Abstract

Diffraction limit is manifested in the loss of high spatial frequency information that results from decay of evanescent waves. As a result, conventional far-field optics yields no information about an object’s subwavelength features. Here we propose a novel approach to recovering evanescent waves in the far field, thereby enabling subwavelength-resolved imaging and spatial spectroscopy. Our approach relies on shifting the frequency and the wave vector of near-field components via scattering on acoustic phonons. This process effectively removes the spatial frequency cut-off for unambiguous far field detection. This technique can be adapted for digital holography, making it possible to perform phase-sensitive subwavelength imaging. We discuss the implementation of such a system in the mid-IR and THz bands, with possible extension to other spectral regions.

© 2011 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  4. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Scie. U.S.A. 102, 13,081–6 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399, 134–137 (1999).
    [CrossRef]
  9. N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. Acoustooptic diffraction efficiency, and hence the signal-to-noise ratio varies as 1/q.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  26. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]

2010 (1)

M. E. Testorf and M. A. Fiddy, “Superresolution Imaging Revisited,” Adv. Imag. Electron. Phys. 163, 165–218 (2010).
[CrossRef]

2008 (2)

2007 (2)

Y. Kuznetsova, A. Neumann, and S. R. Brueck, “Imaging interferometric microscopy-approaching the linear systems limits of optical resolution.” Opt. Express 15, 6651–63 (2007).
[CrossRef] [PubMed]

M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
[CrossRef]

2006 (2)

S. Alexandrov, T. Hillman, T. Gutzler, and D. Sampson, “Synthetic Aperture Fourier Holographic Optical Microscopy,” Phys. Rev. Lett. 97, 168,102 (2006).
[CrossRef]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, “Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit,” J. Opt. Soc. Am. B 23, 2383–2392 (2006).
[CrossRef]

2005 (3)

R. Lanz and P. Muralt, “Bandpass filters for 8 ghz using solidly mounted bulk acoustic wave resonators,” IEEE Trans. Ultrasonic. Ferroelec. Freq. Control 52, 938 – 948 (2005).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Opt. Lett. 30, 75–77 (2005).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Scie. U.S.A. 102, 13,081–6 (2005).

2002 (2)

N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
[CrossRef]

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143 (2002).
[CrossRef]

2001 (1)

B. Dragnea, J. Preusser, J. M. Szarko, S. R. Leone, and W. D. J. Hinsberg, “Pattern characterization of deep-ultraviolet photoresists by near-field infrared microscopy,” J. Vac. Sci. Technol. B 19, 142–152 (2001).
[CrossRef]

2000 (2)

1999 (3)

1997 (2)

1994 (1)

U. Schnars and W. Jüptner, “Direct recording of holograms by a ccd target and numerical reconstruction,” Appl. Opt. 33, 179181 (1994).
[CrossRef]

1967 (2)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

W. Lukosz, “Optical Systems with Resolving Powers Exceeding the Classical Limit II,” J. Opt. Soc. A. 57, 932 (1967).
[CrossRef]

Alexandrov, S.

S. Alexandrov, T. Hillman, T. Gutzler, and D. Sampson, “Synthetic Aperture Fourier Holographic Optical Microscopy,” Phys. Rev. Lett. 97, 168,102 (2006).
[CrossRef]

Alnot, P.

M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
[CrossRef]

Assouar, M. B.

M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
[CrossRef]

Bo, F.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143 (2002).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003), 2nd ed.

Brueck, S. R.

Collot, L.

Cuche, E.

De Nicola, S.

Depeursinge, C.

Dragnea, B.

B. Dragnea, J. Preusser, J. M. Szarko, S. R. Leone, and W. D. J. Hinsberg, “Pattern characterization of deep-ultraviolet photoresists by near-field infrared microscopy,” J. Vac. Sci. Technol. B 19, 142–152 (2001).
[CrossRef]

Durant, S.

Elmazria, O.

M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
[CrossRef]

Ferraro, P.

Fiddy, M. A.

M. E. Testorf and M. A. Fiddy, “Superresolution Imaging Revisited,” Adv. Imag. Electron. Phys. 163, 165–218 (2010).
[CrossRef]

Finizio, a.

Garcia, J.

Garcia Martinez, P.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Grilli, S.

Gross, M.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Scie. U.S.A. 102, 13,081–6 (2005).

Gutzler, T.

S. Alexandrov, T. Hillman, T. Gutzler, and D. Sampson, “Synthetic Aperture Fourier Holographic Optical Microscopy,” Phys. Rev. Lett. 97, 168,102 (2006).
[CrossRef]

Hillman, T.

