Fields and Waves I

Fields and Waves I Lecture 22 Wave Polarization K. A. Connor Electrical, Computer, and Systems Engineering Department Rensselaer Polytechnic Institute, Troy, NY

These Slides Were Prepared by Prof. Kenneth A. Connor Using Original Materials Written Mostly by the Following: • Kenneth A. Connor – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY • J. Darryl Michael – GE Global Research Center, Niskayuna, NY • Thomas P. Crowley – National Institute of Standards and Technology, Boulder, CO • Sheppard J. Salon – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY • Lale Ergene – ITU Informatics Institute, Istanbul, Turkey • Jeffrey Braunstein – Chung-Ang University, Seoul, Korea Materials from other sources are referenced where they are used. Those listed as Ulaby are figures from Ulaby’s textbook. Fields and Waves I

Polarization http://www.bungie.org/archives/news-Oct_02.html http://www.3dglassesonline.com/how-do-3d-glasses-work/ http://www.maximumeyewear.com/productfolder/military-glasses/polarized-glasses.html Fields and Waves I

Overview • EM Waves in Lossless Media • Wave Equation • General Solution (similarity to Transmission Lines) • Lossless vs lossy materials (complex permittivity) • Energy and Power • EM Waves in Lossy Media • Skin Depth • Approximate wave parameters • Low Loss Dielectrics • Good Conductors • Power and Power Deposition • Microwave Heating • Wave Polarization • Reflection and Transmission at Normal Incidence • Plane Waves at Oblique Incidence Fields and Waves I

Wave Polarization describes the shape and locus of tip of the vector at a given point in space as a function of time The locus of , may have three different polarization states depends on conditions • Linear • Circular • Elliptical Fields and Waves I

Wave Polarization Laser light is polarized (can check a laser pointer) http://www.mic-d.com/java/argonionlaser/index.html Fields and Waves I

Wave Polarization Antennas usually have a dominant polarization. Antenna design must take this into account. Polarized light can illuminate or clarify objects in ways that non-polarized light cannot. Propagation through most media and scattering of waves can significantly affect polarization. Thus, polarized light can be very effective in the characterization of materials and physical objects. Polarization is the basis of one method for 3D photography. Polarization losses can be a significant issue is optical communications. Polarization direction is one option for the representation of ones and zeros for optical computing. The list goes on … Fields and Waves I

Wave Polarization Encarta Fields and Waves I

Polarization • For a +z-propagating wave, there are two possible directions of • Direction of is called as polarization • They are two independent solutions for the wave equation • Linear combinations make all possibilities Missing Image Reference Fields and Waves I

Polarization a uniform plane wave traveling in the +z direction may have x and y components Complex amplitudes The phase difference between the complex amplitudes of x and y components of electric field can be defines with angle δ Ex0=ax Ey0=ayejδax,ayare the magnitudesof Ex0 and Ey0 Fields and Waves I

Polarization The phasor of electric field The corresponding instantaneous field Fields and Waves I

Intensity and Inclination Angle The intensity of The inclination angleψ generally they both are function of t and z Fields and Waves I

Linear Polarization E +z B Can make any angle from the horizontal and vertical waves Missing Image Reference Fields and Waves I

Linear Polarization A wave is said to be linearly polarized if and Are in phase (δ=0) or out of phase (δ=π) In phase Out of phase Fields and Waves I

Linear Polarization (out of phase) Ulaby Fields and Waves I

Linear Polarization Looking up from +z x-polarized or horizontal polarized ay=0 ψ=0° or 180° y-polarized or vertical polarized ax=0 ψ=90° or -90° Fields and Waves I

Circular Polarization • A wave is said to be circularly polarized if • the magnitudes of and are equal and • The phase difference is δ=±π/2 δ=-π/2 δ=π/2 Ulaby Fields and Waves I

Elliptical Polarization Generally ax≠ay≠0 and δ≠0. the tip of traces an elliptical path in x-y plane rotation angle, γ -π/2≤γ≤π/2 Ellipticity angle, χ -π/4≤χ≤π/4 Ulaby Fields and Waves I

