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x z , . , a, , . , = a sin = :

2 2a , , < 2a :: = 2a:

z:

= = p = s :

cos 1 ; sin1 ;

, , ,.. .

s p v = c cos = c 1 ; sin2 = c 1 ; :

Hmn Emn , z.

, . , .

3.8. , . . , , , . -.

. , ~ 0 ~ Em e; z, Hm e; z. : E e; z, H e; z. , . , .

, :

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

z0 ~ = ;, { .

0 ~ ~ ~ ~ div (Em H) + div (E Hm) = ~ ~ ~ ~ ~ ~ ~ ~ = H rot Em ; Em rot H + Hm rot E ; E rot Hm = ~ ~ ~ = H (j! Hm ; ~ Em) + Em (j!"0E + ~ H) ;

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

:

I Z ~ ~ ~ ~ ~ ~ ~ ~ (Em H + E Hm) ~ = ( ; ) (Em H + E Hm) ~ dS ndC zC S H ~ ~ ~ ~ (Em H + E Hm) ~ ndC C = + R :

~ ~ ~ ~ (Em H + E Hm) ~ dS zS ~ { , , C { n , S { .

I ~ ~ (Em H)~ = ndC C ~ Em.

, , ~ ~ ~ Et = (H ~ (Hm ~ n) n) C. , .

I I I h i ~ ~ ~ ~ ~ (E Hm)~ = (Hm ~ Hm ~ = jHmj2 dC:

ndC n) ndC C C C ~ ~ ~ E H Em ~ Hm:

Z Z ~ ~ ~ ~ ~ ~ ~ ~ (Em H + E Hm) ~ dS (Em Hm + Em Hm) ~ dS = z0 zS S Z ~ ~ = 2Re (Em Hm) ~ dS :

zS , H ~ jHmj2 dC C + R :

~ ~ 2Re (Em Hm) ~ dS zS :

H ~ Re jHmj2 dC C = R ~ ~ Re (Em Hm) ~ dS zS H ~ Im jHmj2 dC C = R :

~ ~ Re (Em Hm) ~ dS zS , 1 + j = I ~ P1 = jHmj2 dC | C Z ~ ~ P = Re (Em Hm) ~ dS | zS , P1 = = :

2P P1 P1 = = 2P 2vW Z ~ W = jHmj2 dS | S s v = c 1 ; | .

, :

H H ~ ~ jHmj2 dC jHmj2 dC 1 C C = s = s :

R ~ 2 2 c R 0 jHmj2 dS ~ 2 jHmj2 dSc 1 ; 1 ;

S 2 S = :

! , H ~ jHmj2 dC C = = s :

R ~ 2 0 jHmj2 dS 1 ;

S , . , . :

) , ) .

, . H ~ ~ ~ ~ (Em H + E Hm) ~ ndC C = + R :

~ ~ ~ ~ (Em H + E Hm) ~ dS zS . ~ Hm = ~ Em:

z0 ~ j! . ~ ~ H Hm , . ~ ~ , H E , :

~ H = ~ E:

z0 ~ j! ~ ~ E Em :

H ~ ~ ~ ~ j! (Em H + E Hm) ~ ndC C ; = = R ~ ~ ( jEmj2 + jEmj2) dS S H ~ ~ ~ ~ j! (Em H + E Hm) ~ ndC C = R :

~ ( + ) jEmj2 dS S +, H ~ ~ ~ ~ j! (Em H + E Hm) ~ ndC C 2 ; = :

R ~ jEmj2 dS S . = 0. . , .

.

.

3.8.1. . H10{ x Hz = cos a a j x Hx = sin a a Hy = 0:

x x jHj2 = cos2 + sin2 :

a a a a ( ) Z 4 2 a a ab jHj2 dS = b + = + = 2 a 2 a 2 a a S ab 4 = 2 a 4 2 + = g2 + = k2 = :

a " # I 4 4 a 4ajHj2 dC = 2 b +2 + = 2b + = a 2 a a a C ! = 2b + a :

a , 2b + a a = s = 2 0 ab 4 1 ;

2 a 2b 1 + a = s :

b 0 1 ;

: 10 23 2, . = 3 , =, b = 1 , a =2:3 , =4:6 , 0:64 10;4 , f =1010.

