Title: Wave Incidence at Oblique angles
1Wave Incidenceat Oblique angles
- Sandra Cruz-Pol
- ECE Dept. UPRM
2Quiz VIERNES
- Uno de los problemas asignados en el prontuario
- Enviar contestaciones a preguntas en Word por
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3Wave Incidence
- Normal incidence
- Wave arrives at 90o from the surface
- Standing waves
- Oblique incidence (lossless)
- Wave arrives at an angle
- Snells Law and Critical angle
- Two types Parallel or Perpendicular
- Brewster angle
4Oblique incidence
- First, we need to define
- Expression for uniform plane wave traveling in
any direction - The Normal , an
- Plane of incidence
- Angle of incidence
x
Medium 2 e2, m2
Medium 1 e1 , m1
qr
qt
y
qi
z
z0
5Oblique incidence
- Uniform plane wave in general form
- the radius or position
vector - the wave number or propagation vector
- Where
- For lossless unbounded media, k b
6Oblique Incidence
x
Medium 2 e2, m2
Medium 1 e1 , m1
kr
kt
qr
qt
z
y
qi
z0
ki
7Look at the direction of travel
x
Medium 2 e2, m2
Medium 1 e1 , m1
kr
kt
qr
qt
z
y
qi
kix
z0
ki
kiz
8Expression for Waves
9Tangential E must be Continuous
- From this we know that frequency is a property
of the wave. So is color. - So 700nm is not always red!!
- Give example of bathing suit.
10Snell Law
- Equating, we get
- or
- where, the index of refraction of a medium, ni
, is defined as the ratio of the phase velocity
in free space (c) to the phase velocity in the
medium.
11Critical angle, qc All is reflected
- When qt 90o, the refracted wave flows along the
surface and no energy is transmitted into medium
2. - The value of the angle of incidence corresponding
to this is called critical angle, qc. - If qi gt qc, the incident wave is totally
reflected.
12Fiber optics
- Light can be guided with total reflections
through thin dielectric rods made of glass or
transparent plastic, known as optical fibers. - The only power lost is due to reflections at the
input and output ends and absorption by the fiber
material (not perfect dielectric).
13- Optical fibers have cylindrical fiber core with
index of refraction nf, surrounded by another
cylinder of lower, nc lt nf , called a cladding. - For total reflection
Figure from Ulaby, 1999
Acceptance angle
Use Snell and critical angle to derive
14Exercise optical fiber
- An optical fiber (in air) is made of fiber core
with index of refraction of 1.52 and a cladding
with an index of refraction of 1.49. - Find the acceptance angle
Answer 17.5o
15Parallel polarization
- Its defined as E is to incidence plane
x
Medium 1 e1 , m1
Er
Et
kt
kr
qr
qt
z
y
z
qi
Ei
z0
ki
Medium 2 e2, m2
16Equating for continuity, the tangent fields
- Which components are tangent to the interface
between two surfaces? - y and x
- At z 0 (interface)
17Reflection and Transmission Coefficients
Parallel Incidence
18Reflection and Transmission Coefficients
Perpendicular Incidence
19Java Animation
- http//www.amanogawa.com/archive/Oblique/Oblique-2
.html
20Exercise
- A plane wave in air with
- Is incident upon planar surface of nonmagnetic
dielectric material with er4, on zgt0, Find - The incidence polarization of this wave
- The angle of incidence
- The time-domain expressions for the reflected
electric and magnetic fields. - The average power density carried by the wave in
the dielectric medium.
21Brewster angle, qB
- Is defined as the incidence angle at which the
reflection coefficient is 0 (all transmission). - The Brewster angle does not exist for
perpendicular polarization for nonmagnetic
materials.
qB is known as the polarizing angle
22Exercise
- A plane wave in free space with
- Is incident upon planar surface of nonmagnetic
lossless dielectric material with er4, on zgt0,
Find - The polarization of the incident wave
- The angle of incidence and transmission
- The reflection and transmission coefficients.
- The E field that is reflected and in dielectric
- Brewster angle
23Reflection vs. Incidence angle.
Reflection vs. incidence angle for different
types of soil and parallel or perpendicular
polarization.
24Exercise (Brewster angle)
- A wave in air is incident upon the flat boundary
of a nonmagnetic soil medium with er4, at
qi50o. - Find reflection and transmission coefficients for
both incident polarizations, and the Brewster
angle. - Answers
EMAG
25Summary wave incidence
Property Normal Incidence Perpendicular Parallel
Reflection coefficient
Transmission coefficient
Relation
Power Reflectivity
Power Transmissivity
Snells Law Snells Law Snells Law Snells Law