lecture 02 : chapter1. the propagation of light

Changhee Lee, SNU, Korea

Optoelectronics

EE 430.423.001

2016. 2nd Semester

1/20

2016. 9. 6.

Changhee Lee

School of Electrical and Computer Engineering

Seoul National Univ.

[email protected]

Lecture 02 : Chapter1. The propagation of light


Optoelectronics

EE 430.423.001

2016. 2nd Semester

2/20

Maxwell equations for the vacuum

0

0

H

E

• Gauss' laws

• Faraday's law: electromagnetic induction

t

HE o

H/m10261H/m104 66 . μo

• Ampere-Maxwell equation: Maxwell added the time rate of change of electric field (displacement current)

t

EH o

At a point in empty space, the EM state of the vacuum is specified by two vectors, the electric field E and

the magnetic field H.

t

EJB ooo

F/m 10854.8 12o

Permeability of the vacuum

Permittivity of the vacuum


Optoelectronics

EE 430.423.001

2016. 2nd Semester

3/20

Maxwell’s wave equations

2

2

2

2

2

22

2

Laplacian

) () () (

zyx

• From the Maxwell equations, we can get EM wave equations

• Maxwell's discovery merged the fields of electricity, magnetism, and optics.

2

2

2

2

2

2 1 ,)(

t

E

cE

t

EE oo

2

2

2

2

2

2 1 ,)(

t

H

cH

t

HH oo

smcoo

/ 1031 8

speed of EM wave (light) http://micro.magnet.fsu.edu/primer/java/wavebasics/index.html


Optoelectronics

EE 430.423.001

2016. 2nd Semester

4/20

Measurement of speed of light: Interferometry

A coherent beam of light (e.g. from a laser), with a known

frequency (n), is split to follow two paths and then recombined.

By adjusting the path length while observing the interference

pattern and carefully measuring the change in path length, the

wavelength of the light (λ) can be determined. The speed of light

is then calculated using the equation c = λ n.

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


Optoelectronics

EE 430.423.001

2016. 2nd Semester

5/20

Measurement of speed of light: rotating mirror

Fizeau–Foucault apparatus : On the way from the source to the mirror, the beam

passes through a rotating cogwheel. At a certain rate of rotation, the beam passes

through one gap on the way out and another on the way back, but at slightly

higher or lower rates, the beam strikes a tooth and does not pass through the

wheel. Knowing the distance between the wheel and the mirror, the number of

teeth on the wheel, and the rate of rotation, the speed of light can be calculated.


https://en.wikipedia.org/wiki/File:Michelson_speed_of_light_measurement_1930.jpg

https://en.wikipedia.org/wiki/File:Michelson_speed_of_light_measurement_1930.jpg

https://en.wikipedia.org/wiki/File:Fizeau.JPG

https://en.wikipedia.org/wiki/File:Fizeau.JPG


Optoelectronics

EE 430.423.001

2016. 2nd Semester

6/20


Optoelectronics

EE 430.423.001

2016. 2nd Semester

7/20

mKKu

cn

index of refraction

Speed of light in a medium

o

mμ

μK

o

K

Relative permeability

Relative permittivity

speed of light in a medium

KKc

KKu

moom

111


Optoelectronics

EE 430.423.001

2016. 2nd Semester

8/20

Dispersion

dispersion : The refractive index of materials varies with the wavelength (and frequency) of light.

This causes prisms and rainbows to divide white light into its constituent spectral colors.

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

chromatic aberration: Dispersion also causes the focal length of lenses to be wavelength dependent.

normal dispersion: The refractive index decreases with increasing wavelength.

https://en.wikipedia.org/wiki/File:Dispersion-curve.png

https://en.wikipedia.org/wiki/File:Dispersion-curve.png

https://en.wikipedia.org/wiki/File:Prism_rainbow_schema.png

https://en.wikipedia.org/wiki/File:Prism_rainbow_schema.png

https://en.wikipedia.org/wiki/File:WhereRainbowRises.jpg

https://en.wikipedia.org/wiki/File:WhereRainbowRises.jpg


Optoelectronics

EE 430.423.001

2016. 2nd Semester

9/20


redblue

yellow

nn

nV

1

Abbe number

Abbe number

In optics and lens design, the Abbe number, also known as the V-number or constringence of a transparent

material, is a measure of the material's dispersion (variation of refractive index versus wavelength), with high

values of V indicating low dispersion.

