Abstract

We propose a source of multimode squeezed light that can be used for superresolving microscopy. This source is an optical parametric amplifier with a properly chosen diaphragm on its output and a Fourier lens. We demonstrate that such an arrangement produces squeezed prolate spheroidal waves that are the eigenmodes of the optical imaging scheme used in microscopy and discuss the conditions of the degree of squeezing and of the number of spatial modes in illuminating light.

© 2004 Optical Society of America

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References

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  1. M. I. Kolobov, Rev. Mod. Phys. 71, 1539 (1999).
    [CrossRef]
  2. J. Eschner, A. Gatti, A. Maître, and G. Morigi, eds., “Quantum fluctuations and coherence in optical and atomic structures,” special issue of the Eur. Phys. J. D 22, 311–530 (2003).
    [CrossRef]
  3. http://sucima.dipscfm.uninsubria.it/quantum.
  4. M. I. Kolobov and C. Fabre, Phys. Rev. Lett. 85, 3789 (2000).
    [CrossRef] [PubMed]
  5. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
    [CrossRef] [PubMed]
  6. P. Kok, H. Lee, and J. P. Dowling, Phys. Rev. A 65, 052104 (2002).
    [CrossRef]
  7. D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).
    [CrossRef]
  8. B. R. Frieden, in Progress in Optics, Vol. IX, E. Wolf, ed. (North-Holland, Amsterdam, 1971), p. 311.
    [CrossRef]
  9. M. I. Kolobov, C. Fabre, P. Scotto, P. Colet, and M. San Miguel, in Coherence and Quantum Optics VIII, N. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, eds. (Plenum, New York, 2003).
  10. M. I. Kolobov and I. V. Sokolov, JETP 69, 1097 (1989).

2003

J. Eschner, A. Gatti, A. Maître, and G. Morigi, eds., “Quantum fluctuations and coherence in optical and atomic structures,” special issue of the Eur. Phys. J. D 22, 311–530 (2003).
[CrossRef]

M. I. Kolobov, C. Fabre, P. Scotto, P. Colet, and M. San Miguel, in Coherence and Quantum Optics VIII, N. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, eds. (Plenum, New York, 2003).

2002

P. Kok, H. Lee, and J. P. Dowling, Phys. Rev. A 65, 052104 (2002).
[CrossRef]

2000

M. I. Kolobov and C. Fabre, Phys. Rev. Lett. 85, 3789 (2000).
[CrossRef] [PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

1999

M. I. Kolobov, Rev. Mod. Phys. 71, 1539 (1999).
[CrossRef]

1989

M. I. Kolobov and I. V. Sokolov, JETP 69, 1097 (1989).

1971

B. R. Frieden, in Progress in Optics, Vol. IX, E. Wolf, ed. (North-Holland, Amsterdam, 1971), p. 311.
[CrossRef]

1961

D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).
[CrossRef]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Colet, P.

M. I. Kolobov, C. Fabre, P. Scotto, P. Colet, and M. San Miguel, in Coherence and Quantum Optics VIII, N. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, eds. (Plenum, New York, 2003).

Dowling, J. P.

P. Kok, H. Lee, and J. P. Dowling, Phys. Rev. A 65, 052104 (2002).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Fabre, C.

M. I. Kolobov, C. Fabre, P. Scotto, P. Colet, and M. San Miguel, in Coherence and Quantum Optics VIII, N. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, eds. (Plenum, New York, 2003).

M. I. Kolobov and C. Fabre, Phys. Rev. Lett. 85, 3789 (2000).
[CrossRef] [PubMed]

Frieden, B. R.

B. R. Frieden, in Progress in Optics, Vol. IX, E. Wolf, ed. (North-Holland, Amsterdam, 1971), p. 311.
[CrossRef]

Kok, P.

P. Kok, H. Lee, and J. P. Dowling, Phys. Rev. A 65, 052104 (2002).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Kolobov, M. I.

