οπτικη 4

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4.

&

! , . , . ; , , . , , 33 ! , . , , , , . , , ; ; , ( ) ( , ), . ! , . . . , . . . material dispersion. , .

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4.1. , . ; , , , (bound) . , - . , . , . , , c - . , , . , , , .

4-1-1 : . , . . , , ( ) . , 0 2, .

4.2

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&

. , ! . . , , 1014 Hz. , , . , , : 2 E 0 0 2E =0 t 2

(4.1.1)

. (4.1.1) (1.2.2) : =c=1

0 0

(4.1.2)

(0) (0) . , () () . [ 1.2.]. (4.1.1) : 2 E 2E =0 t 2

(4.1.3)

:

=

1

(4.1.4)

, = ik & / t = i , :

=

k

= ph

(4.1.5)

(phase velocity). n (c) . : n = c/ph (4.1.6)

4.3

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e= /0 m= /0, :n = 1/ o 1/

=

= e m e

(4.1.7)

- . , ( 3.5). e , 0, e = 0, :n = e

n 2 = e = 1 + e

(4.1.8)

, , , e, . , . , .. , () (). , , , . , , . ( ) , , (4.1.7), , . , ( 4.3.2.). . , , , . , , . x, :p = qx

(4.1.9)

P . , :P = N p = Nqx

(4.1.10)

4.4

fysikoblog.blogspot.com

&

- - , :

P

=

&

o e

E

(4.1.11)

- . o e , . , -: ( ) ( ). , 7.4.3. o e , ( 3.5.). . , , :D = o E + o e E = o E

(4.1.12)

:n 2 = e = 1 + e = 1 + P o E

(4.1.13)

4.1.1. Lorentz , Lorentz. [ Hendrik Antoon Lorentz 1878, Nobel 1902]. : , , . xyz, . , , .

4.5

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4-1-2 : . , (resonant frequencies) , . - 0 s m :

0 =

sm

s = m02

(4.1.14)

E = E0 exp ( it ) Coulomb :Fe = qE = qE0 exp ( it )

(4.1.15)

x . - ,

:Fs = s x = m02 x

(4.1.16)

(damping force) :FT = m = m dx dt

(4.1.17)

:d 2x F = Fe + Fs + FT = m 2 dt

(4.1.18)

Fe Fs

Coulomb

E

q x

4-1-3 : , . H :

4.6

fysikoblog.blogspot.comqE0 exp ( it ) m02 x m dx d 2x =m 2 dt dt

&

qE d 2x dx + + 02 x = 0 exp ( it ) (4.1.19) 2 dt dt m

:x = x0 exp ( it ) = q E0 exp ( it ) qE = 2 2 2 m (0 i ) m (0 2 i )

(4.1.20)

. 0 . (4.1.20), , :P = N p = Nqx = Nq 2 E m (02 2 i )

(4.1.21)

(4.1.13) :

p Nq 2 1 2 = 1+ 2 n ( ) = 1 + 2 0 2 i m o 0 i2 2

(4.1.22) (4.1.23)

:

p = Nq 2 m o

(plasma frequency) . , . , (dispersion relation). , i. n = n + i n . n , : n 2 1 = ( n + 1) ( n 1) 2 ( n 1) :n ( ) = 1 +2 p

(4.1.24)

2

(02

02 22 2

)

+ ( )

2

&

( ) =

2 p

2

(02 2 ) + ( )2

2

(4.1.25)

. , 02. .

4.7

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( f1 01, f2 02 ), (4.1.22) :fj fj Nq 2 2 n ( ) = 1 + 2 = 1+ p 2 2 m o j 0 j 2 + i j j 0 j + i j2

(4.1.26) (4.1.27)

:

fj

j

=1

, q B . , . ( ) . . , .

4.8

fysikoblog.blogspot.com

&

4.2. , :k =

c

n =

c

( n i ) =

k i

c

(4.2.1)

z, :

E = E0 exp i t kz + = E0 exp

(

)

z exp i ( t kz + ) c

(4.2.2)

z : z ' E0 = E0 exp c

(4.2.3)

m k0 0 k0

0

km

4-2-1 : . , , :I E E* = Eo2 exp 2

z = I o exp ( a ( ) z ) c

(4.2.4) (4.2.5)

:

a ( ) =

2 ( ) c

o (absorption coefficient) . : 1 c = (4.2.6) a ( ) 2 ( ) , (absorption depth), 1/e .

4.9

fysikoblog.blogspot.com

. (), (absorption index), . (4.1.19) , . , August Beer Johann Heinrich Lambert : eer-Lambert: .

(4.2.4) :I ln = a ( ) z I0

(4.2.7)

4-2-2, . I0 d1 ( 4-2-2). Id1, , z d1. d2 ( 4-2-2), Id2 (4.2.4) , z d2.d1

A (R)

A (R)

d2

(T)

(T)

4-2-2 : . Id /I0 d , Beer. .

4.10

fysikoblog.blogspot.com4.3.

&

( ) , : =dn ( ) d

(4.3.1)

, =2 =2c/, n(), n(), n() . , n .

4.3.1. (4.1.24) n() () :n ( ) = 1 +2 p

2

(

02 22 0

2 2

) + ( )

2

( ) =

2 p

2

(

2 0

2 2

) + ( )

2

(4.3.2)

, ^, =0. , . ; . (4.3.2) :n =0 ( ) = 1+2 p

2

(02

02 2

2 2

)

= 1+

2 p

1 2 2 2 0

(4.3.3)

- . : , :n =0 ( = 0 ) =

(4.3.4)

0, .. n(=0) ! =0, , . (normal dispersion). , , .

4.11

fysikoblog.blogspot.com

n

0

4-3-1 : . . . , 0 ( .. 0) , . , , , . , , , . - 7.1.2. 4-3-2 n , (4.3.2).

n 1

4-3-2: . . .

4.12

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&

.. n , .. , (anomalous dispersion). , . , . , j 0, |0| ^ 0 202j 2 0(-0), (4.3.2) :2 2 p p 0 & ( ) = n ( ) = 1 + 2 2 2 4 0 ( 0 ) + ( / 2 ) 80 (0 ) + ( / 2 )2

(4.3.5)

() = 0, . ( ) (4.3.5) , :2 p n ( ) MAX = 1 + 40

&

2 p n ( ) MIN =1 40

(4.3.6)

=0!/2, . +0, p, .

4.3.3. : ( , h=21) , . .

4.16

fysikoblog.blogspot.com

&

h1 4-3-4 : .

h1

( , h21) . . . .

h1 4-3-4 : .

h1

. (continuous spectrum) ( 4-3-5) , ( ..). (. ) , . , (linear discrete spectrum) . , , convoluted . (.. ) , . . , . (emission spectrum) ( 4-3-5) . , (absorption spectrum) , ( 4-35). . !

4.17

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, . , ( 7.1.2). , . .

4-3-5 : () () () . . % ( , % ) . , 100% , 600 nm, . , . . , 500 nm, 100% 500 nm, 550 nm. . , , . , . : , , . , . 450 nm 650 nm, ,

4.18

fysikoblog.blogspot.com

&

. - , !100

(%)

50

(nm)400 500 600 700

0

(%)

100

50

(nm)400 500 600 700

0

4-3-6 : () () . , . , , . , (carotenoids), , (anthocyanins), , . , .

Newton (Optiks, 135).