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Polarization of Light: from Basics to Instruments (in less than 100 slides)

Polarization of Light: from Basics to Instruments (in less than 100 slides). Originally by N. Manset, CFHT, Modified and expanded by K. Hodapp. Part I: Different polarization states of light. Light as an electromagnetic wave Mathematical and graphical descriptions of polarization

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Polarization of Light: from Basics to Instruments (in less than 100 slides)

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  1. Polarization of Light:from Basics to Instruments(in less than 100 slides) Originally by N. Manset, CFHT, Modified and expanded by K. Hodapp

  2. Part I: Different polarization states of light Light as an electromagnetic wave Mathematical and graphical descriptions of polarization Linear, circular, elliptical light Polarized, unpolarized light N. Manset / CFHT Polarization of Light: Basics to Instruments

  3. Light as an electromagnetic wave Light is a transverse wave, an electromagnetic wave Part I: Polarization states N. Manset / CFHT Polarization of Light: Basics to Instruments

  4. Graphical representation of the EM wave (II) Part I: Polarization states An ellipse can be represented by 4 quantities: size of minor axis size of major axis orientation (angle) sense (CW, CCW) Light can be represented by 4 quantities... N. Manset / CFHT Polarization of Light: Basics to Instruments

  5. Vertically polarized light If there is no amplitude in x (E0x = 0), there is only one component, in y (vertical). Part I: Polarization states, linear polarization N. Manset / CFHT Polarization of Light: Basics to Instruments

  6. Polarization at 45º (I) If there is no phase difference (e=0) and E0x = E0y, then Ex = Ey Part I: Polarization states, linear polarization N. Manset / CFHT Polarization of Light: Basics to Instruments

  7. Circular polarization (II) Part I: Polarization states, circular polarization N. Manset / CFHT Polarization of Light: Basics to Instruments

  8. Circular polarization (IV) Part I: Polarization states, circular polarization... see it now? N. Manset / CFHT Polarization of Light: Basics to Instruments

  9. Elliptical polarization Part I: Polarization states, elliptical polarization • Linear + circular polarization = elliptical polarization N. Manset / CFHT Polarization of Light: Basics to Instruments

  10. Part II: Stokes parameters and Mueller matrices Stokes parameters, Stokes vector Stokes parameters for linear and circular polarization Stokes parameters and polarization P Mueller matrices, Mueller calculus Jones formalism N. Manset / CFHT Polarization of Light: Basics to Instruments

  11. Stokes parameters (III)described in geometrical terms Part II: Stokes parameters N. Manset / CFHT Polarization of Light: Basics to Instruments

  12. Stokes vector Part II: Stokes parameters, Stokes vectors The Stokes parameters can be arranged in a Stokes vector: • Linear polarization • Circular polarization • Fully polarized light • Partially polarized light • Unpolarized light N. Manset / CFHT Polarization of Light: Basics to Instruments

  13. Pictorial representation of the Stokes parameters Part II: Stokes parameters N. Manset / CFHT Polarization of Light: Basics to Instruments

  14. Stokes vectors for linearly polarized light Part II: Stokes parameters, examples LHP light LVP light +45º light -45º light N. Manset / CFHT Polarization of Light: Basics to Instruments

  15. Stokes vectors for circularly polarized light Part II: Stokes parameters, examples RCP light LCP light N. Manset / CFHT Polarization of Light: Basics to Instruments

  16. (Q,U) to (P,Q) Part II: Stokes parameters In the case of linear polarization (V=0): N. Manset / CFHT Polarization of Light: Basics to Instruments

  17. Mueller matrices Part II: Stokes parameters, Mueller matrices If light is represented by Stokes vectors, optical components are then described with Mueller matrices: [output light] = [Muller matrix] [input light] N. Manset / CFHT Polarization of Light: Basics to Instruments

  18. Mueller calculus (I) Part II: Stokes parameters, Mueller matrices Element 1 Element 2 Element 3 I’= M3M2M1I N. Manset / CFHT Polarization of Light: Basics to Instruments

