Abstract

Abstract

We propose diffractive optical elements with a spatially-varying nonlinear refractive index. Such a component acts as a diffractive optical element whose properties depend on the intensity of the incoming beam. We present a method for designing such elements, and as specific examples we study three types of nonlinear diffractive optical elements: Nonlinear Fresnel Zone Plates, Two-foci Nonlinear Fresnel Zone Plates, and Fresnel Zone Plate to Grating interpolator.

© 2007 Optical Society of America

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References

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  1. T. H. Bett, C. N. Danson, P. Jinks, D. A. Pepler, I. N. Ross, and R. M. Stevenson, "Binary phase zone-plate arrays for laser-beam spatial-intensity distribution conversion," Appl. Opt. 34, 4025-4036 (1995).
    [CrossRef] [PubMed]
  2. H. I. Smith, "A proposal for maskless zone-plate-array lithography," J. Vac. Sci. Technol. B 14, 4318-4322 (1996).
    [CrossRef]
  3. R. W. Boyd, Nonlinear Optics, 2 ed. (Academic Press, New York, 2002).
  4. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 2.
    [CrossRef]
  5. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik. 35, 237-246 (1972).
  6. N. Peyghambarian and R. A. Norwood, "Organic optoelectronics materials and devices for photonic applications, part one," Opt. Photonics News 16, 30-35 (2005).
    [CrossRef]
  7. X. Wang, D. Wilson, R. Muller, P. Maker, and D. Psaltis, "Liquid-crystal blazed-grating beam deflector," Appl. Opt. 39, 6545-6555 (2000).
    [CrossRef]
  8. L. J. Guo, X. Cheng, and C. Y. Chao, "Fabrication of photonic nanostructures in nonlinear optical polymers," J. Mod. Opt. 49, 663-673 (2002).
    [CrossRef]
  9. M. Morin, G. Duree, G. Salamo, and M. Segev, "Waveguides formed by quasi-steady-state photorefractive spatial solitons," Opt. Lett. 20, 2066-2068 (1995).
    [CrossRef] [PubMed]

2005

N. Peyghambarian and R. A. Norwood, "Organic optoelectronics materials and devices for photonic applications, part one," Opt. Photonics News 16, 30-35 (2005).
[CrossRef]

2002

L. J. Guo, X. Cheng, and C. Y. Chao, "Fabrication of photonic nanostructures in nonlinear optical polymers," J. Mod. Opt. 49, 663-673 (2002).
[CrossRef]

2000

1996

H. I. Smith, "A proposal for maskless zone-plate-array lithography," J. Vac. Sci. Technol. B 14, 4318-4322 (1996).
[CrossRef]

1995

1972

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik. 35, 237-246 (1972).

Bett, T. H.

Chao, C. Y.

L. J. Guo, X. Cheng, and C. Y. Chao, "Fabrication of photonic nanostructures in nonlinear optical polymers," J. Mod. Opt. 49, 663-673 (2002).
[CrossRef]

Cheng, X.

L. J. Guo, X. Cheng, and C. Y. Chao, "Fabrication of photonic nanostructures in nonlinear optical polymers," J. Mod. Opt. 49, 663-673 (2002).
[CrossRef]

Danson, C. N.

Duree, G.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik. 35, 237-246 (1972).

Guo, L. J.

L. J. Guo, X. Cheng, and C. Y. Chao, "Fabrication of photonic nanostructures in nonlinear optical polymers," J. Mod. Opt. 49, 663-673 (2002).
[CrossRef]

Jinks, P.

Maker, P.

Morin, M.

Muller, R.

Norwood, R. A.

N. Peyghambarian and R. A. Norwood, "Organic optoelectronics materials and devices for photonic applications, part one," Opt. Photonics News 16, 30-35 (2005).
[CrossRef]

Pepler, D. A.

Peyghambarian, N.

N. Peyghambarian and R. A. Norwood, "Organic optoelectronics materials and devices for photonic applications, part one," Opt. Photonics News 16, 30-35 (2005).
[CrossRef]

Psaltis, D.

Ross, I. N.

Salamo, G.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik. 35, 237-246 (1972).

Segev, M.

Smith, H. I.

H. I. Smith, "A proposal for maskless zone-plate-array lithography," J. Vac. Sci. Technol. B 14, 4318-4322 (1996).
[CrossRef]

Stevenson, R. M.

Wang, X.

Wilson, D.

Appl. Opt.

J. Mod. Opt.

L. J. Guo, X. Cheng, and C. Y. Chao, "Fabrication of photonic nanostructures in nonlinear optical polymers," J. Mod. Opt. 49, 663-673 (2002).
[CrossRef]

J. Vac. Sci. Technol. B

H. I. Smith, "A proposal for maskless zone-plate-array lithography," J. Vac. Sci. Technol. B 14, 4318-4322 (1996).
[CrossRef]

Opt. Lett.

Opt. Photonics News

N. Peyghambarian and R. A. Norwood, "Organic optoelectronics materials and devices for photonic applications, part one," Opt. Photonics News 16, 30-35 (2005).
[CrossRef]

Optik.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik. 35, 237-246 (1972).

Other

R. W. Boyd, Nonlinear Optics, 2 ed. (Academic Press, New York, 2002).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 2.
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

NDOE implemented with the two-layer approach: One layer deals with the nonlinear properties and the other handles the linear properties, by spatially varying the linear refractive index (left), or the surface relief (right).

Fig. 2.
Fig. 2.

Nonlinear Fresnel Zone Plate: (a) NFZP pattern: the nonlinear refractive index is different from zero only at the dark rings. (b) The on-axis intensity normalized to the intensity of the incoming plane wave, plotted for low intensity (red line), moderate intensity (blue line), and high intensity (green line). (c) Calculated intensity at the focus as a function of the intensity of the incoming beam (blue line) and power-law fit (red line). (d) Intensity at the focus as a function of the intensity of the incoming beam for a complementary NFZP.

Fig. 3.
Fig. 3.

Two-foci Nonlinear Fresnel Zone Plate: Radial cross-sections of the required phase functions for (a) a 3mm FZP and (b) a 5mm FZP, and the resulting (c) linear and (d) nonlinear refractive indices. (e) Normalized on-axis intensity for low-intensity (red line), moderate-intensity (black line), and high- intensity (blue line) incoming beam. (f) Normalized intensity at the two foci - 3mm (red line) and 5mm (blue line), as a function of the intensity of the incident beam.

Fig. 4.
Fig. 4.

FZP to Grating Interpolator: Computed linear (a) and nonlinear (b) refractive indices. (c) 2D cross section of the intensity at the focal-plane and 1D cross section of the intensity (blue line) through the focal point. (d) Intensity cross section after short propagation of a moderate-intensity beam, and (e) after longer propagation, showing the combination of diffraction to multiple angles and partial focusing.

Equations (4)

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ϕ 1 ( x , y ) = Lk [ Δ n L ( x , y ) + n 2 ( x , y ) g ( I 1 ( x , y ) ) ] ,
ϕ 2 ( x , y ) = Lk [ Δ n L ( x , y ) + n 2 ( x , y ) g ( I 2 ( x , y ) ) ] .
n 2 ( x , y ) = 1 kL Δ ϕ Δ g ,
Δ n L ( x , y ) = 1 kL ϕ 1 g 2 ϕ 2 g 1 Δ g ,

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