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. S1 ( ) ~ ~ ~ E = U1 ~(x y) H = I1 h(x y):

e , S1. S1 S1 :

~ ~ ~ Ke = H ~ = ; H ~ n z~ ~ ~ Km = ; E ~ = E ~ n z ~ { .

z 6.7, ~ ~ H = Bs Hs:

Bs { :

as! ; bs!s Bs = j(!2 ; !s ) R R ~ ~ ~ ~ KeEs dS KmHs dS S1 Sas = ; R bs = R :

~ ~ ~ ~ HsHs dV HsHs dV V V ~ ~ , as = 0, Es = Est = 0 S1. H S1 , ~ ~ ~ H = Bs Hs = Bs Hst = Bs jk1s ~ y):

h(x ~ H, I1 = j Bs :

1s Bs U1, , S1.

Bs, bs ~ ~ Km = E ~ z0:

R R R ~ ~ ~ ~ ~ ~ KmHs dS (E ~ dS (E Hs )~ dS z0)Hs zS1 S1 Sbs = = = = R R R ~ ~ ~ ~ ~ ~ HsHs dV HsHs dV HsHs dV V V V R ~ jk1s U1 (~ h)~ dS e zS= :

R ~ ~ HsHs dV V ~ ~ ~ , Hs = ;Hs, Hs { .

~ ~ h, bs e j U1s bs = R :

~ ~ HsHs dV V Bs, U1 !s 1s Bs = ; R :

~ ~ !2 ; !s HsHs dV V , !s 1s I1 = jBs = U1:

R 1s ~ ~ j(!2 ; !s ) HsHs dV V , ( ) :

I1 !s 1s Y1 = = R :

~ ~ U1 j(!2 ; !s ) HsHs dV V , 1 Qs 1s Y1 = R :

~ ~ 1 + jQsx !s HsHs dV V , Qs 1s G1 = R ~ ~ !s HsHs dV V . , { . 1s , :

~ ~ Hst = j h(x y):

1s ( ), , Hst ~ { , h { , .

1s , SGY1 = :

1 + jQsx C, SL (. ). S2, S =4,..

G . 2 Z0 2 Z0 G1 RZ2 = = Z0 Y1 = = :

Z1 1 + jQsx 1 + jQsx , C L R 2 S2 (.

.). , !s. .

, , .

, , .

C LR Z R { , Z0 { . PZ R Y= = :

PR Z0 G PZ Q= :

PR Q , Q0 R Y= = :

Q Z0 G :

Q0 R Y0 PZ = = = = :

Q Z0 G PR 1 1 1 1 Q0 = + = (1 + ) = (1 + ) Q Q0 Q Q0 Q Q QQ = :

1 + , Y0:

Y0 ; Yk ; = Y0 + Yk Yk Yk = G (1 + jQ0x) G =1=R.

x =0, Y0 ; G Y0=G ; 1 ; ;0 = = = :

Y0 + G Y0=G + 1 + :

1 + j;0j + 1 + j ; 1j = = :

1 ; j;0j + 1 ; j ; 1j > 1 ( ) + 1 + ; = = :

+ 1 ; + < 1 ( ) + 1 ; + 1 = = :

+ 1 + ; ( ) =1,.. = 1. .

x =0 Y0 ; G (1 + jQ0x) 2Y0 ; [Y0 + G (1 + jQ0x)] ; = = = Y0 + G (1 + jQ0x) Y0 + G (1 + jQ0x) 2Y0 2Y= ; 1 = ; Y0 + G (1 + jQ0x) Y0 + G + jGQ0x) ;0 + ; = ; 1 + jQx 2Y0 Y0 Q ;0 +1 =, =, Q = { .

Y0 + G G 1 + (..).

x= P= P0 (x=x) :

;0 + ; + 1 = :

1 + jQx S2. ; + 1 . > 1, ;0 > 0, . < 1, ;0 < 0, . = 1 (; = 0).

, :

P = P (1 ; j;j2):

+ ;0 + 1 ; 1 ; jQx ;2 + Q2 x0 j;j2 = = :

1 + jQx 1 + Q2 x P, ;2 + Q2 x2 1 ; ;0 P = P(1 ; ) = P = 1 + Q2 x2 1 + Q2 x P= :

1 + Q2 x P0 = P(1 ; ;2) { , .

, Qx = 2 f1=x1=2 = = :

f0 Q 6.8.2. , .

, (..).

. ,.. Q0 = = 1:

QQ0 Q0 Q2:

1 1 1 1 Q0 1 + = + = (1 + ) = :

Q0 Q2 Q0 Q0 Q2 Q QQ0 = :

1 + , Q= Q1 (1 + ) = 1:

1 + { 1 .

