Download Polarization

Physics 272
December 2
Fall 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_fall_272_uhm.html
Prof. Philip von Doetinchem
[email protected]
Phys272 - Fall 14 - von Doetinchem - 139
Standing electromagnetic waves
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Electromagnetic waves
can be reflected on
surfaces
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Dielectrics or conductors
can serve as reflectors
Superposition principle of
electric and magnetic
fields also applies to
electromagnetic waves
Superposition of incident
and reflected wave forms
a standing wave
Electric force is
conservative → it is not
possible to do work on a
test charge like that:
Phys272 - Fall 14 - von Doetinchem - 140
Standing electromagnetic waves
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Electric field cannot have a net component parallel to the surface
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Superposed incident and reflected wave must be zero at all times on the conductor
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Incident wave is not zero at all times on the conductor
→ oscillating currents are induced in surface
→ additional field that cancels out the electric field of the incident electromagnetic wave
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This also creates the reflected wave:
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The sum of incident and reflected wave must be 0 at all times on the surface:
Phys272 - Fall 14 - von Doetinchem - 141
Standing electromagnetic waves
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The sum of incident and reflected wave must be 0
at all times on the surface:
Position and time factorize for electric field
Phys272 - Fall 14 - von Doetinchem - 142
Standing electromagnetic waves
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What does the magnetic field look like?
→ Faraday's law still applies
Integrate:
A standing wave that was reflected on a conductor shows a 90deg phase
angle between electric and magnetic field
Phys272 - Fall 14 - von Doetinchem - 143
Standing waves in a cavity
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Insert a second conducting plane: cavity
→ example: microwave oven
On both planes the electric field has to vanish
A standing wave is created
when the electromagnetic
wave wavelength is an
integer multiple of /2
Measuring the node positions
→ measurement of
wavelength
Reflections generally also
happen on surfaces of two
materials:
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Part of the wave is transmitted and a part is reflected
Phys272 - Fall 14 - von Doetinchem - 144
The nature and propagation of light
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Understanding the
properties of light:
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Blue color of the sky
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Red color of a sunset
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Rainbows
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Cameras
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Glasses
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Human eye
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lasers
Wave properties of light
began to be discovered
1665
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The wave picture is only
describing one side of
light
Several aspects reveal
particle properties
Particles and wave
properties combined
→ photon
Propagation can be well
understood in wave
picture
Phys272 - Fall 14 - von Doetinchem - 146
Waves, wave fronts, and rays
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A wave front is the leading edge of a wave
All points on a wave front are at the same part of the cycle of
their variation
Electromagnetic waves emitted by a point-like source:
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spherical surface concentric with
source is a wave front
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Far away from the source
(i.e., the radius is large)
→ spherical wave front can be
treated as plane wave
Light rays use the particle properties
of light and denote the direction of
travel of the wave front
Light rays are straight lines in a homogeneous material
→ we will study what happens when light travels from one
medium into another
Phys272 - Fall 14 - von Doetinchem - 147
Reflection and refraction
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When a light ray strikes a plane
→ light is partly reflected
→ light is partly transmitted
Incident, reflected, and refracted rays and the
normal to the surface all lie in the same plane
Incident angle = reflected angle
Keep in mind most objects we see do not emit
light → they reflect light in a diffuse manner
No reflection
→ no wonderful mirror selfies
→ what a sad world that would be
Phys272 - Fall 14 - von Doetinchem - 148
The laws of reflection and refraction
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Optical materials have
an important property
→ index of refraction
air
glass
Incident light ray




Source: http://en.wikipedia.org/wiki/Refractive_index
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Light travels slower in a
material than in vacuum
Index of refraction is 1
for vacuum and larger
than 1 for any other
material
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Snell's law: Ratio of sines of
the angles and is equal to
the inverse ratio of the two
indexes of refraction
Phys272 - Fall 14 - von Doetinchem - 149
The laws of reflection and refraction
air
glass
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If a ray passes into a
material with higher index
of refraction
→ refraction angle is
smaller in material
Incident light ray




Source: http://en.wikipedia.org/wiki/Refractive_index
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At normal incident on the surface: zero refraction angle
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The path of a refracted ray is reversible
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Intensities of reflected and refracted rays depend on angle of
incidence, index of refraction, polarization
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Index of refraction of air: ~1.0003 (increases with density)
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Glasses have index of refraction of 1.5-2.0
Phys272 - Fall 14 - von Doetinchem - 150
Index of refraction and the wave aspects of light
