# Polarization of Light: from Basics to Instruments (in less than 100 slides) N. Manset CFHT.

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Polarization of Light: from Basics to Instruments (in less than 100 slides)
N. Manset CFHT

Polarization of Light: Basics to Instruments
Introduction Part I: Different polarization states of light Part II: Stokes parameters, Mueller matrices Part III: Optical components for polarimetry Part IV: Polarimeters Part V: ESPaDOnS N. Manset / CFHT Polarization of Light: Basics to Instruments

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

Light as an electromagnetic wave
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

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

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

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

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

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

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

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

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

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

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

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

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

Polarization of Light: Basics to Instruments
Part I: Polarization states A cool Applet Electromagnetic Wave Location: N. Manset / CFHT Polarization of Light: Basics to Instruments

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

Stokes parameters A tiny itsy-bitsy little bit of history...
Part II: Stokes parameters Stokes parameters A tiny itsy-bitsy little bit of history... 1669: Bartholinus discovers double refraction in calcite 17th – 19th centuries: Huygens, Malus, Brewster, Biot, Fresnel and Arago, Nicol... 19th century: unsuccessful attempts to describe unpolarized light in terms of amplitudes 1852: Sir George Gabriel Stokes took a very different approach and discovered that polarization can be described in terms of observables using an experimental definition N. Manset / CFHT Polarization of Light: Basics to Instruments

Polarization of Light: Basics to Instruments
Part II: Stokes parameters Stokes parameters (I) The polarization ellipse is only valid at a given instant of time (function of time): To get the Stokes parameters, do a time average (integral over time) and a little bit of algebra... N. Manset / CFHT Polarization of Light: Basics to Instruments

Stokes parameters (II) described in terms of the electric field
Part II: Stokes parameters Stokes parameters (II) described in terms of the electric field The 4 Stokes parameters are: N. Manset / CFHT Polarization of Light: Basics to Instruments

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

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

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

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

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

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

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

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

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

Polarization of Light: Basics to Instruments
Part II: Stokes parameters, Jones formalism, not that important here... Jones formalism Stokes vectors and Mueller matrices cannot describe interference effects. If the phase information is important (radio-astronomy, masers...), one has to use the Jones formalism, with complex vectors and Jones matrices: Jones vectors to describe the polarization of light: Jones matrices to represent optical components: BUT: Jones formalism can only deal with 100% polarization... N. Manset / CFHT Polarization of Light: Basics to Instruments

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

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

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

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

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

Dichroic crystals [dichroism]
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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(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

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

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

Retardation on total internal reflection
Part III: Optical components, retarders Retardation on total internal reflection Total internal reflection produces retardation (phase shift) In this case, retardation is very achromatic since it only depends on the refractive index Application: Fresnel rhombs N. Manset / CFHT Polarization of Light: Basics to Instruments

Polarization of Light: Basics to Instruments
Part III: Optical components, retarders Fresnel rhombs Quarter-wave and half-wave rhombs are achieved with 2 or 4 reflections N. Manset / CFHT Polarization of Light: Basics to Instruments

Polarization of Light: Basics to Instruments
Part III: Optical components, retarders Other retarders Soleil-Babinet: variable retardation to better than 0.01 waves Nematic liquid crystals... Liquid crystal variable retarders... Ferroelectric liquid crystals... Piezo-elastic modulators... Pockels and Kerr cells... N. Manset / CFHT Polarization of Light: Basics to Instruments

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

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

Polaroid-type polarimeter for linear polarimetry (II)
Part IV: Polarimeters, polaroid-type Polaroid-type polarimeter for linear polarimetry (II) Move the polaroid to 2 positions, 0º and 45º (to measure Q, then U) Advantage: very simple to make Disadvantage: half of the light is cut out Other disadvantages: non-simultaneous measurements, cross-talk... N. Manset / CFHT Polarization of Light: Basics to Instruments

