Abstract

We found that the distances between isolated scatterers with similar columnar shapes could be measured by taking a single Fourier transform of their diffraction intensity. If the scatterers have different shapes, the distances between similar shapes can be selected from the distances between all the shapes. The distance from a specific scatterer can be measured with a resolution of 0.8 wavelengths and a precision of 0.01 wavelengths. This technique has the potential to be used in a novel optical memory that has a memory density as high as that of holographic memory, while can be fabricated by simple transfer molding. We used rigorous coupled-wave analysis to calculate the diffraction intensity. Some of the results were verified by nonstandard finite-difference time-domain simulations and experiments.

© 2012 OSA

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2011 (1)

T. Hoshino, S. Banerjee, J. B. Cole, M. Itoh, and T. Yatagai, “Shape analysis of wavelength-insensitive grating in the resonance domain,” Opt. Commun. 284(10-11), 2466–2472 (2011).
[CrossRef]

2009 (2)

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[CrossRef] [PubMed]

T. Hoshino, S. Banerjee, M. Itoh, and T. Yatagai, “Diffraction pattern of triangular grating in the resonance domain,” J. Opt. Soc. Am. A 26(3), 715–722 (2009).
[CrossRef] [PubMed]

2007 (3)

2005 (1)

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

2004 (1)

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

2003 (2)

T. Kashiwa, Y. Sendo, K. Taguchi, T. Ohtani, and Y. Kanai, “Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods,” IEEE Trans. Magn. 39(4), 2125–2128 (2003).
[CrossRef]

Y. Takahashi, K. Hayashi, and E. Matsubara, “Complex X-ray holography,” Phys. Rev. B 68(5), 052103 (2003).
[CrossRef]

2002 (2)

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89(8), 088303 (2002).
[CrossRef] [PubMed]

E. N. Glytsis, “Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis,” J. Opt. Soc. Am. A 19(4), 702–715 (2002).
[CrossRef] [PubMed]

2000 (2)

P. Lalanne and E. Silberstein, “Fourier-modal methods applied to waveguide computational problems,” Opt. Lett. 25(15), 1092–1094 (2000).
[CrossRef] [PubMed]

J. Nakayama, ““Periodic fourier transform and its application to wave scattering from a finite periodic surface,” IEICE Trans. Electron,” E 83-C, 481–487 (2000).

1999 (1)

1997 (1)

1995 (1)

1994 (1)

1992 (1)

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

1982 (1)

M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. A 72(10), 1385–1392 (1982).
[CrossRef]

1972 (1)

1971 (1)

D. E. Sayers, E. A. Stern, and F. W. Lytle, “New technique for investigating noncrystalline structures: Fourier analysis of the extended x-ray-absorption fine structure,” Phys. Rev. Lett. 27(18), 1204–1207 (1971).
[CrossRef]

1970 (1)

J. A. Rajchman, “Promise of optical memories,” J. Appl. Phys. 41(3), 1376–1383 (1970).
[CrossRef]

1963 (1)

Anderson, E. H.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89(8), 088303 (2002).
[CrossRef] [PubMed]

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

Banerjee, S.

Boher, P.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Chandezon, J.

Chaton, P.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Chon, J. W. M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[CrossRef] [PubMed]

Cole, J. B.

T. Hoshino, S. Banerjee, J. B. Cole, M. Itoh, and T. Yatagai, “Shape analysis of wavelength-insensitive grating in the resonance domain,” Opt. Commun. 284(10-11), 2466–2472 (2011).
[CrossRef]

Desieres, Y.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

du Pau, P.

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

El-Husseini, M.

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

Foucher, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Fukumoto, A.

Gaylord, T. K.

Germer, T. A.

Glytsis, E. N.

Granet, G.

Grann, E. B.

Gu, M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[CrossRef] [PubMed]

Hara, M.

Hayashi, K.

Y. Takahashi, K. Hayashi, and E. Matsubara, “Complex X-ray holography,” Phys. Rev. B 68(5), 052103 (2003).
[CrossRef]

Hazart, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Hill, B.

Hirayama, K.

Hirooka, K.

Hobbelen, D.

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

Hodgson, K. O.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89(8), 088303 (2002).
[CrossRef] [PubMed]

Hoshino, T.

Howells, M. R.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

Ishikawa, T.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89(8), 088303 (2002).
[CrossRef] [PubMed]

Ishioka, K.

Itoh, M.

Jabben, L.

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

Jacobsen, C.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

Johnson, B.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89(8), 088303 (2002).
[CrossRef] [PubMed]

Kanai, Y.

