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<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)

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 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 ×≈×=

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+==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 Young’s Double-Slit Experiment

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

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 << λd ~ λd >> λ

Far-fieldFraunhofer

Near-fieldFresnel

Evanescent-fieldVector diffraction