Документ взят из кэша поисковой машины. Адрес оригинального документа : http://shg.phys.msu.ru/educat/vinogradov/Lesson7-8.pdf Дата изменения: Wed Mar 12 16:11:35 2008 Дата индексирования: Mon Oct 1 20:47:47 2012 Кодировка:

. , D(t ) () , .. . . , , , , , t D(t ) = E = (t - t ) E (t )dt = ( ) E (t - )d
- 0

D( ) = ( ) E ( ) ( ) = ( )ei d
0

= + i =| | e

i


D(t ) = E =

-



t

(t - t ) E (t )dt = ( ) E (t - )d
0




D( ) = ( ) E ( )

= + i =| | e

i

( ) = ( )e d
i 0



( -) = (
*

)

( -) = (

) )

( -) = - (


. ( . . . « » . 1976 ). . x ( t ) = g ( t - t ) F ( t)
-

F (t ) -- , F = F ( )e - i d
-

g ( t - t ) =



-



G e

- i ( t - t )

d

--



x = F G


, < 0 g ( ) = 0 .

-



t

F (t ) x(t )dt > 0

·

, . ,
1 2 mx + m x + m0 x(t ) = F (t ) 2
·· ·

(2)

, t -


t , (2) x(t ) - t :

-



t

F (t ) x(t )dt = E (t ) + 2m

·

-



t

x (t )dt

· 2

, . ( > 0 ) ,
-



t

F (t ) x(t )dt > 0
, t.

·

1 ·2 1 2 E (t ) = m x + m0 x 2 (t ) 0 2 2
E ( - ) = 0


, t - , , . x(t )
F (t ) t > 0 F (t ) = 0 t<0 ,

x(t ) t > 0 x(t ) = 0 t<0


F1 ( t

)

, , F1 ( t ) 0 t < 0

x1 (t ) . ,
, · · ) + F (t ) ) ( F1 (t ( x1 (t ) + x(t ) ) , t < 0
-
-



t

F1 (t ) x1 (t )dt > 0

·

[

t

· · F1 (t ) + F (t )] x1 (t ) + x(t ) dt = =

-



t

F1 (t ) x1 (t )dt +

·

-



t

F1 (t ) x(t )dt 0

·


t < 0

-



t

F1 (t ) x1 (t )dt + F1 (t ) x(t )dt 0
-

·

t

·

, -- , , t < 0 . F1 ( t ) , , t < 0 x(t ) 0. t - , x(t ) 0 t < 0 .
F (t
·

)

t <0

= 0 x(t ) 0 t < 0


-
( x) 1 ( x) - 1 ( ) - 1 = P dx, ( ) = P dx - x - - x -

1



y = -x

( x) 1 ( x) ( ) - 1 = P dx = dx + - x - 0 x -

1



-



0

( x) x -

dx =

1 ( x) (- y ) 1 ( x) ( y ) dx + dy = dx + dy = = y + 0 x - -y - 0 x - 0 0 2 x ( x) dx, = 2 2 0 x -

( -) = - (

)


0 1 ( x) - 1 dx + ( ) = - x - 0 1 (- y ) - 1 dy + = 0 -y - 1 ( y ) - 1 dy + = - 0 y +

( x) - 1 dx = x -



0

( x) - 1 dx = x - ( x) - 1 dx = x -




0

1 1 = ( ( y ) - 1) - dy = 0 y - y + 2 ( y ) - 1 = y 2 - 2 dy 0 1




. G ( ) , : 1. g ( t ) G ( ) t < 0 2. G ( u ) u v 0 + G ( u +,iv , : +

)

3. 4. Re G , Im G :
Re G ( ) = 1


-

G(

u + iv

)

2

du < C




P

-



Im G ( x) 1 dx, Im G ( ) = 1 - P x -

-



Re G ( x ) - 1 dx x -


, ( ) = 0 1 2 >> 1 ,

) 2 2 ( ) - 1 = P 2 dx = 2 0 x -


x ( x

1


0

2 dx + 2 2 x -

x ( x

)



2



x ( x
2

)
2

x -

dx

1 << << 2 , x < 1 << , , << 2 < x . . 1 2 x ( x ) 0 2 2 ( x ) ( ) - 1 = - dx + dx = 0 - 2 2 0 2 x

0 = 1 +

2 ( x )dx / x 2



2 = x ( x )dx 0
2 0

1


( ) - 1 =

2






0

x ( x) dx, 2 2 x -

, 0
2 ( x) (0) - 1 = dx > 0 0 x


(0) > 1

, , , , -1 , 1 - 1 > 0 1 > (0) (0)


.
i ln r = ln R ( ) + i ( ) r = R ( ) e ( ) r . . . « » . 1976.

