Abstract

The exact full-wave generalization of the cylindrically symmetric scalar real-argument Laguerre–Gauss beam is determined. The radiation intensity of the resulting Laguerre–Gauss wave is deduced, and the main characteristics of the radiation intensity pattern are described. The total power Pn is evaluated, where n is the radial mode number. By the use of 1Pn as the quality parameter, the characteristics of the quality of the paraxial beam approximation to the full Laguerre–Gauss wave are discussed.

© 2007 Optical Society of America

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References

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  1. H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  2. T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
    [CrossRef]
  3. S. R. Seshadri, Opt. Lett. 27, 1872 (2002).
    [CrossRef]
  4. S. R. Seshadri, J. Opt. Soc. Am. A 24, 482 (2007).
    [CrossRef]
  5. S. R. Seshadri, Appl. Opt. 45, 5335 (2006).
    [CrossRef] [PubMed]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.
  7. J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B: Photophys. Laser Chem. 71, 549 (2000).
    [CrossRef]

2007 (1)

2006 (1)

2002 (1)

2000 (1)

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B: Photophys. Laser Chem. 71, 549 (2000).
[CrossRef]

1985 (1)

1966 (1)

Arlt, J.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B: Photophys. Laser Chem. 71, 549 (2000).
[CrossRef]

Dholakia, K.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B: Photophys. Laser Chem. 71, 549 (2000).
[CrossRef]

Fukumitsu, O.

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B: Photophys. Laser Chem. 71, 549 (2000).
[CrossRef]

Kogelnik, H.

Li, T.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.

Seshadri, S. R.

Takenaka, T.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.

Yokota, M.

Appl. Opt. (2)

Appl. Phys. B: Photophys. Laser Chem. (1)

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B: Photophys. Laser Chem. 71, 549 (2000).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.

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Figures (3)

Fig. 1
Fig. 1

Radiation intensity pattern of the Laguerre–Gauss wave for the radial mode numbers n = 0 , 2, and 4, and k w 0 = 2.980 .

Fig. 2
Fig. 2

Radiation intensity pattern of the Laguerre–Gauss wave for the radial mode numbers n = 1 , 3, and 5, and k w 0 = 2.980 .

Fig. 3
Fig. 3

1 P n as functions of w 0 λ for n = 0 , 1, and 2 and for 0.05 < w 0 λ < 1 . P n , power in the Laguerre–Gauss wave of radial mode number n.

Equations (23)

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F n ( 0 ) ( ρ , z ) = K n ( 0 ) exp ( i k z ) w 0 w exp [ i ( 2 n + 1 ) tan 1 ( z b ) ] L n ( 2 ρ 2 w 2 ) exp ( q 2 ρ n 2 ) ,
w = w 0 ( 1 + z 2 b 2 ) 1 2 ,
2 b = k w 0 2 ,
q 2 = ( 1 + i z b ) 1 ,
ρ n 2 = ρ 2 w 0 2 .
0 d x L m ( a x ) L n ( a x ) exp ( a x ) = δ m n a ,
K n ( 0 ) = ( 2 π ω b ) 1 2 ,
S n ( 0 ) ( ρ , z ) = K n ( 0 ) exp ( i k z ) ( 1 ) n n ! 2 2 n q 2 ( n + 1 ) × L n ( q 2 ρ n 2 ) exp ( q 2 ρ n 2 ) .
F n ( 0 ) ( ρ , z ) = l = 0 l = n a n , l S n l ( 0 ) ( ρ , z ) ,
a n , l = ( 1 ) n n ! 2 n l ( n l ) ! ( n l ) ! l !
S n ( ρ , z ) = K n ( 0 ) b exp ( k b ) 0 d η η J 0 ( η ρ ) ( η 2 w 0 2 ) n ζ 1 exp [ i ζ ( z i b ) ]
ζ = ( k 2 η 2 ) 1 2 .
F n ( ρ , z ) = l = 0 l = n a n , l S n l ( ρ , z ) .
z , n ( ρ , z ) = 1 2 Re [ i ω F n * ( ρ , z ) z F n ( ρ , z ) ] ,
P n = 0 2 π d ϕ 0 d ρ ρ z , n ( ρ , z ) .
P n = 0 2 π d ϕ 0 π 2 d θ sin θ Φ n ( θ , ϕ ) ,
Φ n ( θ , ϕ ) = ( 2 π f 0 2 ) 1 [ G n ( k 2 w 0 2 sin 2 θ ) ] 2 exp [ k 2 w 0 2 ( 1 cos θ ) ] ,
G n ( k 2 w 0 2 sin 2 θ ) = l = 0 l = n a n , l ( k 2 w 0 2 sin 2 θ ) ( n l ) ,
Φ 0 ( θ , ϕ ) = ( 2 π f 0 2 ) 1 exp [ k 2 w 0 2 ( 1 cos θ ) ] .
P 0 = 1 exp ( k 2 w 0 2 ) ,
P 1 = 1 4 f 0 2 + 6 f 0 4 + ( k 4 w 0 4 4 + k 2 w 0 2 2 f 0 2 6 f 0 4 ) exp ( k 2 w 0 2 ) ,
P 2 = 1 14 f 0 2 + 120 f 0 4 450 f 0 6 + 630 f 0 8
× ( k 8 w 0 8 64 + k 6 w 0 6 4 9 k 4 w 0 4 8 + k 2 w 0 2 2 + 7 4 + 14 f 0 2 + 15 f 0 4 180 f 0 6 630 f 0 8 ) exp ( k 2 w 0 2 ) .

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