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

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1 Polarization of Light: from Basics to Instruments (in less than 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 2

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

4 Part I: Polarization states Mathematical description of the EM wave Light wave that propagates in the z direction: E E x y (z, t) (z, t) E E x y cos(kz -t) x cos(kz -t ) y N. Manset / CFHT Polarization of Light: Basics to Instruments 4

5 Part I: Polarization states Graphical representation of the EM wave (I) One can go from: E E to the equation of an ellipse (using trigonometric identities, squaring, adding): x y (z, t) (z, t) E E x y cos(kz -t) x cos(kz -t ) y E E x x 2 E E y y 2 2 E E x x E E y y cos sin 2 N. Manset / CFHT Polarization of Light: Basics to Instruments 5

6 Part I: Polarization states Graphical representation of the EM wave (II) An ellipse can be represented by 4 quantities:. size of minor axis 2. size of major axis 3. orientation (angle) 4. sense (CW, CCW) Light can be represented by 4 quantities... N. Manset / CFHT Polarization of Light: Basics to Instruments 6

7 Part I: Polarization states, linear polarization Vertically polarized light E E x y (z, t) (z, t) E E x y cos(kz -t) x cos(kz -t ) y If there is no amplitude in x (E x = ), there is only one component, in y (vertical). N. Manset / CFHT Polarization of Light: Basics to Instruments 7

8 Part I: Polarization states, linear polarization Polarization at 45º (I) E E x y (z, t) (z, t) E E x y cos(kz -t) x cos(kz -t ) y If there is no phase difference (=) and E x = E y, then E x = E y N. Manset / CFHT Polarization of Light: Basics to Instruments 8

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

10 Part I: Polarization states, circular polarization Circular polarization (I) E E x y (z, t) (z, t) E E x y cos(kz -t) x cos(kz -t ) y If the phase difference is = 9º and E x = E y then: E x / E x = cos, E y / E y = sin and we get the equation of a circle: 2 2 E E x y 2 2 E x E y cos sin N. Manset / CFHT Polarization of Light: Basics to Instruments

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

12 Part I: Polarization states, circular polarization Circular polarization (III) N. Manset / CFHT Polarization of Light: Basics to Instruments 2

13 Part I: Polarization states, circular polarization... see it now? Circular polarization (IV) N. Manset / CFHT Polarization of Light: Basics to Instruments 3

14 Part I: Polarization states, elliptical polarization Elliptical polarization Linear + circular polarization = elliptical polarization N. Manset / CFHT Polarization of Light: Basics to Instruments 4

15 Part I: Polarization states, unpolarized light Unpolarized light (natural light) N. Manset / CFHT Polarization of Light: Basics to Instruments 5

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 N. Manset / CFHT Polarization of Light: Basics to Instruments 6

17 N. Manset / CFHT Polarization of Light: Basics to Instruments 7 Stokes parameters (III) described in geometrical terms sin2 sin2 cos2 cos2 cos2 V U Q I a a a a Part II: Stokes parameters

18 Part II: Stokes parameters, Stokes vectors Stokes vector The Stokes parameters can be arranged in a Stokes vector: I E Q E U 2E V 2E 2 x 2 x x x Linear polarization Circular polarization 2 Ey 2 Ey I E ycos ε I E sin ε y I intensity I9 45 I35 RCP ILCP Fully polarized light 2 I 2 2 Q U V Partially polarized light 2 I 2 2 Q U V Unpolarized light Q U V N. Manset / CFHT Polarization of Light: Basics to Instruments 8 Q Q, U, U, V, V 2 2

19 Part II: Stokes parameters Pictorial representation of the Stokes parameters N. Manset / CFHT Polarization of Light: Basics to Instruments 9

20 N. Manset / CFHT Polarization of Light: Basics to Instruments 2 Stokes vectors for linearly polarized light LHP light I LVP light +45º light -45º light I I I Part II: Stokes parameters, examples

21 Part II: Stokes parameters, examples Stokes vectors for circularly polarized light RCP light I LCP light I N. Manset / CFHT Polarization of Light: Basics to Instruments 2

22 Part II: Stokes parameters (Q,U) to (P,) In the case of linear polarization (V=): P Q 2 I U 2 2 arctan U Q Q P cos2 U P sin2 N. Manset / CFHT Polarization of Light: Basics to Instruments 22

23 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] I' Q' U' V' m m m m m m m m m m m m m m m m I Q U V N. Manset / CFHT Polarization of Light: Basics to Instruments 23

24 Part II: Stokes parameters, Mueller matrices Mueller calculus (I) Element Element 2 Element 3 M M M 2 3 I = M 3 M 2 M I N. Manset / CFHT Polarization of Light: Basics to Instruments 24

25 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: R( ) cos2 sin2 sin2 cos2 N. Manset / CFHT Polarization of Light: Basics to Instruments 25

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

27 Part III: Optical components Complex index of refraction The index of refraction is actually a complex quantity: m n ik 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 27

28 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. N. Manset / CFHT Polarization of Light: Basics to Instruments 28

29 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 N. Manset / CFHT Polarization of Light: Basics to Instruments 29

