Electromagnetic theory of propagation, interference and diffraction of light

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4 6 7 8 & 3 5 /

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1.1 The electromagnetic ®eld

1.1.1 Maxwell's equations

he

EB

j D

H

{

H

D_ ˆ ð

j !"

E_‡

B_ ˆ# !$ "

EH

DB %

& ' !"(! " '

' !) " EB

' !) " DH

! * " '

' j=r )

E B D H ) ! " +

! % "

!DH" % H

B , -

{ ) . ' !E Dj r"

' !H B"

!" !$ " ,

D_ˆ ðr !/"

B_ˆ#: ! "

1 ' !/" ' r ! "

2 !" ! # "

j_ˆ

ð D_ !/"

@r

@‡jˆ#: !3"

4 !3"

2 !3" .5

…

r _‡

…

j . n_ˆ# !6"

-

n '

_ˆ

…

r !7"

%

J ˆ …

j . n: !8"

'

!j_ˆ# " '

!j_6ˆ# " -

-

0

% ! "

1.1.2 Material equations

' % -

! " ,

) ! } /"

!

" -

{

j_ˆóE !9 "

D_ˆåE !# "

B_ˆìH: !"

: ó å - !

" ì

1 ' !9 " ;5 + ó 6ˆ# !

,

" &

' :

- ! "

+ ó

å ì 2

ì

ì

ì. _!

" ì, _!

"

) '

{

'óå ì ,

' åˆ=

ìˆ=! D EB H,

<

{ =

óE rv v

r ! 9 "

{ > D E

? 0 2- 0 1 : < = ? . = " #$#%7!9 6" 8

2 > 4& ' !> @- = 0

4 9 63" ? > 4 A < ( & ' !< < B ? 9 9 # " C = 4& ' !4 0 ? 9 9 $ "

1.1.3 Boundary conditions at a surface of discontinuity

H!". tä‡H!$ ". t$ä$ ‡ ˆ

1.1.4 The energy law of the electromagnetic ®eld

v !8"

83# 2 2

v

0

è

è$

!2 /" '

vv_$

è è$ ˆ

v

v_$: !# "

}3 : '

) - -

!v9 "

=

v ˆv9è v_$ ˆv9è_$ !"

v9 !# "

:5 !}//"

!# " $

=

G 5 ,

_ˆ

v: !$ "

$ !"

$

$ _ˆ$ ˆ

v

v_$: !/"

Refracted wave-front

Incident wave-front θ2

θ1

v₂, n₂ v

1, n1

2 /

< !$ " !8" & 5

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+ ì

! " ' ' ;

)-

> '

& 5 å

'

å ' -

% }$ /

& 5 ! å ' "

C

* 4 1 ' ! "

' , <6:6_ˆ: 8$

 å p

ˆ: 89 ;

! " ' $

1.3 Scalar XaveS

!r " }$ !7"

'

* 4 0 # # OC!87 " 79 3," # )# 155 !873" # /,0 # )# " 14# $#1 > $ 6 3/7

$

! " p_å

0 # # # $ 9 # # # $ 9 3

: :$ # # # /8 # # # /$

< <;$ # # # 9 # # # 7/

< <; # # # / # # # # / 3

$ $

! " 

å

p

& <:/;: / 37

1 <$:3;: /6 3#

!3" -

@$

@@ˆ#: !7"

'

_ˆ!"‡$!"

ˆ!r . S v"‡$!r . S‡v" !8"

$

= !æ " !æ‡vô

_‡ô" ô :

v æ + $!æ‡v" )

v æ

1.3.2 Spherical waves

>

_ˆ! " !9 "

_{ˆ jj ˆ}p$ _‡$_‡,$

B @=@_ˆ!@=@"!@=@"_ˆ!="!@=@"

=$ _ˆ

@$

@$!" !# "

' !"

@$ @$!"

v$

@$

@$!"ˆ#: !"

> ' !3" æ

: !" !8"

_ˆ! v"

‡

$!_‡v"

!$ "

$ ) !$ "

v

1.3.3 Harmonic waves. The phase velocity

0 r#

!r# "ˆ +!": !/"

0 - +

0 +

* ) 0

) ' ù

'

!r "_ˆ!r" Hù !r"I !$ /"

!._{# "}

!r"_ˆ !$ "

!$ /"

+

< 1 ' !$ /"

!r "_{ˆ Rf}5!r" ù_g !$ 3"

5!r"_ˆ!r"!r" !$ 6"

_R ; !$ 6" ' !"

5 '

=$_{5 ‡}$_1#$_{5 ˆ#: !$ 7"}

5

!r"_ˆù r . S v

ä_ˆ 1!r . S" ä_ˆL . r ä: !$ 8"

_R !$ 3"

' ' : ' ! ) " -

{

B - !$ 3"

ù !r" !r "

!r_‡r _‡"

ù !".r_ˆ#: !$ 9 "

T r r_ˆT !$ 9 "

ˆ

ù

T .: !/# "

T

T_ˆ=_jj

ä

1.

v!"!_r"ˆ ù

1.3.4 Wave packets. The group velocity