Physical & Electromagnetic Optics: Basic Principles ...users.ntua.gr/eglytsis/OptEng/Interference_p.pdf · Physical & Electromagnetic Optics: Basic Principles & ... • Interference

Physical & Electromagnetic Optics: Basic Principles &

Interference

Optical Engineering Prof. Elias N. Glytsis

School of Electrical & Computer Engineering National Technical University of Athens

29/05/2017

Prof. Elias N. Glytsis, School of ECE, NTUA 2

Quantum Optics

Electromagnetic Optics Wave (Physical) Optics

Geometrical Optics

Wave and Electromagnetic Optics


Electromagnetic Spectrum

https://en.wikipedia.org/wiki/File:EM_Spectrum_Properties_edit.svg

Maxwells Equations Differential Form

Integral Form

4 Prof. Elias N. Glytsis, School of ECE, NTUA

Boundary Conditions

S

Region +

Region -


Maxwells Equations Time Harmonic Form

Constitutive Relations



1D-Wave Equation

c c A A A

z ct ct

t = 0 t = t t = t

General Solution

z

x y

E

H

|k| = k0n

Maxwells Equations Plane Wave Solutions Isotropic Case


Polarization of Electromagnetic Waves

Polarization is the phenomenon in which electromagnetic waves are restricted in direction of vibration

Polarization is a property of waves that describes the orientation of their oscillations


Two beams, otherwise identical, may interact differently with matter if their polarization states are different.

Interference only occurs when EM waves have the same frequency and polarization (i.e., they are coherent)

Polarization of Electromagnetic Waves

Linear

Circular

Elliptical

Random or unpolarized

Polarization Types


Linear Polarization

Plane EM wave linearly polarized Trace of electric field vector is linear Also called plane-polarized light Convention is to refer to the electric field vector

http://www.univie.ac.at/mikroskopie/1_grundlagen/optik/wellenoptik/6_polarisation.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html


http://en.wikipedia.org/wiki/Image:Linear_polarization_schematic.png

Linear Polarization (Animation)

http://bestanimations.com/Science/Physics/45degree-polarized-light-wave.gif https://userscontent2.emaze.com/images/cac94365-b9dc-4762-9121-96c69882485b/458fc46b-b8bd-43e1-b3db-f7ae1667d4e0image20.gif

Linear Polarization (Horizontal) Linear Polarization (45 degrees)


Circular Polarization

Two perpendicular electric field components of equal amplitude with 90 difference in phase Electric vector rotates counterclockwise right-hand circular polarization Electric vector rotates clockwise left-hand circular polarization




http://en.wikipedia.org/wiki/Image:Circular_polarization_schematic.png

Circular Polarization (Animation)

http://i.imgur.com/3bjXjMd.gif

Left Handed Circular Polarization (LHC)


Elliptical Polarization

Two perpendicular eletric field components not in phase, either with different amplitudes and/or not 90 out of phase Electric vector rotates counterclockwise right-hand elliptical polarization Electric vector rotates clockwise left-hand elliptical polarization The most general state of complete polarization is elliptical




http://en.wikipedia.org/wiki/Image:Elliptical_polarization_schematic.png

Animation showing four different polarization states and two orthogonal projections.

By de:Benutzer:Averse - http://www.radartutorial.eu/06.antennas/pic/zirkulanim.gif via de.wikipedia.org, CC BY-SA 2.0, https://commons.wikimedia.org/w/index.php?curid=4849061

A circularly polarized wave as a sum of two linearly polarized components 90 out of phase

By Davidjessop - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=48021939

Polarization Animation


Scattering by molecules Reflection and transmission

at interfaces

Polarization States Occurring Naturally

By DrBob Bob Mellish - English Wikipedia repository., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=724505


http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polabs.html

Polarization Applications

Dichroism Polarizing Glasses


Photographic Filters When light reflects off water it becomes polarized. Such light is often called glare and can make it harder to see what's behind it. Photographers often use filters to cut out glare and get better pictures.

3 D films When you watch a 3D film you are actually watching two films shot with different cameras, looking at the same thing but from slightly different angles. When the films are projected the light is polarised and polaroid filters, worn as glasses, can let just one of the films into each eye.

Liquid Crystal (LCD) Displays There are some crystals that become aligned when an electric field is put across them. When this happens they act as polarising filters.

Stress Analysis When light passes through some materials its plane of polarisation is rotated. The thicker the material the more it is rotated and different colours are rotated by different amounts. To investigate the stresses in an engineering part you could make a model of it in plastic, pass light through and then put it under stress. The patterns produced which may give an indication of where the material has been deformed.

