Physical & Electromagnetic Optics: Basic Principles & Interference

Home , Elliptical polarization

25/05/2021

Optical Engineering Prof. Elias N. Glytsis

School of Electrical & Computer Engineering National Technical University of Athens Wave and Electromagnetic Optics

Originally from the Book: B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Ed., J. Wiley 2007

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

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

Prof. Elias N. Glytsis, School of ECE, NTUA 3 Maxwell’s Equations Differential Form

Integral Form

Prof. Elias N. Glytsis, School of ECE, NTUA 4 Electromagnetic Boundary Conditions

Region +

Region -

Prof. Elias N. Glytsis, School of ECE, NTUA 5 Maxwell’s Equations Time Harmonic Form

Constitutive Relations

Prof. Elias N. Glytsis, School of ECE, NTUA 6 Wave Equation

Maxwell Equations in vacuum– no sources (ρ = 0, J = 0)

Homogeneous Vector Wave Similarly: Equations

Prof. Elias N. Glytsis, School of ECE, NTUA 7 Simple Solutions of Wave Equation

Let

Light Velocity in Vacuum

Solution:

Prof. Elias N. Glytsis, School of ECE, NTUA 8 1D-Wave Equation

t = Δt t = 0 t = Δt A A A −c c

General Solution

z0 z cΔt cΔt

Prof. Elias N. Glytsis, School of ECE, NTUA 9 Simple Solutions of 1D Wave Equation

Let t = t0 λ0 λ0

ε0

μ0 z y

Prof. Elias N. Glytsis, School of ECE, NTUA 10 Maxwell’s Equations Plane Wave Solutions – Isotropic Case

Prof. Elias N. Glytsis, School of ECE, NTUA 11 Maxwell’s Equations Plane Wave Solutions – Isotropic Case Wavevector Surfaces (Isotropic)

Prof. Elias N. Glytsis, School of ECE, NTUA 12 Maxwell’s Equations Plane Wave Solutions – Anisotropic Case

Prof. Elias N. Glytsis, School of ECE, NTUA 13 Maxwell’s Equations Plane Wave Solutions – Anisotropic Case Wavevector Surfaces (Biaxial)

Prof. Elias N. Glytsis, School of ECE, NTUA 14 Maxwell’s Equations Plane Wave Solutions – Anisotropic Case Wavevector Surfaces (Biaxial)

Prof. Elias N. Glytsis, School of ECE, NTUA 15 Maxwell’s Equations Plane Wave Solutions – Uniaxial Anisotropic Case Wavevector Surfaces (Uniaxial)

Prof. Elias N. Glytsis, School of ECE, NTUA 16 Maxwell’s Equations Plane Wave Solutions – Uniaxial Anisotropic Case Wavevector Surfaces (Uniaxial)

Prof. Elias N. Glytsis, School of ECE, NTUA 17 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

Prof. Elias N. Glytsis, School of ECE, NTUA 18 Polarization of Electromagnetic Waves

• 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 Types • Linear • Circular • Elliptical • ‘Random’ or unpolarized

Prof. Elias N. Glytsis, School of ECE, NTUA 19 Polarization of Electromagnetic Waves

Prof. Elias N. Glytsis, School of ECE, NTUA 20 Polarization of Electromagnetic Waves

Transformation

Selection of α

Prof. Elias N. Glytsis, School of ECE, NTUA 21 Linear Polarization

φ = mπ

Prof. Elias N. Glytsis, School of ECE, NTUA 22 Linear Polarization

• Plane EM wave – linearly polarized • Trace of electric field vector is linear http://www.univie.ac.at/mikroskopie/1_grundlagen/optik/wellenoptik/6_polarisation.htm • Also called plane-polarized light • Convention is to refer to the electric field vector

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

Prof. Elias N. Glytsis, School of ECE, NTUA 23 Linear Polarization (Animation)

Linear Polarization (Horizontal) Linear Polarization (45 degrees)

