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(x y), ( e; z ):

2 n m n m Hz = (k2 + g2) (x y) = + cos x cos y a b a b @ n n m n n m Hx = ; = sin x cos y = j sin x cos y @x a a b a a b @ m n m m n m Hy = ; = cos x sin y = j cos x sin y @y b a b b a b @ m n m Ex = ; j! = j! cos x sin y @y b a b @ n n m Ey = j! = ; j! sin x cos y:

@x a a b , a > b.

. , , n m . . , a > b, H10:

= 2a:

. , , .

H10 :

Hz = cos x a a Hx = j sin x a a Hy = Ex = Ey = ;j! sin x:

a a , . , , .

H10 (..):

y Hx yE y 000000000000000000000000000 111111111111111111111111111 E y 000 111 111 Hz 111 x x , Hz Hx 90o. .

Hn0 n- H10 x.

Hn0 , y. , , , b:

= 2 a=n n = 1 2 : : : :

n H10. , .

H11. y (..).

, , Ez.

Hnm n- H11 x m- y.

. ~ ~ K = H ~ n ~ { , . n, , , .

H10 (.. ..).

H11 H10. Hnm , H11, n m .

, H10. . :

Z Z 1 ~ ~ P = Re (E H ) ~ dS = Re (ExHy ; EyHx ) dS:

z2 S S H10 Ey Hx:

Ey = ; Aj! sin x a a Hx = Aj sin :

a a Ey Hx , ! b P = A4 a :

s 2 P a A = :

! b E0:

s EP = ab 1 ;

p = =".

3.2.2. E- , , @2 @+ + g2 = @x2 @y =0.

(x y) = X(x) Y(y):

X Y X = A cos gxx + B sin gxx Y = C cos gyy + D sin gyy:

. , x = 0 X = 0, , A = 0 X = sin gxx y =0 Y = 0, C = 0 Y = sin gyy x = a X =0,.. sin gxa = 0, n gxa = n gx = n = 0 1 2 : : :

a y = b Y = 0,.. sin gyb = 0, m gyb = m gy = m = 0 1 2 : : : :

b (x y) n m (x y) = sin x sin y:

a b , n m , .

, 2 n m gnm = + n = 1 2 : : : m = 1 2 : : : :

a b ( ):

2 2 = = s s :

= nm 2 2 2 gnm n m n m + + a b a b :

Hz = @ m n m Hx = j!" = j!" sin x cos y @y b a b @ n n m Hy = ;j!" = ; j!" cos x sin y @x a a b 2 n m n m Ez = (k2 + ) (x y) = + sin x sin y a b a b @ n n m Ex = ; = ; j cos x sin y @x a a b @ m n m Ey = ; = ; j sin x cos y:

@y b a b n m , E11, 2 2ab = s = p :

2 a2 + b1 + a b H10, 2a.

, gnm nm . , .

E11 Hz = Hx = j!" sin x cos y b a b Hy = ;j!" cos x sin y a a b 2 Ez = + sin x sin y a b a b Ex = ;j cos x sin y a a b Ey = ;j sin x cos y:

b a b E11 (..).

y y y 00 11 00 11 00 11 00 11 00 00 11 11 00 11 00 11 00000000000 11111111111 00 00000000000000000000 11 11111111111111111111 00 11 00000000000 11111111111 x x 00 00000000000000000000 11 11111111111111111111 00 11 00000000000000000000000 11111111111111111111111 x 111111111111 E E z y E x y b x a E11.

. E- , , , (..).

3.3. 3.3.1. :

1 @ @ 1 @ = r + :

xy r @r @r r2 @' , @2 1 @ 1 @+ + + g2 = 0:

@r2 r @r r2 @' . , = R(r) ('):

R, 1 d2R 1 dR 1 d+ + + g2 = 0:

R dr2 rR dr r2 d' :

1 d= ;

d'1 d2R 1 dR + ; + g2 = 0:

R dr2 rR dr r d+ = 0:

d' sin ' = :

cos ' ', ' =2 2 = 2 m m = 0 1 2 : : :

= m m .

