Abstract

We investigate output mode purities of Laguerre–Gaussian (LG) beams generated from four typical simultaneous amplitude and phase modulation methods with phase-only spatial light modulators (SLMs). Numerical simulations supposing the practical SLM, i.e., stepwise phase modulation with a pixelated device, predict an output mode purity of beyond 0.969 for the LG beams of less than radially and azimuthally fifth order. Experimental results of generating LG beams are also shown to demonstrate the effects of the simultaneous phase and amplitude modulation.

© 2008 Optical Society of America

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References

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2008

2007

2006

2005

1999

1971

Anderson, J. E.

Ando, T.

Arrizón, V.

Barnett, S. M.

Bos, P. J.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Campos, J.

Carrada, R.

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cottrell, D. M.

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, New J. Phys. 7, 55 (2005).
[CrossRef]

Davis, J. A.

Dennis, M. R.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, New J. Phys. 7, 55 (2005).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Esposito, E.

Flossmann, F.

Franke-Arnold, S.

Fukuchi, N.

Gibson, G. M.

Girkin, J. M.

González, L. A.

Götte, J. B.

Hara, T.

Inoue, T.

Ito, H.

Jones, A. L.

Kirk, J. P.

Leach, J.

Matsumoto, N.

McConnell, G.

Miranda, F. A.

Moreno, I.

O'Holleran, K.

Ohtake, Y.

Padgett, M. J.

Pouch, J. J.

Preece, D.

Ruiz, U.

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Wang, B.

Wang, X.

Wright, A. J.

Yzuel, M. J.

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Figures (3)

Fig. 1
Fig. 1

Examples of holographic phase patterns for generating the LG 2 1 beam via the four complex-amplitude modulation methods ( d = 6 , beam radius 100   pixels ).

Fig. 2
Fig. 2

Output mode purity of LG 2 1 beams generated via four methods varying the pitch d of the BPG pattern.

Fig. 3
Fig. 3

Observed beam patterns of the LG 2 1 beam via (a) phase-only modulation of a top-hat input beam and (b)–(e) four complex-amplitude modulation schemes. Intensity is enhanced 25 times in the left-bottom corner of each pattern (marked by dashed squares) to observe beam patterns in surrounding areas.

Tables (1)

Tables Icon

Table 1 Maximum η Values for Typical LG p l Beams Generated Holographically via Four Complex-Amplitude Modulation Methods and Phase-Only Modulation of a Top-Hat Input Beam a

Equations (2)

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u p l ( r , ϕ ) = ( 1 ) p w 0 [ 2 π p ! ( p + l ) ! ] 1 2 ( 2 r w 0 ) l × exp ( r 2 w 0 2 ) L p l ( 2 r 2 w 0 2 ) × exp { i [ l ϕ π θ ( L p l ( 2 r 2 w 0 2 ) ) ] } ,
ϕ i BG = π ( 2 r d + 1 ) d ( r i mod d ) .

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