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Wave Incidence at Oblique angles

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Wave Incidence at Oblique angles Sandra Cruz-Pol ECE Dept. UPRM Dr. S. Cruz Wave incidence at oblique angles * Dr. S. Cruz Wave incidence at oblique angles * Dr. S ... – PowerPoint PPT presentation

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Title: Wave Incidence at Oblique angles


1
Wave Incidenceat Oblique angles
  • Sandra Cruz-Pol
  • ECE Dept. UPRM

2
Quiz VIERNES
  • Uno de los problemas asignados en el prontuario
  • Enviar contestaciones a preguntas en Word por
    email

3
Wave 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

4
Oblique 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
5
Oblique 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

6
Oblique Incidence
x
Medium 2 e2, m2
Medium 1 e1 , m1
kr
kt
qr
qt
z
y
qi
z0
ki
7
Look 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
8
Expression for Waves
9
Tangential 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.

10
Snell 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.

11
Critical 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.

12
Fiber 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
14
Exercise 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
15
Parallel 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
16
Equating for continuity, the tangent fields
  • Which components are tangent to the interface
    between two surfaces?
  • y and x
  • At z 0 (interface)

17
Reflection and Transmission Coefficients
Parallel Incidence
  • Reflection

18
Reflection and Transmission Coefficients
Perpendicular Incidence
19
Java Animation
  • http//www.amanogawa.com/archive/Oblique/Oblique-2
    .html

20
Exercise
  • 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.

21
Brewster 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
22
Exercise
  • 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

23
Reflection vs. Incidence angle.
Reflection vs. incidence angle for different
types of soil and parallel or perpendicular
polarization.
24
Exercise (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
25
Summary wave incidence
Property Normal Incidence Perpendicular Parallel
Reflection coefficient
Transmission coefficient
Relation
Power Reflectivity
Power Transmissivity
Snells Law Snells Law Snells Law Snells Law
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