Abstract

We obtain an analytical expression in the form of a finite sum of plane waves that describes the paraxial scalar Fraunhofer diffraction of a limited plane wave by a multilevel (quantized) spiral phase plate (SPP) bounded by a polygonal aperture. For several topological charges of the SPP we numerically obtain the minimal number of SPP sectors for which the RMS between the Fraunhofer diffraction patterns for multilevel and continuous SPP does not exceed 2%.

© 2008 Optical Society of America

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References

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2007 (1)

2006 (6)

2005 (2)

2004 (2)

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, J. Mod. Opt. 51, 2167 (2004).
[CrossRef]

K. Sueda, G. Miyaji, N. Miyanaga, and M. Nakatsuka, Opt. Express 12, 3548 (2004).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 182, 205 (2000).
[CrossRef]

1997 (1)

1987 (1)

N. Saga, Opt. Commun. 64, 4 (1987).
[CrossRef]

Appl. Opt. (1)

J. Mod. Opt. (1)

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, K. Jefimovs, J. Simonen, and J. Turunen, J. Mod. Opt. 51, 2167 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (3)

C. Guo, D. Xue, Y. Han, and J. Ding, Opt. Commun. 268, 235 (2006).
[CrossRef]

N. Saga, Opt. Commun. 64, 4 (1987).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, Opt. Commun. 182, 205 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

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Figures (3)

Fig. 1
Fig. 1

DOE with aperture in the form of regular polygon.

Fig. 2
Fig. 2

Fraunhofer diffraction pattern of the plane wave by the continuous limited SPP ( n = 6 ) : (a) amplitude and (b) phase.

Fig. 3
Fig. 3

Fraunhofer diffraction pattern of the plane wave by the multilevel limited SPP ( n = 6 ) : (a), (d), (g) DOE phase; (b), (e), (h) amplitude; and (c), (f), (i) phase in the Fraunhofer diffraction zone. The number of sectors: (a)–(c) 18, (d)–(f) 30, (g)–(i) 42.

Tables (2)

Tables Icon

Table 1 RMS as a Function of the Number of SPP Sectors ( Topological Change n = 6 )

Tables Icon

Table 2 Minimal Number of Sectors versus the Topological Charge of the SPP

Equations (3)

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E ( ξ , η ) = i f 2 π k p = 1 P ( y p + 1 y p ) ( x p x p 1 ) ( y p y p 1 ) ( x p + 1 x p ) [ ξ ( x p + 1 x p ) + η ( y p + 1 y p ) ] [ ξ ( x p x p 1 ) + η ( y p y p 1 ) ] exp [ i k f ( ξ x p + η y p ) ] ,
E ( ρ , θ ) = i f cos π P 2 π k ρ 2 p = 0 P 1 exp ( i Ψ p ) sin ( φ p θ ) cos α p cos α p + 1 × [ 2 sin π P sin ( φ p θ ) + cos α p + 1 exp ( i k R ρ f cos α p ) cos α p exp ( i k R ρ f cos α p + 1 ) ] ,
E ( ρ 0 , θ ) i k R 2 sin 2 π P 4 π f p = 0 P 1 exp ( i Ψ p ) k 2 R 3 ρ sin 2 π P cos π P 6 π f 2 p = 0 P 1 exp ( i Ψ p ) cos ( φ p θ ) .

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