, , .
Ψ(, t) = A(r) cos (ωt ), A(r) =
(, ). , ρ .
Ψ(, t) = A(ρ) cos (ωt ),
1.2
,
= υ2 (1.2)
, Ψ(, t) = A cos (ωt - kx + φo) Ψ(, t) =
(1.2) - . . .
= -ω2 cos (ωt - kx + φo); = - k2 cos (ωt - kx + φo); = υ2
= kxx + kyy + kzz
ψ(x, y,z) = ψ() :
ψ(x, y,z) =
+ + = (1.2.) |
!
υ2 = , . . . ( ) . .
, ( ).
.
1.3 (1.3.1) (1.3.2)
1.3.1.
.. - , ( ) ( ) .
Ψ12 = 1 Ψ1 + 2 Ψ2 (*); ψ =
(*) -.
.
( ) :
Ψ(, t) =
1.3.2.
.
. .
.. , 2 ω.
. 2
. () ,
.
2.1
, ,
|
|
Ψ(, t) = ,
- n .
υ s = ,
, KF . , m .
.
= s2 ,
.. .
, (x,t) :
= s2 ,
cs = . , k , γ γ = .
cs = .
()
cs =
ρ , - ( , ).
2.2
.
Ψ(, t) = A cos (ωt - kx)
wk = ρυ2 = sin2 (ωt - kx)
wp = ()2 = sin2 (ωt - kx)
, () !
. ( )
w = wk + wp = sin2 (ωt kx)
( )
= w
Is = ρ cs2 ω2 A2
, () (.. , ).
- .
.3
3.1 .-.
3.1.1.
.-. . . . .
. . :
rot = - (I); div = ρ (III);
rot = + (II); div = 0 (IV);
= εo ε (V); = μo μ (VI); = γ (VII).
.
.-. , , .
3.1.2.
: (j = 0, ρ = 0).
, .
: (,t) (,t) z , , ( i= z,,x) .
, :
[ rot ] x = - - μo μ ,
[ rot ]z [ rot ] z,
:
- μo μ = , εo ε = - (*)
εo ε = , - μo μ = - , (**)
(*) Ey Hz, Ex Hx
(. . , = 0). Ez Hy .
|
|
t - (*), ( = ) (*)
:
=
υ2 (,t). z (,t) . :
= υ2 (2.1) = υ2 |
- .-. (,t) z (,t), (2.1):
(,t) = m cos(ω t - kx + φoE)
Hz (,t) = Hm cos(ω t - kx + φoH)
(,t) = m
Hz (,t) = Hm
2.2 .-.
.-.
, 0
: = y ; = Hz ^ , .
0 . 0Z.
υ υ =υ 0. υ = =
, - .
ε =1, μ =1, υ =
υ = .
(,t) Hz (,t)
(*),
k Hm = εoε ω Em (***)
,
=
(***) ω, υ k
Em = m
, .
.-.
. , . Z.
[ ] 0
, . .
. . , c υ
= ,
c .
2.3 .-.
2.3.1.
. . :
w = εoε E2, w = μμo 2
w = w
w = w + w = εoε E2 = μoμ 2
: = (ωt kx) dx =
= εεo = μμo
: W = dV
2.3.2. .
= -
.
=
. υ.
, w,
= w
= =
w, :
= εoε = = [ ]
:
= [ ] (2.3) |
I, .
I =
. - .
I = dt = εεo c = Em Hm
I = Em Hm (2.4) |
2.3.3. .
, S
Ns = dSn
,
N* = dSn
Nω = Nλ =
. . , () .
2.4 .-. . .
.-. . j, .
.. = [ ] = μ μ [ ]
: = .. = =
|
|
= = =
. . ( ) :
. =
. ρ
. = (1 + ρ) = w (1 + ρ)
.4
4.1 (4.1.1). (4.1.2)
4.1.1.
. . (!) .
(ω) = ω dω.
((k) = Ak dk) . .
, , ,
, . , υ = f (ω),
.
4.1.2.
, :
1 = 2 = ; ω1 = ω dω, ω2 = ω + dω; k1 = k dk, k2 = k + dk
:
Ψ1 (x,t) = 1 cos [(ω dω) t (k dk) x ]
Ψ2 (x,t) = 2 cos [(ω + dω) t (k +dk) x ]
cos α + cos β = 2 cos cos , ,
Ψ (x,t) = Ψ1 + Ψ2 = 2 cos (tdω - xdk) cos (ωt -k x)
- .
Ψ(t) , . = .
4.2 .