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

Prof. Elias N. Glytsis, School of ECE, NTUA 24 Circular Polarization

φ = -π/2 ή +π/2 & Εox = Εoy

RHCP = right-handed circular polarization LHCP = left-handed circular polarization

Prof. Elias N. Glytsis, School of ECE, NTUA 25 Circular Polarization

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html http://www.univie.ac.at/mikroskopie/1_grundlagen/optik/wellenoptik/6_polarisation.htm

• Two perpendicular electric field components of equal amplitude with 90° difference in phase • Electric vector rotates in the right-hand direction • Electric vector rotates in the left-hand direction

Prof. Elias N. Glytsis, School of ECE, NTUA 26 Circular Polarization (Animation)

Left Handed Circular Polarization (LHC)

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

Prof. Elias N. Glytsis, School of ECE, NTUA 27 Elliptical Polarization

φ = -π/2 ή +π/2 & Εox , Εoy άνισα

RHEP = right-handed elliptical polarization LHEP = left-handed elliptical polarization

Prof. Elias N. Glytsis, School of ECE, NTUA 28 Elliptical Polarization

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html http://www.univie.ac.at/mikroskopie/1_grundlagen/optik/wellenoptik/6_polarisation.htm • Two perpendicular eletric field components not in phase, either with different amplitudes and/or not 90ο out of phase • Electric vector rotates in the right-hand direction • Electric vector rotates in the left-hand direction • The most general state of complete polarization is elliptical

Prof. Elias N. Glytsis, School of ECE, NTUA 29 Polarization Animation

A circularly polarized wave as a sum of two linearly polarized components 90° out of Animation showing four different polarization phase 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 By Davidjessop - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=48021939

Prof. Elias N. Glytsis, School of ECE, NTUA 30 Elliptical Polarization

Prof. Elias N. Glytsis, School of ECE, NTUA 31 Polarization Example

Prof. Elias N. Glytsis, School of ECE, NTUA 32 Polarization Examples

https://www.youtube.com/watch?v=Q0qrU4nprB0 Prof. Elias N. Glytsis, School of ECE, NTUA 33 Polarization States Occurring Naturally

Reflection and transmission Scattering by molecules at interfaces

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

Prof. Elias N. Glytsis, School of ECE, NTUA 34 Polarization Applications

Dichroism Polarizing Glasses

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

Prof. Elias N. Glytsis, School of ECE, NTUA 35 Polarization Applications

Liquid Crystal (LCD) Displays Photographic Filters There are some crystals that become aligned when an electric field is When light reflects off water it becomes polarized. Such light is often put across them. When this happens they act as polarising filters. 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.

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 3 D films amounts. To investigate the stresses in an engineering part you could make a model of When you watch a 3D film you are actually watching two films shot with it in plastic, pass light through and then put it under stress. The patterns produced different cameras, looking at the same thing but from slightly different which may give an indication of where the material has been deformed. angles. When the films are projected the light is polarized and polaroid filters, worn as glasses, can let just one of the films into each eye. http://www.stokesleyscience.org/A%20level%20Physics/EM%20Waves/applications.htm Prof. Elias N. Glytsis, School of ECE, NTUA 36 Stress Analysis using Polarization

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

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.

Prof. Elias N. Glytsis, School of ECE, NTUA 37 Stress Analysis using Polarization

Stress in plastic glasses

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

Prof. Elias N. Glytsis, School of ECE, NTUA 38 Polarizing Filters

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

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

Prof. Elias N. Glytsis, School of ECE, NTUA 39 Birefringent Crystals

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

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

Prof. Elias N. Glytsis, School of ECE, NTUA 40 Measuring the concentration of solutions using Polarization

https://chem.libretexts.org/@api/deki/files/53868/a337ad5ab915a2785a17ae18073a40a9.jpg?revision=1

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.

Prof. Elias N. Glytsis, School of ECE, NTUA 41 Liquid Crystal Displays

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

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.

