Abstract

This Letter presents the analysis of a new class of diffractive optical element, the odd-symmetry phase grating, which creates wavelength- and depth-robust features in its near-field diffraction pattern.

© 2013 Optical Society of America

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References

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  1. A. Wang, P. Gill, and A. Molnar, Appl. Opt. 48, 5897 (2009).
    [CrossRef]
  2. P. R. Gill, C. Lee, D.-G. Lee, A. Wang, and A. Molnar, Opt. Lett. 36, 2949 (2011).
    [CrossRef]
  3. P. R. Gill and A. C. Molnar, in Computational Optical Sensing and Imaging 2012 (Optical Society of America, 2012), p. JW3A.3.
  4. A. Wang and A. Molnar, IEEE J. Solid-State Circuits 47, 257 (2012).
    [CrossRef]
  5. P. R. Gill and D. G. Stork, “Lensless ultra-miniature imagers using odd-symmetry spiral phase gatings”, in Imaging Systems and Applications (Optical Society of America, to be published).
  6. Y. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12, 24 (2001).
    [CrossRef]
  7. A. Ostrovsky, V. Arrizón, and C. Rickenstorff-Parrao, Opt. Lett. 38, 534 (2013).
    [CrossRef]
  8. R. L. Morrison, J. Opt. Soc. Am. A 9, 464 (1992).
    [CrossRef]

2013 (1)

2012 (1)

A. Wang and A. Molnar, IEEE J. Solid-State Circuits 47, 257 (2012).
[CrossRef]

2011 (1)

2009 (1)

2001 (1)

Y. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12, 24 (2001).
[CrossRef]

1992 (1)

Arrizón, V.

Gill, P.

Gill, P. R.

P. R. Gill, C. Lee, D.-G. Lee, A. Wang, and A. Molnar, Opt. Lett. 36, 2949 (2011).
[CrossRef]

P. R. Gill and A. C. Molnar, in Computational Optical Sensing and Imaging 2012 (Optical Society of America, 2012), p. JW3A.3.

P. R. Gill and D. G. Stork, “Lensless ultra-miniature imagers using odd-symmetry spiral phase gatings”, in Imaging Systems and Applications (Optical Society of America, to be published).

Kivshar, Y. S.

Y. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12, 24 (2001).
[CrossRef]

Lee, C.

Lee, D.-G.

Molnar, A.

Molnar, A. C.

P. R. Gill and A. C. Molnar, in Computational Optical Sensing and Imaging 2012 (Optical Society of America, 2012), p. JW3A.3.

Morrison, R. L.

Ostrovskaya, E. A.

Y. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12, 24 (2001).
[CrossRef]

Ostrovsky, A.

Rickenstorff-Parrao, C.

Stork, D. G.

P. R. Gill and D. G. Stork, “Lensless ultra-miniature imagers using odd-symmetry spiral phase gatings”, in Imaging Systems and Applications (Optical Society of America, to be published).

Wang, A.

Appl. Opt. (1)

IEEE J. Solid-State Circuits (1)

A. Wang and A. Molnar, IEEE J. Solid-State Circuits 47, 257 (2012).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (2)

Opt. Photon. News (1)

Y. S. Kivshar and E. A. Ostrovskaya, Opt. Photon. News 12, 24 (2001).
[CrossRef]

Other (2)

P. R. Gill and A. C. Molnar, in Computational Optical Sensing and Imaging 2012 (Optical Society of America, 2012), p. JW3A.3.

P. R. Gill and D. G. Stork, “Lensless ultra-miniature imagers using odd-symmetry spiral phase gatings”, in Imaging Systems and Applications (Optical Society of America, to be published).

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Figures (2)

Fig. 1.
Fig. 1.

Odd-symmetry, binary phase grating shown in cross-section. A phase grating at the intersection of two optical media introduces a phase delay of a half-wavelength between light passing through a thick versus a thin portion of the grating. One robust null is shown as a dashed vertical line; if the grating were to repeat, then both the left and right borders would also exhibit robust nulls. The optical media have refractive indices and dispersions such that the phase delay is roughly constant across λs of interest. The grating in this example has only two depths (making it easy to manufacture), whereas in general the phase delay at any point need not belong to a discrete set.

Fig. 2.
Fig. 2.

Phase delay (solid line) induced by a 0.9 μm tall phase grating made from a high-dispersion, low-n optical plastic above a low-dispersion, high-n optical glass. Phase delays are roughly equal to π (dashed line) for all visible light.

Equations (15)

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Eλ,y0,z,ψ=PC(x,yy0,z)e2πirλeiϕ(x,y,ψ,λ)dydx.
Eλ,y0,z,ψ=HC(x,yy0,z)e2πirλ(eiϕ(x)+eiϕ(x))Grating effectsdydx,
ϕ(x,y,λ,ψ)=ϕ(x,y,λ,ψ)+π+2πm,mZ,
p(x)ϕ(x)+ϕ(x)+π2,
q(x)ϕ(x)ϕ(x)π2,
ϕ(x)=p(x)+q(x),
p(x)=p(x),
q(x)=q(x)π,
(eiϕ(x)+eiϕ(x))=2ieip(x)sin(q(x)).
Eλ,y0,z,ψ=HF(x,y)e2πirλG(x,y)dydx.
Eν,y0,z,ψ=12πHF(r)e2πiν·rG(r)dr.
F(r){F(r)ifx>00ifx0,
G(r){G(r)ifx>01ifx0,
Eν,y0,z,ψ=12πPF(r)e2πiν·rG(r)dr.
P|Eν,y0,z,ψ|2dν=P|F(r)G(r)|2dr.

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