Abstract

We propose a new method of optically reconstructing binary data formed by nanostructures with an elemental size several tens of nanometers smaller than the diffraction limit, implemented with an interference microscope and a complex-amplitude image pattern matching method. We examine the size dependency of the data reconstruction capacity using a light propagation simulation based on the finite-difference time-domain (FDTD) method and the Fourier spatial frequency filtering method. We demonstrated that the readable size of the binary nanostructure depends on the magnitude of noise.

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    [CrossRef]
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    [CrossRef]
  8. J. Fang and Z. Wu, “Closed-form expression of closed numerical reflection coefficient at PML Interfaces and optimization of PML Performance,” IEEE Microw. Guided Wave Lett.6(9), 332–334 (1996).
    [CrossRef]
  9. W. S. Torgerson, “Multidimensional scaling: I. Theory and method,” Psychometrika17(4), 401–419 (1952).
    [CrossRef]
  10. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt.13(11), 2693–2703 (1974).
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    [CrossRef]

1998

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett.73(15), 2078–2080 (1998).
[CrossRef]

1997

1996

J. Fang and Z. Wu, “Closed-form expression of closed numerical reflection coefficient at PML Interfaces and optimization of PML Performance,” IEEE Microw. Guided Wave Lett.6(9), 332–334 (1996).
[CrossRef]

1994

J.-P. Berenger, “A perfectly matched layer for the absorption of electro-magnetic waves,” J. Comput. Phys.114(2), 185–200 (1994).
[CrossRef]

1991

K. P. Bishop, S. M. Gasper, L. M. Milner, S. S. H. Naqvi, and J. R. McNeil, “Grating line shape characterization using scatterometry,” Proc. SPIE1545, 64–73 (1991).
[CrossRef]

J. H. Strickler and W. W. Webb, “Three-dimensional optical data storage in refractive media by two-photon point excitation,” Opt. Lett.16(22), 1780–1782 (1991).
[CrossRef] [PubMed]

1974

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

1963

1952

W. S. Torgerson, “Multidimensional scaling: I. Theory and method,” Psychometrika17(4), 401–419 (1952).
[CrossRef]

Atoda, N.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett.73(15), 2078–2080 (1998).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electro-magnetic waves,” J. Comput. Phys.114(2), 185–200 (1994).
[CrossRef]

Bishop, K. P.

K. P. Bishop, S. M. Gasper, L. M. Milner, S. S. H. Naqvi, and J. R. McNeil, “Grating line shape characterization using scatterometry,” Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Fang, J.

J. Fang and Z. Wu, “Closed-form expression of closed numerical reflection coefficient at PML Interfaces and optimization of PML Performance,” IEEE Microw. Guided Wave Lett.6(9), 332–334 (1996).
[CrossRef]

Gallagher, J. E.

Gasper, S. M.

K. P. Bishop, S. M. Gasper, L. M. Milner, S. S. H. Naqvi, and J. R. McNeil, “Grating line shape characterization using scatterometry,” Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Hayashi, S.

Herriott, D. R.

Ichimura, I.

Kino, G. S.

McNeil, J. R.

K. P. Bishop, S. M. Gasper, L. M. Milner, S. S. H. Naqvi, and J. R. McNeil, “Grating line shape characterization using scatterometry,” Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Milner, L. M.

K. P. Bishop, S. M. Gasper, L. M. Milner, S. S. H. Naqvi, and J. R. McNeil, “Grating line shape characterization using scatterometry,” Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Nakano, T.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett.73(15), 2078–2080 (1998).
[CrossRef]

Naqvi, S. S. H.

K. P. Bishop, S. M. Gasper, L. M. Milner, S. S. H. Naqvi, and J. R. McNeil, “Grating line shape characterization using scatterometry,” Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Rosenfeld, D. P.

Strickler, J. H.

Tominaga, J.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett.73(15), 2078–2080 (1998).
[CrossRef]

Torgerson, W. S.

W. S. Torgerson, “Multidimensional scaling: I. Theory and method,” Psychometrika17(4), 401–419 (1952).
[CrossRef]

van Heerden, P. J.

Webb, W. W.

White, A. D.

