# Cookbook

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```					ECE 3300 Cookbook: Wave Reflection and Transmission – Oblique Incidence

1) Is E Parallel or Perpendicular to Plane of Incidence? The Plane of incidence
is defined as the plane that includes the DOP and the vector normal to surface.
The plane of incidence is the paper.

2) Find the Angles of incidence , reflection, transmission

θi = θr         k1 sinr = k2 sint (Snell’s law)

k     n        

3) Find the reflection and transmission coefficients (depends on polarization)

E  0  2 cos i  1 cos t
r
  i 
 2 cos t  1 cos i
E  0 2 cos i  1 cos t
|| 
 2 cos t  1 cos i
t
2 2 cos i
 
E0
                                              2 2 cos i
E  0  2 cos i  1 cos t
i
 || 
 2 cos t  1 cos i
   1  
Given E i : E r  E i E t   E i H  E / 
We will not consider loss in this class.
4) Define the direction of propagation (does not depend on polarization).

The direction of propagation is not a vector. It tells how the wave propagates
(how the phase changes), which is expressed as

e  jkx where x is xi ,r ,t  Direction of propagation
xi  x sin  i  z cosi
xr  x sin  r  z cos r
xt  x sin  t  z cost
5) Define the polarization vector y (this is how the field is ‘lying’ in the plane),
and put it all together:

a) Perpendicular Polarization

E i  E i e  jki xi y
ˆ    H i  H i e  jki xi yi
ˆ           yi   x cosi  z sin i
ˆ      ˆ         ˆ
E r  E r e  jkr xr y
ˆ      H r  H r e  jkr xr yr
ˆ        yr  x cos r  z sin  r
ˆ    ˆ          ˆ
E t  E t e  jkt xt y
ˆ    H t  H t e  jkt xt yt
ˆ        yt   x cost  z sin t
ˆ      ˆ         ˆ
b) Parallel Polarization

E i  E i e  jki xi  yi  H i  H i e  jki xi y
ˆ                         ˆ
E r  E r e  jkr xr yr
ˆ           H r  H r e  jkr xr  y 
ˆ
E t  E t e  jkt xt  yt  H t  H t e  jkt xt y
ˆ                         ˆ

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