Abstract

The smallest spot in optical lithography and microscopy is generally limited by diffraction. Quantum lithography, which utilizes interference between groups of N entangled photons, was recently proposed to beat the diffraction limit by a factor N. Here we propose a simple method to obtain N photons interference with classical pulses that excite a narrow multiphoton transition, thus shifting the “quantum weight” from the electromagnetic field to the lithographic material. We show how a practical complete lithographic scheme can be developed and demonstrate the underlying principles experimentally by two-photon interference in atomic Rubidium, to obtain focal spots that beat the diffraction limit by a factor of 2.

© 2004 Optical Society of America

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  1. T. A. Brunner, “Why optical lithography will live forever,” J. Vac. Sci. Technol. B 21, 2632–2637 (2003).
    [CrossRef]
  2. J. W. Goodman, Introduction to Fourier optics, 3rd Ed., (McGraw-Hill, 1996).
  3. S. Kawata, H. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
    [CrossRef] [PubMed]
  4. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
    [CrossRef] [PubMed]
  5. M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
    [CrossRef]
  6. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de-Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
    [CrossRef] [PubMed]
  7. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” quant-ph/p. 0411023 (2004), http://xxx.lanl.gov/abs/quant-ph/0411023
  8. V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, “Temporal coherent control in two-photon transition: from optical interferences to quantum interferences,” Phys. Rev. Lett. 78, 2716–2719 (2002).
    [CrossRef]
  9. D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396, 239 (1998).
    [CrossRef]
  10. S.A. Hosseini and D. Goswami, “Coherent control of multiphoton transitions with femtosecond pulse shaping,” Phys. Rev. A 64, 033410 (2001).
    [CrossRef]
  11. N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Coherent control with real optical fields: a simple route to strong field control,” Submitted to Phys. Rev. Lett (2004).
  12. E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
    [CrossRef]
  13. D. V. Korobkin and E. Yablonovitch, “Twofold spatial resolution enhancement by two-photon exposure of photographic film,” Opt. Eng. 41, 1729–1732(2002).
    [CrossRef]
  14. N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
    [CrossRef] [PubMed]
  15. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two-photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett. 93, 023005 (2004).
    [CrossRef] [PubMed]

2004 (1)

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two-photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef] [PubMed]

2003 (1)

T. A. Brunner, “Why optical lithography will live forever,” J. Vac. Sci. Technol. B 21, 2632–2637 (2003).
[CrossRef]

2002 (3)

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de-Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, “Temporal coherent control in two-photon transition: from optical interferences to quantum interferences,” Phys. Rev. Lett. 78, 2716–2719 (2002).
[CrossRef]

D. V. Korobkin and E. Yablonovitch, “Twofold spatial resolution enhancement by two-photon exposure of photographic film,” Opt. Eng. 41, 1729–1732(2002).
[CrossRef]

2001 (4)

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

S.A. Hosseini and D. Goswami, “Coherent control of multiphoton transitions with femtosecond pulse shaping,” Phys. Rev. A 64, 033410 (2001).
[CrossRef]

S. Kawata, H. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef] [PubMed]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

2000 (1)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef] [PubMed]

1999 (1)

E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
[CrossRef]

1998 (1)

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396, 239 (1998).
[CrossRef]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef] [PubMed]

Blanchet, V.

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, “Temporal coherent control in two-photon transition: from optical interferences to quantum interferences,” Phys. Rev. Lett. 78, 2716–2719 (2002).
[CrossRef]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef] [PubMed]

Bouchene, M. A.

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, “Temporal coherent control in two-photon transition: from optical interferences to quantum interferences,” Phys. Rev. Lett. 78, 2716–2719 (2002).
[CrossRef]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef] [PubMed]

Brunner, T. A.

T. A. Brunner, “Why optical lithography will live forever,” J. Vac. Sci. Technol. B 21, 2632–2637 (2003).
[CrossRef]

Chekhova, M. V.

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

D’Angelo, M.

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Dayan, B.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two-photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” quant-ph/p. 0411023 (2004), http://xxx.lanl.gov/abs/quant-ph/0411023

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef] [PubMed]

Dudovich, N.

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Coherent control with real optical fields: a simple route to strong field control,” Submitted to Phys. Rev. Lett (2004).

Edamatsu, K.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de-Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Friesem, A. A.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two-photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef] [PubMed]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” quant-ph/p. 0411023 (2004), http://xxx.lanl.gov/abs/quant-ph/0411023

Gallagher Faeder, S. M.

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

Girard, B.

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, “Temporal coherent control in two-photon transition: from optical interferences to quantum interferences,” Phys. Rev. Lett. 78, 2716–2719 (2002).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier optics, 3rd Ed., (McGraw-Hill, 1996).

Goswami, D.

S.A. Hosseini and D. Goswami, “Coherent control of multiphoton transitions with femtosecond pulse shaping,” Phys. Rev. A 64, 033410 (2001).
[CrossRef]

Hosseini, S.A.

S.A. Hosseini and D. Goswami, “Coherent control of multiphoton transitions with femtosecond pulse shaping,” Phys. Rev. A 64, 033410 (2001).
[CrossRef]

Itoh, T.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de-Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Kawata, S.

S. Kawata, H. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef] [PubMed]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef] [PubMed]

Korobkin, D. V.

