Abstract

We present electrically controlled wavefront modulators that simultaneously focus and introduce vorticity to an incident beam. These modulators are made out of spiral-shaped 180° ferroelectric domains in lithium niobate; they have a virtually instantaneous response time, withstand high power and can be used throughout the transparency region of the material (0.4 - 5 μm).

© 2009 Optical Society of America

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References

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  19. R. C. Miller. "Optical Second Harmonic Generation in Piezoelectric Crystals," Appl. Phys. Lett. 5, 17 (1964).
    [CrossRef]
  20. G. J. Edwards and M. Lawrence, "A temperature dependent dispersion for congruently grown lithium niobate," Opt. Quantum Electron. 16, 373-374 (1984).
    [CrossRef]

2008

Y.J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, "Generating electrically tunable optical vortices generated by a liquid crystal cell with patterned electrode," App. Phys. Lett. 92, 101114 (2008).
[CrossRef]

2005

2004

2003

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

2002

2001

G. A. Swartzlander, Jr., "Peering into darkness with a vortex spatial filter," Opt. Lett. 26, 1752-1754 (2001).

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

1999

1998

1997

1992

1990

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocations in their wavefronts," JETP Lett. 52, 429-431 (1990).

1984

G. J. Edwards and M. Lawrence, "A temperature dependent dispersion for congruently grown lithium niobate," Opt. Quantum Electron. 16, 373-374 (1984).
[CrossRef]

1964

R. C. Miller. "Optical Second Harmonic Generation in Piezoelectric Crystals," Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

’t Hooft, G. W.

Almazov, A. A.

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocations in their wavefronts," JETP Lett. 52, 429-431 (1990).

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Cabtree, K.

Cudney, R. S.

Davis, J. A.

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Edwards, G. J.

G. J. Edwards and M. Lawrence, "A temperature dependent dispersion for congruently grown lithium niobate," Opt. Quantum Electron. 16, 373-374 (1984).
[CrossRef]

Elfstrom, H.

Eliel, E. R.

Escamilla, H. M.

Gan, X.

Ganic, D.

Grier, D. G.

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Gu, M.

Guo, C.-S.

Hain, M.

Haist, T.

Heckenberg, N. R.

Jazbinsek, M.

M. Jazbinsek and M. Zgonik, "Material tensor parameters of LiNbO3 relevant for electro-and elasto-optics," Appl. Phys. B 74, 407-414 (2002).
[CrossRef]

Khonina, S. N.

Kloosterboer, J. G.

Kotlyar, V. V.

Law, C. T.

Lawrence, M.

G. J. Edwards and M. Lawrence, "A temperature dependent dispersion for congruently grown lithium niobate," Opt. Quantum Electron. 16, 373-374 (1984).
[CrossRef]

Liu, X.

Liu, Y.J.

Y.J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, "Generating electrically tunable optical vortices generated by a liquid crystal cell with patterned electrode," App. Phys. Lett. 92, 101114 (2008).
[CrossRef]

Luo, D.

Y.J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, "Generating electrically tunable optical vortices generated by a liquid crystal cell with patterned electrode," App. Phys. Lett. 92, 101114 (2008).
[CrossRef]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

McDuff, R.

Miller, R. C.

R. C. Miller. "Optical Second Harmonic Generation in Piezoelectric Crystals," Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Moreno, I.

Oemrawsingh, S. S. R.

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Raszewski, Z.

Y.J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, "Generating electrically tunable optical vortices generated by a liquid crystal cell with patterned electrode," App. Phys. Lett. 92, 101114 (2008).
[CrossRef]

Reicherter, M.

Ren, X.-Y.

Ríos, L. A.

Rozas, D.

Sacks, Z. S.

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Smith, C. P.

Soifer, V. A.

Somalingam, S.

Soskin, M. S.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocations in their wavefronts," JETP Lett. 52, 429-431 (1990).

Stankovic, S.

Sun, X. W.

Y.J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, "Generating electrically tunable optical vortices generated by a liquid crystal cell with patterned electrode," App. Phys. Lett. 92, 101114 (2008).
[CrossRef]

Swartzlander, G. A.