Polarization states The wave is traveling out of the slide Ulaby Fields and Waves I

http://www.mic-d.com/curriculum/lightandcolor/polarizedlight.htmlhttp://www.mic-d.com/curriculum/lightandcolor/polarizedlight.html Fields and Waves I

Example 1 – Polarization Consider a wave travelling in the z direction whose electric field is given by Describe the polarization (e.g. linear, right circular, etc.) and on an xy plot sketch the locus of over a cycle for the following cases. a) b) Fields and Waves I

Example 1 Fields and Waves I

Polarization Polarization Applet from Winston Chan (formerly at Iowa) http://home3.netcarrier.com/~chan/ The relationship between circular, linear and elliptical polarization is discussed by Alkwin Slenczka (University of Regensburg) http://www-dick.chemie.uni-regensburg.de/research_slenczka/polspe.html Fields and Waves I

Polarization Linear polarized light is separable as coherent superposition of two linearly polarized waves. As shown in the figure to the right both waves (red and green amplitude) are polarized perpendicular with respect to each other and of identical amplitude. Alkwin Slenczka Fields and Waves I

Polarization In addition, linear polarized light is separable into two circularly polarized waves of opposite sense of rotation (red and green amplitude) of identical amplitude. Alkwin Slenczka Fields and Waves I

Polarization Birefringence, which causes a phase shift between the two linearly polarized components, changes linear into circular polarization (a). Linear dichroism, however, which changes the respective amplitude differently, simply rotates the plane of polarization (b). Both effects together change linear polarized light into elliptically polarized light with main axis rotated with respect to the original plane of polarization (c). Alkwin Slenczka Fields and Waves I

Polarization In contrast, birefringence of circularly polarized components creates a rotation of plane of polarization (d) while circular dichroism in this case changes linear polarization into elliptical (e). Both effects together create elliptically polarized light with main axis rotated with respect to the original plane of polarization (f). Alkwin Slenczka Fields and Waves I

Polarized Light from Olympus* Naturally occurring light is randomly polarized. That is, it is equally probable for the electric field to be in any direction. A polarizing filter can select a particular polarization of light. *http://www.mic-d.com/curriculum/lightandcolor/polarizedlight.html Fields and Waves I

Polarized Light from Olympus As we shall see in a future lecture, reflection of light at oblique incidence (any angle other than normal to the surface) will produce somewhat polarized light. A Brewster’s Angle, the reflected light will be totally polarized. *http://www.mic-d.com/curriculum/lightandcolor/polarizedlight.html Fields and Waves I

Polarized Light from Olympus Sunglasses with polarizing lenses are made to block light that is reflected from highly reflective surfaces and, thus, can greatly reduce the effects of glare. *http://www.mic-d.com/curriculum/lightandcolor/polarizedlight.html Fields and Waves I

Polarized Light from Olympus *http://www.mic-d.com/curriculum/lightandcolor/polarizedlight.html Fields and Waves I

Polarized Light from Olympus An excellent example of the basic application of liquid crystals to display devices can be found in the seven-segment liquid crystal numerical display (illustrated in Figure 9). Here, the liquid crystalline phase is sandwiched between two glass plates that have electrodes attached similar to those depicted in the illustration. In Figure 9, the glass plates are configured with seven black electrodes that can be individually charged (these electrodes are transparent to light in real devices). Light passing through polarizer 1 is polarized in the vertical direction and, when no current is applied to the electrodes, the liquid crystalline phase induces a 90 degree "twist" of the light that enables it to pass through polarizer 2, which is polarized horizontally and is oriented perpendicular to polarizer 1. This light can then form one of the seven segments on the display. When current is applied to the electrodes, the liquid crystalline phase aligns with the current and loses the cholesteric spiral pattern. Light passing through a charged electrode is not twisted and is blocked by polarizer 2. By coordinating the voltage on the seven positive and negative electrodes, the display is capable of rendering the numbers 0 through 9. In this example the upper right and lower left electrodes are charged and block light passing through them, allowing formation of the number "2" by the display device (seen reversed in the figure). Fields and Waves I

