Abstract

We present a mode purity comparison between optical vortices (OVs) generated by a static multilevel phase plate with 16 or 32 phase steps and a vortex generated with a segmented deformable mirror with 37 actuators. Computer simulations show the intensity and phase of the vortices generated with the two methods. The deformable mirror, by being reconfigurable, shows better mode purity for high charge OVs, while the static phase plate mode efficiency declines due to the fixed number phase quantization.

© 2008 Optical Society of America

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  1. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604-612 (1995).
    [CrossRef]
  2. M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
    [CrossRef]
  3. C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates”, Opt. Commun. 268, 235-239 (2006).
    [CrossRef]
  4. M. B. Fleming and M. C. Hutley, “Blazed diffractive optics,” Appl. Opt. 36, 4635-4643 (1997).
    [CrossRef] [PubMed]
  5. D. C.O'Shea, A. D. Kathman, and T. J. Suleski, Diffractive Optics: Design, Fabrication, and Test (SPIE-International Society for Optical Engineering, 2003).
  6. Z. Jaroszewicz, A. Kołodziejczyk, A. Kowalik, and R. Restrepo, “Determination of phase step errors of kinoform gratings from their diffraction efficiencies,” Opt. Eng. 40, 692-697 (2001).
    [CrossRef]
  7. R. K. Tyson, M. Scipioni, and J. Viegas, “Generation of an optical vortex with a segmented deformable mirror,” submitted to Appl. Opt.
    [PubMed]
  8. M. A. Helmbrecht, T. Juneau, M. Hart, and N. Doble, “Segmented MEMS deformable-mirror technology for space applications,” Proc. SPIE 6113, 622-305 (2006).
  9. G. Molina-Terriza, J. Recolons, and L. Torner, “The curious arithmetic of OVs,” Opt. Lett. 25, 1135-1137 (2000).
    [CrossRef]

2006 (2)

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates”, Opt. Commun. 268, 235-239 (2006).
[CrossRef]

M. A. Helmbrecht, T. Juneau, M. Hart, and N. Doble, “Segmented MEMS deformable-mirror technology for space applications,” Proc. SPIE 6113, 622-305 (2006).

2004 (1)

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

2001 (1)

Z. Jaroszewicz, A. Kołodziejczyk, A. Kowalik, and R. Restrepo, “Determination of phase step errors of kinoform gratings from their diffraction efficiencies,” Opt. Eng. 40, 692-697 (2001).
[CrossRef]

2000 (1)

1997 (1)

1995 (1)

V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604-612 (1995).
[CrossRef]

Basistiy, V.

V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604-612 (1995).
[CrossRef]

Dai, G.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Ding, J.

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates”, Opt. Commun. 268, 235-239 (2006).
[CrossRef]

Doble, N.

M. A. Helmbrecht, T. Juneau, M. Hart, and N. Doble, “Segmented MEMS deformable-mirror technology for space applications,” Proc. SPIE 6113, 622-305 (2006).

Ebihura, T.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Fleming, M. B.

Guo, C. S.

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates”, Opt. Commun. 268, 235-239 (2006).
[CrossRef]

Han, Y. J.

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates”, Opt. Commun. 268, 235-239 (2006).
[CrossRef]

Hart, M.

M. A. Helmbrecht, T. Juneau, M. Hart, and N. Doble, “Segmented MEMS deformable-mirror technology for space applications,” Proc. SPIE 6113, 622-305 (2006).

Helmbrecht, M. A.

M. A. Helmbrecht, T. Juneau, M. Hart, and N. Doble, “Segmented MEMS deformable-mirror technology for space applications,” Proc. SPIE 6113, 622-305 (2006).

Hutley, M. C.

Hyashi, N.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Jaroszewicz, Z.

Z. Jaroszewicz, A. Kołodziejczyk, A. Kowalik, and R. Restrepo, “Determination of phase step errors of kinoform gratings from their diffraction efficiencies,” Opt. Eng. 40, 692-697 (2001).
[CrossRef]

Juneau, T.

M. A. Helmbrecht, T. Juneau, M. Hart, and N. Doble, “Segmented MEMS deformable-mirror technology for space applications,” Proc. SPIE 6113, 622-305 (2006).

Kathman, A. D.

D. C.O'Shea, A. D. Kathman, and T. J. Suleski, Diffractive Optics: Design, Fabrication, and Test (SPIE-International Society for Optical Engineering, 2003).

Kolodziejczyk, A.

Z. Jaroszewicz, A. Kołodziejczyk, A. Kowalik, and R. Restrepo, “Determination of phase step errors of kinoform gratings from their diffraction efficiencies,” Opt. Eng. 40, 692-697 (2001).
[CrossRef]

Kowalik, A.

