polarization - The University of Texas at Dallas Erik...

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The University of Texas at Dallas Erik Jonsson School PhoTEC c C. D. Cantrell (09/2004) POLARIZATION The state of polarization (SOP) is the relation between the transverse components of E Assume a plane wave propagating in the + z direction Linear (plane) polarization : E y /E x is real and independent of time The E field vector lies in a fixed plane that includes the direction of propagation (see figure on next page) Circular polarization : The tip of the E vector describes a circle in the x y plane In right circular polarization , E rotates clockwise looking toward the source (looking in the z direction) Elliptical polarization : The tip of the E vector describes an ellipse in the x y plane
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The University of Texas at Dallas Erik Jonsson School PhoTEC c C. D. Cantrell (08/2010) PLANE OF POLARIZATION Y X E Plane of Polarization ψ The direction of the electric field and the direction of propagation determine the plane of polarization
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The University of Texas at Dallas Erik Jonsson School PhoTEC c C. D. Cantrell (09/2004) PLANE POLARIZATION The state of polarization of a plane wave is determined by the value of the relative phase angle, δ , and the ratio E 1 /E 2 , where E x = E 1 cos( ω t β z ) , E y = E 2 cos( ω t β z + δ ) Plane polarization (also called linear polarization ): δ = 0 Real components of the E field of a plane wave: E x = E 1 cos( ω t β z ) , E y = E 2 cos( ω t β z ) The E vector makes an angle ψ = tan 1 ( E 2 /E 1 ) with the x axis Note that the word “plane” has been used with 2 di ff erent meanings on this slide!
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The University of Texas at Dallas Erik Jonsson School PhoTEC c C. D. Cantrell (01/2002) SNAPSHOT OF PLANE-POLARIZED PLANE WAVE 0 5 10 15 -1 0 1 -1 0 1 Y Z X Red curve: Tip of the E vector Blue curve: Tip of the H vector The plane of polarization is the x z plane
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The University of Texas at Dallas Erik Jonsson School PhoTEC c C. D. Cantrell (03/2004) CIRCULAR POLARIZATION Circular polarization: δ = ± π 2 , E 2 = E 1 Real components of E : E x = E 1 cos( ωt βz ) , E y = E 1 sin( ωt βz ) For fixed z , the E vector describes a circle in the x y plane δ = π 2 ( sign on E y ): Right circular polarization δ = π 2 (+ sign on E y ): Left circular polarization The terms “right” and “left” circular polarization are confusing, because a right-circularly-polarized wave actually describes a left-handed screw as the wave propagates in z For right-circularly-polarized light, the tip of the E vector rotates clockwise in the x y plane, from the point of view of someone looking toward the source (in the z direction)
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The University of Texas at Dallas Erik Jonsson School PhoTEC c C. D. Cantrell (01/2002) SNAPSHOT OF CIRCULARLY-POLARIZED PLANE WAVE Z X Y Red lines: E vectors Blue lines: H vectors The light is left-circularly-polarized
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The University of Texas at Dallas Erik Jonsson School PhoTEC c C. D. Cantrell (03/2004) ELLIPTICAL POLARIZATION Elliptical polarization: E 2 = E 1 , or E 2 = E 1 and δ = ± π 2 and δ = 0 Real components of E : E x = E 1 cos( ωt βz
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