M. I. Kolobov, C. Fabre, P. Scotto, P. Colet, and M. San Miguel, in Coherence and Quantum Optics VIII, N. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, eds. (Plenum, New York, 2003).

M. I. Kolobov and C. Fabre, Phys. Rev. Lett. 85, 3789 (2000).
[CrossRef] [PubMed]

M. I. Kolobov, Rev. Mod. Phys. 71, 1539 (1999).
[CrossRef]

M. I. Kolobov and I. V. Sokolov, JETP 69, 1097 (1989).

Lee, H.

P. Kok, H. Lee, and J. P. Dowling, Phys. Rev. A 65, 052104 (2002).
[CrossRef]

Pollak, H. O.

D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).
[CrossRef]

San Miguel, M.

M. I. Kolobov, C. Fabre, P. Scotto, P. Colet, and M. San Miguel, in Coherence and Quantum Optics VIII, N. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, eds. (Plenum, New York, 2003).

Scotto, P.

M. I. Kolobov, C. Fabre, P. Scotto, P. Colet, and M. San Miguel, in Coherence and Quantum Optics VIII, N. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, eds. (Plenum, New York, 2003).

Slepian, D.

D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).
[CrossRef]

Sokolov, I. V.

M. I. Kolobov and I. V. Sokolov, JETP 69, 1097 (1989).

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Bell Syst. Tech. J.

D. Slepian and H. O. Pollak, Bell Syst. Tech. J. 40, 43 (1961).
[CrossRef]

Eur. Phys. J. D

J. Eschner, A. Gatti, A. Maître, and G. Morigi, eds., “Quantum fluctuations and coherence in optical and atomic structures,” special issue of the Eur. Phys. J. D 22, 311–530 (2003).
[CrossRef]

JETP

M. I. Kolobov and I. V. Sokolov, JETP 69, 1097 (1989).

Phys. Rev. A

P. Kok, H. Lee, and J. P. Dowling, Phys. Rev. A 65, 052104 (2002).
[CrossRef]

Phys. Rev. Lett.

M. I. Kolobov and C. Fabre, Phys. Rev. Lett. 85, 3789 (2000).
[CrossRef] [PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys.

M. I. Kolobov, Rev. Mod. Phys. 71, 1539 (1999).
[CrossRef]

Other

B. R. Frieden, in Progress in Optics, Vol. IX, E. Wolf, ed. (North-Holland, Amsterdam, 1971), p. 311.
[CrossRef]

M. I. Kolobov, C. Fabre, P. Scotto, P. Colet, and M. San Miguel, in Coherence and Quantum Optics VIII, N. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, eds. (Plenum, New York, 2003).

http://sucima.dipscfm.uninsubria.it/quantum.

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Figures (1)

Fig. 1
Fig. 1

Schematic of optical imaging with squeezed light.

Equations (13)

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

cˆξ,cˆξ=δξ-ξ,    aˆs,aˆs=δs-s,
aˆs=Tcˆs=c/2π-dξexp-icsξcˆξ,
φks=1λkψkss1,0s>1,χks=0s1,11-λkψkss>1,
cˆξ=k=0cˆkφkξ+k=0dˆkχkξ.
cˆk=-dξcˆξφkξ,    dˆk=-dξcˆξχkξ.
-11dξψkξexp-iqξ=-ik2πλkcψkq/c.
Tφks=-ikλkφks+1-λkχks=-ikψks,Tχks=-ik1-λkφks-λkχks=-ikθks,
aˆs=Tcˆs=k=0Aˆkψks+k=0Nˆkθks,
c˜q=Uqc˜inq+Vqc˜in-q.
Uq±V*-q=exp-iφqexp±rq×cosθq+iexp±rqsin θq.
Aˆk=12πc-dqψkq/cUqc˜inq+Vqc˜in-q.
ΔAˆ1k2=14c-dqψk2q/cexp±2rqcos2 θq+exp2rqsin2 θq,
ΔAˆ2k2=14c-dqψk2q/cexp2rqcos2 θq+exp±2rqsin2 θq.

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