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Modern Optics II – Polarization of light. Special topics course in IAMS Lecture speaker: Wang-Yau Cheng 2006/4. Outline. Wave properties of light Polarization of light Coherence of light Special issues on quantum optics. Polarization of light  Polarization vs. dipole oscillation

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Modern optics ii polarization of light l.jpg

Modern Optics II – Polarization of light

Special topics course in IAMS

Lecture speaker: Wang-Yau Cheng

2006/4


Outline l.jpg
Outline

  • Wave properties of light

  • Polarization of light

  • Coherence of light

  • Special issues on quantum optics


Slide3 l.jpg

  • Polarization of light

     Polarization vs. dipole oscillation

    • Ways to change the polarization status

    • Ways to purify the polarization

    • Polarization in light scattering


Slide4 l.jpg

Neutral atoms

))))))

Higher harmonic radiation

Concepts of induced dipole moment

Interact with EM wave


Scattering by molecules is not spherically symmetric it has a dipole pattern l.jpg

Direction of light excitation

E-field and electron oscillation

Emitted intensity pattern

Scattering by molecules is not sphericallysymmetric. It has a "dipole pattern."

The field emitted by an oscillating dipole excited by a vertically

polarized light wave:

Directions of scat-

tered light E-field

No light is emitted along

direction of oscillation!

Directions of scat-

tered light E-field


Dipole emission pattern from an antenna l.jpg
Dipole Emission Pattern from an Antenna

Analogous to a molecule emitting light, an antenna emits a dipole pattern at much lower frequency and longer wavelength:

The pattern is somewhat distorted by the earth and nearby objects.


Slide8 l.jpg

Linear polarization

Left hand circular polarization

Right hand circular polarization

For stimulation emission process, all the dipoles will becoherently induced and the radiation will go with certain polarization


Slide9 l.jpg

))))))

Note that c could be a tensor

Interact with EM wave


Optical activity l.jpg
Optical Activity

Unlike birefringence, optical activity maintains a linear polarization

throughout. The rotation angle is proportional to the distance.



Slide12 l.jpg

  • Polarization of light

    • Polarization vs. dipole oscillation

      Ways to change the polarization status

    • Ways to purify the polarization

    • Polarization in light scattering


Wave plates l.jpg
Wave plates

When a beam propagates through a birefringent medium, one

polarization experiences more phase delay than the other.

If both polarizations are present, this has the effect of changing

relative phase of the x and y fields, and hence rotating the polarization.

Input:

Polarization state:

}

}

Output:


Wave plates continued l.jpg
Wave plates (continued)

(45-degree input polarization)

Wave plate output polarization state:

“Quarter-wave plate”

“Half-wave plate”

A quarter-wave plate creates circular polarization, and a half-wave plate rotates linear polarization to its orthogonal state.

We can add an additional 2mp without changing the polarization, so the polarization cycles through this evolution as d increases further.


Half wave plate l.jpg
Half-Wave Plate

When a beam propagates through a half-wave plate, one polarizationexperiences half of a wavelength more phase delay than the other.

If the incident polarization is 45° to the principal axes, then theoutput polarization is rotated by 90°.

If the incident polarization is parallel to one of the principal axes of the plate, then no polarization rotation occurs.



Multiplying jones matrices l.jpg

x

z

x-pol

y

y-pol

rotated

x-pol

y-pol

Multiplying Jones Matrices

Crossed polarizers:

so no light leaks through.

Uncrossed polarizers

(slightly):

SoIout≈ e2Iin,x




Phase shifts in reflection glass to air l.jpg

p

0

0° 30° 60° 90°

Incidence angle

p

0

||

0° 30° 60° 90°

Incidence angle

Phase shifts in reflection (glass to air)

Interesting phase above the critical angle

nt < ni

180° phase shift

for angles below

Brewster's angle;

0° for larger angles


Total internal reflection occurs just as the transmitted beam grazes the surface l.jpg
Total Internal Reflection occurs just as thetransmitted beam grazes the surface.

Note that the irradiance of the transmitted beam goes to zero as it

grazes the surface.

Total internal reflection is 100% efficient.




The faraday effect l.jpg
The Faraday Effect

A magnetic field can induce optical activity.

The Faraday effect allows control over the polarization rotation.


Slide26 l.jpg

  • Polarization of light

    • Polarization vs. dipole oscillation

    • Ways to change the polarization status

       Ways to purify the polarization

    • Polarization in light scattering


Phase shifts in reflection air to glass l.jpg

p

0

0° 30° 60° 90°

Incidence angle

p

0

||

0° 30° 60° 90°

Incidence angle

Phase shifts in reflection (air to glass)

ni < nt

180° phase shift

for all angles

180° phase shift

for angles below

Brewster's angle;

0° for larger angles


Phase shifts in reflection glass to air28 l.jpg

p

0

0° 30° 60° 90°

Incidence angle

p

0

||

0° 30° 60° 90°

Incidence angle

Phase shifts in reflection (glass to air)

Interesting phase above the critical angle

nt < ni

180° phase shift

for angles below

Brewster's angle;

0° for larger angles


Glare is horizontally polarized l.jpg
Glare is horizontally polarized

Puddle reflection viewed

through polarizer that

transmits only horizontally

polarized light

Puddle reflection viewed

through polarizer that

transmits only vertically

polarized light

Light reflected

into our eyes

from the puddle

reflects at about

Brewster's Angle.