Z. Jaroszewicz, A. Kołodziejczyk, A. Kowalik, and R. Restrepo, “Determination of phase step errors of kinoform gratings from their diffraction efficiencies,” Opt. Eng. 40, 692-697 (2001).
[CrossRef]

Levenson, M. D.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Molina-Terriza, G.

Morikawa, Y.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

O'Shea, D. C.

D. C.O'Shea, A. D. Kathman, and T. J. Suleski, Diffractive Optics: Design, Fabrication, and Test (SPIE-International Society for Optical Engineering, 2003).

Recolons, J.

Restrepo, R.

Z. Jaroszewicz, A. Kołodziejczyk, A. Kowalik, and R. Restrepo, “Determination of phase step errors of kinoform gratings from their diffraction efficiencies,” Opt. Eng. 40, 692-697 (2001).
[CrossRef]

Scipioni, M.

R. K. Tyson, M. Scipioni, and J. Viegas, “Generation of an optical vortex with a segmented deformable mirror,” submitted to Appl. Opt.
[PubMed]

Soskin, M. S.

V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604-612 (1995).
[CrossRef]

Suleski, T. J.

D. C.O'Shea, A. D. Kathman, and T. J. Suleski, Diffractive Optics: Design, Fabrication, and Test (SPIE-International Society for Optical Engineering, 2003).

Tan, S. M.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Torner, L.

Tyson, R. K.

R. K. Tyson, M. Scipioni, and J. Viegas, “Generation of an optical vortex with a segmented deformable mirror,” submitted to Appl. Opt.
[PubMed]

Vasnetsov, M. V.

V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604-612 (1995).
[CrossRef]

Viegas, J.

R. K. Tyson, M. Scipioni, and J. Viegas, “Generation of an optical vortex with a segmented deformable mirror,” submitted to Appl. Opt.
[PubMed]

Xue, D. M.

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates”, Opt. Commun. 268, 235-239 (2006).
[CrossRef]

Appl. Opt. (2)

R. K. Tyson, M. Scipioni, and J. Viegas, “Generation of an optical vortex with a segmented deformable mirror,” submitted to Appl. Opt.
[PubMed]

M. B. Fleming and M. C. Hutley, “Blazed diffractive optics,” Appl. Opt. 36, 4635-4643 (1997).
[CrossRef] [PubMed]

J. Microlithogr. Microfabr. Microsyst. (1)

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Opt. Commun. (2)

C. S. Guo, D. M. Xue, Y. J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates”, Opt. Commun. 268, 235-239 (2006).
[CrossRef]

V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604-612 (1995).
[CrossRef]

Opt. Eng. (1)

Z. Jaroszewicz, A. Kołodziejczyk, A. Kowalik, and R. Restrepo, “Determination of phase step errors of kinoform gratings from their diffraction efficiencies,” Opt. Eng. 40, 692-697 (2001).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

M. A. Helmbrecht, T. Juneau, M. Hart, and N. Doble, “Segmented MEMS deformable-mirror technology for space applications,” Proc. SPIE 6113, 622-305 (2006).

Other (1)

D. C.O'Shea, A. D. Kathman, and T. J. Suleski, Diffractive Optics: Design, Fabrication, and Test (SPIE-International Society for Optical Engineering, 2003).

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Figures (5)

Fig. 1
Fig. 1

(a) Ideal smooth vortex phase ramp and (b) DM-generated vortex phase ramp.

Fig. 2
Fig. 2

Log plot of mode intensity versus diffraction vortex mode charge for the SPP (continuous line) and DM (segmented line) with design charge = 1 . Note that the SPP produces relatively high efficiencies for m = 16 and m = + 17 , which is given by the relation m = + k N ( k = ± 1 and N = 16 ).

Fig. 3
Fig. 3

Vortex mode purity versus topological charge for the 16 step SPP and DM-generated phase ramp.

Fig. 4
Fig. 4

Vortex mode purity versus topological charge for the 32 step SPP and DM-generated phase ramp.

Fig. 5
Fig. 5

Intensity and phase for vortex beams of charge + 1 , + 6 , and + 10 generated by the SPP (a)–(f). Intensity and phase for vortex beams of charge + 1 , + 6 , and + 10 generated by DM (g)–(l).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

f ( r , θ ) = + C m e i m θ .
C m = 1 2 π 0 2 π f ( r , θ ) e i m θ d θ .
f ( r , θ ) = e i φ quantized ( θ ) = q = 1 N e i 2 π N rect [ θ 2 π N ( q 1 / 2 ) ] .
e i φ quantized ( θ ) = + C m e i m θ ,
C m = 1 2 π 0 2 π e i φ quantized ( θ ) e i m θ d θ .
η m { 1 | m | 2 sin 2 ( m π N ) sin 2 [ π ( m ) ] sin 2 [ π ( m ) / N ] for m = + k N 0 for m + k N ,

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