R d2R 1 dR m+ + (g2 ; ) = 0:

dr2 R dr r . Jm(gr) Nm(gr). , ( r = 0). R = Jm(gr):

@ = 0 .

@n @ @ =. , @n @r Jm(ga) = a { .

t0 :

mn gmna = tmn t0 mn gmn = n = 1 2 : : : :

a , . mn cos m' = Jm(gmnr) :

mn sin m' , gmn , m = 0,.. .

, . ~ H = ; grad + g2 ~ z~ E = ; j! grad ~ z0:

, @ 1 @ 1 @ @ grad ( ) grad ~ ( ; ), z@r r @' r @' @r cos m' 0 Hz = gmn 2 Jm(gmnr) sin m' @ cos m' 0 0 Hr = ; = ; j gmn Jm(gmnr) sin m' @r @ j m sin m' H' = ; = Jm(gmnr) cos m' r @' r j! @ j! m sin m' Er = ; = Jm(gmnr) cos m' r @' r @ cos m' 0 0 E' = j! = j! gmn Jm(gmnr) :

sin m' @r 2 2 a = = :

mn gmn tmn t0. mn H11, t0 1:84. J1 (t) =0 (. 1).

m = 1 n = 1 H11, H10 . 1: Jm (t) = 0.

m 0 1 2 3 4 n 1 3.83 1.84 3.05 4.20 5.32 6.2 7.016 5.33 6.71 8.01 9.286 10.3 10.17 8.53 9.972 11.355 12.68 13.cos ' 0 Hz = g11 2 J1(g11 r) sin ' cos ' 0 0 Hr = ;j g11 J1 (g11r) sin ' j sin ' H' = J1(g11r) cos ' r j! sin ' Er = J1 (g11r) cos ' r cos ' 0 0 E' = j! g11 J1 (g11r) :

sin ' H11 .

HH E , H11 . , 90o. , , . H11 -.

, . . , (.

.), .

Hm1 H11 (..).

H1n (..).

Hmn m> 1, n > 1 . , H01 (n =1).

0 Hz = g01 J0(g01r) 0 0 0 0 Hr = ;j g01 J0(g01 r) = j g01J1 (g01r) H' = Er = 0 0 0 0 E' = ;j! g01 J0(g01r) = j! g01 J1 (g01 r):

.

E H , . , (..).

H01 , .

H01 (, ). , H01 .

3.3.2. , , ,..

cos m' = Jm(gr) :

sin m' = 0 r = a..

Jm(ga) = a { . m- tmn:

gmna = tmn tmn gmn = n = 1 2 : : : :

a cos m' = Jm(gmnr) :

mn sin m' , m =0 .

E-:

Hz = j!" @ j!"m sin m' Hr = = Jm(gmnr) cos m' r @' r @ cos m' H' = ;j!" = ; j!" gmnJm(gmnr) sin m' @r cos m' 2 Ez = gmn = gmnJm(gmnr) sin m' @ cos m' Er = ; = ; j gmnJm(gmnr) sin m' @r @ j m sin m' E' = ; = Jm(gmnr) :

cos m' r @' r E01 :

Hz = Hr = H' = ;j!" g01J0(g01r) = j!"g01J1 (g01r) Ez = g01J0(g01r) Er = ;j g01J0(g01r) = j g01J1 (g01r) E' = 0:

.

E E0n .

E11 (..).

Jm(x) 2.

2: Jm (t) = 0.

m 0 1 2 3 4 n 1 2.40 3.83 5.14 6.38 7.59 8.2 5.52 7.016 8.42 9.76 11.06 12.3 8.65 10.17 11.62 13.015 14.3.3.3. TEM- , .

H- . - @2 1 @ 1 @+ + + g2 = 0:

@r2 r @r r2 @' . , R(r) d2R 1 dR m+ + (g2 ; ) = 0:

dr2 R dr r (r =0) , Jm(gr) Nm(gr):

R = A Jm(gr) + B Nm(gr):

dR = dr 0 r = a r = b (b > a),..

