Fundamentals of PhotonicsBahaa E. A. Saleh, Malvin Carl Teich

송 석 호

Physics Department (Room #36-401)2220-0923, 010-4546-1923, shsong@hanyang.ac.kr

http://optics.hanyang.ac.kr/~shsong

Midterm Exam 30%, Final Exam 30%, Homework 20%, Attend 10%

< 1/4> Course outline

(Supplements)

From Maxwell Eqs to wave equations

Optical properties of materials

Optical properties of metals

< 2/4> Course outline

< 3/4> Course outline

< 4/4> Course outline

Optics

Also, see Figure 2-1, Pedrotti

(Genesis 1-3) And God said, "Let there be light," and there was light.

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

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)

Let’s warm-up

일반물리

전자기학

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 EΦμε+μ=⋅∫ 000

rr

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

( ) BB rrrr 2−∇=×∇×∇ kzjyix ˆˆˆ ∂∂

+∂∂

+∂∂

=∇r

( ) ( ) BBBB rrrrrrrr 22 −∇=∇−⋅∇∇=×∇×∇( ) ( ) ( )CBABCACBA rrrrrrrrr ⋅−⋅=××

2

2

002

tBB

∂∂

=∇r

rεμ

2

2

002

tEE

∂∂

=∇r

rεμ

022

002

2

=∂∂

−∂∂

tB

xB εμ

022

002

2

=∂∂

−∂∂

tE

xE εμ

Wave equations

In vacuum

Scalar wave equation

2 2

0 02 2 0x tμ ε∂ Ψ ∂ Ψ− =

∂ ∂

0 cos( )kx tωΨ = Ψ −

02002 =ωεμ−k cvk

≡==00

1εμ

ωSpeed of Light

smmc /103sec/1099792.2 88 ×≈×=

Transverse Electro-Magnetic (TEM) waves

BEtEB

rrr

rr⊥⇒

∂∂

εμ−=×∇ 00

Electromagnetic Wave

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 Refraction

00

)()(

)(εμλμε

λλ ==

vcnIn dielectric media,

(Material) Dispersion

Interference & Diffraction

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+==δ1

21

21

12

nmmt n

Bright ( m = 0, 1, 2, 3, ···)

tnPhase change: π

No Phase change

( ) ( )λ+=λ+==δn

mmt n 21

212

λ=λ==δnmmt n2

Bright ( m = 0, 1, 2, 3, ···)

Dark ( m = 1, 2, 3, ···)

Interference Young’s Double-Slit Experiment

Interference

The path difference

λ=θ=δ msind( )λ+=θ=δ 21msind

⇒ Bright fringes m = 0, 1, 2, ····

⇒ Dark fringes m = 0, 1, 2, ····

The phase differenceλ

θπ=π⋅

λδ

=φsind22

θ=−=δ sindrr 12

Hecht, Optics, Chapter 10

Diffraction

Diffraction

Diffraction Grating

Diffraction of X-rays by Crystals

d

θθ

θ

dsinθ

Incidentbeam

Reflectedbeam

λθ md =sin2 : Bragg’s Law

Regimes of Optical Diffraction

d > λ

Far-fieldFraunhofer

Near-fieldFresnel

Evanescent-fieldVector diffraction