S. Alexandrov, T. Hillman, T. Gutzler, and D. Sampson, “Synthetic Aperture Fourier Holographic Optical Microscopy,” Phys. Rev. Lett. 97, 168,102 (2006).
[CrossRef]

Hinsberg, W. D. J.

B. Dragnea, J. Preusser, J. M. Szarko, S. R. Leone, and W. D. J. Hinsberg, “Pattern characterization of deep-ultraviolet photoresists by near-field infrared microscopy,” J. Vac. Sci. Technol. B 19, 142–152 (2001).
[CrossRef]

Jüptner, W.

U. Schnars and W. Jüptner, “Direct recording of holograms by a ccd target and numerical reconstruction,” Appl. Opt. 33, 179181 (1994).
[CrossRef]

Keilmann, F.

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399, 134–137 (1999).
[CrossRef]

Kirsch, P.

M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
[CrossRef]

Kiryuschev, I.

Knoll, B.

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399, 134–137 (1999).
[CrossRef]

Konforti, N.

Korpel, A.

A. Korpel, Acoustooptics (Marcel Dekker, New York, 1989).

Kuznetsova, Y.

Lanz, R.

R. Lanz and P. Muralt, “Bandpass filters for 8 ghz using solidly mounted bulk acoustic wave resonators,” IEEE Trans. Ultrasonic. Ferroelec. Freq. Control 52, 938 – 948 (2005).
[CrossRef]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Le Clerc, F.

Leone, S. R.

B. Dragnea, J. Preusser, J. M. Szarko, S. R. Leone, and W. D. J. Hinsberg, “Pattern characterization of deep-ultraviolet photoresists by near-field infrared microscopy,” J. Vac. Sci. Technol. B 19, 142–152 (2001).
[CrossRef]

Liu, C.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143 (2002).
[CrossRef]

Liu, Z.

Lohmann, A. W.

Lukosz, W.

W. Lukosz, “Optical Systems with Resolving Powers Exceeding the Classical Limit II,” J. Opt. Soc. A. 57, 932 (1967).
[CrossRef]

Marquet, P.

Mendlovic, D.

Merola, F.

Mortet, V.

M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
[CrossRef]

Muralt, P.

R. Lanz and P. Muralt, “Bandpass filters for 8 ghz using solidly mounted bulk acoustic wave resonators,” IEEE Trans. Ultrasonic. Ferroelec. Freq. Control 52, 938 – 948 (2005).
[CrossRef]

Narimanov, E. E.

Neumann, A.

Paturzo, M.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Planken, P. C. M.

N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
[CrossRef]

Podolskiy, V. A.

Preusser, J.

B. Dragnea, J. Preusser, J. M. Szarko, S. R. Leone, and W. D. J. Hinsberg, “Pattern characterization of deep-ultraviolet photoresists by near-field infrared microscopy,” J. Vac. Sci. Technol. B 19, 142–152 (2001).
[CrossRef]

Sampson, D.

S. Alexandrov, T. Hillman, T. Gutzler, and D. Sampson, “Synthetic Aperture Fourier Holographic Optical Microscopy,” Phys. Rev. Lett. 97, 168,102 (2006).
[CrossRef]

Schnars, U.

U. Schnars and W. Jüptner, “Direct recording of holograms by a ccd target and numerical reconstruction,” Appl. Opt. 33, 179181 (1994).
[CrossRef]

Shemer, A.

Steele, J. M.

Szarko, J. M.

B. Dragnea, J. Preusser, J. M. Szarko, S. R. Leone, and W. D. J. Hinsberg, “Pattern characterization of deep-ultraviolet photoresists by near-field infrared microscopy,” J. Vac. Sci. Technol. B 19, 142–152 (2001).
[CrossRef]

Testorf, M. E.

M. E. Testorf and M. A. Fiddy, “Superresolution Imaging Revisited,” Adv. Imag. Electron. Phys. 163, 165–218 (2010).
[CrossRef]

Tiusan, C.

M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
[CrossRef]

van der Valk, N. C. J.

N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
[CrossRef]

Wang, Y.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143 (2002).
[CrossRef]

Yamaguchi, I.

Zalevsky, Z.

Zhang, T.

Zhang, X.

Zheludev, N. I.

