Before this lecture there were two lectures:
1. Qualitative description of polarization and generation of various polarized light.
2. Quantitative derivation and explaining the observations. 08/08/2017 How to generate Polarized Light?
1.Dichroic materials
3.Birefringent materials
4.Reflection
5.Scattering
Wire grid polarizer
Birefringence
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 Reflected ray ray
p n 90o 1 n2
r
n1sin P = n2sin r 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
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 Gas molecule
z O
Unpolarized x sunlight
Light scattered at right angles is plane-polarized
Polarization by Scatterings 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.
28 Phase shift of half wavelength Quarter Wave plate
Circular polarization (IV)
32
END 11/08/2017 Orientations of Polarizers Mathematics of Polarization, Malus’s Law Example 1
• Two polarizers are After the first polarizer: orientated with their 1 I I axes at an angle of 1o2 o 35.0 , what proportion After the second polarizer: of the original light 2 remains? First polarizer I21 I cos
reduce the intensity 1 2 o II2 o cos 35.0 half of original intensity. 2
II2 0.336 o Birefringence
Refractive Index in Isotropic and Anisotropic Crystal 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 Hexagonal, trigonal, tetragonal – All axes c are equal but c is unique Biaxial 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 high- order symmetry axis Dependence of refractive index on the angel of Incidence:
The refractive index for extra-ordinary 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 o 0 θ = 0 to n(θ) = ne for θ = 90 Index Ellipsoid and classification of Crystal
ne
n0 n0
n0 = n 0 > ne
For Uniaxial crystal Relation Between angle of propagation and refractive index of extraordinary ray
Z Propagation
ne() ne Y n0 n0 n0
Projection of ellipsoid along Y-Z plane
= angle between direction of propagation and the optic axis.
So, the maximum value of ne() = n0 at = 0 degree
The minimum value of ne() = ne at = 90 degree
The refractive index for extraordinary ray depends on the direction of propagation relative to optic axis. Effect of Incident Angle
Wave surfaces of Ordinary and Extraordinary rays Wave surfaces of Ordinary and Extraordinary rays 17/08/2017 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. Rhombohedron Calcite Crystal Nicol Prism Nicol Prism Glan–Thompson polarizing prism Glan–Foucault polarizing prism Glan–Foucault polarizing prism Glan–Taylor polarizing prism
END 18/08/2017
Einstein Coefficients, absorption, spontaneous emission and Stimulated Emission 22/08/2017
• Population Inversion in two level and three level systems 24/08/2017 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
2 4 Laser light due to transition from E state to A2 state Example of a 4 level system
E4 Rapid decay
E3
LASING
E2
Rapid decay
E1
• 14 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 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) Incandescent vs. Laser Light
Light from bulbs are due to spontaneous emission
1. Many wavelengths 1. Monochromatic 2. Multidirectional 2. Directional 3. Incoherent 3. Coherent
Coherence
The concept of coherence is related to the stability, or predictability, of the phase of an electromagnetic wave.
1. Temporal or Longitudinal Coherence
2. Spatial Coherence Temporal Coherence
Spatial Coherence Perfect temporal coherence
Direction of wave propagation Temporal coherence t
t “Bad” (limited) temporal coherence Wavefront
20 Temporal Coherence:
Temporal coherence is the measure of the average correlation between wave trains separated by a delay . The delay over which the phase or amplitude diverges significantly (is
defined as the coherence time coh
21 Temporal Coherence:
22 Longitudinal or Temporal Coherence
lcoh Michelson Interferometer 25