Catalogação na fonte Universidade Federal de Alagoas Biblioteca Central Divisão de Tratamento Técnico

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Catalogação na fonte

Universidade Federal de Alagoas Biblioteca Central

Divisão de Tratamento Técnico Bibliotecária Responsável: Helena Cristina Pimentel do Vale

S586c Silva, Willamys Cristiano Soares.

Geração e Caracterização de feixes possuindo momento angular orbital / Willamys Cristiano Soares Silva. – 2011.

69 f.: il.

Orientador: Jandir Muguel Hickmann. Co-Orientador: Dilson Pereira Caetano.

Tese (doutorado em Física da Matéria Condensada) – Universidade Federal de Alagoas. Instituto de Física. Maceió, 2011.

Bibliografia. f. 67-69.

1. Difração. 2. Feixes Laguerre-gauss. 3. Feixes Bessel. 4. Momento Angular orbital. I. Título.

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HG d) HG e)HG f) HG ?D

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. V? GA

φ >

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∂t ∇φ+ ∂

∂t = . V? JA

6 ∇×× =()∇ # >

−∇ +ε

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∂t = . V? DA

# V? BA V? CA 8 >

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∂t =ρ, V? @IA

>

∇ φ+∂

∂t(∇ ) =− ρ

ε . V? @@A

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∂t = 0, V? @?A

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#/( $ 9 & 0

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ǫ V? @CA

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j

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#/( $ 9 & #:

x, y z * & # V? @BA V? @GA # >

m = ε ×

j

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= ε

j

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6 9 * >

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j

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8 >

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j

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* # >

[∇j(Ej × )]dv =

s

Ej( × )dsj. V? ?CA

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#/(/ $ #

, ( ,

, >

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j

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m = + V? ?EA

= ε ( × )dv 5

= ε

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)Aj]dv

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$

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l , 5 9

8 9 3 $ 9 !

* >

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, * 3 8 x k = π

(24)

#/(/ $ ##

8 ω, P u( ), 8

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8 8 , ∂ u

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∂z ku 8 ,

>

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∂u

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∂x +

∂y , - *

, * "

1.2 ,

*3 # # V # # , P

8 A , >

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9 N $ V? BA ,

9 N 8

=

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W V? @GA

W 8 * ×

! >

Re ( × ⋆) = 1 2(

× + × ⋆). V? ?DA

(25)

#/(/ $ #(

, >

=

∂t =iωuexp [i(kz−ωt)]x V? CIA

= ∇× = ∂u

∂z +iku exp [i(kz−ωt)]y− ∂u

∂y exp [i(kz−ωt)]z. V? C@A

× =iωu⋆ ∂u

∂yy+ ∂u

∂zz +ωk|u| z, V? C?A

∂u

∂x = 0 >

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*

× ⋆ =iωu

∇u⋆+ωk

|u| z. V? CEA

, "

, , >

= Re [ε × ⋆] = ε 2 [

× + × ⋆] = iωε

2 (u∇u ⋆

−u⋆u) +ε ωk|u| z.

V? CFA

7 ,

8 * # 8 u ! >

u(r, φ, z) =u (r, z) exp(ilφ), V? CGA

8 5 l , 5 9

7 # V? CGA * V? ?BA , 8

* 8 8 - 8 L?GM 8

(26)

#/(/ $ #,

6 9 8 8 9 ∂u

∂z

ku ,

, 8 >

= iωε 2 u

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⋆∂u

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r |u | φ+ε ωk|u | z, V? CBA

r φ z * 3 5 7

, * + , c * "

! $ r

3 8 φ , 3*

# z "

z

, >

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r z|u | r+ iωε

2 u

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4 8 3

,

8 z 3 * 8

& # 8 ,u=cpz =ε ω |u | , *

9 L?BM

# 8 , >

z

U =

dv

u dv

=

lε ω|u | dv

ε ω |u | dv

= l

(27)

#/(/# * " #1 # ,> z z = dv dv =

lε ω|u | dv

ε ωk|u | dv

= l

k =l λ

2π. V? EIA

8 , 9 *

& 8 N # ,

Nl , N ω R 9

# 8 U 8 #

U 8 ! l ω V? CDA 3

8 0 0 8 *

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8 #

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#/(/#

*

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- "; ' # V? ?GA "

5 , * 3* ρ φ L?JM

- "; , >

upl(r, φ, z) ∝ (−1)p r √

2

w(z) l

exp r

w (z) exp −i

kr

2R(z) exp(ilφ)

×Ll p

2r

w (z) exp −i(2p+l+ 1) arctan

z zr

, V? E@A

(28)

#/(/# * " #'

w(z) =w 1 + z

zr

V? E?A

R(z) =z 1 + zr

z V? ECA

* 8 * z w

, 5 8 zr =kw 2 , 2 + $ Llp , K

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z , ; + .

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Q 2π 9 (p+ 1) 3 Q

, *, # , ( V? @A

- "; p= 0 * l= 0 8 - ";

$ N

8 * z

(29)

#/(/# * " #7

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* p A p= 0 #Ap= 1 A p= 2 A p= 3

( > V?I@@A

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l = 1 #A l= 2 A l= 3 A l= 4

(30)

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p "

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p = min(m, n) HGmn , N =m+n . HGmn

: 8 8 LGl

p

9

# . "; >

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w (z) Hm

2 x

w(z) Hn

2 y

w(z) exp(ikz)

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z zr

, V? EEA

Hn(ξ) , K n .

(31)

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d) HG e) HG f) HG

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8

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* * k = α +β ρ φ z

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$ 3

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( $ ,

IlN ∝ N−

n

exp (ilαn) exp ika

z (xcosαn+ysinαn) VC CA

k = 2π/λ , * αn = 2πn/N , 9

, a , N , Q ( VC @@A

9 : 4 N

8 - "; 5 9 l VC CA 7

( VC @@A V A V#A V A N = 5 ( VC @@A V A V A V A N = 6

l = 0,1,2 *

# * 4

8 $ , 5*

# 8

( C @@> # 4

( > V?I@@A

(48)

(/, & ! * $ % ,'

l l+pN p , Q N , Q 4

Il pNN ∝ N−

n

exp [i(l+pN)αn] exp ika

z (xcosαn+ysinαn)

IN

l pN ∝

N−

n

exp (ilαn) exp(ipNαn) exp ika

z (xcosαn+ysinαn) VC EA

7 exp(ipNαn) = 1 VC EA 9 $ IN

l =Il pNN

! # 8 - ";

l 4 # 8 - "

; l = l+pN 8 8

l = 1 4 N = 6 #

8 l´= ...11,5,7,13, ... ( VC @?A

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4 N = 6 8 - "

; l =5,1,7 *

( C @?> 4 N = 5

8 - "; 9 > A l = 1 #A l = 4 A l = 9

(49)

(/1 ! ,7

( C @C> 4 N = 6

8 - "; 9 > A l = 5 #A l = 1 A

l = 7

( > V?I@@A

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8 * # P

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2

w

l

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w , 5 8 r = x +y , φ= tan− y

x

, 9 l , 8 #

τ(x , y )

8 ( $ V A 8 - "; "

# , LCIM>

E(x, y, z) = −i

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x +y

2z U (x , y , z = 0)τ(x , y )

×exp ik

z (xx +yy ) dx dy VE ?A

9 # : VE ?A kx = kzx ky = kzy kx

ky * * # * VE ?A

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7 VE CA !3 "

8 z #

, # ( * # "

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Figure

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References

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