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When light passes from one medium to the other:
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Frequency stays constant:
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number of wave cycles per time is conserved
A surface cannot destroy or create waves
The wavelength changes:
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Wavelength becomes shorter after refraction into medium with
higher index of refraction
Wave gets squeezed at lower velocities and stretched at higher
velocities
Phys272 - Fall 14 - von Doetinchem - 151
Reflection and refraction
Phys272 - Fall 14 - von Doetinchem - 152
Total internal reflection
Source: http://en.wikipedia.org/wiki/Optical_fiber
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AMS-02
AntiCoincidence Counter
All the light can be reflected from a surface
→ no transmission
Important effect to transport light without losses from one
place to the other → light guides
Used in cars for sending signals to sensors → does not feel
electric interference → more reliable signal
Phys272 - Fall 14 - von Doetinchem - 156
Total internal reflection
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If a ray passes from a higher
refractive index medium to a
lower refractive index medium
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At a certain critical incident
angle the refracted angle in the
second medium becomes 90deg
→ no transmission possible
Phys272 - Fall 14 - von Doetinchem - 157
Applications of total internal reflection
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In contrast to polished metallic
surfaces total reflection can really
totally reflect light without losses
(inhomogeneities in material make
this statement a bit weaker)
Diamonds have a large refractive
index
(2.417 → critical angle: 24.4deg):
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light enters a cut diamond
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internal total reflection on the back
surface
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light leaves the light in the front
→ wonderful sparkle!
Phys272 - Fall 14 - von Doetinchem - 158
Dispersion
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White light is a superposition of
electromagnetic waves with a wide
variety of wavelength
Speed of light is the same for all
wavelength in vacuum
Speed of light in matter is different
for different wavelength
→ index of refraction depends on
wavelength (dispersion)
Source: http://de.wikipedia.org/wiki/Prisma_%28Optik%29
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In most materials the index of refraction decreases with longer wavelengths
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Violet light is the slowest in this case, red light the fastest inside the prism
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Different wavelengths (colors) have different refractive angles
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Prism reveals the spectrum of colors
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Diamonds also have a large dispersion → wide spectrum of colors adds to
the sparkling effect
Phys272 - Fall 14 - von Doetinchem - 160
Rainbows
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Dispersion, refraction, and reflection are important
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White light is reflected on the back of a water droplet
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Waves of different wavelength feel different index of refraction
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Exit angle of water droplet is different for different wavelength
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Observation at a quite narrow angle: the refracted, reflected spectrum from the water
droplets meet in observer's eye
Rainbow is visible from different locations: for example the red color is now coming from a
different region of the sky → angle between sun, water droplet and sun has to be just right
(reason for arc)
Double rainbow comes from two internal reflections in water droplet (→ reversed colors)
Phys272 - Fall 14 - von Doetinchem - 161
Rainbow
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How large is the angle
between incident and exit ray
→ add up all refraction angles:
Snell's law:
depends on
wavelengths
Water droplet is spherical:
Angle between incident and
deflected ray:
Phys272 - Fall 14 - von Doetinchem - 162
Rainbow
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This is the deflection
angle for a particular
wavelength using the
index of refraction
for this particular
wavelength
Deflection angle
Change of deflection
angle is small
Change of deflection
angle is too large to
form one bright region
on the sky
Incident angle
the deflection angle
varies with the incident angle of the light on the water droplet
To form a bright region on the sky in a particular color: incident
light needs to be reflected at the same (or very similar)
deflection angle:
Larger index of refraction → lower deflection angle
→ light comes from a lower position on the sky
Phys272 - Fall 14 - von Doetinchem - 163
Polarization
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If an electromagnetic wave has an electric field that only varies in
one direction: linear polarization
Electromagnetic waves can be composed of different modes with
different polarizations
Unpolarized light can be filter in a way such that is polarized
Waves from a radio transmitter are usually linearly polarized
(electric field only changes in vertical direction of the antenna)
Electromagnetic waves from light are different
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The total composition of light waves is not emitted from a single antenna
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Waves are emitted from different sources (atoms, molecules) with random
order → light from (e.g., a light bulb) is the superposition of
electromagnetic waves with different polarizations
Please don't confuse a polarized wave with shifting of electric
charges inside material
Phys272 - Fall 14 - von Doetinchem - 164
Polarizing filters
https://www.youtube.com/watch?v=nCAKQQjfOvk
Phys272 - Fall 14 - von Doetinchem - 165
Polarizing filters
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Simple filter for microwaves (~cm wavelength) with isolated
conducting wires:
Polaroid material → sun glasses:
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Selective absorption of different polarization directions