Prof. Elias N. Glytsis, School of ECE, NTUA 42 Liquid Crystal Displays

http://indexxit.com/wp-content/uploads/2017/12/archaicfair-liquid-crystal-display-active-matrix- working-ebecfabfdd-not-ppt-of-monitor-pdf-adt-construction-and-970x774.jpg

Prof. Elias N. Glytsis, School of ECE, NTUA 43 Polarizing Microscopy

Inclusion of a fly in Baltic amber. Although Cobalt, cold-rolled, Beraha etch, polarization. amber is an amorphous substance and in theory The examination of microstructure morphology optically isotropic, the flow structures of the plays a decisive role in materials science and resin due to internal strain as well as the strain failure analysis. Color contrast and specific caused by the inclusions can be visualized in microstructure formations can frequently be polarized light. The use of polarized light and enhanced by optical polarization of the etched the first-order red compensator lead to samples under the polarizing microscope. intensive colors in the otherwise golden amber. Courtesy of Ursula Christian, University of Courtesy of Michael Hügi, Swiss Gemological Pforzheim, Germany. Society, Bern, Switzerland.

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

Prof. Elias N. Glytsis, School of ECE, NTUA 44 Polarization Camera

Dark Objects Transparent Objects

https://www.ricoh.com/technology/tech/051_polarization.html

Prof. Elias N. Glytsis, School of ECE, NTUA 45 3D Movies

https://i.kinja-img.com/gawker- media/image/upload/c_scale,fl_progressive,q_80,w_800/j3x9oiaqcnqub9twruqu.jpg

https://www.thorlabs.com/images/TabImages/3D_Cinema_A1-450.jpg

Prof. Elias N. Glytsis, School of ECE, NTUA 46 Reflection and Refraction at a Planar Boundary

Prof. Elias N. Glytsis, School of ECE, NTUA 47 Reflection and Refraction at a Planar Boundary

TE polarization case

Electric Field Region 1 Region 2

Prof. Elias N. Glytsis, School of ECE, NTUA 48 Reflection and Refraction at a Planar Boundary

TE polarization case Magnetic Field

Prof. Elias N. Glytsis, School of ECE, NTUA 49 Reflection and Refraction at a Planar Boundary

TE polarization case

Boundary Condition (electric field)

Prof. Elias N. Glytsis, School of ECE, NTUA 50 Reflection and Refraction at a Planar Boundary

Boundary Condition (magnetic field)

Prof. Elias N. Glytsis, School of ECE, NTUA 51 Reflection and Refraction at a Planar Boundary

Boundary Conditions

Fresnel Equations (ΤΕ polarization)

Prof. Elias N. Glytsis, School of ECE, NTUA 52 Reflection and Refraction at a Planar Boundary

TM polarization case

Prof. Elias N. Glytsis, School of ECE, NTUA 53 Reflection and Refraction at a Planar Boundary

Boundary condition (electric field)

Boundary condition (magnetic field)

Prof. Elias N. Glytsis, School of ECE, NTUA 54 Reflection and Refraction at a Planar Boundary

Boundary conditions

Fresnel Equations (ΤM polarization)

Prof. Elias N. Glytsis, School of ECE, NTUA 55 Fresnel Equations (non-magnetic media)

Power Conservation

Prof. Elias N. Glytsis, School of ECE, NTUA 56 Fresnel Equations

Brewster Angles

https://en.wikipedia.org/wiki/Brewster%27s_angle Critical Angle

Prof. Elias N. Glytsis, School of ECE, NTUA 57 Planar Interface - Wavevector Diagrams

Prof. Elias N. Glytsis, School of ECE, NTUA 58 Planar Interface - Wavevector Diagram for Total Internal Reflection

Prof. Elias N. Glytsis, School of ECE, NTUA 59 Planar Interface - Wavevector Diagram for Total Internal Reflection

(evanescent wave)

