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Ch 3. The Quantum Theory of Light Ch 3. The Quantum Theory of Light

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(1)

Ch 3. The Quantum Theory of Light Ch 3. The Quantum Theory of Light

이 병 호

서울대 전기공학부

byoungho@snu.ac.kr

(2)

하나님이 이르시되 빛이 있으라 하니 빛이 있었고

빛이 하나님이 보시기에 좋았더라 하나님이 빛과 어둠을 나누사 (창세기 1:3-4)

And God said, “Let there be light,” and there was light.

God saw that the light was good, and he separated the light from the darkness.

(Genesis 1:3-4)

Light

Light

(3)

•We all know what light is; but it is not easy to tell what it is.

- Samuel Johnson

• 파동성 (Wave : 전자파(Electromagnetic Wave)의 일종)

• 입자성 (Particle : Photon; 光子 )

Light

Light

(4)

History of the Study on Light History of the Study on Light

-- 1665 Grimaldi1665 Grimaldi -- 1678 Huygens1678 Huygens -- 1704 Newton1704 Newton

-- 1804 Young1804 Young -- 1818 Fresnel1818 Fresnel -- 1860 Maxwell1860 Maxwell -- 1905 Einstein1905 Einstein

(5)

Newton Newton

Isaac Newton Isaac Newton (1642

(1642--1727)1727)

J. Hakim, The Story of Science

J. Hakim, The Story of Science Newton at the Center, Newton at the Center, Smithsonian Books, Washington DC, USA, 2005

Smithsonian Books, Washington DC, USA, 2005

(6)

Young

Young

(7)

Electromagnetic Wave Electromagnetic Wave

James Clerk Maxwell (1831-1879) Heinrich Hertz (1857-1894)

(8)

Tragically, Hertz was as unfortunate with his health as he was fortunate with his talent. The first sign of trouble was a series of toothaches in 1888, which led to removal of all his teeth in 1889. By 1892, he was suffering from pains in his nose and throat, and was often depressed. His doctors could give him no satisfactory diagnosis. Several operations failed to provide permanent relief. By December 1893, he knew he would not recover, and in a letter he asked his parents "not to mourn... rather you must be a little proud and

consider that I am among the especially elect destined to live for only a

short while and yet to live enough. I did not choose this fate, but since it has overtaken me, I must be content; and if the choice had been left to me,

perhaps I should have chosen it myself."

Hertz died of blood poisoning on New Year's Day, 1894; he was thirty-six years old.

--- From 'Great Physicists' by W. H. Cropper

(9)

Fig. 3-2, p. 67

Electromagnetic Wave

Electromagnetic Wave

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파장과 주파수 파장과 주파수

주기 주파수 파장

진공에서의 빛의 속력 f

T

λ

c

T f c

f T

λ = λ

=

= 1

위치

시간 진폭

파장 물리량

주기

진폭 물리량

주기

(11)

전자파의 스펙트럼

전자파의 스펙트럼

(12)

Thermal Radiation

Thermal Radiation

(13)

Fig. 3-4, p. 69

Blackbody

Blackbody

(14)

Fig. 3-3, p. 68

Blackbody Radiation

Blackbody Radiation

(15)

Fig. 3-11, p. 78

Harmonic Oscillator

Harmonic Oscillator

(16)

Cavity Modes I Cavity Modes I

2 2 f

k c c

π π ω

= λ = =

( )

2

( )

2

2 2

1 ,

, t

t c t

∇ = ∂

Ε r Ε r

( ) , t E ( ) ( ) t k x ( ) k y ( ) k

z

z

E

x

r =

x

cos

x

sin

y

sin

( ) , t E ( ) ( ) t k x ( ) k y ( ) k

z

z E

y

r =

y

sin

x

cos

y

sin

( ) , t E ( ) ( ) t k x ( ) k y ( ) k

z

z E

z

r =

z

sin

x

sin

y

cos

0 ) ,

( =

E r t

(17)

Cavity Modes II Cavity Modes II

0 )

( =

⋅ t E k

, … 3 , 2 , 1 , 0 ,

,

y z

=

x

n n

n

kx

ky

kz

← Lπ

L n

k L

n k

L n

k

x

= π

x

/ ,

y

= π

y

/ ,

z

= π

z

/

(18)

Mode Density I Mode Density I

( ) k

22

( ) k

22

N k dk dk N k

π π

= =

( )

( )

2

3

1 4

8 2

k dk L π

π ×

Mode density ( )

Number of modes between and (per unit volune) ( ) N k

k k + dk = N k dk

Many books use the notation of ( ) rather than ( ). ρ k N k

(19)

Mode Density II Mode Density II

( ) ( )

N f df = N k dk 2

f ck

= π

( ) ( ) dk k

22

2 8

3

f

2

N f N k

df c c

π π

= = π =

Mode density ( )

Number of modes between and (per unit volune) ( ) N f

f f + df = N f df

(20)

Spectral Energy Density Spectral Energy Density

( , ) ( )

u f T df = EN f df

Spectral energy density ( , )

Energy of radiation fields between and (per unit volune) ( , ) u f T

f f + df = u f T df

(21)

Rayleigh-Jeans Law Rayleigh-Jeans Law

2 2 3

( , ) ( ) 8 f

B

u f T df EN f df k Tdf c

= = π

/( ) 0

/( ) 0

B

B

E k T E k T B

Ee dE

E k T

e dE

= ∫

∞ −

=

(By Boltzmann Distribution

or by the equipartition principle)

4

( , ) ( ) 8

B

u λ T d λ EN f df π k Td λ

= = λ

(22)

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