Module 4 b

# Module 4 b - Module 4 Lecture 2 EM waves across interfaces...

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Page 1 Module 4 Lecture 2 EM waves across interfaces at oblique incidence

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Page 2 On the program today (Sadiku 10.9 • Review of definitions • How does the polarization of EM waves impact the reflection coefficient? • Reflection and transmission at oblique incidence. • Fresnel coefficients • TIR (total internal reflection) • Brewster’s angle
Page 3 Definitions Reflection/transmission coefficient: refers to wave amplitudes ( G ranges from -1 to +1, can be complex): 1+ G = t Reflectivity/Transmissivity: Usually identified by R and T respectively. Both R and T are positive, real numbers and refer to the average power. R and T range from 0 to 1, and R+T=1

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Page 4 Polarization dependence of G • The reflection coefficient G , is derived (and calculated) by matching tangential fields ( E T and H T ) at boundaries. • For a TEM wave incident normally on the interface, regardless of the state of polarization (orientation of the E vector in the plane of the interface), the full vectors of both E and H are completely tangential to the interface. • So G is polarization-independent at normal incidence.
Page 5 Reflection and transmission of plane waves on a plane interface between two media Regardless of the orientation of E in the x-y plane, E r + E i = E t

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Page 6 Reflections at boundaries under non- normal incidence • When a TEM wave strikes a boundary at non- normal incidence, its E and H fields cannot be all tangential to the interface. • Matching tangential fields at boundaries will yield different equations than the normal incidence case, hence different reflection coefficients. • The values of the tangential components of E and H , for a given angle of incidence, will depend on the state of polarization.
Page 7 Reflection and transmission of plane waves on a plane interface between two media For this orientation, H is tangential at the boundary,but not E media 2

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Page 8 How do we match E fields in this case ( H is along y )? z x y E field We must find the tangential component of E in the two media and match them.
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## This note was uploaded on 09/27/2011 for the course ENGINEERIN 3600 taught by Professor Victor during the Spring '11 term at Carleton CA.

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Module 4 b - Module 4 Lecture 2 EM waves across interfaces...

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