Polarization Applications

http://www.stokesleyscience.org/A%20level%20Physics/EM%20Waves/applications.htm


At places where the internal stresses are greatest, the colored bands change more rapidly (with distance). Engineers wishing to predict where a mechanical component might fail, when placed under stress, can make a model of the component out of, for example, Perspex and observe the stress patterns (the colored bands are more concentrated where the stresses are greatest. The design of the model can then be modified accordingly before the actual component is manufactured.

Certain plastics rotate the plane of polarization of light passing through them. The angle through which the plane of polarization is rotated is found to vary when the sample is placed under stress, for example by bending it. The angle also depends on the wavelength of the light. The photograph on the right shows a small part of a plastic set square viewed under normal conditions

Stress Analysis using Polarization


Stress Analysis using Polarization

By Spigget - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=9587846

Stress in plastic glasses


By PiccoloNamek at the English language Wikipedia, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1103795

The effects of a polarizing filter (right image) on the sky in a photograph.

Polarizing Filters


http://plc.cwru.edu/tutorial/enhanced/files/lc/biref/graphics/birefringence.JPG

Birefringent Crystals


http://www.olympusmicro.com/primer/images/birefringence/crystalpencil.jpg

Measuring the concentration of solutions using Polarization

Certain solutions rotate the plane of polarization of light passing through them. The angle through which the plane of polarization is rotated depends on the concentration of the solution.


On the under-side of the top plate of the liquid crystal container, A, are fine lines etched parallel to the plane of polarization of the top Polaroid. Similarly there are lines etched into face B parallel to the plane of the lower Polaroid. The liquid crystals line up with these fine lines but also tend to line up with each other so there is a gradual change in the alignment of the crystals from A to B. The crystals change the plane of polarization of the light so that the light can pass through the lower polarizer and be reflected by the mirror. The display appears light. When a voltage is applied, the crystals line up along the direction of the electric field and they therefore no longer allow light to pass through. The display appears dark.

Liquid crystal displays

http://www.connessioni.biz/website/categoria-tecnologie/tecnologia-lcd-inorganici-guida-alla-tecnologia-parte-1.html?lang=en


Inclusion of a fly in Baltic amber. Although amber is an amorphous substance and in theory optically isotropic, the flow structures of the resin due to internal strain as well as the strain caused by the inclusions can be visualized in polarized light. The use of polarized light and the first-order red compensator lead to intensive colors in the otherwise golden amber . Courtesy of Michael Hgi, Swiss Gemological Society, Bern, Switzerland.

Cobalt, cold-rolled, Beraha etch, polarization. The examination of microstructure morphology plays a decisive role in materials science and failure analysis. Color contrast and specific microstructure formations can frequently be enhanced by optical polarization of the etched samples under the polarizing microscope. Courtesy of Ursula Christian, University of Pforzheim, Germany.

Polarizing Microscopy

http://www.leica-microsystems.com/science-lab/polarization-contrast/


Fresnel Equations

1, 0

1

2, 0

x

z 2

TE polarization

TM polarization

Ei

Er Et

Power Conservation



Fresnel Equations

Brewster Angles

Critical Angle

Planar Interface - Wavevector Diagrams

1, 0

1

2, 0

x

z 2

TE polarization TM polarization

Ei

Er Et


Example of Fresnel Equations

n1 = 1, n2 = 1.5


n1 = 1, n2 = 1.5



n1 = 1.5, n2 = 1



Example of Evanescent Field n1 = 1.5, n2 = 1


n1 = 1.5, n2 = 1



n1 = 1.0, n2 = 0.855 - j1.8955 (Gold at 0 =0.5m)



+ =

Constructive interference (In phase)

+ =

( out of phase)

(Waves cancel)

Destructive interference

Wave Interference


+ =

Constructive interference results when light paths differ by an integer multiple of the wavelength: r = m

Mirror

1

2 *

When light waves travel different paths, and are then recombined, they interfere.

Wave Interference


Destructive interference results when light paths differ by an odd multiple of the half wavelength: r = (2m+1) /2

Mirror

1

2 *

When light waves travel different paths, and are then recombined, they interfere.