;

2 1 + 0:64 10; 2:3 4: = q 1:14 10; 4 = = ;

1 1 ;

4:= 9:9 10;4 = = 9:9 10;2 =:

.

kp 3.8.2. . H0 Hz = g01 J0(g01r) 0 Hr = j g01 J1 (g01 r) 0 E' = ;j! g01 J1 (g01 r):

z- (Hz = 0), I 0 2 jHj2 dC = 2 a g01 J0 (g01a):

C R , jHj2 dS S R jEj2 dS, E :

S Z Z Z "0 "0 2 0 2 2 jHj2 dS = jEj2 dS = !2 g01 J1 (g01r)2 r dr = 0 S S S a Z 2 !0 2 = g01 J1 (g01r)r dr:

c a Z a2 0 2 J1 (g01 r)r dr = J0 (g01 a):

, Z !0 2 jHj2 dS = g01 a2 J0 (g01 a):

cS ( = ):

0 2 1 2 a g01 4 J0 (g01a) = s = 2 2 !0 2 g01 2a2 J0 (g01a) 2c 1 ;

2 c = s :

a 1 ;

, 3=2 1= ( ). , , .

, , , .

, P = :

2vW Z P1 = jEj2 dS S { . Z " W = E2dS S ! tg tg = = s = s 2v" 2 2c 1 ; 1 ;

2 =tg.

!" 4. 4.1. . .

, , . .

, , j z e.

( ). , , (.

.).

, , , . , . , .

, . : , - . , .

;, :

b ; = a a b { . , ():

jaj + jbj = :

jaj ; jbj , , . . , . , @ @ (Ey = ;j!, Hx = ;j ).

@x @y ;1.

\ " .

, . , = 1. , =4 , .

, , TEM-, . . , TEM-.

4.2. H- ~ ~ rot E = ;j! H ~ ~ rot H = j!"E:

. H- (, Ez =0 H ) ~ ~ E = E = V(z) ~(x y) e ~ ~ ~ ~ ~ H = H + Hz = I(z) h(x y) + Hz ~ ~ h e .

, ~ [rot (V ~ )] = ; j! I h:

e , rot(V ~ ) = V rot ~ + grad V ~. e e e dV . grad V = ~ z0, dz dV ~ ~ ~ = ; j! I h:

z0 e dz ~ h:

dV ~ (~ h) ~ = ; j! (~ I:

e z0 h)dz :

dI ~ (~ h) + [rot Hz] = j!"V ~ z0 ~ e dz ~ h = ; grad, rot~ =0.

h ~ , rot Hz . , ~ Hz = gm ~ e; z z~ E = ;j! rot ( ~ e; z ) z j! ~ ~ E = ; rot Hz gm 2 gm ~ gm ~ rot Hz = ; E = ; V ~ e:

j! j! ~ e, dI gm ~ (~ h) ~ = ; + j!" ~ V:

e z0 e dz j! S. .

Z Z 1 ~ ~ ~ P = Re (E H ) ~ dS = Re V I (~ h) ~ dS:

z0 e z2 S S ~ ~ h , e Z ~ (~ h) ~ dS = 1:

e zS , Z 1 C1jVjjVj2 "~ dS = We = | e 2 S . Z C1 = "~ dS | e S . Z 1 LjIj ~ Wh = jIj2 h2 dS = | 2 S , Z ~ L = h2 dS | S . C1 L , dV dI V = ; j!LI = ; j!C1 V ; :

dz dz j! "=gmC " = = L | 2 gmC1 !mC1 .

dV = ;j!LI dz dI = ;(j!C1 + ) V:

dz j!L H- .

E- ( L C1 ).

, Z1 = j!L Y1 = j!C1 + :

j!L , . , , . . Z1 Y1 , (.. ), ,.. , . , . , ( H10) .

