Lect 3.5 - Department of Electrical and Computer...

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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 13.4 @Andrew Kirk 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. 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 ECSE 352 3.5-3 Contents • Definition of oblique incidence • Reflection coefficients • Implications ECSE 352 3.5-4
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Snell’s law ECSE 352 3.5-5 Example: Why do swimming pools appear to be deeper than they really are? ECSE 352 3.5-6 Example: Why do swimming pools appear to be deeper than they really are? ECSE 352 3.5-7 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 ++ = ECSE 352 3.5-8
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Review: Transverse EM waves Write the wave as: k k = Wave vector (m -1 ) () ( ) 0 exp j =− ER E kr W r P a n k = a x k x + a y k y + a z k z k 2 = ω 2 2 k 2 + k 2 + k z 2 = 2 με REVIE 0z u y 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 ECSE 352 3.5-9 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 + and k 1 - ) E-field 1 arallel polarization (TM H- olarization vertical p) ECSE 352 3.5-10 Parallel polarization (TM, H polarization, vertical, p), Parallel and perpendicular polarization H 10 + H 10 - k 1 - k 1 + θ 1 θ r E 10 + E 10 - η 1 η 1 z θ 2 E 20 H 20 z η 2 η 2 x x k 2 •Parallel •p-polarization •Perpendicular •s-polarization • Note that the signs of E and H fields are bit •Transverse magnetic (TM) •Transverse electric (TE) ECSE 352 3.5-11 arbitrary Parallel and perpendicular polarization E 10 + E 10 - k 1 - k 1 + H 10 + H 10 - k 1 - k 1 + θ 1 θ r H 10 + H 10 - θ 1 θ r E 10 + E 10 - η 1
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This note was uploaded on 02/14/2011 for the course ECSE 352 taught by Professor Mi during the Fall '10 term at McGill.

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Lect 3.5 - Department of Electrical and Computer...

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