+ =

Wave Interference



Two Plane Wave Interference x

z 1

2

k1

k2

n

Special Case: 1= - 2 =


Special Case: 1= 60deg and 2= 0deg

Two Plane Wave Interference

Double-Slit Experiment (Youngs Experiment)


https://upload.wikimedia.org/wikipedia/commons/1/18/%D0%97%D0%B5%D1%80%D0%BA%D0%B0%D0%BB%D0%BE_%D0%9B%D0%BB%D0%BE%D0%B9%D0%B4%D0%B0.png

Lloyds Mirror


z

x

L

D

mirror

Lloyds Mirror

S

A


i

t

i

A

B

C

D

E

t nf

n0

n0

Transmitted Waves

Reflected Waves

Fabry-Perot Interferometer


Asymmetric Fabry-Perot Interferometer with Gain or Loss

G = et

Gain Loss


Symmetric Fabry-Perot Interferometer

m m+1 m-1

FSR

Resonant Frequencies



Coefficient of Finesse



/k0 m01 m02

2m 2m

1

1/2

Minimum Wavelength Separation


m m+1 m-1

FSR


Resolving Power

Finesse

Thin Film Interference Examples

http://www.explainthatstuff.com/thin-film-interference.html

Soap Bubbles Oil Thin Films

R. A. Serway and J. W. Jewett, Physics for Scientists and Engineers, Thomson Brooks/Cole, 6th Ed. 2004

Oil film

Incident Sunlight

Multiple Colors

Red Orange Green Blue

Internal Reflection

External Reflection


http://en.wikipedia.org/wiki/Morpho

Morpho butterflies

Thin Film Interference Examples

Peacock Feathers

http://www.microscopyu.com/articles/polarized/interferenceintro.html http://www.rowland.harvard.edu/organization/past_research/optics/default.html


Michelson Interferometer

http://www.britannica.com/EBchecked/topic/380060/Michelson-interferometer

http://skullsinthestars.com/2008/10/16/fabry-perot-and-their-wonderful-interferometer-1897-1899/



Michelson Interferometer

http://cnx.org/contents/APKEiCUR@3/The-Michelson-Interferometer

With Compensators

Michelson Interferometer Sample Patterns


http://physics.aps.org/articles/v9/17

Gravitational Waves Measurement LIGO (Light Interferometer Gravitational-Wave Observatory)

Observation of Gravitational Waves from a Binary Black Hole Merger B.P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration) Phys. Rev. Lett. 116, 061102 (2016)

Video: A schematic depiction of LIGOs interferometric gravitational wave detector. Light from a laser is split in two by a beam splitter; one half travels down the vertical arm of the interferometer, the other half travels down the horizontal arm. The detector is designed so that in the absence of gravitational waves (top left) the light takes the same time to travel back and forth along the two arms and interferes destructively at the photodetector, producing no signal. As the wave passes (moving clockwise from top right) the travel times for the lasers change, and a signal appears in the photodetector. (The actual distortions are extremely small, but are exaggerated here for easier viewing.) Inset: The elongations in a ring of particles show the effects of a gravitational wave on spacetime.


http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102


First Experimental Measurement of Gravitational Waves on September 14, 2015 at 09:50:45 UTC (coordinated universal time)



http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102


http://blogs.scientificamerican.com/sa-visual/ligo-and-gravitational-waves-a-graphic-explanation/



http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102http://link.aps.org/doi/10.1103/PhysRevLett.116.061102

Evolved Laser Interferometer Space Antenna (eLISA)

eLISA would be the first dedicated space-based gravitational wave detector. It aims to measure gravitational waves directly by using laser interferometry. The LISA concept has a constellation of three spacecraft, arranged in an equilateral triangle with million-kilometre arms (5 million km for classic LISA, 1 million km for eLISA) flying along an Earth-like heliocentric orbit.

Proposed for launch in 2034

https://en.wikipedia.org/wiki/Evolved_Laser_Interferometer_Space_Antenna


Antireflection Layer

n1 n2 nc

dc

1

x

z antirelection

layer

http://www.pveducation.org/pvcdrom/anti-reflection-coatings

Comparison of surface reflection from a silicon solar cell, with and without a typical anti-reflection coating.



Antireflection Layer Amorphous Silicon (Solar Cells)

0 = 0.6m, = 0 deg

http://www.filmetrics.com/refractive-index-database/Si/Silicon Amorphous Silicon Data 2

Amorphous Silicon Data 1 https://refractiveindex.info/?shelf=main&book=Si&page=Pierce

D. T. Pierce and W. E. Spicer, Electronic structure of amorphous Si from photoemission and optical studies, Phys. Rev. B 5, 3017-3029 (1972)

Amorphous Silicon Data 1 Amorphous Silicon Data 2

https://doi.org/10.1103/PhysRevB.5.3017https://doi.org/10.1103/PhysRevB.5.3017https://doi.org/10.1103/PhysRevB.5.3017https://doi.org/10.1103/PhysRevB.5.3017https://doi.org/10.1103/PhysRevB.5.3017https://doi.org/10.1103/PhysRevB.5.3017https://doi.org/10.1103/PhysRevB.5.3017

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Physical & Electromagnetic Optics: Basic Principles ...users.ntua.gr/eglytsis/OptEng/Interference_p.pdf · Physical & Electromagnetic Optics: Basic Principles & ... • Interference