Wu, Z.

J. Fang and Z. Wu, “Closed-form expression of closed numerical reflection coefficient at PML Interfaces and optimization of PML Performance,” IEEE Microw. Guided Wave Lett.6(9), 332–334 (1996).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. Tominaga, T. Nakano, and N. Atoda, “An approach for recording and readout beyond the diffraction limit with an Sb thin film,” Appl. Phys. Lett.73(15), 2078–2080 (1998).
[CrossRef]

IEEE Microw. Guided Wave Lett.

J. Fang and Z. Wu, “Closed-form expression of closed numerical reflection coefficient at PML Interfaces and optimization of PML Performance,” IEEE Microw. Guided Wave Lett.6(9), 332–334 (1996).
[CrossRef]

IEEE Trans. Antenn. Propag.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

J. Comput. Phys.

J.-P. Berenger, “A perfectly matched layer for the absorption of electro-magnetic waves,” J. Comput. Phys.114(2), 185–200 (1994).
[CrossRef]

Opt. Lett.

Proc. SPIE

K. P. Bishop, S. M. Gasper, L. M. Milner, S. S. H. Naqvi, and J. R. McNeil, “Grating line shape characterization using scatterometry,” Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Psychometrika

W. S. Torgerson, “Multidimensional scaling: I. Theory and method,” Psychometrika17(4), 401–419 (1952).
[CrossRef]

Other

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC, 1993).

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Figures (12)

Fig. 1
Fig. 1

Binary nanostructure representing 4-bit binary digital data.

Fig. 2
Fig. 2

Flow chart for data reconstruction.

Fig. 3
Fig. 3

Interference microscope.

Fig. 4
Fig. 4

FDTD calculation model.

Fig. 5
Fig. 5

Example calculation results, showing (a) reflected near-field distribution, Ex(x, z), (b) near-field complex amplitude distribution on focal plane, unear(x), and (c) complex amplitude distribution on image sensor, u(x), after passing through microscope.

Fig. 6
Fig. 6

Complex amplitude templates (four bits). Solid line indicates the amplitude distribution and dashed lines indicates the phase distribution.

Fig. 7
Fig. 7

Degree of difference (DoD) between all pairs of templates versus the pit size. The curves labeled DoDmax, DoDmin, and DoDave are the maximum, minimum, and average DoD.

Fig. 8
Fig. 8

Relative positions of complex amplitude templates when wp = hp = 100 nm.

Fig. 9
Fig. 9

Relative positions of complex amplitude templates when wp = hp = 70 nm.

Fig. 10
Fig. 10

Relative positions of complex amplitude templates when wp = hp = 40 nm. Inset shows a magnified view of the region where the templates were clustered.

Fig. 11
Fig. 11

Complex-amplitude images with noise: (a) SNR = 30 dB and (b) SNR = 50 dB.

Fig. 12
Fig. 12

BER versus SNR of image sensor in binary data reconstruction with different elemental sizes.

Equations (12)

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DoD( u i , u j )=[ 1Cor( u i , u j ) 2 ],
Cor( u i , u j )= u i (x) u j * (x)dx | u i (x) | 2 dx | u i (x) | 2 dx .
u(x)= F 1 { F[ u near (x) ]H( f x ) },
H( f x )={ 1 if| f x |NA/λ 0 otherwize .
d ij 2 = ( x i x j ) t ( x i x j )= b ii + b jj 2 b ij ,
b ij =( d in 2 + d nj 2 d ij 2 )/2.
X=P Λ 1/2
I n (x)= | u(x)+ u r (x)exp( inπ/2 ) | 2 = | u(x) | 2 + | u r (x) | 2 +2[ i n u(x) u r * (x) ],
u(x)= { I 0 (x) I 2 (x)+i[ I 3 (x) I 1 (x) ] } / [ 4 u r (x) ] .
u (x)=u(x)+ [ N 02 (0,2 σ 2 )+i N 31 (0,2 σ 2 ) ] / [ 4 u r * (x) ] ,
SNR=20log( I max σ )
I max = max i,x [ | u i (x) | 2 + | u r (x) | 2 +2 | u i (x) u r * (x) | 2 ].

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