Рудакова Л.И., Соколова Е.Ю. Практический курс физики. Волновая оптика
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. . , . .
Практический курс физики
. . .
2006
2
16.4.5
43
. ., . .
43 . « ». – .:
« », 2006.–136 .: .
« »
.
ISBN 5-7035-2059-2
© . . , . . . 2006 .
3
I.
.
,
:
, - .
,
,
– .
;
;
. ,
,
.
.
r
:
( )
),krwtcos(
r
A
t,rE
0
α
+−=
(1.1)
E(r,t) –
E
;
)r(A
r
A
0
=
-
;
constA
=
0
,
α
-
.
. 1.1 -
( ) ( )
. ,
:
A
E
=
, – ,
A
E
−
=
.
P
)cos(
111
ϕ
+= wtAE
),cos(
222
ϕ
+= wtAE
111
kr−=
αϕ
,
222
kr−=
αϕ
.
E
P
21
EEE +=
.
4
( . 1.2)
)cos(2
1221
2
2
2
1
2
ϕϕ
−++= AAAAA
(1.2)
,
).cos(2
122121
ϕϕ
−++= IIIII
(1.3)
, ,
)(
12
ϕ
ϕ
−
.
,
...,,2,1,0,2)(
12
±
±
=
=
−
π
ϕ
ϕ
(1.4)
21
AAA +=
,
. . ,
. . 1.1 , ,
1
2
, .
,
π
ϕϕ
)12()(
12
+=−
,
...,
,
2
,
1
,
0
±
±
=
(1.5)
21
AAA −=
- ,
( , ,
).
( ) ( )
211212
2
rr −+−=−
λ
π
ααϕϕ
. (1.6)
.
(
)
12
ϕϕ
−
P
;
.
–
.
(
)
21
αα
=
.
(1.4) (1.6)
...,2,1,0m,mrr
21
±
±
=
=
−
λ
(1.7)
(1.5) (1.6)
( )
2
1m2rr
21
λ
+=−
...
,
2
,
1
,
0
m
±
±
=
(1.8)
5
. 1.1
. 1.2
. 1.3
6
,
0
λ
λ
=
(
0
λ
- ), (1.7)
0
λ
m=∆
,
,...
2
,
1
,
0
m
±
±
=
(1.9)
( (1.8))
( )
2
1m2
0
λ
∆
+=
,
,...
2
,
1
,
0
m
±
±
=
(1.10)
(
)
21
rrn
−
=
∆
.
nr
∗
.
1
r
1
n
, –
2
r
2
n
,
2211
rnrn
−
=
∆
.
(1.11)
.
.
( , )
, .
(
)
8
10
−
≈
τ
.
,
, ,
.
,
,
τ
ω
1
≈∆
.
,
.
τ
ω
1
∆
.
ω
ω
∆
;
.
∗
1
2
=
2
1
.)( dxxnl
7
[
]
,)t,r(twcos)t,r(A)t,r(E
ϕ
+=
(1.12)
w
- .
,
,
τ
.
,
τ
( . 1.3).
π
≈
.
ω
τ
∆
≈
1
(1.13)
,
τ
,
l
υτ
=
.
, (1.3)
∗
:
(
)
(
)
[
]
ttIIIItI
122121
cos2)(
ϕϕ
−++=
(1.14)
(
)
t
1
ϕ
(
)
t
2
ϕ
τ
.
, , ,
, ,
τ
:
(
)
(
)
[
]
−++= ttIIIItI
122121
cos2)(
ϕϕ
(1.15)
,
1
ϕ
2
ϕ
;
(1.15)
1
+
1
−
, (1.15)
∗
,
.
8
0. <I>
21
II
+
=
;
.
( ) , .
( )
,
.
,
)()(
12
tt
ϕϕ
−
.
)(
1
t
ϕ
)(
2
t
ϕ
, .
.
.
,
.
,
, .
,
.
∆
>
l
, .
– ( .
. 1.4).
S
1
S
2
S
. (
).
1
S
2
S
, ,
,
, .
(1.7) (1.8),
,
(
)
λ
mrr =−
21
, -
( )
2
12
21
λ
+=− mrr
.
...
,
2
,
1
,
0
m
±
±
=
. ,
21
rr =
,
, , , .
( ) ( . 1.4)
l
L
x
λ
=∆
, (1.16)
x
∆
.
. 1.4
9
.
, lrr ≈−
21
.
, .
,
.
,
.
,
.
.
, .
,
.
x
∆
,
.
,
∆
≈
, ( . 1.8).
.
S
( . 1.5).
,
.
P
SABCP
( 1)
SFP
( 2).
d
,
S
.
1 2
P
( . 1.11)
β
cos2
⋅
=
∆
dn
, (1.17)
. 1.5
10
n
- ,
β
- .
,
,
π
.
, 1
B
, , ,
2
F
(
n
).
:
πβ
λ
π
ϕϕ
+=− cosdn2
2
0
12
2
cosdn2
0
λ
β∆
+=
. (1.18)
(1.9) (1.10),
,...2,1,0m
m
2
cosdn2
0
0
=
=+
λ
λ
β
(1.19)
( )
2
1m2
2
cosdn2
00
λ
λ
β
+=+
,
,...
2
,
1
,
0
m
=
(1.20)
.
, (1.18), (1.19), (1.20)
.
1 2 (
– ),
π
.
( 1.13 1.14), (
(1.15)).
.
1.1. , ,
d 1
=
,
0
30=
α
.
?
.5,1
=
n