Wave Optics – Outline What’s it all about? · combustion-physics-and-non-linear-optics/teaching Intro Brooker, Modern Classical Optics Hecht, Optics Klein and Furtak, Optics Smith,

Wave Optics Propagation, interference and diffraction of waves

Axel Kuhn, Oxford 2016

Paul Ewart’s lecture notes and problem sets:

https://www2.physics.ox.ac.uk/research/combustion-physics-and-non-linear-optics/teaching

Intro

Brooker, Modern Classical Optics Hecht, OpticsKlein and Furtak, OpticsSmith, King & Wilkins, Optics and PhotonicsBorn and Wolf, Principles of Optics

Wave Optics – Literature

Intro

Wave Optics – Outline

What’s it all about?Revision of geometrical opticsPropagation of waves Fourier methods

➙ Fresnel-Kirchhoff integral, theory of imaging

Diffraction-based optical instruments ➙ 2-slit, grating, Michelson and Fabry-Perot Interferometer

Dielectric surfaces and boundaries ➙ multilayer (anti)reflection coatings

Polarized Light

Intro

What’s it all about?

Imaging Visualization (projection, lithography)SpectroscopyMatter-wave propagation & imagingLasers and applicationsModern devices(opto-electronics, display technology, optical coatings, telecommunication, consumer electronics)

Intro

Astronomical observatory, Hawaii, 4200m above sea level.

What’s it all about?

Intro

Hubble space telescope, 2.4 m mirror

What’s it all about?

Intro

Classical Optics – Relevance

Optical Microscopefru

it fly

What’s it all about?

Intro

CD/DVD player optical pickup system

What’s it all about?

Intro

What’s it all about?

photo lithography

cutting & welding

Intro

Coherent Light ➙ Laser Physics

spectroscopymetrology (clocks)quantum opticsquantum computinglaser nuclear ignitionmedical applicationsengineeringtelecommunication

What’s it all about?

Intro

Geometrical Optics – Revision

Fermat’s principle (shortest path)reflection & refractionspherical & thin lensesparaxial approximationlensmaker’s formulacombining lensesprincipal planesoptical instrumentsAperture and field stopsPinhole camera ➙ wave optics

Geometric

Fermat‘s PrincipleLight propagating between two points follows a path, or paths, for which the time taken is an extremum (minimum)

Ignoring the wave nature of lightBasic theory for optical instruments

Geometrical Optics – Revision

Geometric

focussing with spherical surfaces

parallel bundles↓

image sphere

object sphere↓

image sphere

Geometrical Optics – Revision

Geometric

axis

Focal point

Focal point

u v

thin lens formula

Geometrical Optics – Revision

1u

+1v

=1f

Geometric

location of equivalent thin lens

Geometrical Optics – Instruments

Prin

cipa

l pla

nes

Geometric

location of equivalent thin lens

Prin

cipa

l pla

nes

Geometrical Optics – Instruments

Geometric

u v

lenssystem

1u

+1v

=1f

thin lens equation applies with u and vmeasured from the two principal planes

Geometrical Optics – Instruments

Prin

cipa

l pla

nes

Geometric

Objective magnification = v/u Eyepiece magnifies real image of object

Com

poun

d m

icro

scop

e

Geometrical Optics – Instruments

Geometric

angular magnification = β/α = fo/fE

Astro

nom

ical

tele

scop

e

Geometrical Optics – Instruments

Geometric

angular magnification = β/α = fo/fE

1.3.4 Telescope (Galilean)

!"!#

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!Figure 1.6

"#$%&'(!)'$#*+*,'-*.#/!! $ " !!" " ! %!!# !!!

1.3.5 Telescope (Newtonian)

!

!%

!#

!Figure 1.7

"#$%&'(!)'$#*+*,'-*.#/!! $ " !!" " ! %!!# !!

! ! % !!*0!-12!+.,'&!&2#$-1!.+!-12!.342,-*52!)*((.(!'#6!7+.(!'!0812(*,'&!)*((.(!0%(+',29!2:%'&0!

1'&+!-12!('6*%0!.+!,%(5'-%(2;!

!

1.3.6 Compound Microscope

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!Figure 1.8

!

<12!.342,-!'-!6*0-'#,2!&!+(.)!.342,-*52!=*-1!+.,'&!&2#$-1!!%!*0!*)'$26!'-!6*0-'#,2!';!>2'&!

*)'$2!*0!'-!+.,'&!&2#$-1!!#!+(.)!2?28*2,2!$*5*#$!'#$%&'(!)'$#*+*,'-*.#(!#$%!=12(2!$!!*0!-12!'#$&2!0%3-2#626!3?!-12!(2'&!*)'$2!*+!*-!='0!'-!-12!#2'(!8.*#-!.+!-12!2?2;!

!

Gal

ilean

tele

scop

eGeometrical Optics – Instruments

Geometric

Field stop

Apertures and Field Stops

limiting thefield-of-view

Aperture stop

limiting theIntensity

f/no. =

focal leng

th

entran

ce pupil dia

meter

Geometric

Camera Obscura

optimum pinhole size

contradicts expectations from geometrical optics

from Hecht, Optics

Geometric

Maxwell’s equations ⟼ waves

equivalence to matter waves

plane and spherical waves

energy flow / intensity

Huygen’s principle

The Wave Nature of Light

EM waves

Maxwell’s Equations

~r · ~B = 0 ~r⇥ ~H =d

dt~D

~r · ~D = 0 ~r⇥ ~E = � d

dt~B

linear isotropic medium⇢ = 0 ~J = 0

~D = ✏r✏0 ~E~B = µrµ0

~H

r2 ~E =⇣nc

⌘2 d2

dt2~E and r2 ~H =

⇣nc

⌘2 d2

dt2~H

EM waves

Plane and Spherical Waves

plane wave

spherical wave

n =p ✏rµr

c = 1/p ✏0µ0

vp= c/n

= !/k= ⌫�

~S =~E ⇥ ~H

k =2⇡

�= nk0

EM waves

u → amplitude of E, H, ψ …(�+ k2)u = 0

u(~r, t) = u0ei(~k~r�!t)

u(~r, t) = u0ei(kr�!t)/r

Huygen’s Principle

Huygens’ wavelet ebcid:com.britannica.oec2.identifier.AssemblyIdentifier?assemblyId=...

1 of 1 23.11.2008 19:56 Uhr

Figure 2: Huygens' wavelets. Originating along the fronts of (A) circular waves and (B) plane waves, wavelets recombine to produce the propagating wave front. (C) The diffraction of sound around a corner

arising from Huygens' wavelets.

Huygens’ wavelet

print articles

Every point on a wave frontcan be considered as a sourceof secondary spherical waves

u(~R) /Z

u(~r)eik|

~R�~r|

|~R� ~r|dS

Huygens

Interference of Waves