Tiziani, H. J.

Tschudi, T.

Turunen, J.

van Houwelingen, J. A. W.

Vasnetsov, M. V.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocations in their wavefronts," JETP Lett. 52, 429-431 (1990).

Verstegen, E. J. K.

Wageman, E. U.

Wang, H.-T.

White, A. G.

Woerdman, J. P.

Zgonik, M.

M. Jazbinsek and M. Zgonik, "Material tensor parameters of LiNbO3 relevant for electro-and elasto-optics," Appl. Phys. B 74, 407-414 (2002).
[CrossRef]

App. Phys. Lett.

Y.J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, "Generating electrically tunable optical vortices generated by a liquid crystal cell with patterned electrode," App. Phys. Lett. 92, 101114 (2008).
[CrossRef]

Appl. Opt.

Appl. Phys. B

M. Jazbinsek and M. Zgonik, "Material tensor parameters of LiNbO3 relevant for electro-and elasto-optics," Appl. Phys. B 74, 407-414 (2002).
[CrossRef]

Appl. Phys. Lett.

R. C. Miller. "Optical Second Harmonic Generation in Piezoelectric Crystals," Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

JETP Lett.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocations in their wavefronts," JETP Lett. 52, 429-431 (1990).

Nature

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

G. J. Edwards and M. Lawrence, "A temperature dependent dispersion for congruently grown lithium niobate," Opt. Quantum Electron. 16, 373-374 (1984).
[CrossRef]

Science

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd edition (McGraw-Hill, New York, 1996).

Supplementary Material (8)

» Media 1: MOV (1080 KB)     
» Media 2: MOV (1069 KB)     
» Media 3: MOV (1072 KB)     
» Media 4: MOV (1059 KB)     
» Media 5: MOV (285 KB)     
» Media 6: MOV (736 KB)     
» Media 7: MOV (1551 KB)     
» Media 8: MOV (1625 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Vorticity-producing transmittance function. Black and white zones correspond to +Δϕ and −Δϕ, respectively. (a) q = 2; (b) q = 8.

Fig. 2.
Fig. 2.

Single-frame excerpts from theoretical animations of the evolution of the beam with propagation distance z. In both cases q = 2 and Δϕ = π/2, λ=515 nm and f =48 cm. (a) w 2 / λf = 4 (Media 1); (b) w 2 / λf = 16 (Media 2).

Fig. 3.
Fig. 3.

Single-frame excerpts from theoretical animations of the evolution of the beam with propagation distance z. (a) q = 8 (Media 3); (b) q = 20 (Media 4). In both cases w 2 / λf = 16, Δϕ = π/2, λ = 515 nm and f = 48 cm.

Fig. 4.
Fig. 4.

Vortex lens with q = 2. (a) Photoresist pattern; (b) ferroelectric domain pattern. Dimensions: 1.8 × 1.3 mm.

Fig. 5.
Fig. 5.

Single-frame excerpts from movies of the evolution of the beam with propagation distance for ∣Δϕ∣ = π/2. The lenses were illuminated by a collimated 515 nm beam. (a) q = 2, w 2 / λf ≈ 4 (Media 5); (b) q = 2, w 2 / λf≈ 16 (Media 6); (c) q = 20, w 2/λf ≈ 16 (Media 7).

Fig. 6.
Fig. 6.

Single-frame excerpt from a movie of the apparent rotating pattern (Media 8).

Equations (8)

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

ϕV(r,θ)=exp[iqθ],
Δϕ(V)=πno3r13Vλ,
tFZP(r,θ)={exp[+iΔϕ]ifsin(πr2)>0exp[iΔϕ]ifsin(πr2)<0,
z=±f/m,
t(r,θ)={exp[+iΔϕ]ifsin(πr2+)>0exp[iΔϕ]ifsin(πr2+)<0.
E(z,x,y)=1iλzexp[ikz]exp[ikx2+y22z]×
×++E(0,x,y)t(x,y)exp[ikx2+y22z]exp[ikxx+yyz] dxdy ,
I(z,x,y)E(z,x,y)21z2{E(0,x,y)t(x,y)exp[ikx2+y22z]},

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