  19. Mueller calculus (II) Part II: Stokes parameters, Mueller matrices Mueller matrix M’ of an optical component with Mueller matrix M rotated by an angle a: M’ = R(- a) M R(a) with: N. Manset / CFHT Polarization of Light: Basics to Instruments

  20. Part III: Optical components for polarimetry Complex index of refraction Polarizers Retarders N. Manset / CFHT Polarization of Light: Basics to Instruments

  21. Complex index of refraction Part III: Optical components The index of refraction is actually a complex quantity: • real part • optical path length, refraction: speed of light depends on media • birefringence: speed of light also depends on P • imaginary part • absorption, attenuation, extinction: depends on media • dichroism/diattenuation: also depends on P N. Manset / CFHT Polarization of Light: Basics to Instruments

  22. Polarizers Part III: Optical components, polarizers Polarizers absorb one component of the polarization but not the other. The input is natural light, the output is polarized light (linear, circular, elliptical). They work by dichroism, birefringence, reflection, or scattering. N. Manset / CFHT Polarization of Light: Basics to Instruments

  23. Wire-grid polarizers (I)[dichroism] Mainly used in the IR and longer wavelengths Grid of parallel conducting wires with a spacing comparable to the wavelength of observation Electric field vector parallel to the wires is attenuated because of currents induced in the wires Part III: Optical components, polarizers N. Manset / CFHT Polarization of Light: Basics to Instruments

  24. Wide-grid polarizers (II)[dichroism] Part III: Optical components, polarizers N. Manset / CFHT Polarization of Light: Basics to Instruments

  25. Dichroic crystals[dichroism] Part III: Optical components, polarizers Dichroic crystals absorb one polarization state over the other one. Example: tourmaline. N. Manset / CFHT Polarization of Light: Basics to Instruments

  26. Polaroids[dichroism] Part III: Optical components, polarizers – Polaroids, like in sunglasses! Made by heating and stretching a sheet of PVA laminated to a supporting sheet of cellulose acetate treated with iodine solution (H-type polaroid). Invented in 1928. N. Manset / CFHT Polarization of Light: Basics to Instruments

  27. Crystal polarizers (I)[birefringence] Part III: Optical components, polarizers • Optically anisotropic crystals • Mechanical model: • the crystal is anisotropic, which means that the electrons are bound with different ‘springs’ depending on the orientation • different ‘spring constants’ gives different propagation speeds, therefore different indices of refraction, therefore 2 output beams N. Manset / CFHT Polarization of Light: Basics to Instruments

  28. Crystal polarizers (II)[birefringence] isotropic crystal (sodium chloride) Part III: Optical components, polarizers anisotropic crystal (calcite) The 2 output beams are polarized (orthogonally). N. Manset / CFHT Polarization of Light: Basics to Instruments

  29. Crystal polarizers (IV)[birefringence] Part III: Optical components, polarizers • Crystal polarizers used as: • Beam displacers, • Beam splitters, • Polarizers, • Analyzers, ... • Examples: Nicol prism, Glan-Thomson polarizer, Glan or Glan-Foucault prism, Wollaston prism, Thin-film polarizer, ... N. Manset / CFHT Polarization of Light: Basics to Instruments

  30. Mueller matrices of polarizers (I) Part III: Optical components, polarizers • (Ideal) linear polarizer at angle c: N. Manset / CFHT Polarization of Light: Basics to Instruments

  31. Mueller matrices of polarizers (II) Part III: Optical components, polarizers Linear (±Q) polarizer at 0º: Linear (±U) polarizer at 0º : Circular (±V) polarizer at 0º : N. Manset / CFHT Polarization of Light: Basics to Instruments

  32. Mueller calculus with a polarizer Part III: Optical components, polarizers Input light: unpolarized --- output light: polarized Total output intensity: 0.5 I N. Manset / CFHT Polarization of Light: Basics to Instruments

  33. Retarders Part III: Optical components, 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. N. Manset / CFHT Polarization of Light: Basics to Instruments

