fundamental of photonic
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Transcript of fundamental of photonic
Fundamentals of PhotonicsBahaa E. A. Saleh, Malvin Carl Teich
송 석 호
Physics Department (Room #36-401)2220-0923, 010-4546-1923, [email protected]
http://optics.hanyang.ac.kr/~shsong
Midterm Exam 30%, Final Exam 30%, Homework 20%, Attend 10%
(Supplements)
From Maxwell Eqs to wave equations
Optical properties of materials
Optical properties of metals
< 2/4> Course outline
A Bit of History
1900180017001600 200010000-1000
“...and the foot of it of brass, of the lookingglasses of the women
assembling,” (Exodus 38:8)
Rectilinear Propagation(Euclid)
Shortest Path (Almost Right!)(Hero of Alexandria)
Plane of IncidenceCurved Mirrors(Al Hazen)
Empirical Law of Refraction (Snell)
Light as PressureWave (Descartes)
Law of LeastTime (Fermat)
v<c, & Two Kinds of Light (Huygens)
Corpuscles, Ether (Newton)
Wave Theory (Longitudinal) (Fresnel)
Transverse Wave, Polarization Interference (Young)
Light & Magnetism (Faraday)
EM Theory (Maxwell)
Rejection of Ether, Early QM (Poincare, Einstein)
(Chuck DiMarzio, Northeastern University)
More Recent History
2000199019801970196019501940193019201910
Laser(Maiman)
Quantum Mechanics
Optical Fiber(Lamm)
SM Fiber(Hicks)
HeNe(Javan)
Polaroid Sheets (Land)Phase Contrast (Zernicke)
Holography (Gabor)
Optical Maser(Schalow, Townes)
GaAs(4 Groups)
CO2(Patel)
FEL(Madey)
Hubble Telescope
Speed/Light (Michaelson)
Spont. Emission (Einstein)
Many New Lasers
Erbium Fiber Amp
Commercial Fiber Link (Chicago)
(Chuck DiMarzio, Northeastern University)
Question
How does the light propagate through a glass medium?
(1) through the voids inside the material.(2) through the elastic collision with matter, like as for a sound.(3) through the secondary waves generated inside the medium.
Construct the wave front tangent to the wavelets
Secondaryon-going wave
Primary incident wave
What about –r direction?
Electromagnetic Waves
0εQAdE =⋅∫
rr
0=⋅∫ AdBrr
dtdsdE BΦ
−=⋅∫rr
dtdisdB EΦ
με+μ=⋅∫ 000rr
Gauss’s Law
No magnetic monopole
Faraday’s Law (Induction)
Ampere-Maxwell’s Law
Maxwell’s Equation
Maxwell’s Equation
Gauss’s Law
No magnetic monopole
Faraday’s Law (Induction)
Ampere-Maxwell’s Law
∫∫∫ ερ
=⋅∇=⋅ dvdvEAdE0
rrrr
0=⋅∇=⋅ ∫∫ dvBAdBrrrr
∫∫∫ ⋅−=⋅×∇=⋅ AdBdtdAdEsdE
rrrrrrr
∫∫
∫∫
⋅εμ+⋅μ=
Φεμ+μ=⋅×∇=⋅
AdEdtdAdj
dtdiAdBsdB E
rrrr
rrrrr
000
000
tEjB∂∂
εμ+μ=×∇r
rrr000
djtE rr
=∂∂
ε0 ( )djjBrrrr
+μ=×∇ 0
0ερ
=⋅∇ Err
⇒
0=⋅∇ Brr
⇒
tBE∂∂
−=×∇r
rr⇒
⇒
⇒
Wave equations
tBE∂∂
−=×∇r
rr
tEB∂∂
=×∇r
rr00εμ
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
−∂∂
=×∇∂∂
=×∇×∇tB
tE
tB
rrrrrr
0000 εμεμ
( ) BBrrrr
2−∇=×∇×∇k
zj
yi
xˆˆˆ
∂∂
+∂∂
+∂∂
=∇r
( ) ( ) BBBBrrrrrrrr
22 −∇=∇−⋅∇∇=×∇×∇
( ) ( ) ( )CBABCACBArrrrrrrrr
⋅−⋅=××
2
2
002
tBB
∂∂
=∇r
rεμ
2
2
002
tEE
∂∂
=∇r
rεμ
02
2
002
2
=∂∂
−∂∂
tB
xB εμ
02
2
002
2
=∂∂
−∂∂
tE
xE εμ
Wave equations
In vacuum
Scalar wave equation
2 2
0 02 2 0x t
μ ε∂ Ψ ∂ Ψ− =
∂ ∂
0 cos( )kx tωΨ = Ψ −
0200
2 =ωεμ−k cvk
≡==00
1εμ
ωSpeed of Light
smmc /103sec/1099792.2 88 ×≈×=
Energy carried by Electromagnetic Waves
Poynting Vector : Intensity of an electromagnetic wave
BESrrr
×=0
1μ
2
0
2
0
0
1
1
BcEc
EBS
μ=
μ=
μ=
(Watt/m2)
⎟⎠⎞
⎜⎝⎛ = c
EB
202
1 EuE ε=Energy density associated with an Electric field :
2
021 BuB μ
=Energy density associated with a Magnetic field :
n1n2
Reflection and Refraction
11 θ′=θReflected ray
Refracted ray 2211 sinsin θθ nn =
Smooth surface Rough surface
Reflection and Interference in Thin Films
• 180 º Phase changeof the reflected light by a media with a larger n
• No Phase changeof the reflected light by a media with a smaller n
Interference in Thin Films
tn1
Phase change: π
n2 Phase change: π
n2 > n1
λ=λ==δ1
12
nmmt n
Bright ( m = 1, 2, 3, ···)
( ) ( )λ
+=λ+==δ
1
21
21
12
nmmt n
Bright ( m = 0, 1, 2, 3, ···)
tnPhase change: π
No Phase change
( ) ( )λ
+=λ+==δ
nmmt n
21
212
λ=λ==δnmmt n2
Bright ( m = 0, 1, 2, 3, ···)
Dark ( m = 1, 2, 3, ···)
Interference
The path difference
λ=θ=δ msind( )λ+=θ=δ 2
1msind
⇒ Bright fringes m = 0, 1, 2, ····
⇒ Dark fringes m = 0, 1, 2, ····
The phase differenceλ
θπ=π⋅
λδ
=φsind22
θ=−=δ sindrr 12