission WIRE GRID POLARIZER

9. crystals may similarly show absorption which depends upon linear polarization • absorption also depends upon wavelength • polarization therefore determines crystal colour Linear dichroism • pleochroism, dichroism, trichroism TOURMALINE

10. CUTTLEFISH (sepia officinalis) MAN’S VIEW CUTTLEFISH VIEW • the European cuttlefish also has polarization-sensitive vision • … and can change its colour and polarization! Polarization in nature (red = horizontal polarization)

11. SCARAB BEETLE LEFT CIRCULAR POLARIZED LIGHT RIGHT CIRCULAR POLARIZED LIGHT • absorption may also depend upon circular polarization • the scarab beetle has polarization-sensitive vision, which it uses for navigation Circular dichroism • the beetle’s own colour depends upon the circular polarization

12. CH3 CH3 CH3 CH3 CH2 CH2 H H • optical activity is birefringence for circular polarizations • an asymmetry between right and left allows opposing circular polarizations to have differing refractive indices Optical activity (circular birefringence) l-limonene (orange) r-limonene (lemon) • optical activity rotates the polarization plane of linearly polarized light CHIRAL MOLECULES • may be observed in vapours, liquids and solids

13. 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 13

14. Polarizing components LINEAR CIRCULAR POLARIZER (filter/separator) WAVEPLATE (retarder) 14

15. Waveplates (retarders) • at normal incidence, a birefringent material retards one polarization relative to the other • linearly polarized light becomes elliptically polarized WAVEPLATE 15

16. 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

17. Polarization by scattering cdoswell.com/tips3.htm

18. Brewster’s angle • reflected light fully (s-) polarized

19. www.paddling.net/sameboat/archives/sameboat496.html Brewster’s angle • reflected light fully (s-) polarized

20. Malus’ law • amplitude transmission • intensity transmission WIRE GRID POLARIZER

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

22. 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

23. 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

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

25. 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 25

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

27. 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

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

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