06/08/2018
Before this lecture there were two lectures:
1. Introduction about this course.
2. Qualitative description about the various
polarizations.
Retarders
• In
retarders, one polarization gets ‘retarded’, or
delayed, with respect to the other one. There is a final
phase difference between the 2 components of the
polarization. Therefore, the polarization is changed.
• Most retarders are based on birefringent materials
(quartz, mica, polymers) that have different indices of
refraction depending on the polarization of the incoming
light.
3
Phase shift of half wavelength
Quarter Wave plate
Circular polarization (IV)
7
How to generate Polarized Light?
1.Dichroic materials
2.Polarizer
3.Birefringent materials
4.Reflection
5.Scattering
Wire grid polarizer
Polaroid
How to generate Polarized Light?
1.Dichroic materials
2.Polarizer
3.Birefringent materials
4.Reflection
5.Scattering
Birefringence
How to generate Polarized Light?
1.Dichroic materials
2.Polarizer
3.Birefringent materials
4.Reflection
5.Scattering
Polarized Reflecting Light
• When an unpolarized light wave reflects off a
non-metallic surface, it can be completely
polarized, partially polarized or unpolarized
depending on the angle of incidence. A
completely polarized wave occurs for an angle
called Brewster’s angle (named after Sir David
Brewster)
Snell's law
Incident
ray
Reflected
ray
p p
90
o
r
n1sin P = n2sin r
n1
n2
n1sin P = n2sin r = n2sin (90-P) = n2cos P
tan P = n2/n1
P = Brewster’s angel
Reflection
• When an unpolarized wave reflects off a nonmetallic surface, the
reflected wave is partially plane polarized parallel to the surface. The
amount of polarization depends upon the angle (more later).
The reflected ray contains
more vibrations parallel to
the reflecting surface while
the transmitted beam
contains more vibrations at
right angles to these.
Applications
• Knowing that reflected light or glare from
surfaces is at least partially plane polarized,
one can use Polaroid sunglasses. The
polarization axes of the lenses are vertical as
the glare usually comes from reflection off
horizontal surfaces.
Polarized Lens on a Camera
Reduce Reflections
How to generate Polarized Light?
1.Dichroic materials
2.Polarizer
3.Birefringent materials
4.Reflection
5.Scattering
Polarization by Scattering
• When a light wave passes through a gas, it will be
absorbed and then re-radiated in a variety of
directions. This process is called scattering.
y
z
Unpolarized
sunlight
Gas molecule
O
x
Light scattered at right angles
is plane-polarized
Polarization by Scatterings
3D Movie Projection and Viewing
• Modern 3D movies are projected using
different polarizations instead of different
colors.
• Without glasses, the images look like this:
3D Movie Projection and Viewing
• The two overlapping images are actually
projected through a polarizing filter, alternating
in rapid succession
• The glasses separate the polarized light and each
eye sees something different, creating the illusion
of depth
• The system actually uses circularly polarized light,
so the glasses won’t work like your polarized
sunglasses
08/08/2018
08/08/2018
• Concept of polarizer and analyzer
Mathematics of Polarization, Malus’s Law
Orientations of Polarizers
Example 1
• Two polarizers are
orientated with their
axes at an angle of
35.0o, what proportion
of the original light
remains? First polarizer
reduce the intensity
half of original intensity.
After the first polarizer:
1
I1  Io
2
After the second polarizer:
I 2  I1cos 2
1  2
I 2   I o  cos 35.0o
2 
I 2  0.336 I o
Birefringence
Refractive Index in Isotropic and Anisotropic Crystal
Optic Axis
Beam propagation in anisotropic crystals
Optic axis of a crystal is the direction in which a ray of transmitted
light suffers no birefringence (double refraction). Light propagates
along that axis with a speed independent of its polarization
However, if the light beam is not parallel to the optical axis, then, when
passing through the crystal the beam is split into two rays: the ordinary
and extraordinary, to be mutually perpendicular polarized.
A crystal which has only one optic axis is called uniaxial crystal.
A crystal which has only two optic axis is called biaxial crystal.
Calcite experiment and double refraction
O
E
Fig 6-8 Bloss, Optical
Crystallography, MSA
Fig 6-7 Bloss, Optical
Crystallography, MSA
How light behaves depends on crystal structure
(there is a reason you took mineralogy!)
Isotropic
Isometric
– All crystallographic axes are equal
Uniaxial
Biaxial
Hexagonal, trigonal, tetragonal
– All axes  c are equal but c is unique
Orthorhombic, monoclinic, triclinic
– All axes are unequal
Let’s use all of this information to help us identify minerals
Thin layer of balsam cement
with n = 1.55
Other Crystallographic systems: Orthorhombic,
monoclinic, and triclinic have two optic axes and
are biaxial.
For example, Mica KH2Al3(SiO4)3 has three
different indices n.
Birefringent devices – Separation
of the o- and e- rays.