T. Kashiwa, Y. Sendo, K. Taguchi, T. Ohtani, and Y. Kanai, “Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods,” IEEE Trans. Magn. 39(4), 2125–2128 (2003).
[CrossRef]

Kashiwa, T.

T. Kashiwa, Y. Sendo, K. Taguchi, T. Ohtani, and Y. Kanai, “Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods,” IEEE Trans. Magn. 39(4), 2125–2128 (2003).
[CrossRef]

Kern, D. P.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

Kirz, J.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

Lai, B.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89(8), 088303 (2002).
[CrossRef] [PubMed]

Lalanne, P.

Leroux, T.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Li, L.

Lytle, F. W.

D. E. Sayers, E. A. Stern, and F. W. Lytle, “New technique for investigating noncrystalline structures: Fourier analysis of the extended x-ray-absorption fine structure,” Phys. Rev. Lett. 27(18), 1204–1207 (1971).
[CrossRef]

Matsubara, E.

Y. Takahashi, K. Hayashi, and E. Matsubara, “Complex X-ray holography,” Phys. Rev. B 68(5), 052103 (2003).
[CrossRef]

McNulty, I.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

Miao, J.

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89(8), 088303 (2002).
[CrossRef] [PubMed]

Moharam, M. G.

Nakayama, J.

J. Nakayama, ““Periodic fourier transform and its application to wave scattering from a finite periodic surface,” IEICE Trans. Electron,” E 83-C, 481–487 (2000).

Ohtani, T.

T. Kashiwa, Y. Sendo, K. Taguchi, T. Ohtani, and Y. Kanai, “Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods,” IEEE Trans. Magn. 39(4), 2125–2128 (2003).
[CrossRef]

Overschie, P.

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

Petit, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Plumey, J.-P.

Polinder, H.

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

Pommet, D. A.

Rajchman, J. A.

J. A. Rajchman, “Promise of optical memories,” J. Appl. Phys. 41(3), 1376–1383 (1970).
[CrossRef]

Sayers, D. E.

D. E. Sayers, E. A. Stern, and F. W. Lytle, “New technique for investigating noncrystalline structures: Fourier analysis of the extended x-ray-absorption fine structure,” Phys. Rev. Lett. 27(18), 1204–1207 (1971).
[CrossRef]

Sendo, Y.

T. Kashiwa, Y. Sendo, K. Taguchi, T. Ohtani, and Y. Kanai, “Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods,” IEEE Trans. Magn. 39(4), 2125–2128 (2003).
[CrossRef]

Silberstein, E.

Spronck, J.

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

Stern, E. A.

D. E. Sayers, E. A. Stern, and F. W. Lytle, “New technique for investigating noncrystalline structures: Fourier analysis of the extended x-ray-absorption fine structure,” Phys. Rev. Lett. 27(18), 1204–1207 (1971).
[CrossRef]

Taguchi, K.

T. Kashiwa, Y. Sendo, K. Taguchi, T. Ohtani, and Y. Kanai, “Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods,” IEEE Trans. Magn. 39(4), 2125–2128 (2003).
[CrossRef]

Takahashi, Y.

Y. Takahashi, K. Hayashi, and E. Matsubara, “Complex X-ray holography,” Phys. Rev. B 68(5), 052103 (2003).
[CrossRef]

Tanaka, K.

Tokuyama, K.

van Eijk, J.

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

van Heerden, P. J.

Watanabe, K.

Yatagai, T.

Zijlstra, P.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[CrossRef] [PubMed]

Appl. Opt. (4)

Assembly Autom. (1)

J. Spronck, M. El-Husseini, L. Jabben, P. Overschie, D. Hobbelen, P. du Pau, H. Polinder, and J. van Eijk, “Mastering high-density optical disks: a new concept design,” Assembly Autom. 24(4), 406–415 (2004).
[CrossRef]

E (1)

J. Nakayama, ““Periodic fourier transform and its application to wave scattering from a finite periodic surface,” IEICE Trans. Electron,” E 83-C, 481–487 (2000).

