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Zkk Ik Ik = 2j! (Wh ; We) , Zkk { .

, In , Ik =0 Im =0. :

6 fIk Ik Zkk + ImImZmm + ImZmkIk + Ik ZkmImg = 2j! (Wh ; We ):

Zmk = Zkm, Re (ImIk + Ik Im)Zmk = 0:

ImIk + Ik Im , , Re Zmk = .

, .

4.4.4. () () . , .

Z I ZI = 4j! (Wh ; We ) = j! ( jHj2 ; "jEj2) dV V Z Z 1 jHj2 1 "jEjWh = dV We = dV:

2 2 2 V V V, S, , .

, , ~ ~ E = rot H:

j!" Z " ~ ~ I ZI = j! jHj2 ; jrot Hj2 dV = !2"V Z Z j j ~ ~ ~ ~ ~ ~ = k2jHj2 ; jrot Hj2 dV = k2HH ; rot H rot H dV:

!" !" V V :

Z j ~ ~ ~ ~ I ZI + I ZI + I Z I = k2H H + k2 H H ;

!" V ~ ~ ~ ~ ; rot H rot H ; rot H rot H dV:

~ ~ ~ ~ ~ ~ div (rot H H ) = H rot rot H ; rot H rot H , ~ ~ ~ ~ ~ ~ ;rot H rot H = div (rot H H ) ; H rot rot H ~ ~ ~ ~ ~ ~ ;rot H rot H = div (rot H H) ; H rot rot H :

, Z h j ~ ~ ~ I ZI + I ZI + I Z I = (k2H ; rot rot H) H + !" V I i h i ~ ~ ~ ~ ~ ~ ~ + (k2H ; rot rot H ) H dV ; (rot H H ) ~ +(rot H H) ~ dS:

n n S ~ { .

n ~ ~ , rot H = j!"E :

Z h j ~ ~ ~ I ZI + I ZI + I Z I = (k2H ; rot rot H) H + !" V I i h i ~ ~ ~ ~ ~ ~ ~ + (k2H ; rot rot H ) H dV + E H + E H ~ dS:

n S ~ , H ~ ~ k2H ; rot rot H = ~ ~ rot H ~ = 0 E ~ = n n ( ), Z = 0. , . , , , . , :

I ZI + I ZI + I Z I = I ZI ; I Z I:

Z = ;Z. , I Z I = 0:

Z =0.

, :

~ 1. H ~ ~ k2H ; rot rot H = 0:

~ 2. rot H , , ~ E .

~ , H . , Z, , . , .

. , :

Z h j ~ ~ ~ I ZI + I ZI + I Z I = (k2E ; rot rot E) E + ! V I i h i ~ ~ ~ ~ ~ ~ ~ + (k2E ; rot rot E) E dV + H E + H E ~ ndS:

S Z , ~ E . ~ , E . , , ~ ~ E. E , . .

, .

, :

~ 1. E .

~ 2. E S .

~ , E , . ( ).

4.4.5. , , () . .

, . , , Z ~ ~ (Em Hk ) ~ dS m = k z0 S S { , ~ { z z.

, N , N .

4.4.6. , ,.. .

:

Un = pn(an + bn) In = (an ; bn):

pn pn . , , p2 = Z0n n p pn = Z0n. , . Un = an + bn In = an ; bn an = (Un + In) bn = (Un ; In):

X Un = ZnmIm:

m an bn, ! X X 1 an = ZnmIm + In = (Znm + ) Im nm 2 m m ! X X 1 bn = ZnmIm ; In = (Znm ; ) Im nm 2 m m 0 n = m = nm 1 n = m:

:

a = (Z + 1) I b = (Z ; 1) I:

I:

I = 2(Z + 1); 1a:

b, b = (Z ; 1)(Z + 1); 1a:

S = (Z ; 1)(Z + 1); , . , :

S = (1 ; Y)(1 + Y); 1:

{ , ,.. , , . { .

4.4.7. (Z +1):

(Z + 1) S = (Z + 1)(Z ; 1)(Z + 1); 1:

, Z +1 Z ; 1 . . , (Z + 1) S = (Z ; 1)(Z + 1)(Z + 1); , , (Z + 1) S = Z ; 1:

(Z +1); 1, S = (Z + 1);1 (Z ; 1):

, Z ; 1 (Z +1);1 . , . , , , , . , , ST = S ST { .