  34. Half-Wave plate (I) Retardation of ½ wave or 180º for one of the polarizations. Used to flip the linear polarization or change the handedness of circular polarization. Part III: Optical components, retarders N. Manset / CFHT Polarization of Light: Basics to Instruments

  35. Half-Wave plate (II) Part III: Optical components, retarders N. Manset / CFHT Polarization of Light: Basics to Instruments

  36. Quarter-Wave plate (I) Retardation of ¼ wave or 90º for one of the polarizations Used to convert linear polarization to elliptical. Part III: Optical components, retarders N. Manset / CFHT Polarization of Light: Basics to Instruments

  37. Quarter-Wave plate (II) Part III: Optical components, retarders • Special case: incoming light polarized at 45º with respect to the retarder’s axis • Conversion from linear to circular polarization (vice versa) N. Manset / CFHT Polarization of Light: Basics to Instruments

  38. Mueller matrix of retarders (I) Part III: Optical components, retarders • Retarder of retardance t and position angle y: N. Manset / CFHT Polarization of Light: Basics to Instruments

  39. Mueller matrix of retarders (II) Part III: Optical components, retarders • Half-wave oriented at ±45º • Half-wave oriented at 0º or 90º N. Manset / CFHT Polarization of Light: Basics to Instruments

  40. Mueller calculus with a retarder Part III: Optical components, retarders • Input light linear polarized (Q=1) • Quarter-wave at +45º • Output light circularly polarized (V=1) N. Manset / CFHT Polarization of Light: Basics to Instruments

  41. (Back to polarizers, briefly)Circular polarizers Part III: Optical components, polarizers • Input light: unpolarized --- Output light: circularly polarized • Made of a linear polarizer glued to a quarter-wave plate oriented at 45º with respect to one another. N. Manset / CFHT Polarization of Light: Basics to Instruments

  42. Achromatic retarders (I) Retardation depends on wavelength Achromatic retarders: made of 2 different materials with opposite variations of index of refraction as a function of wavelength Pancharatnam achromatic retarders: made of 3 identical plates rotated w/r one another Superachromatic retarders: 3 pairs of quartz and MgF2 plates Part III: Optical components, retarders N. Manset / CFHT Polarization of Light: Basics to Instruments

  43. Achromatic retarders (II) Part III: Optical components, retarders t=140-220º not very achromatic! t= 177-183º much better! N. Manset / CFHT Polarization of Light: Basics to Instruments

  44. Part IV: Polarimeters Polaroid-type polarimeters Dual-beam polarimeters N. Manset / CFHT Polarization of Light: Basics to Instruments

  45. Polaroid-type polarimeterfor linear polarimetry (I) Part IV: Polarimeters, polaroid-type • Use a linear polarizer (polaroid) to measure linear polarization ... [another cool applet]Location:http://www.colorado.edu/physics/2000/applets/lens.html • Polarization percentage and position angle: N. Manset / CFHT Polarization of Light: Basics to Instruments

  46. Dual-beam polarimetersPrinciple Instead of cutting out one polarization and keeping the other one (polaroid), split the 2 polarization states and keep them both Use a Wollaston prism as an analyzer Disadvantages: need 2 detectors (PMTs, APDs) or an array; end up with 2 ‘pixels’ with different gain Solution: rotate the Wollaston or keep it fixed and use a half-wave plate to switch the 2 beams Part IV: Polarimeters, dual-beam type N. Manset / CFHT Polarization of Light: Basics to Instruments

  47. Dual-beam polarimetersSwitching beams Part IV: Polarimeters, dual-beam type • Unpolarized light: two beams have identical intensities whatever the prism’s position if the 2 pixels have the same gain • To compensate different gains, switch the 2 beams and average the 2 measurements N. Manset / CFHT Polarization of Light: Basics to Instruments

  48. Dual-beam polarimetersSwitching beams by rotating the prism Part IV: Polarimeters, dual-beam type rotate by 180º N. Manset / CFHT Polarization of Light: Basics to Instruments

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