30 Part III: Optical components, polarizers Wide-grid polarizers (II) [dichroism] N. Manset / CFHT Polarization of Light: Basics to Instruments 3

31 Part III: Optical components, polarizers Dichroic crystals [dichroism] Dichroic crystals absorb one polarization state over the other one. Example: tourmaline. N. Manset / CFHT Polarization of Light: Basics to Instruments 3

32 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 928. N. Manset / CFHT Polarization of Light: Basics to Instruments 32

$with different springs depending on the orientation different spring constants gives different propagation speeds, therefore different indices of refraction, therefore 2 output beams N.$

33 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 33

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

35 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,... N. Manset / CFHT Polarization of Light: Basics to Instruments 35

36 Part III: Optical components, polarizers Mueller matrices of polarizers (I) (Ideal) linear polarizer at angle : 2 cos2χ sin2χ cos2χ cos 2 2χ sin2χ cos2χ sin2χ sin2χ cos2χ sin 2 2χ N. Manset / CFHT Polarization of Light: Basics to Instruments 36

37 N. Manset / CFHT Polarization of Light: Basics to Instruments 37 Mueller matrices of polarizers (II) Linear (±Q) polarizer at º:.5 Linear (±U) polarizer at º :.5 Part III: Optical components, polarizers Circular (±V) polarizer at º :.5

38 N. Manset / CFHT Polarization of Light: Basics to Instruments 38 Mueller calculus with a polarizer Input light: unpolarized --- output light: polarized I - I.5 I.5 V' U' Q' I' Total output intensity:.5 I Part III: Optical components, polarizers

39 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 39

40 Part III: Optical components, retarders Half-Wave plate (I) Retardation of ½ wave or 8º 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 4

41 Part III: Optical components, retarders Half-Wave plate (II) N. Manset / CFHT Polarization of Light: Basics to Instruments 4

42 Part III: Optical components, retarders Quarter-Wave plate (I) Retardation of ¼ wave or 9º for one of the polarizations Used to convert linear polarization to elliptical. N. Manset / CFHT Polarization of Light: Basics to Instruments 42

43 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) N. Manset / CFHT Polarization of Light: Basics to Instruments 43

44 Part III: Optical components, retarders Mueller matrix of retarders (I) Retarder of retardance and position angle : G with : G H sin4ψ sinτ H cos4ψ sin2ψ 2 G H sin4ψ sinτ H cos4ψ cos2ψ sinτ sin2ψ sinτ cos2ψ cosτ 2 cosτ and H cosτ N. Manset / CFHT Polarization of Light: Basics to Instruments 44

45 N. Manset / CFHT Polarization of Light: Basics to Instruments 45 Mueller matrix of retarders (II) Half-wave oriented at º or 9º Half-wave oriented at ±45º k k Part III: Optical components, retarders

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

47 N. Manset / CFHT Polarization of Light: Basics to Instruments 47 Mueller calculus with a retarder V' U' Q' I' k k Input light linear polarized (Q=) Quarter-wave at +45º Output light circularly polarized (V=) Part III: Optical components, retarders

Part III: Optical components, polarizers (Back to polarizers, briefly) Circular polarizers Input light: unpolarized --- Output light: circularly polarized Made

48 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 48

49 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 MgF 2 plates N. Manset / CFHT Polarization of Light: Basics to Instruments 49

50 Part III: Optical components, retarders Achromatic retarders (II) =4-22º not very achromatic! = 77-83º much better! N. Manset / CFHT Polarization of Light: Basics to Instruments 5

51 Part IV: Polarimeters Polaroid-type polarimeters Dual-beam polarimeters N. Manset / CFHT Polarization of Light: Basics to Instruments 5

52 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: P I I max max (I N. Manset / CFHT Polarization of Light: Basics to Instruments 52 I I I min min max )

53 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 53

54 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 54

55 Part IV: Polarimeters, dual-beam type Dual-beam polarimeters Switching beams by rotating the prism rotate by 8º N. Manset / CFHT Polarization of Light: Basics to Instruments 55

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

57 UH DBIP (Masiero, 27) Polarization of Light: Basics to Instruments 57

58 Part IV: Polarimeters, example of circular polarimeter A real circular polarimeter Semel, Donati, Rees (993) Quarter-wave plate, rotated at -45º and +45º Analyser: double calcite crystal N. Manset / CFHT Polarization of Light: Basics to Instruments 59

59 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 2 positions minimum analyzer + half-wave plate Circular polarimetry: position minimum analyzer + quarter-wave plate N. Manset / CFHT Polarization of Light: Basics to Instruments 6

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 N. Manset / CFHT Polarization of Light: Basics to Instruments 6

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 2 N. Manset / CFHT Polarization of Light: Basics to Instruments 62

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 N. Manset / CFHT Polarization of Light: Basics to Instruments 63

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 N. Manset / CFHT Polarization of Light: Basics to Instruments 64

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 N. Manset / CFHT Polarization of Light: Basics to Instruments 65

Basic Polarization Techniques and Devices 1998, 2003 Meadowlark Optics, Inc

Basic Polarization Techniques and Devices 1998, 2003 Meadowlark Optics, Inc This application note briefly describes polarized light, retardation and a few of the tools used to manipulate the polarization