1. Originally by N. Manset, CFHT, Modified and expanded by K. Hodapp
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
Part I: Polarization states
Light as an electromagnetic wave
Light is a transverse wave,
an electromagnetic wave
?!?
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Polarization of Light: Basics to Instruments

4. Mathematical description of the EM wave
Part I: Polarization states
Mathematical description of the EM wave
Light wave that propagates in the z direction:
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Polarization of Light: Basics to Instruments

5. Graphical representation of the EM wave (I)
Part I: Polarization states
Graphical representation of the EM wave (I)
One can go from:
to the equation of an ellipse (using trigonometric identities, squaring, adding):
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Polarization of Light: Basics to Instruments

6. Graphical representation of the EM wave (II)
Part I: Polarization states
Graphical representation of the EM wave (II)
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...
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Polarization of Light: Basics to Instruments

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

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

9. Polarization of Light: Basics to Instruments
Part I: Polarization states, linear polarization
Polarization at 45º (II)
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Polarization of Light: Basics to Instruments

10. Circular polarization (I)
Part I: Polarization states, circular polarization
Circular polarization (I)
If the phase difference is = 90º and E0x = E0y
then: Ex / E0x = cos  , Ey / E0y = sin 
and we get the equation of a circle:
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Polarization of Light: Basics to Instruments

11. Circular polarization (II)
Part I: Polarization states, circular polarization
Circular polarization (II)
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Polarization of Light: Basics to Instruments

12. Circular polarization (III)
Part I: Polarization states, circular polarization
Circular polarization (III)
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Polarization of Light: Basics to Instruments

13. Circular polarization (IV)
Part I: Polarization states, circular polarization... see it now?
Circular polarization (IV)
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Polarization of Light: Basics to Instruments

14. Elliptical polarization
Part I: Polarization states, elliptical polarization
Elliptical polarization
Linear + circular polarization = elliptical polarization
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Polarization of Light: Basics to Instruments

15. Unpolarized light (natural light)
Part I: Polarization states, unpolarized light
Unpolarized light (natural light)
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Polarization of Light: Basics to Instruments

16. 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
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Polarization of Light: Basics to Instruments

17. Stokes parameters (III) described in geometrical terms
Part II: Stokes parameters
Stokes parameters (III) described in geometrical terms
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Polarization of Light: Basics to Instruments

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

19. Pictorial representation of the Stokes parameters
Part II: Stokes parameters
Pictorial representation of the Stokes parameters
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Polarization of Light: Basics to Instruments

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

21. Stokes vectors for circularly polarized light
Part II: Stokes parameters, examples
Stokes vectors for circularly polarized light
RCP light
LCP light
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Polarization of Light: Basics to Instruments

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

23. Polarization of Light: Basics to Instruments
Part II: Stokes parameters, Mueller matrices
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

24. Polarization of Light: Basics to Instruments
Part II: Stokes parameters, Mueller matrices
Mueller calculus (I)
Element Element Element 3
I’ = M3 M2 M1 I
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Polarization of Light: Basics to Instruments

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

26. Part III: Optical components for polarimetry
Complex index of refraction
Polarizers
Retarders
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Polarization of Light: Basics to Instruments

27. Complex index of refraction
Part III: Optical components
Complex index of refraction
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
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Polarization of Light: Basics to Instruments

28. Polarization of Light: Basics to Instruments
Part III: Optical components, polarizers
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.
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Polarization of Light: Basics to Instruments

29. Wire-grid polarizers (I) [dichroism]
Part III: Optical components, polarizers
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
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Polarization of Light: Basics to Instruments

30. Wide-grid polarizers (II) [dichroism]
Part III: Optical components, polarizers
Wide-grid polarizers (II) [dichroism]
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Polarization of Light: Basics to Instruments

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

32. Polaroids [dichroism]
Part III: Optical components, polarizers – Polaroids, like in sunglasses!
Polaroids [dichroism]
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.
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Polarization of Light: Basics to Instruments

33. Crystal polarizers (I) [birefringence]
Part III: Optical components, polarizers
Crystal polarizers (I) [birefringence]
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

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

35. Crystal polarizers (IV) [birefringence]
Part III: Optical components, polarizers
Crystal polarizers (IV) [birefringence]
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, ...
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Polarization of Light: Basics to Instruments

36. Mueller matrices of polarizers (I)
Part III: Optical components, polarizers
Mueller matrices of polarizers (I)
(Ideal) linear polarizer at angle :
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Polarization of Light: Basics to Instruments

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

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

39. Polarization of Light: Basics to Instruments
Part III: Optical components, retarders
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

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

41. Polarization of Light: Basics to Instruments
Part III: Optical components, retarders
Half-Wave plate (II)
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Polarization of Light: Basics to Instruments

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

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

44. Mueller matrix of retarders (I)
Part III: Optical components, retarders
Mueller matrix of retarders (I)
Retarder of retardance  and position angle :
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Polarization of Light: Basics to Instruments