Photography with a Polarizing Filter http://www.tifaq.com/images/ http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/filter/polarizer.html http://www.canfieldsci.com/photography/polarizer.shtml Fields and Waves I

Photography with a Polarizing Filter http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/filter/polarizer.html Fields and Waves I

Nikon – Polarized Light Polarized Light Microscopy: Can distinguish between isotropic and anisotropic materials. The technique exploits optical properties of anisotropy to reveal detailed information about the structure and composition of materials, which are invaluable for identification and diagnostic purposes. http://www.microscopyu.com/articles/polarized/polarizedintro.html Fields and Waves I

Nikon – Polarized Light Isotropic materials, which include gases, liquids, unstressed glasses and cubic crystals, demonstrate the same optical properties in all directions. They have only one refractive index and no restriction on the vibration direction of light passing through them. Anisotropic materials, in contrast, which include 90 percent of all solid substances, have optical properties that vary with the orientation of incident light with the crystallographic axes. They demonstrate a range of refractive indices depending both on the propagation direction of light through the substance and on the vibrational plane coordinates. More importantly, anisotropic materials act as beam splitters and divide light rays into two parts. The technique of polarizing microscopy exploits the interference of the split light rays, as they are re-united along the same optical path to extract information about these materials. http://www.microscopyu.com/articles/polarized/polarizedintro.html Fields and Waves I

Nikon – Polarized Light http://www.microscopyu.com/articles/polarized/polarizedintro.html Fields and Waves I

Nikon – Polarized Light http://www.microscopyu.com/tutorials/java/polarized/polarizerrotation/index.html Fields and Waves I

Birefringence The incoming ray of light is broken into two rays (whose polarization is at 90 degrees to each other and whose velocities through the material is different--hence birefringence) that travel through and exit the crystal. http://webphysics.davidson.edu/alumni/MiLee/JLab/Crystallography_WWW/birefringence.htm Fields and Waves I

Stress Birefringence http://www.oberlin.edu/physics/catalog/demonstrations/optics/birefringence.html Fields and Waves I

Birefringence on Plastic Boxes http://www.engl.paraselene.de/html/birefringence_on_plastic_boxes.html Fields and Waves I

Birefringence on Plastic Film http://www.engl.paraselene.de/html/birefringence_on_plastic_film.html Fields and Waves I

Quantitative analysis of the colors observed in birefringent samples is usually accomplished by consulting a Michel-Levy chart. The polarization colors visualized can be correlated with the actual retardation, thickness, and birefringence of the specimen. Olympus Fields and Waves I

3D Photography http://www.stereoscopy.com/library/waack-ch-5.html Fields and Waves I

Some Movies • Aspirin 1 • Aspirin 2 • DNA Fields and Waves I

Faraday Rotation http://www.unifiedphysics.com/ http://www.teachspin.com/instruments/faraday/index.shtml The rotation in the plane of polarization is caused by circular birefringence and their relationship with the magnetic field in terms of Zeeman Effect. The rotation is given by the following expression: where is the angle of rotation, B is the strength of the magnetic field in Gauss, d is the length of the medium and V is Verdet constant. http://www.wooster.edu/physics/JrIS/Files/kash-webarticle.pdf Fields and Waves I

Faraday Rotation The phenomenon of the Faraday effect was first observed by Michael Faraday in 1845. He found out that when a block of glass is subjected to a strong magnetic field, it becomes optically active. The effect occurs when the rotation of a linearly polarized wave passes through a thickness of a transparent medium. The beam should be plane polarized, that is, it can pass through an analyzer without attenuation only when its axis is parallel to that of the analyzer. The propagation of the beam of light has to be parallel to the direction of the magnet field in order to observe the rotation in its plane of polarization. If the field is perpendicular to the beam, then there is no rotation. There should be a medium present where the beam and the magnetic fields will interact. When non-magnetic materials like copper, lead, tin and silver are placed between the magnet, they cause no effect to polarized waves. http://www.wooster.edu/physics/JrIS/Files/kash-webarticle.pdf Fields and Waves I

Faraday Rotation Wikipedia Fields and Waves I

Fields and Waves I