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

Fundamentals of Photonics

Bahaa 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

1900 1800

1700

1600 2000

1000 0

-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 Incidence Curved Mirrors (Al Hazen)

Empirical Law of Refraction (Snell)

Light as Pressure Wave (Descartes)

Law of Least Time (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

2000 1990

1980 1970

1960 1950

1940 1930

1920 1910

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

Secondary on-going wave

Primary incident wave

What about –r direction?

Electromagnetic Waves

ε

0

A Q d E ⋅ =

∫ ^{r r}

= 0

∫ ^{B r} ⋅ ^{d A r}

dt s d

d

E ⋅ = − Φ

^B

∫ ^{r r}

dt i d

s d

B Φ

^E

μ ε + μ

=

∫ ^r ⋅ ^r

^{0 0 0}

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

∫

∫

∫ ^{E ⋅ d A = ∇ ⋅ E dv =} _ε ^{ρ dv}

0

r r r

r

= 0

⋅

∇

=

⋅ ∫

∫ ^{B r d A r r B r dv}

∫

∫

∫ ^{⋅ = ∇ × ⋅ = − B ⋅ d A}

dt A d

d E s

d

E r r r r r r r

∫

∫

∫

∫

⋅ ε

μ +

⋅ μ

=

ε Φ μ + μ

=

⋅

×

∇

=

⋅

A d dt E

A d d j

dt i d

A d B s

d

B

^E

r r r r

r r r r

r

0 0 0

0 0 0

t j E

B ∂

ε ∂ μ + μ

=

×

∇

r r r

r

0 0 0

j

d

t

E r r

∂ =

ε

₀

∂ r B r ( r j r j

d

)

+ μ

=

×

∇

₀

ε

0

= ρ

⋅

∇ E r r

⇒

= 0

⋅

∇ B r r

⇒

t E B

∂

− ∂

=

×

∇ r r

⇒ r

⇒

⇒

Wave equations

t E B

∂

− ∂

=

×

∇ r r r

t B E

∂

= ∂

×

∇ r r r

0 0

ε μ

( ) _⎟⎟

⎠

⎜⎜ ⎞

⎝

⎛

∂

− ∂

∂

= ∂

×

∂ ∇

= ∂

×

∇

×

∇ t

B E t

B t

r r r r

r r

0 0 0

0

ε μ ε

μ

( ^{r B r} ) ^{B r}

r

₂

−∇

=

×

∇

×

∇

^{x iˆ y ˆj ∂z kˆ}

+ ∂

∂ + ∂

∂

= ∂

∇r

(

^{r Br}

) ( )

^{r r Br Br Br}

r _{2 2}

−∇

=

∇

−

⋅

∇

∇

=

×

∇

×

∇

(

^{B C}

) ( ) ( )

^{A C B A B C}

Ar r r r r r r r r

⋅

−

⋅

=

×

×

2 2 0 0 2

t B B

∂

= ∂

∇

r μ ε r

2 2 0 0 2

t E E

∂

= ∂

∇

r μ ε r

2

0

2 0 2 0

2

=

∂

− ∂

∂

∂

t B x

B μ ε

2

0

2 0 2 0

2

=

∂

− ∂

∂

∂

t E x

E μ ε

Wave equations

In vacuum

Scalar wave equation

2 2

0 0

2 2

0

x μ ε t

∂ Ψ − ∂ Ψ =

∂ ∂

0

cos( kx ω t )

Ψ = Ψ −

2

0

0 0

2

− μ ε ω =

k v c

k = = ≡

0 0

1 ε μ

ω Speed of Light

s m m

c = 2 . 99792 × 10

⁸

/ sec ≈ 3 × 10

⁸

/

Transverse Electro-Magnetic (TEM) waves

B t E

B E r r r

r

r ⇒ ⊥

∂ ε ∂ μ

−

=

×

∇

_{0 0}

Electromagnetic

Wave

Energy carried by Electromagnetic Waves

Poynting Vector : Intensity of an electromagnetic wave

B E S r r r

×

=

0

1 μ

2 0 2

0 0

1 1

c B c E

EB S

= μ

= μ

= μ

(Watt/m²)

⎟⎠

⎜ ⎞

⎝⎛ = c E B

2

2

0

1 E u

_E

= ε

Energy density associated with an Electric field :

2

2

0

1 B u

_B

= μ

Energy density associated with a Magnetic field :

n₁ n₂

Reflection and Refraction

1 1

= θ′

θ

Reflected ray

Refracted ray n

₁

sin θ

₁

= n

₂

sin θ

₂

Smooth surface Rough surface

Reflection and Refraction

0 0

) ( )

) (

( μ ε

λ με λ = λ =

v n c

In dielectric media,

(Material) Dispersion

Interference & Diffraction

Reflection and Interference in Thin Films

• 180 º Phase change of the reflected light by a media

with a larger n

• No Phase change of the reflected light by a media

with a smaller n

Interference in Thin Films

t n

₁

Phase change: π

n

₂ Phase change: π

n

₂ > n₁

λ

= λ

=

= δ

1

2

1

n m m

t

_n

Bright ( m = 1, 2, 3, ···)

( ⁺ ) ^{λ = ( + ) λ}

=

= δ

1 2 1 2

1

2

1

n m m

t

_n

Bright ( m = 0, 1, 2, 3, ···) n t

Phase change: π

No Phase change

( ⁺ ) ^{λ = ( + ) λ}

=

=

δ n

m m

t

_n ²

1 2

2

1

λ

= λ

=

=

δ n

m m

t

_n

2

Bright ( m = 0, 1, 2, 3, ···)

Dark ( m = 1, 2, 3, ···)

Interference

Young’s Double-Slit Experiment

Interference

The path difference

λ

= θ

=

δ d sin m

( ⁺ ) ^λ

= θ

=

δ d sin m

₂¹

⇒ Bright fringes m = 0, 1, 2, ····

⇒ Dark fringes m = 0, 1, 2, ····

The phase difference

λ θ

= π π λ ⋅

= δ

φ 2 d sin

2

θ

=

−

=

δ r

₂

r

₁

d sin

Hecht, Optics, Chapter 10

Diffraction

Diffraction

Diffraction Grating

Diffraction of X-rays by Crystals

d θ θ

θ

dsinθ Incident

beam

Reflected beam

λ θ m d sin =

2 : Bragg’s Law

Regimes of Optical Diffraction

d << λ d ~ λ

d >> λ

Far-field Fraunhofer

Near-field Fresnel

Evanescent-field

Vector diffraction