notes 18 3317.pptx - ECE 3317 Prof Ji Chen Spring 2019 Notes 18 Reflection and Transmission of Plane Waves 1 General Plane Wave Consider a plane wave

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Prof. Ji Chen Notes 18 Reflection and Transmission of Plane Waves ECE 3317 1 Spring 2019
General Plane Wave Consider a plane wave propagating at an arbitrary direction in space. Denote so 2 x y z z jkz e sin cos sin sin cos z x y z ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ z xx yy zz z x z x y z y z z z x r x y r y z r z ˆ r ˆ ˆ ˆ ˆ sin cos sin sin cos r x y z , , x y z
General Plane Wave (cont.) Hence x y z z Note: (wavenumber equation) or 3 x y z j k x k y k z e sin cos sin sin cos x y z k k k k k k ˆ r 2 2 2 2 2 2 2 2 2 sin cos sin cos x y z k k k k k 2 2 2 2 x y z k k k k
General Plane Wave (cont.) We define the wavevector: The k vector tells us which direction the wave is traveling in. (This assumes that the wavevector is real.) 4 x y z z sin cos sin sin cos x y z k k k k k k ˆ ˆ ˆ x y z k x k y k z k 2 2 2 2 2 2 x y z x y z k k k k k k k k  ˆ r
TM and TE Plane Waves The electric and magnetic fields are both perpendicular to the direction of propagation. There are two fundamental cases: Transverse Magnetic (TM z ) H z = 0 Transverse Electric (TE z ) E z = 0 x TM z y z E H S x TE z y z E H S Note: The word “transverse” means “perpendicular to.” 5 ˆ ˆ TM : E E H H ˆ ˆ TE : E E H H z z
Reflection and Transmission As we will show, each type of plane wave (TE z and TM z ) reflects differently from a material. #1 x z i r t #2 Incident Reflected Transmitted 6
Boundary Conditions Here we review the boundary conditions at an interface (from ECE 2317). ++++ Note: The unit normal points towards region 1. No sources on interface: The tangential electric and magnetic fields are continuous. The normal components of the electric and magnetic flux densities are continuous. 7 1 2 1 2 1 2 1 2 ˆ D D ˆ E E 0 ˆ B B 0 ˆ H H J s s n n n n ˆ n 1 1 , 2 2 , s J s 1 2 1 2 1 2 1 2 ˆ ˆ D D ˆ ˆ E E ˆ ˆ B B ˆ ˆ H H n n n n n n n n
Reflection at Interface First we consider the ( x , z ) variation of the fields. (We will worry about the polarization later.) Assume that the Poynting vector of the incident plane wave lies in the xz plane ( = 0 ). This is called the plane of incidence .

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