waves, light & quanta

29
Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London

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Waves, Light & Quanta. Tim Freegarde. Web Gallery of Art; National Gallery, London. . where. Sinusoidal waves. z. simple harmonic motion. circular motion. wavenumber. spectroscopists’. at ,. wavenumber. wavelength. Sinusoidal waves. angular frequency. frequency. - PowerPoint PPT Presentation

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Page 1: Waves, Light & Quanta

Waves, Light & QuantaTim Freegarde

Web Gallery of Art; National Gallery, London

Page 2: Waves, Light & Quanta

2

Sinusoidal waves

kztrtxy sin,

• simple harmonic motion

• circular motion

,r kzt where

kztrkztr sin,cos

z

Page 3: Waves, Light & Quanta

3

Sinusoidal waves

0tt

0tt at ,

• wavenumber

2k

x

y

000 sin, tkxytxy

• spectroscopists’

1~ wavenumb

er

00~2sin txy

002sin txy • wavelength

kxtytxy sin, 0

Page 4: Waves, Light & Quanta

4

Sinusoidal waves

0xx

0xx at ,

• angular frequency

2

t

y

000 sin, kxtytxy

• frequency

1 00 2sin kxty

002sin kxty • period

kxtytxy sin, 0

Page 5: Waves, Light & Quanta

5

Birefringence• asymmetry in crystal

structure causes two different refractive indices

• opposite polarizations follow different paths through crystal

• birefringence, double refraction

Page 6: Waves, Light & Quanta

6

Optical polarization

• for any wavevector, there are two field components

• light is a transverse wave: perpendicular to E k

• any wave may be written as a superposition of the two polarizations

Page 7: Waves, Light & Quanta

7

Linear dichroism• conductivity of wire grid depends

upon field polarization• electric fields perpendicular to the

wires are transmitted

WIRE GRID POLARIZER

• fields parallel to the wires are absorbed

Page 8: Waves, Light & Quanta

8

Malus’ law

WIRE GRID POLARIZER

• amplitude transmission

cos

• intensity transmission

2cos

Page 9: Waves, Light & Quanta

9

Linear dichroism• crystals may similarly show

absorption which depends upon linear polarization• absorption also depends upon wavelength• polarization therefore determines crystal colour

TOURMALINE

• pleochroism, dichroism, trichroism

Page 10: Waves, Light & Quanta

10

Polarization in nature• the European cuttlefish also has

polarization-sensitive vision• … and can change its colour and

polarization!

MAN’S VIEW CUTTLEFISH VIEW (red = horizontal polarization)

CUTTLEFISH (sepia officinalis)

Page 11: Waves, Light & Quanta

11

Circular dichroism• absorption may also depend

upon circular polarization• the scarab beetle has

polarization-sensitive vision, which it uses for navigation

• the beetle’s own colour depends upon the circular polarization SCARAB BEETLE LEFT CIRCULAR

POLARIZED LIGHT

RIGHT CIRCULAR

POLARIZED LIGHT

Page 12: Waves, Light & Quanta

12

Optical activity (circular birefringence)

l-limonene(orange)

r-limonene(lemon)

CH2

CH3

HCH3 CH2

CH3

HCH3

CHIRAL MOLECULES

• optical activity is birefringence for circular polarizations

• an asymmetry between right and left allows opposing circular polarizations to have differing refractive indices• optical activity rotates the polarization plane of linearly polarized light• may be observed in vapours, liquids and solids

Page 13: Waves, Light & Quanta

13

Categories of optical polarization

• linear (plane) polarization• non-equal components in phase

• circular polarization• equal components 90° out of

phase• elliptical polarization

• all other cases

Page 14: Waves, Light & Quanta

14

Polarizing components

POLARIZER(filter/

separator)

LINEAR CIRCULAR

WAVEPLATE

(retarder)yx

yx TT

RL

RL TT

Page 15: Waves, Light & Quanta

15

Waveplates (retarders)