So parallel

(i.e., vertical)

polarization sees

zero reflection.

Polarizer sunglasses transmit only vertically polarized light.


Brewster s angle l.jpg
Brewster's Angle

When the reflected beam makes a

right angle with the transmitted beam,

and the polarization is parallel, then

no scattering can occur, due to the

scattered dipole emission pattern.

But our right-angle assumption

implies that qi+ qt= 90°. So:

Thus,

A complex trigonometric calcu-lation reveals that the reflection

coefficient for parallel-polarized

light goes to zero for Brewster's

angle incidence, tan(qi) = nt / ni

qi

qi

ni

nt

qi +qt = 90°

qt


Slide31 l.jpg

BREWSTER ANGLE

Extinction 5*10-5



Slide33 l.jpg

BROAD BAND POLARIZING CUBES

The extinction of transmitted -p component is at least 1 part in 500


Slide34 l.jpg

GLAN THOMPSON

The Glan Thompson polarizer is made of two calcite prisms cemented together. Two types of Glan Thompsons are available. One is the standard form and the other is the long form. Their length to aperture ratios are 2.5 : 1 and 3.0 : 1 respectively. Glan Thompsons tend to have higher extinction ratio than air spaced polarizers. In the ultra violet spectrum, their transmission is limited by absorption in calcite as well as the cement layer. These polarizers can be used from about 350 to 2300 nm.

Extinction 5*10-5


Slide35 l.jpg

GLAN TAYLOR

The Glan Taylor prism polarizer is made of two calcite prisms which are assembled with an air space . It has a length to aperture ratio of approximately 1.0 which makes it a relatively thin polarizer. It is made of UV selected calcite. A 10 mm thick calcite  plate having 50% or more transmission at 250 nm is considered UV selected. The spectral range of this polarizer is from 250-2300 nm. Below 250 nm, transmission cutoff wavelength varies from crystal to crystal.

Extinction 1*10-4


Slide36 l.jpg

CALCITE WOLLASTON

Calcite Wollaston prism polarizer is made of two prisms of calcite which are cemented together. The two output beams in a Wollaston polarizer exit with unequal beam deviation ( asymmetry ) which is given in the table below. The beam separation angle is dependent on wavelength. Useable range of this polarizer is from 350 nm to 2300 nm.

Extinction 1*10-5


Slide37 l.jpg

MAGNESIUM FLUORIDE ROCHON

extinction ratio of at least  10-3

The magnesium fluoride Rochon polarizer is made of two prisms of single crystal magnesium fluoride which are optically contacted. This polarizer can be used over the spectral range of 140 to 6000 nm and has an extinction ratio of at least  10-3.


Slide38 l.jpg

CALCITE BEAM DISPLACER

A calcite Beam Displacer splits the input unpolarized beam of light into two orthogonally polarized components which exit parallel to each other. The ordinary polarization transmits straight through while the extraordinary transmits through the crystal making approximately 6 degree angle with the straight through beam and emerges parallel to it. The beam displacement varies slightly with wavelength. Non standard beam displacers are available by special order.


Slide39 l.jpg

Polarizer used in camera

The extinction of transmitted -p component is at least 1 part in 200


Slide40 l.jpg

  • Polarization of light

    • Polarization vs. dipole oscillation

    • Ways to change the polarization status

    • Ways to purify the polarization

       Polarization in light scattering


Scattering of polarized light l.jpg
Scattering of polarized light

No light is scattered along the input field direction, i.e. with k parallel to E.

Vertically polarized

input light

Horizontally polarized

input light


Scattering of unpolarized light l.jpg
Scattering of unpolarized light

Again, no light is scattered along the input field direction,

i.e. with k parallel to Einput.


Scattering in the earth s atmosphere leads to interesting polarization properties of skylight l.jpg
Scattering in the Earth's atmosphere leads to interesting polarization properties of skylight.

Sun's rays


Skylight is polarized if the sun is to your side l.jpg
Skylight is polarized if the sun is to your side. polarization properties of skylight.

Right-angle scattering

is polarized

This polarizer transmits

horizontal polarization

(of which there is very little).

Multiple scattering yields some light of the other polarization.

In clouds, much multiple scattering occurs, and light there is

unpolarized.

Polarizer transmitting vertical polarization


Polarization spectroscopy l.jpg
Polarization Spectroscopy polarization properties of skylight.

The 45°-polarized “Pump” pulse reorients molecules, which induces some birefringence into the medium, which then acts like a wave plate until the molecules re-orient back to their initial random distribution.


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