lecture 02 : chapter1. the propagation of light
TRANSCRIPT
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.
Lecture 02 : Chapter1. The propagation of light
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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.
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2
2
2
2
2 1 ,)(
t
E
cE
t
EE oo
2
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t
H
cH
t
HH oo
smcoo
/ 1031 8
speed of EM wave (light) http://micro.magnet.fsu.edu/primer/java/wavebasics/index.html
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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/Speed_of_light
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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.
Changhee Lee, SNU, Korea
Optoelectronics
EE 430.423.001
2016. 2nd Semester
9/20
https://en.wikipedia.org/wiki/Speed_of_light
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)
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
Optoelectronics
EE 430.423.001
2016. 2nd Semester
12/20
Sources of EM waves
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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)
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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
Changhee Lee, SNU, Korea
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)(