Prof. Elias N. Glytsis, School of ECE, NTUA 60 Example of Fresnel Equations

n1 = 1, n2 = 1.5

Prof. Elias N. Glytsis, School of ECE, NTUA 61 Example of Fresnel Equations

n1 = 1, n2 = 1.5

Prof. Elias N. Glytsis, School of ECE, NTUA 62 Example of Fresnel Equations

n1 = 1, n2 = 1.5

Prof. Elias N. Glytsis, School of ECE, NTUA 63 Example of Fresnel Equations

n1 = 1.5, n2 = 1

Prof. Elias N. Glytsis, School of ECE, NTUA 64 Example of Fresnel Equations

n1 = 1.5, n2 = 1

Prof. Elias N. Glytsis, School of ECE, NTUA 65 Example of Evanescent Field

n1 = 1.5, n2 = 1

Prof. Elias N. Glytsis, School of ECE, NTUA 66 Example of Fresnel Equations

n1 = 1.5, n2 = 1

Prof. Elias N. Glytsis, School of ECE, NTUA 67 Example of Fresnel Equations

n1 = 1.0, n2 = 0.855 - j1.8955 (Gold at λ0 =0.5μm)

Prof. Elias N. Glytsis, School of ECE, NTUA 68 Example of Fresnel Equations

n1 = 1.0, n2 = 0.855 - j1.8955 (Gold at λ0 =0.5μm)

Prof. Elias N. Glytsis, School of ECE, NTUA 69 Example of Fresnel Equations n1 = 1.0, n2 = 0.855 - j1.8955 (Gold at λ0 =0.5μm)

Prof. Elias N. Glytsis, School of ECE, NTUA 70 Fresnel Equations Generalization

Prof. Elias N. Glytsis, School of ECE, NTUA 71 Fresnel Equations Generalization

Prof. Elias N. Glytsis, School of ECE, NTUA 72 Wave Interference

(In phase)

+ =

Constructive interference ( π out of phase)

+ =

Destructive interference

Prof. Elias N. Glytsis, School of ECE, NTUA 73 Two-Wave Interference (collinear) When light waves travel different paths, and are then recombined, they interfere.

(In phase)

+ =

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

Prof. Elias N. Glytsis, School of ECE, NTUA 74 Two-Wave Interference (collinear) When light waves travel different paths, and are then recombined, they interfere.

( π out of phase)

+ =

Destructive interference results when light paths differ by an odd multiple of the half wavelength: ∆r = (2m+1) λ/2 Prof. Elias N. Glytsis, School of ECE, NTUA 75 Two-Wave Interference (collinear)

Prof. Elias N. Glytsis, School of ECE, NTUA 76 Two-Wave Interference (collinear)

Most detectors use only electric field

Application for two collinear waves

Prof. Elias N. Glytsis, School of ECE, NTUA 77 Two-Wave Interference (collinear)

Fringe Visibility

Prof. Elias N. Glytsis, School of ECE, NTUA 78 Two Plane Wave Interference

Prof. Elias N. Glytsis, School of ECE, NTUA 79 Two Plane Wave Interference

Prof. Elias N. Glytsis, School of ECE, NTUA 80 Two Plane Wave Interference

Special Case: θ1= - θ2 = θ

Prof. Elias N. Glytsis, School of ECE, NTUA 81 Two Plane Wave Interference

Special Case: θ1= 60deg and θ2= 0deg

Prof. Elias N. Glytsis, School of ECE, NTUA 82 Double-Slit Experiment (Young’s Experiment)

Prof. Elias N. Glytsis, School of ECE, NTUA 83 Double-Slit Experiment (Young’s Experiment)

Exact Values Approximate Values

Prof. Elias N. Glytsis, School of ECE, NTUA 84 Double-Slit Experiment (Young’s Experiment)

Prof. Elias N. Glytsis, School of ECE, NTUA 85 Double-Slit Experiment (Young’s Experiment)

Prof. Elias N. Glytsis, School of ECE, NTUA 86 Double-Slit Experiment (Young’s Experiment)

Prof. Elias N. Glytsis, School of ECE, NTUA 87 Double-Slit Experiment (Young’s Experiment)