( ) = ( ) =
2


2






0

ln R dy 2 2 y -




0

y + d ln R dy ln y - dy

, .



1 1 rot E =- B =- rot A c t c t

1 rot E + A = 0 c t

E+

1 A = - c t B = rot A

1 A = -4 c t 1 1 4 2 A- 2 A - A + j =- c t c t c , . 2 +


,
= - 1 c t

A A = A +

1 + 2 =0 c t
2

.

1 A+ =0 c t

1 2 2 - 2 2 = -4 c t 1 2 4 2 j A- 2 2 A = - c t c




A = 0

2 = -4
1 1 4 A- 2 A = j - c t c t c
2

x, t ) 1 1 t ( 4 1 ' j ( x, t ) 3 4 3 ( x, t ) = - d x = d x = jl c t c | x - x | c 4 | x - x | c j ( x ') 21 2 j =- (1/ | x - x |) = -4 ( x - x ) | x - x |d ( x ') 4
в = ( ) -
j = jl + jt
2

j ( x, t ) 3 1 jt ( x, t ) = d x вв 4 | x - x |


, j


,
= 4jl t 1 4 2 A- 2 A=- jt c t c

jt , , , "" , , . , , , .


.

, , . . . . , , .


. . , , , . , dS ( dS n , , ) dq = jdtdS = jndtdS jn dtdS = dS = Pn , , dP = = ( jdt ) cos ds


, . 4 E = Eext - P. 3 4 j = Eext - P 3
= Eext - t P 4 P = Eext - t 3 1 P= E0 = (1 - i) ( 4 / 4 3 P cos P (t = 0 ) = 0





= Pn = P cos

P (t ) = 1 - e

{

- t ( 4 / 3)

}

E0

1 E0 3) (1 - i)

= 1/ ( 4 / 3

)


[ (1863-1906) ]

, . , , l. , , , , . , .
8kT 8 в 1.38 в 10-23 в 300 < v >= = 105 m (T = 300 K ) s m 3.14 в 0.91в 10-30


. ,

j = ne < u >
107 A 1029 m
-3

m

2

j 107 < u >= en 1.6 в10-19 в10

29

10-3 m

s


, , . u . eE m
u
max

eE = m

l = vcp

u eEl ne 2l ne 2l < u >= j= E = 2mvcp 2mvcp 2mvcp


. t p (t ) t+dt . , dt / , (1 - dt / ) . f(t) f(t)dt. . . dt ( p (t ) + f (t )dt ) = p (t ) - dt p (t ) + f (t ) dt + O ( dt 2 ) p (t + dt ) = 1 -

(

)

p (t + d t ) - p ( t ) d p p (t ) = =- + f (t ) dt dt


E (t ) = Re ( E ()e

- i t

)

p (t ) = Re ( p ()e

- i t

)

p () -ip () = - - eE ()

j () =- nep ()

m E () = m 1 - i

(

ne

2

)

0 ne 2 () = , c 0 = ( 0) = 1 - i m

l = v<<


0 ne 2 () = , c 0 = ( 0) = 1 - i m 40 4 , () = p + i = p + i (1 - i )
() = p + i 40 (1 + i 1 + (

(

)

2

)

)

= p -

(1

40 + (

)

2

)

+i

1 + (
0

(

4

0

)

2

)

() = p -

(1

40 + (

)

2

)

,

() =

1 + (

(

4

)

2

)

l = u<< = 2c / << c / u
0 4ne 2 >> 1 () = p - 2 c p = = m 40 () = p - 4 0 , () = << 1 2 p


l = u<< = 2c / << c / u
>> 1
p =
0 4ne () = p - 2 c p = = m 2 p
2

1 = 2 = 1018-30 = 2.510 p 36
() = p - 4 0 ~ p - 3 105 , 40 1018 () = ~ f (1010 ) ~ 10
8

