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3.5 - Department of Electrical and Computer Engineering...

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Department of Electrical and Computer Engineering ECSE 352 Electromagnetic Waves and Optics 3.5 Wave reflection at oblique incidence References: Section 13.5 AGK 2005 3.5-1 Overview In this class we will examine the case of waves incident onto a boundary at oblique incidence. We will see that waves can be refracted (i.e. their paths will be deviated) when they enter a medium of different dielectric constant. We will also see that the reflection and transmission coefficients are now a unction of angle and polarization as well as material function of angle and polarization as well as material parameters. ©AGK 2005 ECSE 352 3.5-2 Learning outcomes After taking this class you should be able to: • Calculate the E and H field distribution in the case of oblique incidence onto a dielectric ecognize and apply the definitions of parallel and Recognize and apply the definitions of parallel and perpendicularly polarized waves • Calculate the transmission and reflection coefficients for any polarization state • Recognize that waves incident at an angle onto a ielectric are refracted dielectric are refracted • Calculate the angle of refraction using Snell's law ©AGK 2005 ECSE 352 3.5-3 Contents • Definition of oblique incidence • Reflection coefficients • Implications ©AGK 2005 ECSE 352 3.5-4

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Snell’s law ©AGK 2005 ECSE 352 3.5-5 Example: Why do swimming pools appear to be deeper than they really are? ©AGK 2005 ECSE 352 3.5-6 Review: Normal incidence • Reflection coefficient Γ : 21 j e φ η Γ= • Transmission coefficient τ : ηη + W 2 2 j e τ == E 1 + E + Air Dielectric REVIE + E 1 - 2 10 10 x x EE −+ 20 10 x x ++ = ©AGK 2005 ECSE 352 3.5-7 Review: Transverse EM waves Write the wave as: k k = Wave vector (m -1 ) () ( ) 0 exp j =− ER E kr r P a n k = a x k x + a y k y + a z k z k 2 = ω 2 2 k x 2 + k y 2 + k z 2 = 2 με 0z u h t is th l f hi h th h s st t ? What is the plane for which the phase is constant ? Plane of constant phase Æ k r is constant AVEFRONT ©AGK 2005 ECSE 352 3.5-8 k is always normal to wave-front Æ WAVEFRONT
Oblique incidence Perpendicular polarization (also y x pp ( called TE, E-polarzation, horizontal, s), interface Resolve polarization into two components: k 1 - k 2 η 2 z l f i id k + η 1 Plane of incidence (Plane of k 1 +

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3.5 - Department of Electrical and Computer Engineering...

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