N. I. Zheludev, “What diffraction limit?” Nature Mat. 7, 420–2 (2008).
[CrossRef]

Zhu, J.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143 (2002).
[CrossRef]

Adv. Imag. Electron. Phys. (1)

M. E. Testorf and M. A. Fiddy, “Superresolution Imaging Revisited,” Adv. Imag. Electron. Phys. 163, 165–218 (2010).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (3)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
[CrossRef]

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143 (2002).
[CrossRef]

IEEE Trans. Ultrasonic. Ferroelec. Freq. Control (1)

R. Lanz and P. Muralt, “Bandpass filters for 8 ghz using solidly mounted bulk acoustic wave resonators,” IEEE Trans. Ultrasonic. Ferroelec. Freq. Control 52, 938 – 948 (2005).
[CrossRef]

J. Appl. Phys. (1)

M. B. Assouar, O. Elmazria, P. Kirsch, P. Alnot, V. Mortet, and C. Tiusan, “High-frequency surface acoustic wave devices based on aln/diamond layered structure realized using e-beam lithography,” J. Appl. Phys. 101, 114507 (2007).
[CrossRef]

J. Opt. Soc. A. (1)

W. Lukosz, “Optical Systems with Resolving Powers Exceeding the Classical Limit II,” J. Opt. Soc. A. 57, 932 (1967).
[CrossRef]

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

J. Vac. Sci. Technol. B (1)

B. Dragnea, J. Preusser, J. M. Szarko, S. R. Leone, and W. D. J. Hinsberg, “Pattern characterization of deep-ultraviolet photoresists by near-field infrared microscopy,” J. Vac. Sci. Technol. B 19, 142–152 (2001).
[CrossRef]

Nature (1)

B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399, 134–137 (1999).
[CrossRef]

Nature Mat. (1)

N. I. Zheludev, “What diffraction limit?” Nature Mat. 7, 420–2 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

S. Alexandrov, T. Hillman, T. Gutzler, and D. Sampson, “Synthetic Aperture Fourier Holographic Optical Microscopy,” Phys. Rev. Lett. 97, 168,102 (2006).
[CrossRef]

Proc. Natl. Acad. Scie. U.S.A. (1)

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Scie. U.S.A. 102, 13,081–6 (2005).

Other (3)

Acoustooptic diffraction efficiency, and hence the signal-to-noise ratio varies as 1/q.

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003), 2nd ed.

A. Korpel, Acoustooptics (Marcel Dekker, New York, 1989).

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Figures (3)

Fig. 1
Fig. 1

Schematics of the proposed system.

Fig. 2
Fig. 2

(a) Optical test target and its modified version (inset). In the modified target, the “5” label of every column has been replaced by another digit. (b) Computed output of the system in the presence of noise (shown in grayscale) assuming a realistic, noisy detector with 400 active photocells. The modified optical target is superimposed for illustration purposes. The output of the system clearly identifies the location of every modified digit, even for regions far below the diffraction limit.

Fig. 3
Fig. 3

(a) Schematics of the proposed system. Note the Bragg-shifted reference beam that aids in providing phase information. (b) The computed output of the system with optical test target as the object in the presence of noise.

Equations (9)

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

ɛ ( x ) = ɛ ¯ + Δ ɛ cos ( q x Ω t ) ,
E = j A j ( z ) exp [ i ( k x + j q ) x i ( ω + j Ω ) t ] .
A j ( z ) + k z j 2 A j ( z ) = Δ ɛ 2 c 2 ω j 2 [ A j 1 ( z ) + A j + 1 ( z ) ] ,
A ± ( z ) + k z j 2 A ± ( z ) = Δ ɛ 2 c 2 ω j 2 A 0 ( z ) .
E out ( k x ) = [ A ˜ exp ( i Ω t ) + A ˜ + exp ( i Ω t ) + A ˜ 0 ] exp [ i ( k x x ω t ) ] ,
t ± = t 0 Δ ɛ 2 ( ω c ) 2 1 k z ± ( k z ± ) 2 + κ 2 t 0 Δ ɛ 2 ( ω c ) 2 1 k z ± q ( q 2 k x ) ,
| t ± | ω / c 2 k x in Δ ɛ n ( 1 + n ) ,
I out = | A ˜ 0 | 2 + 2 ( | A ˜ i A ˜ | 2 + | A ˜ i A ˜ + | 2 ) 1 / 2 cos ( Ω t + γ ) .
I out ( k x ) = | E i exp ( i k 0 z ) + A ˜ b exp ( i k r ) + [ A ˜ exp ( i Ω t ) + A ˜ + exp ( i Ω t ) + A ˜ 0 ] exp ( i k r ) | 2 = + 2 | A ˜ A ˜ b | cos [ ( Ω b + Ω ) t + Δ Φ ] + 2 | A ˜ + A ˜ b | cos [ ( Ω b Ω ) t + Δ Φ + ] + ,

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