Abstract

We introduce the orbital Stokes parameters as a linear combination of a beam’s second-order moments. Similar to the ones describing the field polarization and associated with beam energy and its spin angular momentum, the orbital Stokes parameters are related to the total beam width and its orbital angular momentum. We derive the transformation laws for these parameters during beam propagation through first-order optical systems associated with phase-space rotations. The values of the orbital Stokes parameters for Gaussian modes and arbitrary fields expressed as their linear superposition are obtained.

© 2009 Optical Society of America

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References

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Agarwal, G. S.

Alieva, T.

Arsenault, H. H.

Bastiaans, M. J.

Bekshaev, A. Ya.

A. Ya. Bekshaev, Fotoelektronika 8, 22 (1999).

Calvo, G. F.

Courtial, J.

Hsu, Y. N.

Martínez-Herrero, R.

Mejías, P. M.

Mukunda, N.

Padgett, M. J.

Serna, J.

Simon, R.

Sundar, K.

Wolf, K. B.

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Equations (20)

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W ( r , q ) = Γ ( r + 1 2 r , r 1 2 r ) exp ( i 2 π q t r ) d r .
M = 1 E [ r q ] [ r t , q t ] W ( r , q ) d r d q ,
M = [ M r r M r q M r q t M q q ] = [ m x x m x y m x u m x v m x y m y y m y u m y v m x u m y u m u u m u v m x v m y v m u v m v v ] = M t .
[ r o q o ] = T [ r i q i ] = [ A B C D ] [ r i q i ] .
r o i q o = U ( r i i q i ) ,
U r ( α ) = [ cos α sin α sin α cos α ] , U g ( ϑ ) = [ cos ϑ i sin ϑ i sin ϑ cos ϑ ] ,
U f ( γ x , γ y ) = [ exp ( i γ x ) 0 0 exp ( i γ y ) ] ,
M = 1 E ( r i q ) ( r i q ) W ( r , q ) d r d q = M r r + M q q + i ( M r q M r q t ) = [ Q 0 + Q 1 Q 2 + i Q 3 Q 2 i Q 3 Q 0 Q 1 ] ,
Q 0 = 1 2 [ ( m x x + m u u ) + ( m y y + m v v ) ] ,
Q 1 = 1 2 [ ( m x x + m u u ) ( m y y + m v v ) ] ,
Q 2 = m x y + m u v ,
Q 3 = m x v m y u
M o = U M i U = U M i U 1
det ( M ν I ) = 0 = ν 2 2 Q 0 ν + Q 0 2 Q 2 = ( ν Q 0 ) 2 Q 2 ,
( Q 2 + i Q 3 ) o = exp [ i ( γ x γ y ) ] ( Q 2 + i Q 3 ) i .
L p ± l ( r , ϕ ) = 2 1 2 [ ( min { m , n } ) ! ( max { m , n } ) ! ] 1 2 ( 2 π r ) m n × exp [ ± i ( m n ) ϕ ] L min { m , n } m n ( 2 π r 2 ) exp ( π r 2 ) ,
f ( x , y ) = m , n = 0 a m , n H m , n ( x , y ) , m , n = 0 a m , n 2 = 1 .
Q 0 = m , n = 0 a m , n 2 ( m + n + 1 ) ,
Q 1 = m , n = 0 a m , n 2 ( m n ) ,
Q 2 + i Q 3 = 2 m , n = 0 a m , n + 1 a m + 1 , n * ( m + 1 ) ( n + 1 ) .

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