IEEE Trans. Magn. (1)

T. Kashiwa, Y. Sendo, K. Taguchi, T. Ohtani, and Y. Kanai, “Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods,” IEEE Trans. Magn. 39(4), 2125–2128 (2003).
[CrossRef]

J. Appl. Phys. (1)

J. A. Rajchman, “Promise of optical memories,” J. Appl. Phys. 41(3), 1376–1383 (1970).
[CrossRef]

J. Opt. Soc. Am. A (7)

Nature (1)

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[CrossRef] [PubMed]

Opt. Commun. (1)

T. Hoshino, S. Banerjee, J. B. Cole, M. Itoh, and T. Yatagai, “Shape analysis of wavelength-insensitive grating in the resonance domain,” Opt. Commun. 284(10-11), 2466–2472 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

Y. Takahashi, K. Hayashi, and E. Matsubara, “Complex X-ray holography,” Phys. Rev. B 68(5), 052103 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89(8), 088303 (2002).
[CrossRef] [PubMed]

D. E. Sayers, E. A. Stern, and F. W. Lytle, “New technique for investigating noncrystalline structures: Fourier analysis of the extended x-ray-absorption fine structure,” Phys. Rev. Lett. 27(18), 1204–1207 (1971).
[CrossRef]

Proc. SPIE (1)

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Science (1)

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High-resolution imaging by Fourier transform x-ray holography,” Science 256(5059), 1009–1012 (1992).
[CrossRef] [PubMed]

Other (7)

J. B. Cole, “High accuracy nonstandard finite-difference time-domain algorithms for computational electromagnetics: applications to optics and photonics,” in Advances in the Applications of Nonstandard Finite Difference Schemes, R. E. Mickens, ed. (World Scientific, Singapore, 2006), pp. 89–189.

S. Banerjee, “Nonstandard finite-difference time-domain algorithm: application to the design of subwavelength diffractive optical elements,” Ph.D. thesis, Univ. of Tsukuba (2006).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, Greenwood Village USA, 2005).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram depicting arrangement of two convex scatterers. There is only one boundary between regions 1 and 2, which both extend to infinity. The plate and the scatterers have a refractive index n2 of 1.5, while the refractive index of air n1 is 1.0.

Fig. 2
Fig. 2

Diffraction efficiency against Λ/λ for various θ (w/λ = 3, v/λ = 1.5, and d/v = 2).

Fig. 3
Fig. 3

(a) Diffraction intensity for two rectangles as a function of diffraction angle for various d/w (w/λ = 3, v/w = 0.5, and Λ/λ = 31). Auxiliary line that connects diffraction intensity is the envelope. (b) FT of diffraction intensity for various w/λ (v/w = 0.5, d/w = 0.5, and Λ/λ = 31).

Fig. 4
Fig. 4

Distance obtained from diffraction intensity by the NS-FDTD method as a function of diffraction angle. (a) Comparison of NS-FDTD and RCWA results for diffraction intensity from two rectangular scatterers as a function of diffraction angle (w/λ = 3, v/w = 0.5, d/w = 0.5, and Λ/λ = 31). Auxiliary line that connects diffraction intensity for RCWA is the envelope. (b) Result of FT of diffraction intensity by the NS-FDTD method for various w/λ (v/w = 0.5 and d/w = 0.5).

Fig. 5
Fig. 5

Distance obtained from the FT of the diffraction intensity against 1/λ. (a) Diffraction intensity for two triangular scatterers as a function of 1/λ for a specific angle θ (w = 1, v/w = 1, d/w = 1, and Λ = 30). (b) FT of (a).

Fig. 6
Fig. 6

Measured diffraction intensity for a triangular grating. (a) Schematic profile of the grating showing the definitions of w, d, and ds. Fill factor = 0.5 and aspect ratio d/w = 0.48; θ' is the incident angle. w is 3 or 5 μm. (b) Diffraction intensity from triangular gratings against 1/λ at a diffraction angle of 0° for grating periods of 3 and 5 μm. θ' is set to 45°, n2 = 1.52, and ds = 2 mm. The numbers 5–9 denote the diffraction order of the grating with period 5 μm. “EXP” indicates the experimental results and “CAL” indicates the calculated results.

Fig. 7
Fig. 7

(a) Rectangular scatterers with two different heights. r is the parameter which changes the distance between scatterers. The distance from scatterer 1 to the others is 3, 4, and 5. All v values are 0.2λ, d for scatterer 1 is 0.1λ, and d for the others is 0.05λ. Λ/λ = 31. (b) FT of angular distribution of diffraction intensity. The arrows indicate the peaks for scatterers 2, 3, and 4 in the case r = 1.

Fig. 8
Fig. 8

Collection of scatterers with different shapes and sizes. (a) Array consisting of triangular, rectangular and sinusoidal scatterers. Distances between convex 1 and the other convexes are 3, 4, 5, and 6 from the left of the array. Λ = 43. v = 1 for scatterer 1, 0.5 for scatterers 3 and 5, and 0.25 for scatterers 2 and 4. d for scatterer 1 is 1, and for the others is 0.5. (b) FT of diffraction intensity for a specific angle θ. The arrows indicate the peaks associated with scatterers 2, 3, 4, and 5.

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