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~80% are transmitted when light is polarized parallel to the polarizing
axis
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~1% for other directions
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Explanation goes back to certain long-chain molecules
→ similar to the filter above
Phys272 - Fall 14 - von Doetinchem - 166
Using polarizing filters
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Ideal polarizer definition:
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100% of incident light polarized parallel to polarizing axis transmitted
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0% transmission in all other directions
Polarized wave carries exactly 50% of the energy of the incident waves
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Superposition of incoming waves can be decomposed into a parallel and perpendicular
component with respect to polarizer
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If light is completely unpolarized
→ all directions appear equally often
→ perpendicular and parallel component have the same value
Phys272 - Fall 14 - von Doetinchem - 167
Using polarizing filters
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A combination of two filters allows to find the polarization direction:
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Intensity is at maximum when both polarizing axis are align
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Intensity is zero when polarizing axis are perpendicular
Intensity of light transmitted (Malus's law):
Phys272 - Fall 14 - von Doetinchem - 168
Polarization by reflection
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Unpolarized light can be polarized by reflection
Components that are polarized perpendicular to the plane of
incidence are stronger reflected than parallel components
Assumption in the following:
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Light composed of a linear polarized component parallel to the
plane of incidence
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and a component linear polarized to the plane of incidence
Example on water:
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The polarization of most reflected light is aligned with the water
surface
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Sun glasses with polarization have vertical polarizing axis and filter
the reflections from the water
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At the same time the intensity is also reduced by ~50%.
Phys272 - Fall 14 - von Doetinchem - 170
Polarization by reflection
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Reflection can be described by inducing Hertzian dipole in the reflecting
surface
Reflection can only occur if the induced Hertzian dipoles actually emit
electromagnetic waves in the direction of reflection angle
When induced dipoles in material do not emit in the direction of the
reflected ray
→ reflected parallel ray disappears when the reflected ray and the
refracted ray enclose 90deg
→ only perpendicular component left → polarized
Phys272 - Fall 14 - von Doetinchem - 171
Polarization by reflection
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=0 for vanishing of parallel component:
Brewster angle
Phys272 - Fall 14 - von Doetinchem - 172
Polarization filter in photography
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without polarization filter
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with polarization filter
reflecting surface is not horizontal
incidence plane is determined for
each drop by the plane containing
the sun, the drop, and the
observer → the rainbow is
polarized tangential to the arch
vertical polarizing filter will
produce a gap at the top of the
rainbow and enhances the
contrast of the sides
Grey sky is not polarized
→ filter reduces background
Phys272 - Fall 14 - von Doetinchem - 173
Additional Material
Phys272 - Fall 14 - von Doetinchem - 175
Flattened sun at sunset
Deviation from circular shape
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Rays path through atmosphere
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Atmosphere gets denser at lower altitudes
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rays from the lower limb of the sun and from the
upper limb path through different densities of the
atmosphere → different refraction
Phys272 - Fall 14 - von Doetinchem - 176
AMS-02 AntiCoincidence Counter
Plastic optical fiber light guides
are part of a detector for cosmic
ray measurement
AMS-02 during ground testing
Connecting plastic optical
fiber light guides
AMS-02 on the International Space Station
Phys272 - Fall 14 - von Doetinchem - 177
Reflection from a swimming pool
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Sunlight reflects from a
smooth swimming pool
surface
Reflected light is completely
polarized at this incident angle:
Corresponding refraction angle:
If you would turn on a spot under water during the night
→ completely polarized reflected beam under water at 36.9deg
→ angles are reversed
Phys272 - Fall 14 - von Doetinchem - 178
Circular and elliptical polarization
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Circular polarized light can be produced when
running two antennas in a 90deg angle at a quarter
cycle phase difference
The two electric fields superpose in the following
way at a fixed position:
If the phase angle is different from 90deg, the light
is elliptically polarized
Phys272 - Fall 14 - von Doetinchem - 179
Circular and elliptical polarization
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Nature is also able to produce circular polarized light:
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Light composed of two perpendicular polarizations
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enters a material with different indexes of refraction for
different directions of polarization (e.g., calcite)
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Light travels at different velocities through material
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After leaving material
→ light not any longer in phase
→ circular/elliptical polarization
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If such a material has the right thickness to produce
quarter-wave phase angle → circular polarization
It also works in reverse → circular polarized light is
linear polarized after going through a quarter-wave
plate
Phys272 - Fall 14 - von Doetinchem - 180