• Optic axis of a uniaxial crystal is the highorder symmetry axis
Extent of Birefringence
09/08/2018
Index Ellipsoid and classification of Crystal
ne
n0
n0
n0 = n0 > ne
For Uniaxial crystal
Wave surfaces of Ordinary and Extraordinary rays
Dependence of refractive index of extraordinary ray:
The refractive index of ‘e’ ray depends on the direction
of propagation relative to optic axis.
Where  is angle between propagation vector and
Optic axis
The index of refraction varies from
n(θ) = no for θ = 0o
n(θ) = ne for θ = 900
Wave surfaces of Ordinary and Extraordinary rays
Huygen’s Explanation of Double Refraction
• Spherical wavelet associated with ordinary waves
• Ellipsoidal wavelet associated with extraordinary waves.
Dependence of incident angle and propagation properties of light
a) When optic axis is inclined to some angle to the incident light.
b) When optic axis is perpendicular to incident light.
c) When optic axis is parallel to incident light direction.
Huygen’s wavefront theory
Every point on a wave-front may be considered a source of secondary spherical wavelets
which spread out in the forward direction at the speed of light. The new wave-front is the
tangential surface to all of these secondary wavelets.
Effect of Incident Angle
END
12/08/2018
Total Internal Reflection
Total Internal Reflection
Fiber Optics
Total Internal Reflection
Total Internal Reflection
Prisms
Polarising Prism: Nicol Prism
The so-called “Nicol prism”. It is made of two pieces of calcite
with a gap between, filled with “Canada Balsam” (a transparent
glue). Due to the different refractive indices of the ordinary and
the extraordinary waves, the ordinary undergoes a total internal
reflection and is removed from the prism, while the extraordinary
gets through.
The Nicol Prism is an extremely efficient polarizer, but very expensive.
Therefore, it is used only in apparatus in which high precision is crucial.
Nicol Prism
Glan–Thompson polarizing prism
Glan–Foucault polarizing prism
Glan–Taylor polarizing prism
A ray of light makes a transition from a sample of benzene to water.
What is the minimum angle the light must make with respect the
normal in order for the light to be completely reflected back into the
sample of benzene?
The index of refraction for water is 1.33 and for benzene is 1.50.
Correct answer: 62.5 degree
Consider an optical fiber having a core index of 1.46 and a cladding
index of 1.45. What is the critical angle for this core-cladding interface?
Correct answer: 83.3 degree
END
16/08/2018
Einstein Coefficients, absorption,
spontaneous emission and
Stimulated Emission
16/08/2018
• Population Inversion in two level and three
level systems
20/08/2018
Absorption
E1
E2
Spontaneous Emission
Stimulated Emission
Stimulated vs Spontaneous Emission
Stimulated emission requires the presence of a photon.
An “incoming” photon stimulates a molecule in an excited
state to decay to the ground state by emitting a photon.
The stimulated photons travel in the same direction as the
incoming photon.
Spontaneous emission does not require the presence of a
photon.
Instead a molecule in the excited state can relax to the
ground state by spontaneously emitting a photon.
Spontaneously emitted photons are emitted in all directions.
For stimualted emission to be the dominant process, the
excited state population must be larger than the lower state
population.
In other words, for a medium to produce laser light, there
must be a “population inversion” where Nupper > Nlower
How can a population inversion be created when the
population in the ground state is always greater that the
population in the excited state?
What kinds of materials will “allow” for an inversion of
population in its electronic states?
How can a population inversion be created?
By excitation of the lasing atoms or molecules - this is
called PUMPING.
If the pump source is very intense, the number of atoms or
molecules excited can be large.
However, once excited, the atoms and molecules must say
in the excited state long enough to create an excited
population > ground state population
Two-Level System
Em, Nm
Em, Nm
En, Nn
En, Nn
Even with very a intense pump source, the best one can
achieve with a two-level system is
excited state population = ground state population
Example of a 3 level system
E3
Rapid decay
E2
LASING
E1
Three-Level System
The first laser, the ruby laser, was a three-level system
upper lasing
state
lower lasing
state
Laser light due to transition from 2E state to 4A2 state
Example of a 4 level system
E4
Rapid decay
E3
LASING
E2
Rapid decay
E1
• 1→4 transition is pumped.
• Rapid decay from 4 →3.
• A population inversion is produced between states 3 and 2.
• Laser action is therefore possible between 3 →2.
• Molecules decay rapidly from 2 →1, replenishing population of 1.
Four-Level System
He-Ne laser
Four-Level System
Nd:YAG laser
upper laser state
lower laser state
Laser light due to transition from 4F to 4I
Nd:YAG (neodymium-doped yttrium aluminum garnet; Nd:Y3Al5O12) is a crystal
that is used as a lasing medium for solid-state lasers
Dye Lasers: Four-level systems
A short sketch of laser history
1917: Einstein – stimulated absorption and
emission of light
1954: Charles Townes and Schawlow – maser,
prediction of the optical laser
Nobel Prize (1964)
1960: Theodore Maiman – first demonstration of a laser:
Ruby laser
Rapid progress in the 1960s:
1961: first gas laser, first Nd laser
1962: first semiconductor laser
1963: CO2 laser (IR)