Prof. Elias N. Glytsis, School of ECE, NTUA 88 Double-Slit Experiment (Young’s Experiment)

λ1 = 0.45μm

λ2 = 0.65μm

Prof. Elias N. Glytsis, School of ECE, NTUA 89 Double-Slit Experiment (Young’s Experiment) – White Light

With diffraction Effects (s = d/20)

Prof. Elias N. Glytsis, School of ECE, NTUA 90 Lloyd’s Mirror

Maxima

Minima

Prof. Elias N. Glytsis, School of ECE, NTUA 91 Lloyd’s Mirror

Prof. Elias N. Glytsis, School of ECE, NTUA 92 Fabry-Perot Interferometer

Reflected Waves

Prof. Elias N. Glytsis, School of ECE, NTUA 93 Stokes Relations

Prof. Elias N. Glytsis, School of ECE, NTUA 94 Fabry-Perot Interferometer

Transmitted Waves

Prof. Elias N. Glytsis, School of ECE, NTUA 95 Fabry-Perot Interferometer

Prof. Elias N. Glytsis, School of ECE, NTUA 96 Symmetric Fabry-Perot Interferometer

n1 = n3 = n0 and n2 = nf

Prof. Elias N. Glytsis, School of ECE, NTUA 97 Electromagnetic Analysis of Fabry-Perot Interferometer

Prof. Elias N. Glytsis, School of ECE, NTUA 98 Electromagnetic Analysis of Fabry-Perot Interferometer Οριακές Συνθήκες

Prof. Elias N. Glytsis, School of ECE, NTUA 99 Electromagnetic Analysis of Fabry-Perot Interferometer

Prof. Elias N. Glytsis, School of ECE, NTUA 100 Fabry-Perot Interferometer (lossless)

Prof. Elias N. Glytsis, School of ECE, NTUA 101 Asymmetric Fabry-Perot Interferometer with Gain or Loss G = eγd

Gain Loss

Prof. Elias N. Glytsis, School of ECE, NTUA 102 Symmetric Fabry-Perot Interferometer

Resonant Frequencies

Prof. Elias N. Glytsis, School of ECE, NTUA 103 Symmetric Fabry-Perot Interferometer

Coefficient of Finesse

Prof. Elias N. Glytsis, School of ECE, NTUA 104 Symmetric Fabry-Perot Interferometer

Minimum Wavelength Separation

Prof. Elias N. Glytsis, School of ECE, NTUA 105 Symmetric Fabry-Perot Interferometer

Resolving Power

Finesse

Prof. Elias N. Glytsis, School of ECE, NTUA 106 Fabry-Perot Interferometer

Prof. Elias N. Glytsis, School of ECE, NTUA 107 Thin Film Interference Examples

Soap Bubbles Oil Thin Films

R. A. Serway and J. W. Jewett, “Physics for Scientists and Engineers”, Thomson Brooks/Cole, 6th Ed. 2004 Multiple Colors Incident Sunlight

Blue Green Orange Red External Reflection

Oil film Internal Reflection

http://www.explainthatstuff.com/thin-film-interference.html Prof. Elias N. Glytsis, School of ECE, NTUA 108 Thin Film Interference Examples

Morpho butterflies Peacock Feathers

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

http://www.microscopyu.com/articles/polarized/interferenceintro.html http://www.rowland.harvard.edu/organization/past_research/optics/default.html Prof. Elias N. Glytsis, School of ECE, NTUA 109 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/

Prof. Elias N. Glytsis, School of ECE, NTUA 110 Michelson Interferometer With Compensators

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

Compensation with a cube beamsplitter

Prof. Elias N. Glytsis, School of ECE, NTUA 111 Michelson Interferometer Folded version of Michelson Interferometer

Prof. Elias N. Glytsis, School of ECE, NTUA 112 Michelson Interferometer Folded version of Michelson Interferometer