D. V. Korobkin and E. Yablonovitch, “Twofold spatial resolution enhancement by two-photon exposure of photographic film,” Opt. Eng. 41, 1729–1732(2002).
[CrossRef]

Meshulach, D.

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396, 239 (1998).
[CrossRef]

Nicole, C.

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, “Temporal coherent control in two-photon transition: from optical interferences to quantum interferences,” Phys. Rev. Lett. 78, 2716–2719 (2002).
[CrossRef]

Pe’er, A.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two-photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef] [PubMed]

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Coherent control with real optical fields: a simple route to strong field control,” Submitted to Phys. Rev. Lett (2004).

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” quant-ph/p. 0411023 (2004), http://xxx.lanl.gov/abs/quant-ph/0411023

Polack, T.

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Coherent control with real optical fields: a simple route to strong field control,” Submitted to Phys. Rev. Lett (2004).

Shih, Y.

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Shimizu, R.

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de-Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Silberberg, Y.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two-photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396, 239 (1998).
[CrossRef]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” quant-ph/p. 0411023 (2004), http://xxx.lanl.gov/abs/quant-ph/0411023

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Coherent control with real optical fields: a simple route to strong field control,” Submitted to Phys. Rev. Lett (2004).

Sun, H.

S. Kawata, H. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef] [PubMed]

Takada, K.

S. Kawata, H. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef] [PubMed]

Tanaka, T.

S. Kawata, H. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef] [PubMed]

Vrijen, R. B.

E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
[CrossRef]

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef] [PubMed]

Yablonovitch, E.

D. V. Korobkin and E. Yablonovitch, “Twofold spatial resolution enhancement by two-photon exposure of photographic film,” Opt. Eng. 41, 1729–1732(2002).
[CrossRef]

E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
[CrossRef]

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

T. A. Brunner, “Why optical lithography will live forever,” J. Vac. Sci. Technol. B 21, 2632–2637 (2003).
[CrossRef]

Nature (2)

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396, 239 (1998).
[CrossRef]

S. Kawata, H. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices,” Nature 412, 697–698 (2001).
[CrossRef] [PubMed]

Opt. Eng. (2)

E. Yablonovitch and R. B. Vrijen, “Optical projection lithography at half the Rayleigh resolution limit by two-photon exposure,” Opt. Eng. 38, 334–338 (1999).
[CrossRef]

D. V. Korobkin and E. Yablonovitch, “Twofold spatial resolution enhancement by two-photon exposure of photographic film,” Opt. Eng. 41, 1729–1732(2002).
[CrossRef]

Phys. Rev. A (1)

S.A. Hosseini and D. Goswami, “Coherent control of multiphoton transitions with femtosecond pulse shaping,” Phys. Rev. A 64, 033410 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling., “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef] [PubMed]

M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de-Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001).
[CrossRef] [PubMed]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two-photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett. 93, 023005 (2004).
[CrossRef] [PubMed]

V. Blanchet, C. Nicole, M. A. Bouchene, and B. Girard, “Temporal coherent control in two-photon transition: from optical interferences to quantum interferences,” Phys. Rev. Lett. 78, 2716–2719 (2002).
[CrossRef]

Other (3)

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear interactions with an ultrahigh flux of broadband entangled photons,” quant-ph/p. 0411023 (2004), http://xxx.lanl.gov/abs/quant-ph/0411023

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Coherent control with real optical fields: a simple route to strong field control,” Submitted to Phys. Rev. Lett (2004).

J. W. Goodman, Introduction to Fourier optics, 3rd Ed., (McGraw-Hill, 1996).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic setup for generation of sub diffraction limited spots by quantum interference. A glass plate delays half of a planar ultrashort pulse with respect to the other half. As a result, the non-linear lithographic medium at the focus is excited by two consecutive pulses with a space-variant relative delay; thus generating a space-dependent two-photon interference. Fine tuning the delay can be performed by a small tilt of the glass.

Fig. 2.
Fig. 2.

Calculated sub diffraction-limit spots (line), as compared to the diffraction-limited single-photon spot (dashed). (a), (b) are the two-photon and four-photon spots respectively of the two segment configuration of Fig. 1. (c), (d) show the same spots assuming four equal non-overlapping segments instead of two. (e), (f) show these spots when a third pulse with two offset foci is used to suppress the side lobes. All segments are assumed to be illuminated by a uniform plane wave pulse.

Fig. 3.
Fig. 3.

Experimental configuration and relevant level diagram for atomic Rb. The cylindrical telescope weakly focuses the beam into the Rb Cell, the delay line controls the interference and the CCD records the image of the fluorescence spot. The cylindrical lens in front of the cell tightly focuses the beam in the perpendicular dimension.

Fig. 4.
Fig. 4.

Experimental results. (a) images and transverse cross sections of “dark spots” (destructive at the center) for a short relative delay (crosses - data, gray line - theoretical fit) and a long relative delay (circles - data, line - theoretical fit), demonstrating the double resolution of two-photon interference compared to one-photon interference. (b) is the corresponding two-photon “bright spot” as compared to the diffraction limited one-photon spot (dashed). All experimental cross sections were averaged over the center portion of the image (18 pixel lines) to reduce noise. The theoretical fits assume a Gaussian beam profile with a narrow gap in the middle.

Equations (2)

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I ( x ) E 1 N ( x ; ω A ) + E 2 N ( x ; ω A ) 2 ,
k = 1 M E k N ( x f ) 2 = I ( x f ) ,

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