1. 8-9 Normal Incidence at Multiple Dielectric Interfaces
Antireflection coating for eye glasses.
Radome (for the protection of radars of ships)
Reflected
wave
Medium 3
(ε3 , μ3)
z=0
z=d
Medium 2
(ε2 , μ2)
Medium 1
(ε1 , μ1) x Er Hr
anr
Unknowns :
Transmitted
wave
Incident
wave
Boundary conditions at z=0 , z=d Hi Ei
ani
The procedure is straightforward and purely algebraic.

2. 8-9.1 Wave Impedance of the total field
(includes the effect of medium 2) O z
In an unbounded medium , for +z direction wave
In an unbounded medium, for -z direction wave
η: intrinsic impedance
Medium 1
Medium 2
z=0
which is the same as the input impedance of a transmission line of length l
that has a characteristic impedance and terminates in a short circuit.

3. 8-9.2 Impedance Transformation with Multiple Dielectrics
We can transform to an arbitrary value
of by choosing and
when , There is no reflection.
Ex p405

4. 8-10 Oblique Incidence at a plane Dielectric Boundary
Reflected
wave x
Refracted
wave
anr
ant O’
Snell’s Law of refraction
-The angle of reflection is equal to the angle of incident) A’ B A θr θt θi O z
ani
Incident
wave
n : refractive index
Medium 1
(ε1,μ1)
Medium 2
(ε2,μ2)
z=0

5. 8.10-1 Total Reflection What happen in Medium 2 when ? x z z=0ε1
Medium 2 ε2
(Total reflection)
Critical Angle θt
What happen in Medium 2 when ? θi O z
z=0
Evanescent wave along z
Propagation in x direction
tightly bound to the surface
⇒ surface wave
If medium 2 is not thick enough,
there is transmitted wave even though TIR condition is met!
z (no power transmission)

6. 8-10.2 Perpendicular Polarizationx
For given incident wave, θr θi O
Find z •
z=0

7. 8-10.2 Perpendicular Polarization (2)x θr θi O z
We know that •
z=0

8. 8-10.2 Perpendicular Polarization (3)
Assume that we found the solutions,
Fresnel’s Equation

9. 8-10.3 Parallel Polarizationx
For given incident wave, x θt θi O
Find •
z=0

10. 8-10.3 Parallel Polarization (2)
Boundary conditions
Z=0

11. 8-10.3 Parallel Polarization (3)
(No reflection)
find such
Snell’s law
(assume μ1= μ2)

12. 8-10.3 Parallel Polarization (4)
- (1)
(1)

13. 8-10.3 Parallel Polarization (5)
Brewster Angle
What about perpendicular polarization?
However this is the rare situation in nature!

14. 8-10.3 Parallel Polarization (6)