Prof. Elias N. Glytsis, School of ECE, NTUA 113 Michelson Interferometer

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

Prof. Elias N. Glytsis, School of ECE, NTUA 114 Michelson Interferometer Sample Patterns

https://upload.wikimedia.org/wikipedia/commons/2/2e/Michelson_interference_laser.jpg http://kenolab.com/images/Interferometer/green_fringes.jpg

https://c1.staticflickr.com/3/2761/4256685428_b03743eb11_b.jpg http://minerva.union.edu/newmanj/physics100/light%20as%20a%20wave/michelson2.JPG

Prof. Elias N. Glytsis, School of ECE, NTUA 115 Gravitational Waves Measurement LIGO (Light Interferometer Gravitational-Wave Observatory)

Video: A schematic depiction of LIGO’s 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.

Observation of Gravitational Waves from a Binary Black http://physics.aps.org/articles/v9/17 Hole Merger B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration) Phys. Rev. Lett. 116, 061102 (2016) Prof. Elias N. Glytsis, School of ECE, NTUA 116 Gravitational Waves Measurement LIGO (Light Interferometer Gravitational-Wave Observatory) First Experimental Measurement of Gravitational Waves on September 14, 2015 at 09:50:45 UTC (coordinated universal time)

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) Prof. Elias N. Glytsis, School of ECE, NTUA 117 Gravitational Waves Measurement LIGO (Light Interferometer Gravitational-Wave Observatory)

Observation of Gravitational Waves from a Binary Black http://blogs.scientificamerican.com/sa-visual/ligo-and-gravitational-waves-a-graphic- explanation/ Hole Merger B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration) Phys. Rev. Lett. 116, 061102 (2016) Prof. Elias N. Glytsis, School of ECE, NTUA 118 Evolved Laser Interferometer Space Antenna (eLISA) Proposed for launch in 2034 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.

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

Prof. Elias N. Glytsis, School of ECE, NTUA 119 Optical Interference Filters

Thin-film optical filters are used to control reflection, transmission, and absorption of light. Their operation is based on waves multiple interference

Applications: Telecommunications Photovoltaics Photonic Devices Sensors Lasers Displays/Lighting Security Devices Ophthalmic Technology Automotive Optics etc.

Prof. Elias N. Glytsis, School of ECE, NTUA 120 Antireflection Layer (Transmission Line Equivalent)

Transmission Line Equivalent

Prof. Elias N. Glytsis, School of ECE, NTUA 121 Antireflection Layer

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

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

Prof. Elias N. Glytsis, School of ECE, NTUA 122 Antireflection Layer Amorphous Silicon (Solar Cells)

λ0 = 0.6μm, θ = 0 deg

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

Amorphous Silicon Data 1 Amorphous Silicon Data 2

nc = 2.0678, dc = 0.0725μm nc = 2.4333, dc = 0.0616μm

Prof. Elias N. Glytsis, School of ECE, NTUA 123 Mutlilayer Antireflection Coatings

Demonstration Example

Antireflection coating for 0.45μm < λ0 < 0.75μm

Merit Function for Optimization Procedure

Optimization Procedures Used

• Simulated Annealing • Genetic Algorithms • Particle-Swarm

Prof. Elias N. Glytsis, School of ECE, NTUA 124 Mutlilayer Antireflection Coatings

Two Layer Coating with [n1,n2]=[nL, nH]=[1.46,2.40] on silicon (nSi=3.9473)

Prof. Elias N. Glytsis, School of ECE, NTUA 125 Mutlilayer Antireflection Coatings for Solar Cells

Prof. Elias N. Glytsis, School of ECE, NTUA 126 Mutlilayer Antireflection Coatings for Solar Cells

Prof. Elias N. Glytsis, School of ECE, NTUA 127 http://resources.yesican-science.ca/trek/scisat/final/grade9/spectrometer2.html Multiple Colors

Incident Sunlight

Blue Green Orange Red External Reflection

Oil film

Internal Reflection

Prof. Elias N. Glytsis, School of ECE, NTUA 128