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

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

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 (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 1 Element 2 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

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) =140-220º not very achromatic! = 177-183º much better! 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: http://www.colorado.edu/physics/2000/applets/lens.html Polarization percentage and position angle: 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 UH DBIP (Masiero, 2007) 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

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

Credits for pictures and movies Christoph Keller’s home page – his 5 lectures http://www.noao.edu/noao/staff/keller/ “Basic Polarisation techniques and devices”, Meadowlark Optics Inc. http://www.meadowlark.com/ Optics, E. Hecht and Astronomical Polarimetry, J. Tinbergen Planets, Stars and Nebulae Studied With Photopolarimetry, T. Gehrels Circular polarization movie http://www.optics.arizona.edu/jcwyant/JoseDiaz/Polarization-Circular.htm Unpolarized light movie http://www.colorado.edu/physics/2000/polarization/polarizationII.html Reflection of wave http://www.physicsclassroom.com/mmedia/waves/fix.html ESPaDOnS web page and documents N. Manset / CFHT Polarization of Light: Basics to Instruments

References/Further reading On the Web Very short and quick introduction, no equation http://www.cfht.hawaii.edu/~manset/PolarIntro_eng.html Easy fun page with Applets, on polarizing filters http://www.colorado.edu/physics/2000/polarization/polarizationI.html Polarization short course http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/u12l1e.html “Instrumentation for Astrophysical Spectropolarimetry”, a series of 5 lectures given at the IAC Winter School on Astrophysical Spectropolarimetry, November 2000 –http://www.noao.edu/noao/staff/keller/lectures/index.html N. Manset / CFHT Polarization of Light: Basics to Instruments

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

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

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