-14

<< 1


,

d2 d m 2 r - b r + ar = eE dt dt

P=



eri i

Ne 2 d2 bd a P- P+ P = E 2 dt m dt m m
P= Ne m
2 2

b - +i m (4Ne 2 ) m = 1 + 4 = 1 + b 2 2 0 - + i m
2 0

E


Elocal =< E > +

4 P 3

Ne 2 d2 bd a P- P+ P = E 2 dt m dt m m

d2 d 4 2 P - P + 0 P = f E + 2 dt dt 3

d2 d 4 2 P 2 P - P + 0 - f P = fE dt dt 3

4 2 2 0 0 - f 3

2 4 e 2 N = 0 - 3m


, - dis d P dt 2e 2 d 3 P - 2 3 3mc dt . , 2 3 p - 3c3 t 3

Elocal
d2 P - 2 dt d2 P - 2 dt

4 2 3 p P- =< E > + 3 3 t 3

dis

2 4 Ne 2 d 2e 2 d 3 P- P - 0 - P = 2 3 3mc dt 3 m dt 4 2 d3 Ne 2 = P- p E+ 3 3 3 dt m

dis

2 4 Ne 2 d Ne 2 P - 0 - E P = 3 m dt m






(Salisbury Screen)

, .

/4



, , .


, . . . , . . 180°.


n
Z
( 0)
input

Z

n +1) input

(

=

Z

(n)
input

- iZ n tan ( kd
( n)
input

Z n - iZ

tan

) ( kd )

Z

n

=0

Z

(1)
input

=-iZ 0 tan ( kd
sheet

)

2 = tan = Z tan ( kd ) = tan 4 2
Z
( 2)
input

<< Z

1 input

=

Z Z

(1)
input sheet

- iZ - iZ
d

sheet (1) input

tan ( k tan ( k

sheet sheet

d d

sheet sheet

) )

Z

sheet

Z sheet i tan ( k sheet d
k
sheet

sheet

)

k

sheet

sheet

<< 1

tan ( k

sheet

d

sheet

)

d

sheet

Z

( 2)
input

i

Z k

sheet

sheet

d

=i

1/ k0 d
sheet

sheet



=

( / c )

i d
sheet

(

c = i 4 / ) 4 d

sheet


R=

Z Z

( 2)
input ( 2) input

c =0 4 d +1

-1

=1
sheet

= 377 ohms
=



propagation

=

d

sheet

c

=

1 4

maxwell




The inherent problems of the Salisbury Screen are poor flexibility, poor environmental resistance and increased thickness, especially at lower frequencies. To diminish the thickness we can put a dielectric material with high permittivity in between the metal surface and conducting sheet. Unfortunately, this restricts the working range. We need use material with proper frequency dispersion. This means that inside the layer there should be losses. A good idea is to use semi-transparent system in order to build up a resonance sheet lying on the metallic substrate.




. . ( ): 0.25 d = cos( )
0



d=


4n
i

, kdn =


2

.

n = n + in = , = + i =| | e

( n << 1 kdn = kdn + ikdn =

)


2

+ i ,

n n = kdn = << 1 n 2 n


metal - i tan ( knd ) in = - i tan ( nkd + i metal tan ( knd ) 0
metal

)

1 - in 1 + i tan ( knd = r= 1 + in 1 - i tan ( knd

) )

1 n + in - 1 / tan(knd ) - , R i n + in + 1/
kdn = /2

n = 1/ = 1/ ( kdn 1 2 n = =, kdn

)


1 2 n = =, kdn

n + in - 1/ R= n + in + 1/ n >> i | r | n

in i 2n + in n + i 1

>> ,

= n2 - n2 + 2inn = 2nn / ( n2 - n2 ) 2n / n n , n = 2 / = 2n / n 4 / n = 4 / = /4

= << 1 , = << 1 | |

2

r i


4

!!!


. , , in =-i tan ( nkd -i tan ( nkd ) = 1

)

in = 1



k , , d , -i tan ( nk d ) = 1
2


-1

tan ( nk d ) = 2 =- 2tan ( knd ) i d) = sin ( 2kn =2 2 1 + tan ( knd ) - 1
(k - k ) tan ( knd ) = tan ( k nd ) + cos 2 ( knd 1 = -i tan ( nk d ) tan ( knd ) - tan ( k nd r= tan ( knd ) + tan ( k nd

k k 1 + i tan ( knd ) r= 1 - i tan ( knd )

)

(k - k ) 2 2 - 1) d) cos ( kn ( (k - k ) r = = (k - k ) 2tan ( knd ) sin ( 2k nd )

) )