WAVEPLATE

• at normal incidence, a birefringent material retards one polarization relative to the other• linearly polarized light becomes elliptically polarized

le 02

Page 16: Waves, Light & Quanta

16

Polarization notation

• circular polarization• right- or left-handed rotation

when looking towards source

• linear (plane) polarization• parallel or perpendicular to

plane of incidence

RCP plane of incidence

perpendicular

parallel

• traces out opposite (right- or left-) handed thread

• plane of incidence contains wavevector and normal to surface

Page 17: Waves, Light & Quanta

17

Polarization by scattering

cdoswell.com/tips3.htm

Page 18: Waves, Light & Quanta

18

Brewster’s angle

ir

ri sincos

isin1

itan

• reflected light fully (s-) polarized

i r

Page 19: Waves, Light & Quanta

19

Brewster’s angle

www.paddling.net/sameboat/archives/sameboat496.html

ii

r

r

itan• reflected light fully (s-) polarized

Page 20: Waves, Light & Quanta

20

Malus’ law

WIRE GRID POLARIZER

• amplitude transmission

cos

• intensity transmission

2cos

Page 21: Waves, Light & Quanta

21

sin,cos iea

Characterizing the optical polarization

• wavevector insufficient to define electromagnetic wave• we must additionally define the polarization vector

k

yx aa ,ax

yz

sin,cosa• e.g. linear polarization at

angle

Page 22: Waves, Light & Quanta

22

Jones vector calculus• if the polarization state may be

represented by a Jones vector

• then the action of an optical element may be described by a matrix

yx aa ,a

2221

1211

aaaa

A

y

x

y

x

aa

aaaa

aa

2221

1211

JONES MATRIX

Page 23: Waves, Light & Quanta

23

Jones vector calculus

y

x

y

x

aa

aaaa

aa

2221

1211

JONES MATRIX

0001

1A transmission by horizontal polarizer

y

x

ii

A

exp00exp

2retardation by

waveplate

cossinsincos

3A projection onto rotated axes

• if the polarization state may be represented by a Jones vector

• then the action of an optical element may be described by a matrix

2221

1211

aaaa

A

yx aa ,a

Page 24: Waves, Light & Quanta

24

Birefringence• asymmetry in crystal

structure causes two different refractive indices

• opposite polarizations follow different paths through crystal

• birefringence, double refraction

Page 25: Waves, Light & Quanta

25

38.5º

Linear polarizers (analyzers)

e-ray

o-ray

e-ray

o-ray

s-ray

p-ray

• birefringence results in different angles of refraction and total internal reflection• many different designs, offering different geometries and acceptance angles

• a similar function results from multiple reflection

Page 26: Waves, Light & Quanta

26

Waveplates (retarders)

WAVEPLATE

• at normal incidence, a birefringent material retards one polarization relative to the other• linearly polarized light becomes elliptically polarized

le 02

Page 27: Waves, Light & Quanta

27

Compensators

adjust

fixed

variable

• a variable waveplate uses two wedges to provide a variable thickness of birefringent crystal

• a further crystal, oriented with the fast and slow axes interchanged, allows the retardation to be adjusted around zero SOLEIL

COMPENSATOR• with a single, fixed first section, this is a ‘single order’ (or ‘zero order’) waveplate for small constant retardation

Page 28: Waves, Light & Quanta

28

Electromagnetic waves• light is a transverse wave: perpendicular to E k

zxE

yBx

y

z

x

y

• Faraday

• Ampère

SBsE d.d.t

SEJsB d.d. 00 t yB

SEsB d.d. 00 t

xE

Page 29: Waves, Light & Quanta

29

Dielectrics

z

• atomic electrons move in response to electric field• resulting atomic dipole radiates field which adds to original

• Faraday

• Ampère

SBsE d.d.t

SEJsB d.d. 00 t

SEJsB d.d. 00 tr