I . :

P = jIj2 ZI :

Z Z 1 1 x x P = Ex Hy dxdy = A! sin A sin dxdy = 2 2 a a S S ab = A2! :

a a Z Z x 2a I = Hx dx = A sin dx = A :

a 0 p 2 2P b ! b =" ZI = = = q :

jIj2 8 a 8 a 2 1 ; = :

p jUj2 b =" ZU = = 2 q :

2P a 2 1 ; = 4.3. () , (..). , , I ~ ~ (EH )~ = P + 2j! (Wh ; We ):

ndS S , , , .

~ ~ E H , U I = P + 2j!(Wh ; We ):

.

4.3.1. :

U I Z = Y = :

I U . , U = ZI, jIj2Z = P + 2j! (Wh ; We ) P + 2j!(Wh ; We ) Z = = R + jX:

jIj , I = Y U, P + 2j!(We ; Wh ) Y = = G + jB:

jUj Z (j!) + Z(;j!) Z (j!) = Z (;j!) R = Re Z = Z(j!) ; Z (;j!) X = Im Z = 2j Y(j!) + Y(;j!) Y (j!) = Y(;j!) G = Re Y = Y(j!) ; Y(;j!) B = Im Y = :

2j , R G { , X B { . :

1. R 0, P 0.

2. P =0, Z { .

3. Wh ; We = 0, X = 0 B = 0, .

4.3.2. . a b. b ; = :

a 1 P = jaj2 P = jbj2:

2 , { , U = p(a + b) = pa(1 + ;) 1 I = (a ; b) = a(1 ; ;):

p p p 1=p . U 1 + ;

Z = = p2 :

I 1 ; ;

; =0 Z = Z0, p2 = Z0.

;, Z ; Z; = :

Z + Z , .

, ,.., , . 1 + ; z ; z = ; = :

1 ; ; z + { .

p, U I, (1 + ;)(1 ; ; ) jaj2 = P + 2j!(We ; Wh ) P + 2j!(We ; Wh ) (1 + ;)(1 ; ; ) = jaj , P 1 ; ; ; = jaj2j!(We ; Wh) (; ; ; ) = :

jaj P 0, ; ; 1 j;j 1. ;:

p j' ; = 1 ; P0 e Im ; P sin ' = P0 = :

j;j jaj4.4. , , .

N . S, , (..). S X Un In = P + 2j! (Wh ; We ) n P { , Wh We { , n { .

4.4.1. X Un = Znm Im:

m Znm Z = fZnmg .

U = ZI U (U1 U2 : : : UN ) I (I1 I2 : : : IN ) { . :

I = Y U Y = fYnmg { . , Y = Z; 1.

UI = P + 2j! (Wh ; We ) , U = ZI, I ZI = P + 2j! (Wh ; We ):

4.4.2. () . .

, V . , , 2.

~ ~ ~ ~ ~ ~ ~ ~ div (E(1) H(2)) ; div (E(2) H(1)) = H(2)rot E(1) ; E(1)rot H(2) ;

~ ~ ~ ~ ; H(1)rot E(2) + E(2)rot H(1) ~ ~ ~ ~ ~ ~ ~ ~ ;j!H(2) H(1) ; j!E(1)"E(2) + j!H(1) H(2) + j!E(2)"E(1) , " { 1.

, ~ ~ ~ ~ div (E(1) H(2)) ; div (E(2) H(1)) = " , , .

.

V, S, ( ):

I ~ ~ ~ ~ fE(1) H(2) ; E(2) H(1)g ~ = 0:

ndS S S , , , . , :

X (1) (2) (2) (1) [Un In ; Un In ] = 0:

n n { . , .

:

U(1) I(2) ; U(2) I(1) = 0:

U I { () . , U = ZI:

, I(2) ZI(1) ; I(1) ZI(2) = 0:

, I(1) ZT I(2) ; I(1) ZI(2) = ZT { . I(1) I(2), , ZT = Z,.. Z . , , " , . Z .

Y.

4.4.3. , .

, , ( ) .

X 1 I ZI = InZnmIm = P + 2j! (Wh ; We ):

2 n m P =X InZnmIm = 2j! (Wh ; We ) n m.. . , Znm . , , , ,.. In = 0, Ik = 0. :

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