,

( - ) ( - r 2 d

)

r ( - ) = 2 d ( -

)


kdn =


2

n =


4d
-2 0

= const , ~ 02 ~

R=

1- / - exp(-2i d ) 1+ / 1- / 1- exp(-2i d ) 1+ /
-1

2

,
-2

k d =


2

, =

4



>>




. . ^ +i r= ^ -i ^ tan(knd ) ^ tan(knd )
| knd |<< 1

^^ n =

^ ^ + i (k r= ^ ^ - i (k

^ d ) 1 - ikd = ^ d ) 1 + ikd


1 - ikd 1 + ikd - kd = r= 1 + ikd 1 - ikd + kd
ikd ikd r= 2 - ikd 2 kd = kd



kd 1,
1

kd << 1 r

d= = k 2

<< 1



<< ,

and



-




~

= - i , = - i
= = - i , = = - i kd = 2 d = 2
d d
^ ^ + i tan(knd ) r= ^ ^ - i tan(knd )

tanh 2 i = 1

(

)




2 i << 1 / 4

tanh 2 i 2 i

(

)

, !!!

tanh 2 i = 2 i = 1 + 2 R

(

)

. d d d - i | R | 0.05 = = 2 = -i (1 + 2 R )







0.9 2

d



1.1

|2

d



| 0.1




9| |

, 1 1 1 = 0.07 | 2 |<< 16 d 16 0.9 2 1.4 1.75 d / = 10 | | 0.16 | | 0.01 / ( d

)




|2 i |>> 1

tanh 2 i = 1

(

)

=


: ,

.


5 : d max d 2 Ez + k 2 n 2 Ez = 0 dx 2

= x/d
p = kd = 2 (d / ) >> 1

d 2 Ez + p 2 n 2 Ez = 0 d 2




ip n ( ) d

A( )e


d



- ip n ( ) d

+ B ( )e


0



d2A dA dn + 2 pin + ipA = 0, 2 d d d d 2B dB dn - 2 pin - ipB =0 2 d d d p>>1, , p,

dA dn 2n +A = 0, d d dB dn n +B =0 d d

dA dn =- 2n A A=

ln A =- ln n

constant constant , B= n n


1 Ez = ae n

ip n ( ) d
d





- ip n ( ) d

+ be


0





­ , ­ . a b .
ip n ( ) d

a =-be


0

d

n(0) = 1,

dn dx

-2 ik
x =0

=0

r =- e


0

d

n ( ) d




Ereflect

ed

( t ) = r ( )
0 0



Einc (t - )d

( ) = r ( ) exp ( -i ) d
Re ( - ) = Re (

) )

( - ) = * (

)

Im ( - ) =- Im (

( - ) = (

)

" " = c /


( ) , . ( ) , 1 ,... , n ,...

( ) =

( ( ) (

* - 1* )... ( - n )...

- 1

)(

- n )...



Im ( ) > 0

( ) = (

)


ln ( ) , ln ( ) , .
Re ln ( ) d = 2 ln d + Re ln ( ) d +
C 0 C

+ Re

C

( (

- 1* )...( - n* )... - 1

)(

- n )...

d = 0


(z)

eff

= =



( z)

eff

=

eff tanh eff eff eff

2 id eff 2 id eff tanh

eff

eff

-1 +1

=-1 +
4 id





eff


Re ln ( ) d = Re
C





0

ln ( e


i

)

ei id =
ei id = i ei id = i - i d = eff e ie
eff

4 id Re ln -1 + eff e - i 0 4 id Re ln ( -1) - eff e - 0 4 id i = Re e i ln ( -1) - 0 = Re





0

i e ln ( -1)d + 4 d
i





0

d =

= Re- =-





0

e d + 4 d

i

eff





0

d = = 4 2 d
eff





0

cos ( )d + 4 2 d

eff


Re ln d = ln d
0 0






0

ln d =-2 2 d

eff

+


i

Im 1

Im i > 0



0

ln d 2 2 d


eff

ln

0

(

max - mi

n

)

< ln d 2 2 d
0

eff





0

ln d =



max




ln d +

max


0

ln d

4 id =-1 +

eff



max



ln d = Re = Re

max




4 id ln -1 + eff d =


max



4 d 4 d eff + eff d = i - i

max



4 d



eff d

( ) - ( ( 0 ) = ( max ) +
2

max

)

=

2







max

x ( x x2 -

)
2

0







max

( x
x

)

0

dx = ( max ) +

2






max

( ) d




max max , , ( 0 ) ( max )



ln d =





4 d

eff d

ln

0

( max - min )
d

2 2 d
n 0

eff

( max )

max >> mi max =-10 dB
> 2 2

ln
eff

( max )
d > max / 17.4



2

R ( d) dB
0 -2 -4 -6 -8 -1 0 -1 2 -1 4 -1 6 0, 0 0,5 1, 0 1,5 2, 0

d cm