PolarizationLecture outlineDefinitionsCoherence and incoherenceWhy is polarization important?Classification of polarizationLinear polarizationCircular polarizationElliptical polarizationNatural EM radiationFresnel-Arago LawsFour ways to polarize EM wavesSelective absorption - dichroismDichroic materialsCrossed polarizersInterposing a third polarizer at 45º…Malus’ LawInterposing a third polarizer…Polarization on reflectionRefractionRefractive IndexSnel’s Law (note spelling!)Law of reflectionReflectivitySlide 25Slide 26Slide 27Polarization on scatteringRayleigh scatteringBirefringenceSlide 31Uniaxial crystals have an optic axisBirefringent MaterialsBirefringence can separate two polarizations into separate beamsInterference colorsPhotoelasticityAirplane windowsPolarizers take advantage of birefringence, Brewster's angle, and total internal reflectionWire Grid PolarizerReflectivity of waterRadar polarizationSlide 46Radar cross-polarizationSlide 48Lidar depolarizationRecapPolarizationLecture outline• Why is polarization important? • Classification of polarization• Four ways to polarize EM waves• Polarization in active remote sensing systemsDefinitions• Polarization is the phenomenon in which waves of light or other radiation are restricted in direction of vibration• Polarization is a property of waves that describes the orientation of their oscillationsCoherence and incoherence• Coherent radiation originates from a single oscillator, or a group of oscillators in perfect synchronization (phase-locked)• e.g., microwave ovens, radars, lasers, radio towers (i.e., artificial sources)• Incoherent radiation originates from independent oscillators that are not phase-locked. Natural radiation is incoherent.Why is polarization important?• Bohren (2006): ‘the only reason the polarization state of light is worth contemplating is that two beams, otherwise identical, may interact differently with matter if their polarization states are different.’• Interference only occurs when EM waves have the same frequency and polarization (i.e., they are coherent)• Used by active remote sensing systems (radar, lidar)Classification of polarization• Linear• Circular• Elliptical• ‘Random’ or unpolarizedLinear polarization• Plane EM wave – linearly polarized• Trace of electric field vector is linear• Also called plane-polarized light• Convention is to refer to the electric field vector• Weather radars usually transmit linearly polarized radiationCircular polarization• Two perpendicular EM plane waves of equal amplitude with 90° difference in phase• Electric vector rotates counterclockwise  right-hand circular polarizationElliptical polarization• Two plane waves not in phase, either with different amplitudes and/or not 90º out of phase• The most general state of complete polarization is ellipticalNatural EM radiation• Generally a mixture of different types of polarization• Randomly polarized component• Direction of the electric field vector changes randomly on very short timescale• ‘Unpolarized’ radiation• Bohren (2006): ‘Light is unpolarized if the successive vibration ellipses traced out over many periods of oscillation of the field exhibit no regular pattern’• Ratio of intensity of polarized component of a beam to the total intensity is the degree of polarization• Any oscillating electric field lying in a plane can be resolved into two orthogonal components, e.g., one vertical, one horizontalFresnel-Arago Laws• French scientists Augustin Fresnel (1788–1827) and Dominique Francois Jean Arago (1786–1853)1. Two orthogonal, coherent linearly polarized waves cannot interfere. (the intensity of the resulting beam is the sum of the intensities of each individual beam) 2. Two parallel coherent linearly polarized waves will interfere in the same way as natural light.3. The two constituent orthogonal linearly polarized states of natural light cannot interfere to form a readily observable interference pattern, even if rotated into alignment (because they are incoherent).• Coherence: two EM waves are coherent if there is a definite and fixed phase relation between them• Intensity is proportional to the square of amplitudeFour ways to polarize EM waves• Selective absorption (dichroism)• Reflection • Scattering• Birefringence (double refraction) in crystalline materialsSelective absorption - dichroism• Some crystalline materials absorb more light in one incident plane than another, so that transmitted light is polarized. This anisotropy in absorption is called dichroism.• There are naturally occurring and artificial dichroic materials (e.g., polaroid)• Such materials are used to produce polarized light in remote sensing instrumentsDichroic materials• Dichroic materials absorb more light in one polarization state than another. The mineral tourmaline (boron silicate) is the best known of natural dichroic materials. • Polaroid is produced by heating and stretching a sheet of polyvinyl alcohol, which aligns the long polymeric molecules in the stretch direction. After dipping in an iodine solution, the iodine atoms provide electrons which can move easily along the chains, but not perpendicular to them. Thus the material becomes an efficient electrical conductor along the chains. Light waves with electric fields parallel to these chains are strongly absorbed because the energy is dissipated by the along-chain electron motion. Perpendicular to the chains, the electrons cannot move freely to absorb energy, and light waves pass through.Crossed polarizersNo light is transmitted when two ideal polarizers (e.g., polaroid sheets) are ‘crossed’ (placed at right angles)Interposing a third polarizer at 45º…Malus’ Law• Etienne-Louis Malus (1775-1812): French engineer, physicist and mathematician• I = intensity of light transmitted by a perfect polarizer, I0 = initial light intensity, θ = the angle between the light’s initial plane of polarization and the axis of the polarizer• A beam of unpolarized light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. Since the average value of cos2θ is 1/2, ~50% of such light is transmitted.• For crossed polarizers, θ = 90º so no light is transmitted.€ I = I0cos2θiI0I€ (I0=12cε0E02)Interposing a third polarizer…Using the Law of Malus twice, 25% of the incident light will be transmittedPolarization on