1 1, 1 :

1 . , , Q= :

Q2 2 = = :

1 + 2 1, 1, 1 2 1 1.

, 1 1 1 1 = + + = (1 + + ) 1 Q Q1 Q2 Q0 Q QQ = :

1 + + 1 . . , , { , .

, .

7.

- {, . .

7.1. , . . .

. :

~ me = ; K ~ e = 1:76 1011 / { .

m ~ H, ~ ~ T = (me H) ~ ~ dK ~ ~ = T = (me H):

~ dt ~ me = ; K, ( ~ ) ~ dK ~ ~ = H K:

dt ~ , K ~ H ( ) ~ !0 = jHj ~ H .

;n, n { { , ~ ~ M (M = n me) ~ ~ dM ~ ~ = (H M):

dt , !0.

, . , .

~ !0. , H ~ z, K dKx = ; !0Ky dt dKy = !0Kx dt , Kx Ky, d2Kx + !0Kx = dtd2Ky + !0Ky = dt.. . ~ M.

, ,.. . . , , .

~ M0 ~ H0, .

~ h, , ~ m. m h ~ ~ !.

~ z H0. ~ ~ ~ ~ ~ H = h + H0 M = m + M~ ~ ~ H0 M0 z- . , j!. , , ~ M j!mx = ; (myH0 ; hyM0) j!my = (mxH0 ; hxM0) j!mz = 0:

mx my :

2 M0H0 ! Mmx = ; hx ; j hy 2 2 2 2 !2 ; H0 !2 ; H0 2 ! M0 M0Hmy = j hx ; hy 2 2 2 2 !2 ; H0 !2 ; H0 mz = 0:

!0 = H0 !M = M0 !0 ! !! mx = ; hx ; j hy 2 !2 ; !0 !2 ; !!! !0 ! my = j hx ; hy 2 !2 ; !0 !2 ; !mz = 0:

, , ~ b = (~ + m):

h ~ !0 ! = (1 ; ) !2 ; ! !! k = !2 ; ! bx = hx ; jk hy by = jk hx + hy bz = hz:

, 0 z .

~ ~ b h ^ :

~ ~ b = ^ h ^ ;jk ^ = jk 0 :

0 0 z . ! = !0 = H0.

. , . ~ ~ , H , , H .

z , Ho (..), hy = ; jhx ( hx = jhy ):

hy bx y hx by, x bx = hx ; jkhy = hx ; khx = ( ; k) hx by = jkhx + hy = ; khy + hy = ( ; k) hy :

, ; k 0 ^ = 0 ; k + 0 0 z z- , ^ :

+ !0 ! !! ! = ; k = (1 ; ; ) = (1 ; ):

+ 2 !2 ; !0 !2 ; !0 0 ! ; ! hy = jhx ( hx = ; jhy ):

bx by, bx = hx ; jkhy = hx + khx = ( + k) hx by = jkhx + hy = khy + hy = ( + k) hy + k 0 ^ = 0 + k ;

0 0 z !0 ! !! ! = + k = (1 ; + ) = (1 + ):

; 2 !2 ; !0 !2 ; !0 0 ! + ! + ;

, .

+,m 0 + ) ( , , + . . .

~ dM ~ ~ ~ = (H M) + R:

dt . 1935.:

~ ~ ~ ~ R = ; (M (H M)):

~ jMj .

( ) , . { , . .

, 0 = ; j + + + !(!2 ; !0 )(! + !0) = (1 ; ) + 2 (!2 ; !0 )2 + 4!2!0 !!(! + !0) = 0 :

+ 2 (!2 ; !0 )2 + 4!2!0 0 = ; j ;

; ;

!(!2 ; !0 )(! ; !0) = (1 ; ) ;

2 (!2 ; !0)2 + 4!2!0 !!(! ; !0) = 0 :

;

2 (!2 ; !0 )2 + 4!2!0 .

+ , + + + , , { + ;

.

7.2. 7.2.1. , z.

z.

