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
3.51
Overview
In this class we will examine the case of waves
i
id
t
t
b
d
t bli
i
id
W ill
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
function of angle and polarization as well as material
parameters.
ECSE 352 3.52
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
•
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
dielectric are refracted
•
Calculate the angle of refraction using Snell's law
ECSE 352 3.53
Contents
•
Definition of oblique incidence
•
Reflection coefficients
• Implications
ECSE 352 3.54
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Snell’s law
ECSE 352 3.55
Example: Why do swimming pools appear to
be deeper than they really are?
ECSE 352 3.56
Example: Why do swimming pools appear to
be deeper than they really are?
ECSE 352 3.57
Review: Normal incidence
•
Reflection coefficient
Γ
:
2
1
j
e
φ
η
η
η
η
−
Γ =
= Γ
+
•
Transmission coefficient
τ
:
2
1
W
2
2
j
e
τ
φ
η
τ
τ
η
η
=
=
+
E
1
+
E
2
+
Air
Dielectric
REVIEW
2
1
E
1

10
10
x
x
E
E
−
+
= Γ
20
10
x
x
E
E
τ
+
+
=
ECSE 352 3.58