( m = 2) (tdω - xdk) = const
υ =
:
υ = = υ + k
υ = υ - λ ,
, :
k = , dk = - dλ
, :
υ = υ + k (4.1) υ = υ λ |
.
4.3
ω(k) k - k, k + k,
Ψ (x,t) = (k) cos [ ω(k) ∙ t kx ] dk
, .
/ k . ,
kx , ky , (4.2) kz |
, . .
(4.3) |
( t) , .
:
Ψ (x,t) = (ω) cos [ω t k(ω) ∙ x ] dω
, .
|
|
4.4
-
(z,t) = Exo cos (ωt kz + α)
(z,t) = Eyo cos (ωt kz)
α = 0,
Em =
0 β, β
β = arc tg ()
α = + , :
(z,t) = Exo sin (ωt kz)
(z,t) = Eyo cos (ωt kz)
+ = 1
, z = 0 , ω. α = - .
, Exo = Eyo =Eo . ( .
- .
() I (φ) . η,
η = .
.5
, .
5.1
5.1.1.
, S1 S2, ω1 = ω2 = ω.
ψ(x1,t) = 1 cos (ωt kr1 +α1) = 1 cos t)
ψ(x2,t) = 2 cos (ωt kr2 +α2) = 2 cos t)
:
2 = + +2A1 A2 cos [ t) - t)] (5.1)
, .
5.1.2.
φ = [ t) - t)] = const
, ( ) .
c .
(5.1) [] =0, = 1 + 2;
[] = π, = 1 - 2
. τ (10-11 10-13) π 2π. τ .
τ = .
t τ cos φ =0 I = I1 + I2 .
lk = τ·υ - .
5.1.3. () ()
().
(5.1) , :
os φ = 1, Amax =A1 + A2
k (r1 - r2) = 2 π m, m =0, 1, 2, 3
(r1 - r2) = r . .. k = , :
r = m λ (5.2) |
().
os φ = -1 (5.1) 2 = = (A1 A2)2 Amin = │ A1 A2 │
: k (r1 - r2) = (2 m + 1)π
r = (2 m + 1)
5.1.4.
I A 2 (5.1) :
I = I1 + I2 + 2 cos φ
φ 0
: Imax = ( + )2 φ = 2π m
Imin = ( - )2 φ = (2 m +1) π
.
I1 = I2 = I : Imax = 4 I Imin = 0
5.2
, .
.
5.2.1.
ψ1 = 1 cos (ωt - kx) ψ2 = 2 cos (ωt + kx), 1 = 2 =
|
|
: ψ = ψ1 + ψ2 = ∙2 cos kx cos ωt
. = │2 cos kx │
, . = 0 . .
kx = (2 m +1)
. = (2 m +1) (m =0, 1, 2, 3)
, . = 2 .
kx = π m
.. = m (m =0, 1, 2, 3)
. - ωt. .
5.2.2.
. .
:
(x,t) = Eo cos (ωt kx)
1 (x,t) = H0 cos (ωt kx) -
(x,t) = Eo cos (ωt + kx)
2 (x,t) = - Ho cos (ωt + kx) - ,
: = + = 2 Eo cos kx cos ωt
= + = 2 Ho sin kx sin ωt
, . . , .
5.2.5.
, - () :
= .+ . = w g + w (- g) = 0
, . . , .
.
w k = ()2 = 2ρω2 A2 cos2 kx ∙sin2 ωt
w = ()2 = k2 A2 sin2 kx ∙cos2 ωt
w k = w
. , . . .
w E = = 2 cos 2 kx ∙cos 2ωt
w H = = 2 sin2 kx ∙sin2 ωt
.
5.2.6.
. : .
:
1) Ψ(x,t) ;
2) - .
( z = ρs). (z 1 z 2) , (z 1 z 2) .
z = , ( z = 377 )
(n = ). n1 n2 π, ; n1 n2 , π. , , .
5.2.7.
φ = 2π m
.
( )
Ψ(0 ,t) = 0 Ψ(l,t) = 0
λ = , ω m =
c (x=l)
Ψ(0 ,t) = 0 Ψ(l,t) = Ψ max (t)
λ = , ω m =
; .
5.3
5.3.1.
, , .
, .
(ε μ . ).
, ( ) . ( ) .
μ .
n = =
λ0 λ : = n.
5.3.2.
(λ ).
(, ).
r = r2 - r1 = d sin θ
r . = n (r2 - r1) = n r = n d sin θ
r . = m λ, m = 0, 1,, 2,, 3