Most of the human eye's wavelength sensitivity

curve, shown here, is bracketted by the Abbe

number reference wavelengths of 486.1 nm (blue)

and 656.3 nm (red)


Optoelectronics

EE 430.423.001

2016. 2nd Semester

10/20

Plane harmonic waves.

Waves in 1-dim.

avenumber)(angular w 2

,frequency)(angular 2

velocity)(phase

),cos(),(

n

k

ku

tkzUtzU o

2

2

22

2 1

t

U

uz

U

T

u

kuT

1

2

2

n

tuz


Optoelectronics

EE 430.423.001

2016. 2nd Semester

11/20

Waves in 3-dim.

zyx

o

kkkkzyxr

trkUtzyxU

kji ,kji

)cos(),,,(

Plane harmonic waves.

Surfaces of constant phase

constant tzkykxktrk zyx

222

zyx kkkku


Optoelectronics

EE 430.423.001

2016. 2nd Semester

12/20

Sources of EM waves


Optoelectronics

EE 430.423.001

2016. 2nd Semester

13/20

Alternative ways of representing harmonic waves

sincos iei

• Traveling wave in complex notation

)(),( )cos(),( tkzi

oo eUtzUtkzUtzU

)(),,,( trki

oeUtzyxU

• Spherical wave

)(1 ),cos(

1 tkzier

tkzr


Optoelectronics

EE 430.423.001

2016. 2nd Semester

14/20

Group velocity

• Superposition of two waves

])()[(])()[(),( tzkki

o

tzkki

o eUeUtzU

• Group velocity

dk

d

kug

)cos(2][),( )()()()( tkzeUeeeUtzU tkzi

o

tkzitkzitkzi

o

• phase velocity

ku

dk

dn

n

ku

dk

dn

n

ck

n

c

n

kc

dk

d

dk

dug 1

2

o

o

g

gd

dn

cuud

duuu

11 ,

• For most optical media the index of refraction increases

with increasing frequency (normal dispersion), so that

dn/dk >0 and therefore ug<u.

(Prob. 1.6)


Optoelectronics

EE 430.423.001

2016. 2nd Semester

15/20

Doppler effect

2

2

1'c

u

c

u

uc

cnnn

c

u

c

uc1' nnn

If the source is moving away from the receiver with a velocity u,

If the receiver is moving away

from the source with a velocity u,

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/dopp.html

c

u

n

n

n

nn '

othereach departing when '

other;each gapproachin when '

source

receiver

source

receiver

uc

uc

uc

uc

nn

nn


Optoelectronics

EE 430.423.001

2016. 2nd Semester

16/20

Doppler shifts of spectral lines in astronomy

https://ase.tufts.edu/cosmos/print_images.asp?id=44


Optoelectronics

EE 430.423.001

2016. 2nd Semester

17/20

Relativity correction

From the Einstein's Theory of Special Relativity, the

clock on a moving source runs slow by a factor of

g=(1-u2/c2)-1/2.

Thus, the rate at which new wave crests appear - the

frequency - is slowed down by g=(1-u2/c2)-1/2.

cu

cucu

cucucuuc

c

/1

/1/1

/1

11

/1

1'

/1

1' 22

nn

gnnnnn

2

2

2

11

/1

/1'

c

u

c

u

cu

cunnn

other)each departingwhen : other;each gapproachin when :( ' -uc

uc

nn


Optoelectronics

EE 430.423.001

2016. 2nd Semester

18/20

Experimental verification of relativistic Doppler effect

2

2

2

11

/1

/1'

c

u

c

u

cu

cunnn

H. E. Ives and G. R. Stilwell, J. Opt. Soc. Am. 31, 369 (1941)

2

2

2

2

2

11

2

11

c

u

c

u

c

u

c

u

reflect

direct

Relativistic correction


Optoelectronics

EE 430.423.001

2016. 2nd Semester

19/20

Doppler broadening of spectrum lines

m

kT

c

2ln22

n

nThis widening is due to the random thermal motion of the radiating atoms.

http://astronomy.nju.edu.cn/~lixd/GA/AT4/AT404/HTML/AT4040

4.htm

Molecular speed distribution

dvevkT

mNdvvn kTmv 2/22/3 2

)(4)(


Optoelectronics

EE 430.423.001

2016. 2nd Semester

20/20

Homework set #1.

Solve Problems 1.2, 1.3, 1.4, 1.6, 1.7, 1.10, 1.11.

lecture 02 : chapter1. the propagation of light

Documents