~ ~ ~ ~ ~ = ~ e; z h = h0 e; z b = b0 e; z e e @ @ @ = 0 = 0 = ; :

@x @y @z :

rot ~ = ; j!~ e b rot~ = j!" ~ h e:

~ e, rot rot~ ; !2" ~ = 0:

h b :

~ grad div h ; h ; !2" ~ = 0:

b , @hx @hy @hz ~ div h = + + :

@x @y @z @ @ @ = 0 = 0 = ;

@x @y @z ~ div h = ; hz:

grad z- , :

hx + !2"bx = hy + !2"by = 2 ; hz + hz + !2"bz = 0:

, bz = hz = 0, hz = 0,..

z . , .

bx by hx hy:

bx = mhx ; jk hy by = jk hx + hy ( + !2 ") hx ; j!2"k hy = j!2"k hx + ( + !2 ") hy = 0:

hx, hy ( + !2 ")2 ; (!2"k)2 = + !2 " = !2"k = ; !2" ( k)..

p = j! "( k) = j p p = ! ( ; k)" = ! ( + k)":

+ ;

+ !2"k hx ; j!2"k hy = hx = j hy. , Hz. = ; k:

+ p = ! ( + k)" ;

hx = ; j hy.. { .

, , ( ) .

. ' = ; l ( ; ):

+ ;

' l = = ; ( ; ):

+ ;

2 !0 < !, ! < !, , ! p p ! (1 ; ) (1 ; ) + 0 + ! 2! ! p p ! (1 + ) (1 + ) :

; 0 ; ! 2! h i l p ! p ! ; ! "(1 ; ) ; ! "(1 + ) = 0 2 2! 2! l p = ! ".. . , " { .

. , , - . -.

, , . .

.

, , .

7.2.2. z Ho y,..

(..). y x ~ ~ ~ ~ ~ = ~ e; y h = h0 e; y b = b0 e; y:

e e@ @ @ = 0 = 0 = ; :

@x @z @y rot rot~ ; !2" ~ = h b ~ ~ h + !2" ~ ; grad div h = 0:

b ~ , grad div h y- , hy. hx + !2"bx = 2 hy + !2"by ; hy = hz + !2"bz = 0:

~ b. hx ( + !2" ) ; j!2"k hy = jk hx + hy = hz ( + !2" ) = 0:

z hy , !2"khx ( + !2" ; ) = hz ( + !2" ) = 0:

z hx = 0, !2"k + !2" ; = s ; k = j! " :

, hz = 0,.. ~ H0 ( ). , ; k = :

hz = 0, hx = hy = 0. + !2" = z p = j! ":

2 z ~ H0.

, . { { , hx hy, 90o hx. ; k2 ( ; k) ( + k) + ;

= = = :

{ { . = :

k z 7.3. , , (..).

A ~ . Em, S ~ Hm, { ~ ~ , E, H, { . , = j, 0 = j.

~ ~ ~ rot ( F) = rot F + grad F j z e e;j z ~ ~ rot Em + j ~ Em = j! Hm z0 ~ 0 ~ ~ rot Hm + j ~ Hm = ; j!"0Em z0 ~ ~ ~ rot E ; j ~ E = ; j! H z0 ~ ~ ~ rot H ; j ~ H = j!" E:

z0 ~ ; A = ^ ; A "0 ; A " = " ; A:

^ , , ~ ~ ~ ~ ~ ~ ~ ~ div (Em H) + div (E Hm) = H rot Em ; Em rot H + ~ ~ ~ ~ + Hm rot E ; E rot Hm:

rot , ~ ~ ~ ~ ~ ~ div (Em H) + div (E Hm) = H(j! Hm ; j ~ Em) ;

z0 ~ 0 ~ ~ ~ ; Em(j!"E + j ~ H) + Hm(;j! H + j ~ E) ;

z0 ~ ~ z0 ~ ~ ~ ~ ~ ~ ~ ; E(;j!"0Em ; j ~ Hm) = ; j!Hm( ; )H ; j!Em(" ; "0)E ;

z0 ~ 0 ~ ~ ~ ; j( ; )Em(~ H) ; j( ; )E(~ Hm):

z0 ~ z0 . . Z ~ ~ ~ ~ 0 = ; ! [Hm ( ; ) H + Em (" ; "0) E] dS + S Z ~ ~ ~ ~ + ( ; ) [Em H + E Hm] ~ dS zS , , ; = 0 " ; "0 = 0 6 A, R ~ ~ ~ ~ [Hm ( ^ ; ) H + Em (" ; "0) E] dS ^ A = + ! :

R ~ ~ ~ ~ [Em H + E Hm] ~ dS zS , ~ ~ E H. , .

, : H11 , , . .

2b , ~ ~ ,.. H Hm, ~ ~ E Em, , . :

2a Z Z ~ ~ ~ ~ ~ ~ ~ ~ (Em H + E Hm) ~ dS (Em Hm + Em Hm) ~ dS = z0 zS S Z Z ~ ~ = 2Re (Em Hm)~ dS = jEm j2 dS zZm S S j! ! 0 Zm = = | 0 .

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