( ).

4.4.8. , X (an + bn)(a n ; b n) = P + 2j! (Wh ; We) n , , X (ana n ; bnb n + a nbn ; anb n) = P + 2j! (Wh ; We ):

n , X (ana n ; bnb n) = 2P n X (a nbn ; anb n) = 4j! (Wh ; We ):

n :

a a ; b b = 2P a b ; a b = 4j! (Wh ; We ):

,.. P = 0, jaj2 = jbj : .

:

a a ; Sa S a = 2P:

S S T,.. , a (1 ; S T S)a = 2P:

1 { , ( ik ).

P =0, 1 ; S T S = S T S = 1:

, , .

.

1. , :

X X janj2 = jbnj2:

n n 2. S T S =1 X X T (S T S)ik = Sim Smk = Smi Smk = :

ik m m , X Sim Skm = :

ik m 3. 1.

4. .

, . , , .

a Sa ; a S a = 4j! (Wh ; We ) , a (S ; S T )a = 4j! (Wh ; We ):

, S { , a (S ; S )a = 4j! (Wh ; We ):

S ; S { .

4.4.9. ln an, bn an, b n (.

.). b = Sa. b0 = S0a0.

ln an, bn, a0, b0 n n j nln a0 = ane b0 = bne;j n ln n n j j l nln n n a0 = ane bn = b0 e :

n n L:

0 j le @ A L = j l n n 0 e :

a0 = La b = Lb a = L; 1a0 b = Lb0:

, , Lb0 = S L; 1a0 b0 = L;1S L; 1a0:

, S0 = L; 1SL; 1:

.

4.4.10. , H10 (..).

.

. , , .

, , .

S11 = S22 S13 = S23 S14 = ; S24 S34 = S43 = 0:

, , S12 = S21 S13 = S31 S14 = ;S41 S23 = S32 S24 = S42 S34 = ;S43:

, S11 S12 S13 SS12 S11 S13 ;SS13 S13 S33 S14 ;S14 0 S , X X Sik Sil = Ski Sli = :

kl kl i i .

1. 3 4, . .

, , :

S11 S13 + S12 S13 + S13 S33 = S12 S14 ; S11 S14 ; S14 S44 = 0:

SS11 + S12 = ; SSSS11 ; S12 = ; SS 1 S13 SS11 = ; S33 + S2 S13 S1 S13 SS12 = ; S33 ; S2 S13 S S33 = S44 = 0, , S11 = 0 S12 = 0.

3 4 S S14 . S11 = ; (S33 + S44) S12 = ; (S33 ; S44):

, S11 S12 , S33 = 0 S44 = 0. S33 S44 , .

2. ( S33 = S44 =0) jS13j2 + jS13j2 = jS14j2 + jS14j2 = 1:

p jS13j = jS14j = :

:

S33 = S44 = 0 , , 3 4.

, S33 = S44 = 0, , S11 =0, S22 = 0 S12 = S21 = 0, . , S11 = S22 = S33 = S44 = S34 = S43 = 1 p p S13 = S14 = :

2 0 0 1 0 0 1 ;S = p :

1 1 0 1 ;1 0 , .

, a3 3. 2 , 1 { .

, 4:

b4 = p (a1 ; a2):

a2 = 0, 2 . a1 ;:

a1 = ; b1 :

p b1 = (a3 ; a4):

, 4 .

a4 =p b1 = a3:

a1, 1 a1 = ; p a3 b4 = ; a3:

, 4- 1.

, 1 2 ( ) , 4 . .