0 A Jm(ga) + B Nm(ga) = 0 A Jm(gb) + B Nm(gb) = 0:

A B 0 0 0 Jm(ga) Nm(gb) ; Jm(gb) Nm(ga) = 0:

gmn, . a mn b=a (..).

2 a 2 b .

, Jm(ga) Nm(gb) ; Jm(gb) Nm(ga) = 0:

.

H11, a + b .

, . .

3.4. . , . , .

. , .

, , (..).

, , , , , H .

(..) H11 H01 E (..) H , (..).

a , , . { { (..).

, , { (..).

.

.

. , , .

, , (..). , , .

(..) Z1 = j!L Y1 = j!C1 + :

j!L s p = Z1Y1 = j!L j!C1 + = j!L s = !L ; !C1 :

!L , 1 ; !C1 < 0 :: ! > p = !:

!L LC , s s 1 = j !L !C1 ; = j! LC1 1 ; :

1 !L !2LC1 1 = !, LC1 =.

LCc , r ! ! = j 1 ; = j :

c ! 2 = = s = s 2 ! ! 1 ;

1 ;

c !.. , .

- (..).

b2a b g h "0S1 "0a C1 = = g g L = S = bh (l =1) 0 1 g gc! = = = :

"0a "0 abh abh bh g s 2 c abh = = 2 :

! g , , g, .

, . { , .

: H10 (..).

a a = ! = 2a :

2 3.5. , :

Z ~ ~ P = Re (E H ) ~ dS:

zS H-. ~ E = ;j! grad ~ e; z z~ H = (; grad + g2 ~ e; z:

z0) , ~ ~ (E H ) ~ = j! [(grad ~ grad ] ~ e; z e; z = z0 z0) z= j! (grad )2 e; ( + )z :

, Z P = Re j! (grad )2 e; ( + )z dS:

S < { : = j, = ;j. Z Z 1 2 P = ! (grad )2 dS = ! gm dS:

2 S S > { . P =0.

E- () Z 2 P = !" gm dS < :

S , ~ , E ~ H . , , . .

. H- "jEj2 " = (! )2 (grad )2 jHj4 2 = fgm + (grad )2g:

2 , .

, (.. ) . , Z Z Z "jEj2 " " 2 We = dS = (! )2 (grad )2 dS = (! )2 gm dS 2 2 S S S Z Z Z jHj 4 2 Wh = dS = gm dS + (grad )2 dS = 2 2 S S S Z Z Z 4 2 2 2 2 2 2 2 = gm dS + gm dS = gm(gm + ) dS:

2 2 S S S 2 2 2 gm = k2 + = k2 ; = !2 " ; :

Wh, Z Z " 2 2 2 Wh = gm!2 " dS = (! )2 gm dS:

2 S S , Wh = We.

{ , ( H-) ( E-) , .

3.6. ( ):

f c v = f = s = s > c:

2 1 ; 1 ;

, , , , .

. .

n o j( !1 t; z) j(!2 t; z) j(!1 t; z) j[(!2 ;!1 )t ; ( ; )z] 1 2 1 2 e + e = e 1 + e :

(!2 ; !1 ) t ; ( ; ) z = 0:

2 , ! t z, ! t = z = dz d! v = = dt d ! v =.

d! v = = :

d d =d! s s 2 2 2 = = 1 ; = ; 1 = s 2 ! = ; 1 :

! 2!=! d 2 2 ! = s = s = 2 d! ! ! ! 2 ; 1 ; ! ! 2 1 1 = s = s :

2 ! c ! 1 ; 1 ;

! s v = c 1 ; < c:

, (..):

v v = c2:

v c :

v p P v = W kp P { , W { .

, ( H-) Z 2 P = ! gm dS S Z " 2 W = (! )2 gm dS:

S P v = = :

W ! " , , ! v = :

!= v, v v = = c2:

" , , .

3.7. .

, . .

, H10 8 x x > > < j ; z ;j + z = j! x j! a a Ey = ; sin e;j z = ; e ; e a a 2a > > :

.

H10 . , ( ) (..).

, , z. , z =cos, =sin.

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