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

46. Mueller matrix of retarders (III)
Part III: Optical components, retarders
Mueller matrix of retarders (III)
Quarter-wave oriented at ±45º
Quarter-wave oriented at 0º
N. Manset / CFHT
Polarization of Light: Basics to Instruments

47. Mueller calculus with a retarder
Part III: Optical components, retarders
Mueller calculus with a retarder
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

48. (Back to polarizers, briefly) Circular polarizers
Part III: Optical components, polarizers
(Back to polarizers, briefly) Circular 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

49. Achromatic retarders (I)
Part III: Optical components, retarders
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
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Polarization of Light: Basics to Instruments

50. Achromatic retarders (II)
Part III: Optical components, retarders
Achromatic retarders (II)
= º
not very achromatic!
= º
much better!
N. Manset / CFHT
Polarization of Light: Basics to Instruments

51. Polarization of Light: Basics to Instruments
Part IV: Polarimeters
Polaroid-type polarimeters
Dual-beam polarimeters
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Polarization of Light: Basics to Instruments

52. Polaroid-type polarimeter for linear polarimetry (I)
Part IV: Polarimeters, polaroid-type
Polaroid-type polarimeter for linear polarimetry (I)
Use a linear polarizer (polaroid) to measure linear polarization ... [another cool applet] Location:
Polarization percentage and position angle:
N. Manset / CFHT
Polarization of Light: Basics to Instruments

53. Dual-beam polarimeters Principle
Part IV: Polarimeters, dual-beam type
Dual-beam polarimeters Principle
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
N. Manset / CFHT
Polarization of Light: Basics to Instruments

54. Dual-beam polarimeters Switching beams
Part IV: Polarimeters, dual-beam type
Dual-beam polarimeters Switching beams
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

55. Dual-beam polarimeters Switching beams by rotating the prism
Part IV: Polarimeters, dual-beam type
Dual-beam polarimeters Switching beams by rotating the prism
rotate by 180º
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Polarization of Light: Basics to Instruments

56. Dual-beam polarimeters Switching beams using a ½ wave plate
Part IV: Polarimeters, dual-beam type
Dual-beam polarimeters Switching beams using a ½ wave plate
Rotated by 45º
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Polarization of Light: Basics to Instruments

57. Polarization of Light: Basics to Instruments
UH DBIP (Masiero, 2007)
Polarization of Light: Basics to Instruments

58. A real circular polarimeter Semel, Donati, Rees (1993)
Part IV: Polarimeters, example of circular polarimeter
A real circular polarimeter Semel, Donati, Rees (1993)
Quarter-wave plate, rotated at -45º and +45º
Analyser: double calcite crystal
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Polarization of Light: Basics to Instruments

59. Polarimeters - Summary
Part IV: Polarimeters, summary
Polarimeters - Summary
2 types:
polaroid-type: easy to make but ½ light is lost, and affected by variable atmospheric transmission
dual-beam type: no light lost but affected by gain differences and variable transmission problems
Linear polarimetry:
analyzer, rotatable
analyzer + half-wave plate
Circular polarimetry:
analyzer + quarter-wave plate
2 positions minimum
1 position minimum
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Polarization of Light: Basics to Instruments

60. Credits for pictures and movies
Christoph Keller’s home page – his 5 lectures
“Basic Polarisation techniques and devices”, Meadowlark Optics Inc.
Optics, E. Hecht and Astronomical Polarimetry, J. Tinbergen
Planets, Stars and Nebulae Studied With Photopolarimetry, T. Gehrels
Circular polarization movie
Unpolarized light movie
Reflection of wave
ESPaDOnS web page and documents
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Polarization of Light: Basics to Instruments

61. References/Further reading On the Web
Very short and quick introduction, no equation
Easy fun page with Applets, on polarizing filters
Polarization short course
“Instrumentation for Astrophysical Spectropolarimetry”, a series of 5 lectures given at the IAC Winter School on Astrophysical Spectropolarimetry, November 2000 –
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Polarization of Light: Basics to Instruments

62. References/Further reading Polarization basics
Polarized Light, D. Goldstein – excellent book, easy read, gives a lot of insight, highly recommended
Undergraduate textbooks, either will do:
Optics, E. Hecht
Waves, F. S. Crawford, Berkeley Physics Course vol. 3
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Polarization of Light: Basics to Instruments

63. References/Further reading Astronomy, easy/intermediate
Astronomical Polarimetry, J. Tinbergen – instrumentation-oriented
La polarisation de la lumière et l'observation astronomique, J.-L. Leroy – astronomy-oriented
Planets, Stars and Nebulae Studied With Photopolarimetry, T. Gehrels – old but classic
3 papers by K. Serkowski – instrumentation-oriented
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Polarization of Light: Basics to Instruments

64. References/Further reading Astronomy, advanced
Introduction to Spectropolarimetry, J.C. del Toro Iniesta – radiative transfer – ouch!
Astrophysical Spectropolarimetry, Trujillo-Bueno et al. (eds) – applications to astronomy
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Polarization of Light: Basics to Instruments