4.5. 4.5.1. () ~ ~ ~ ~ rot E = ; j! H rot H = j!"E:

, " . :

~ ~ @E @H ~ rot = ;j H ; j! @! @! ~ ~ @H @E ~ rot = j"E + j!" :

@! @! ~ ~ H, { E . ( " ) ~ ~ @E @H ~ ~ ~ ~ H rot ; E rot = ; j( jHj2 + "jEj2) ;

@! @! ~ ~ @H @E ~ ~ ; rot E + rot H :

@! @! , , ! ! ~ ~ @E @H ~ ~ ~ ~ div H + div E = ; j( jHj2 + "jEj2):

@! @! , , . . , ! !) I( Z ~ ~ @E @H ~ ~ ~ ~ H + E ~ = j( jHj2 + "jEj2) dV:

ndS @! @! S V ~ { . n , , @U @I I + U = 4j (WH + WE ):

@! @! U I { , R R 1 jHj2 1 "jEjWH = dV WE = dV { 2 2 2 V V . U = ZI @U @Z @I = I + Z :

@! @! @! , @Z @I @I I I + I Z + Z I = 4j (WH + WE ):

@! @! @! , Z = ;Z , @Z @I @I I I + I Z ; ZI = 4j (WH + WE ):

@! @! @! , @Z I I = 4j (WH + WE ):

@! @Y U U = 4j (WH + WE ):

@! @Z @Y @Zmn , @! @! @! @Ymn.

@! 4.5.2. :

@U @I I + U = 4j (WH + WE ):

@! @! U = a + b, I = a ; b, , , @a @b @a @b + (a ; b ) + (a + b ) ; = 4j (WH + WE ):

@! @! @! @! , @a @b a ; b = 2j (WH + WE ):

@! @! @b @S @a , b = S a, = a + S. , @! @! @! @a @S @a @a @S @a a ; S a a + S = a ; aS a ; S a S :

@! @! @! @! @! @! @S S { , @! :

@a @S @a @S a ; a S a ; SS a = ; a S a @! @! @! @! S S = 1 .

, , :

@S ;a S a = 2j (WH + WE ):

@! 4.5.3. () @Z W @Y W = 2j = 2j :

@! 1 @! II UU 2 :

j' S = ; = e @S @; d' j' ;a S a = ; a ; a = ; a e;j' je a = 2j (WH + WE ):

@! @! d! d' W = ;

d! P P = aa { .

. , j!1 t j!2 t e e. , :

j(!1 t+'1 ) j(!2 t+'2 ) j(!1 t+'b = e + e = e f1 + ( ) o ' j !(t+ ) j[(!2 ;!1 )t+('2 ;'1 )] j(!1 t+'1 ) ! + e = e 1 +e :

, d' = :

d! , , ,.. . . , d' W = = ; :

d! P , , , , ( , ).

4.6. 4.6.1. , . , (..), l l 1 , S11 SS = S12 = S21 :

S21 S .

, jS11j2 + jS12j2 = jS12j2 + jS22j2 = 1:

, jS11j = jS22j. , S11 = S22. , , S11 S12 + S12 S22 = 0:

, , S11 = S22, S11 S12 + S12 S11 = Re (S11 S12) =0.

, , , S11 = S22 , Re S12 = 0,.. S12 = S21 { . , q p S12 = j 1 ; jS11j2 = j 1 ; S11:

, , jS11j l1 l2, , S11 = S22 ,.. . , S11.

B, S11 1 ; (1 + jB) ;jB S11 = = 1 + 1 + jB 2 + jB 2SjB = ; :

1 + S S11 { B.

, . , .

, , : . { , ,.. , . .

. .

4.6.2. , , e m1 e m III .

, , II I. .

~ ~ E H. ( ).

I ( ) j z ~ ~ EI = Em (e;j 1 z + ;e ) ~ Em z0 ~ j z j z 1 ~ ~ HI = (e;j 1 z ; ;e )Hm = (e;j 1 z ; ;e ) :

ZI II :

~ ~ EII = T Em e;j z ~ Em z z0 ~ 2 ~ ~ HII = T Hm e;j z = T e;j :

ZII z = 0, ( ~ ) z ~ ~ Em (1 + ;) = TEm ~ ~ Em Em (1 ; ;) = T ZI ZII 1 + ; = T 1 ; ; T = :

ZI ZII ;, ZII ; ZI ; = :

ZII + ZI T 2ZII T = 1 + ; = :

ZII + ZI ZI ZII, , . p ! ! ! =" H Z = = p = p = p = 2 2 k2 ; gm !2 " ; gm 1 ; gm=!2 " p =" = q :

2 1 ; = q p 2 ZE = = =" 1 ; = :

!" . " = "0 ; j { .

! 4.6.3. , .

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