2003

- E = hv = Maxwell

hc

h = 6,626 10 34 J S

P : E hv h P c = f = = c c

E = P c

Maxwell

= E x B

(1)1

Edl =

d B dt

FARADAY

dt c dt. xy dB. ac dt dB=Bac dt

. , . c.

2

d B = Bac dt

gh

3

Edl = EaE = cB

1 2 3 Ea = Bac

Faraday

(2)1

Bdl = 0 0

d E dt

Ampere

dt xz E ac dt . , dE=Eac dt.

2

d E = Eac dt

gh

3

Bdl = BaB = 0 0 Ec Ampere

1 2 3 Ba = 0 0 Eac / /

Faraday & Ampere

E = cB

0 0 cE = B

c=

1

0 0

3,00 10 8 m / s

+x

B = Bmax (k )sin (t kx ) E max = cBmax x . t = 0. E xB. x.

E = E max ( j )sin (t kx )

E = y+ B= z+

E = y B= z

-x

B = Bmax (k )sin (t + kx ) E max = cBmax t = 0 , x. x.

E = E max ( j )sin (t + kx )

E = y+ B= z

E = y B= z+

E B

1

u=

1 1 0E2 + B2 2 2 0

2

B=

E = 0 0 E c

1 2 u = 0E2dU = udV = 0 E 2 ( Ac dt ) dt . u Ac dt dt

(

)

1 dU S = = 0 cE 2 A dt S=

0 0 2 EB E2 = E = 0 0 0 01J s m2 S 1 W m2

Poynting- Poynting: S =1

0

EB

:

S=

EB

0

( P) :

P = S dA

Poynting S (W/m2) .

S=

E B

0

=

Emax Bmax

0

sin2 (t kx) =

Emax Bmax [1 cos2(t kx)] 20

E B Sav = max max 20 E2max 1 0 2 1 E max = 0cE2max = I = Sav = 20c 2 0 2

cos2(t-kx) ( )

: cE = B E = cB( Faraday) ( Ampere)

B = E

B = 0 0 cE

= k m 0 , k m =1

1 k

=

1 kk m

1

00= c k

=

c kk m

k m = 1

=

=

1

0 0c

k > 1,

u1 0 < c = 0 n c = f n=

2

1

=

n2 n1

n1 n2

1

2

(2)

(a) ( ) (b) (a) . (c) , .

(a) (b)

1. 2. r = a

= 0 a, b :

sin a nb = na sin a = nb sin b sin b na

Snell

nb > na b < a nb < na b > a

(a) . (b) .

- FERMAT: FERMAT: ( ) s1, s2, s3, ,sm n1, n2, n3, ,nm :

1 m t = = ni si c i =1 i =1 i sim

: FERMAT :

n si =1

m

i i

FRESNEL E0i, E0r E0t , , :

E r 0 r E 0i

n cos i nt cos t = i ni cos i + nt cos t

E 2ni cos i t 0 t = E ni cos i + nt cos t 0i E n cos i ni cos t r || 0 r = t E 0i || ni cos t + nt cos i E 2ni cos i t || 0t = E 0i || ni cos t + nt cos i

.. R T

E R = 0r E 0i

= r2 E 0t E 0i n cos t = t n cos i i2

2

n cos t T= t ni cos i

2 t

na > nb Snell : sin b = na > 1, b > a nb a = crit sin b = 1 na sin a nb

b = 900

sin crit =

nb na

crit = 41.10 crit = 24.40

(a) . , 900, . 1,2 3 , . (b) ( ). , -

: (Evanescent) . . (Evanescent) 1/e

, , .

(a) . (b) , LASER , , , .

:

HUYGENS (1) . ().

r = t

HUYGENS (2)

OPA=AQO r=a

Huygens .

(a) . (b) (a)

AQO : AOB :

sin a =

at

AO t sin b = b AO

sin a a = = (Snell) sin b b

c c

b a

=

nb na

(a) . (b) (a). uba, n>>m, k.

- (2) n100MHz m,k10MHz

-- , . , , . , : (stable resonator) . (unstable resonator) . :

0 g1 g 2 1

gn = 1

L Rn

Rn .

Maxwell ( , ) laser (Transversal Electric Modes). / , . , . . : . x, y :

U mk ( x, y ) = H m H k exp (x2+ y2) L Hm, Hk

Gaussian (0,0) U00(x,y) gaussian :

U 00 ( x, y ) = exp (x2+ y2) L

L w= 2

1/ 2

2z w( z ) = w1 + L

1/ 2

w(z) , w (minimal beam waste).

(divergence) laser , :

=

2 nw

n .

Laser c- Q laser : : laser. : laser. laser (LiNbO3) - (, ). . : . . () n laser : c , L d ca nL E . c = = E c = c dt nL ca n. laser Q, :

Q=

EP

=

EdE dt

= c

P E .

Q (1) ( ns ns) () Q (Q-switching). Q laser laser . , , . Q, , . F N :

N dF = F 1 N dt t

dN N = 2F dt Nt

t laser. , i, .

Q (2) Q, , : - (Pockels shells) (fast rotating galvanometric mirrors-30000rpm) ( BDN) - (LiNbO3 crystals)

(1) (mode locking) ( ps) (Gwatts.) ( n+1-n=c/2L) laser . n n, central. , =2L/c. 1/, . :

E( t ) = En exp i(( 0 + n )t + f n ) ( N/n