Polaroid-type polarimeter for circular polarimetry
Part IV: Polarimeters, polaroid-type Polaroid-type polarimeter for circular polarimetry Polaroids are not sensitive to circular polarization, so convert circular polarization to linear first, by using a quarter-wave plate Polarimeter now uses a quarter-wave plate and a polaroid Same disadvantages as before N. Manset / CFHT Polarization of Light: Basics to Instruments

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

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

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

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

Polarization of Light: Basics to Instruments
Part IV: Polarimeters, dual-beam type Dual-beam polarimeter for circular polarization - Wollaston and quarter-wave plate The measurements V/I is: Switch the beams to compensate the gain effects N. Manset / CFHT Polarization of Light: Basics to Instruments

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

Polarization of Light: Basics to Instruments
Part IV: Polarimeters, example of circular polarimeter A real circular polarimeter free from gain (g) and atmospheric transmission () variation effects First measurement with quarter-wave plate at -45º, signal in the (r)ight and (l)eft beams: Second measurement with quarter-wave plate at +45º, signal in the (r)ight and (l)eft beams: Measurements of the signals: N. Manset / CFHT Polarization of Light: Basics to Instruments

Polarization of Light: Basics to Instruments
Part IV: Polarimeters, example of circular polarimeter A real circular polarimeter free from gain and atmospheric transmission variation effects Build a ratio of measured signals which is free of gain and variable atmospheric transmission effects: average of the 2 measurements N. Manset / CFHT Polarization of Light: Basics to Instruments

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

Polarization of Light: Basics to Instruments
Part V: ESPaDOnS Optical components of the polarimeter part : Wollaston prism: analyses the polarization and separates the 2 (linear!) orthogonal polarization states Retarders, 3 Fresnel rhombs: Two half-wave plates to switch the beams around Quarter-wave plate to do circular polarimetry N. Manset / CFHT Polarization of Light: Basics to Instruments

Part V: ESPaDOnS, circular polarimetry mode ESPaDOnS: circular polarimetry Fixed quarter-wave rhomb Rotating bottom half-wave, at 22.5º increments Top half-wave rotates continuously at about 1Hz to average out linear polarization when measuring circular polarization N. Manset / CFHT Polarization of Light: Basics to Instruments

ESPaDOnS: circular polarimetry of circular polarization
Part V: ESPaDOnS, circular polarimetry mode ESPaDOnS: circular polarimetry of circular polarization half-wave 22.5º positions flips polarization gain, transmission quarter-wave fixed circular to linear analyzer N. Manset / CFHT Polarization of Light: Basics to Instruments

ESPaDOnS: circular polarimetry of (unwanted) linear polarization
Part V: ESPaDOnS, circular polarimetry mode ESPaDOnS: circular polarimetry of (unwanted) linear polarization analyzer half-wave 22.5º positions gain, transmission quarter-wave fixed linear to elliptical circular part goes through not analyzed and adds same intensities to both beams linear part is analyzed! Add a rotating half-wave to “spread out” the unwanted signal N. Manset / CFHT Polarization of Light: Basics to Instruments

Part V: ESPaDOnS, linear polarimetry ESPaDOnS: linear polarimetry Half-Wave rhombs positioned at 22.5º increments Quarter-Wave fixed N. Manset / CFHT Polarization of Light: Basics to Instruments

Part V: ESPaDOnS, linear polarimetry ESPaDOnS: linear polarimetry Half-Wave rhombs positioned as 22.5º increments First position gives Q Second position gives U Switch beams for gain and atmosphere effects Quarter-Wave fixed N. Manset / CFHT Polarization of Light: Basics to Instruments

Polarization of Light: Basics to Instruments
Part V: ESPaDOnS, summary ESPaDOnS - Summary ESPaDOnS can do linear and circular polarimetry (quarter-wave plate) Beams are switched around to do the measurements, compensate for gain and atmospheric effects Fesnel rhombs are very achromatic N. Manset / CFHT Polarization of Light: Basics to Instruments

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

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

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