Abstract

Holographic lithography is an ideal technique for fabricating three-dimensional photonic crystals. However, a critical stage in the fabrication is the minute alignment of the layers with one another. We present a simple moirelike alignment technique with better than 20-nm translation resolution and 45µrad rotation resolution. This technique can easily be extended to other situations when low-cost, high-precision alignment is needed.

© 2002 Optical Society of America

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References

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  1. E. Yablonovich, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef]
  2. S. Jhon, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef]
  3. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
    [CrossRef]
  4. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
    [CrossRef] [PubMed]
  5. A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
    [CrossRef]
  6. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
    [CrossRef] [PubMed]
  7. W. M. Moreau, Semiconductor Lithography (Plenum, New York, 1988).
    [CrossRef]
  8. S. Ishihara, Int. J. Jpn. Soc. Precis. Eng. 30, 103 (1996).
  9. N. Yamamoto and S. Noda, Jpn. J. Appl. Phys. 37, 3334 (1998).
    [CrossRef]
  10. M. C. King and D. H. Berry, Appl. Opt. 11, 11 (1972).
  11. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
    [CrossRef]

2000 (3)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
[CrossRef]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

1998 (2)

N. Yamamoto and S. Noda, Jpn. J. Appl. Phys. 37, 3334 (1998).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

1996 (1)

S. Ishihara, Int. J. Jpn. Soc. Precis. Eng. 30, 103 (1996).

1994 (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

1987 (2)

E. Yablonovich, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

S. Jhon, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

1972 (1)

M. C. King and D. H. Berry, Appl. Opt. 11, 11 (1972).

Arsh, A.

A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
[CrossRef]

Berry, D. H.

M. C. King and D. H. Berry, Appl. Opt. 11, 11 (1972).

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Blur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Feigel, A.

A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
[CrossRef]

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Ho, K. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Ishihara, S.

S. Ishihara, Int. J. Jpn. Soc. Precis. Eng. 30, 103 (1996).

Jhon, S.

S. Jhon, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

King, M. C.

M. C. King and D. H. Berry, Appl. Opt. 11, 11 (1972).

Klebanov, M.

A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
[CrossRef]

Kotler, Z.

A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
[CrossRef]

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Lin, S. Y.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Lyubin, V.

A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
[CrossRef]

Moreau, W. M.

W. M. Moreau, Semiconductor Lithography (Plenum, New York, 1988).
[CrossRef]

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

N. Yamamoto and S. Noda, Jpn. J. Appl. Phys. 37, 3334 (1998).
[CrossRef]

Sfez, B.

A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
[CrossRef]

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Sigalas, M. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

Yablonovich, E.

E. Yablonovich, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

N. Yamamoto and S. Noda, Jpn. J. Appl. Phys. 37, 3334 (1998).
[CrossRef]

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Appl. Opt. (1)

M. C. King and D. H. Berry, Appl. Opt. 11, 11 (1972).

Appl. Phys. Lett. (1)

A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, Appl. Phys. Lett. 77, 3221 (2000).
[CrossRef]

Int. J. Jpn. Soc. Precis. Eng. (1)

S. Ishihara, Int. J. Jpn. Soc. Precis. Eng. 30, 103 (1996).

Jpn. J. Appl. Phys. (1)

N. Yamamoto and S. Noda, Jpn. J. Appl. Phys. 37, 3334 (1998).
[CrossRef]

Nature (2)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, Nature 404, 53 (2000).
[CrossRef] [PubMed]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, Nature 394, 251 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

E. Yablonovich, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

S. Jhon, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Science (1)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

Solid State Commun. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Other (1)

W. M. Moreau, Semiconductor Lithography (Plenum, New York, 1988).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Geometric configuration of the alignment method. The alignment can be accomplished by observation of only two specific diffraction orders, k1n and k2m, corresponding to different incident beams.

Fig. 2
Fig. 2

Typical diffraction pattern for nearly aligned fringes. The fringes and the reference grating have the same periods and directions only when the two diffraction orders (k1n and k2m) of the two interfering beams coincide, in which case the far-field interference pattern is a homogeneous spot. In the experimental conditions the better than 0.004% period and the 45µrad rotational accuracy fittings were achieved for a 1 cm×1 cm grating with a 450-nm period.

Fig. 3
Fig. 3

Measured far-field diffracted intensity as a function of the relative shift between the fringes and the reference grating. Relative shift Rshift between fringes and grating is determined by measurement of the far-field intensity of two coinciding diffraction orders, k1n and k2m. The intensity varies periodically with the maxima when fringes are in phase with the reference grating and with minima in the antiphase case. In the experiment the reference grating was translated by an open-loop piezoelectric transducer. A precision of ΔRshift17 nm was obtained.

Equations (16)

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

Rp,q=R0+pΔr+qΔr,
ΔrΔr.
IRscr=p,qexpik1Rp,q+ik1nRscr-Rp,q2,
IRscr=A expik1-k1nR0+ik1nRscr2,
Δrk1-k1n=2πn, Δrk1-k1n=2πl.
Iintr=E021+expik1-k2r2.
ki=ksin θi cos ϕi,sin θi sin ϕi,cos θi,
kgratfring=ksin θ1 cos ϕ1-sin θ2 cos ϕ2,sin θ1 sin ϕ1-sin θ2 sin ϕ2,0.
kgratref=2π/d,0,0,
sin θ1 cos ϕ1-sin θ1n cos ϕ1n=nλ/d,sin θ1 sin ϕ1-sin θ1n sin ϕ1n=0,sin θ2 cos ϕ2-sin θ2m cos ϕ2m=mλ/d,sin θ2 sin ϕ2-sin θ2m sin ϕ2m=0.
kgratfring=2πλn-mλd+sin θ1n cos ϕ1n-sin θ2m cos ϕ2m,sin θ1n sin ϕ1n-sin θ2m sin ϕ2m,0.
n=m+1, θ1n=θ2m, ϕ1n=ϕ2m.
Δk=k1n-k2m.
Δd/d=Δδ=d/D.
IRscr=E12+E22+2E1E2cos2πRshift/d+Rscr-R0k1n-k2m+φstr,
ΔI122IRshift2|Rshift=0ΔRshiftnoise2ΔRshiftnoised2π2ΔII1/2.

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