Abstract

I propose to use as a window the dark core of an optical vortex to examine a weak background signal hidden in the glare of a bright coherent source. Applications such as the detection of an astronomical object, forward-scattered radiation, and incoherent light are described whereby signal enhancements of at least 7 orders of magnitude may be achieved.

© 2001 Optical Society of America

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References

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  1. S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965).
  2. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  3. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [CrossRef]
  4. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eksp. Teor. Fiz. 33, 206 (1981)JETP Lett. 33, 195 (1981).
  5. J. F. Nye, Proc. R. Soc. London Ser. A 361, 21 (1978).
    [CrossRef]
  6. A. M. Deykoon, M. S. Soskin, and G. A. Swartzlander, Opt. Lett. 24, 1224 (1999).
    [CrossRef]
  7. G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
    [CrossRef]
  8. A. W. Snyder, L. Poladian, and D. J. Mitchell, Opt. Lett. 17, 789 (1992).
    [CrossRef] [PubMed]
  9. For a recent review, see M. Vasnetsov and K. Staliunas, eds. , Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, Huntington, N.Y., 1999).
  10. See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
    [CrossRef]
  11. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  12. Z. S. Sacks, D. Rozas, and G. A. Swartzlander, J. Opt. Soc. Am. B 15, 2226 (1998).
    [CrossRef]
  13. Calculations were made with a DEC Alpha workstation and a fast-Fourier transform algorithm on a 512×512 numerical grid.
  14. C. A. Beichman, ed., A Road Map for the Exploration of Neighboring Planetary SystemsJPL Publ. 96-22 (Jet Propulsion Laboratory, Pasadena, Calif., 1996).
  15. J. R. P. Angel and N. J. Woolf, Astrophys. J. 475, 373 (1997).
    [CrossRef]
  16. The intensity of the planetary signal across a small aperture Rap/Rdiff≪1 is relatively constant, and thus the transmitted power varies as Rap2. However, relation  (2) predicts that the transmitted power for the stellar vortex will increase as Rap8.72 for m=4. Thus we find that when the relative aperture size Rap/Rdiff is decreased from 0.19 to 0.1, the optimum enhancement factor, Pp/Ps, increases by a factor of 1.96.72. In this case we estimate that Pp/Ps≈2×107.

1999 (1)

1998 (1)

1997 (1)

J. R. P. Angel and N. J. Woolf, Astrophys. J. 475, 373 (1997).
[CrossRef]

1994 (1)

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

1992 (2)

A. W. Snyder, L. Poladian, and D. J. Mitchell, Opt. Lett. 17, 789 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

1981 (1)

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eksp. Teor. Fiz. 33, 206 (1981)JETP Lett. 33, 195 (1981).

1978 (1)

J. F. Nye, Proc. R. Soc. London Ser. A 361, 21 (1978).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Angel, J. R. P.

J. R. P. Angel and N. J. Woolf, Astrophys. J. 475, 373 (1997).
[CrossRef]

Baranova, N. B.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eksp. Teor. Fiz. 33, 206 (1981)JETP Lett. 33, 195 (1981).

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Brennan, T. M.

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

de Colstoun, F. B.

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Deykoon, A. M.

Fedorov, A. V.

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Hammons, B. G.

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Khitrova, G.

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Law, C. T.

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

Lowry, C.

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Maker, P. D.

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Mamaev, A. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eksp. Teor. Fiz. 33, 206 (1981)JETP Lett. 33, 195 (1981).

Mitchell, D. J.

Nelson, T. R.

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Nye, J. F.

J. F. Nye, Proc. R. Soc. London Ser. A 361, 21 (1978).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Pilipetskii, N. F.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eksp. Teor. Fiz. 33, 206 (1981)JETP Lett. 33, 195 (1981).

Poladian, L.

Ramo, S.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965).

Rozas, D.

Sacks, Z. S.

Shkunov, V. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eksp. Teor. Fiz. 33, 206 (1981)JETP Lett. 33, 195 (1981).

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Snyder, A. W.

Soskin, M. S.

Swartzlander, G. A.

Van Duzer, T.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965).

Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965).

Woolf, N. J.

J. R. P. Angel and N. J. Woolf, Astrophys. J. 475, 373 (1997).
[CrossRef]

Zel’dovich, B. Ya.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eksp. Teor. Fiz. 33, 206 (1981)JETP Lett. 33, 195 (1981).

Astrophys. J. (1)

J. R. P. Angel and N. J. Woolf, Astrophys. J. 475, 373 (1997).
[CrossRef]

Chaos Solitons Fractals (1)

See pp. 1581–1586 in F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. Lett. (1)

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

Pis’ma Zh. Eksp. Teor. Fiz. (1)

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkunov, Pis’ma Zh. Eksp. Teor. Fiz. 33, 206 (1981)JETP Lett. 33, 195 (1981).

Proc. R. Soc. London Ser. A (2)

J. F. Nye, Proc. R. Soc. London Ser. A 361, 21 (1978).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Other (7)

The intensity of the planetary signal across a small aperture Rap/Rdiff≪1 is relatively constant, and thus the transmitted power varies as Rap2. However, relation  (2) predicts that the transmitted power for the stellar vortex will increase as Rap8.72 for m=4. Thus we find that when the relative aperture size Rap/Rdiff is decreased from 0.19 to 0.1, the optimum enhancement factor, Pp/Ps, increases by a factor of 1.96.72. In this case we estimate that Pp/Ps≈2×107.

Calculations were made with a DEC Alpha workstation and a fast-Fourier transform algorithm on a 512×512 numerical grid.

C. A. Beichman, ed., A Road Map for the Exploration of Neighboring Planetary SystemsJPL Publ. 96-22 (Jet Propulsion Laboratory, Pasadena, Calif., 1996).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1965).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

For a recent review, see M. Vasnetsov and K. Staliunas, eds. , Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, Huntington, N.Y., 1999).

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Figures (5)

Fig. 1
Fig. 1

Direct rays from a star and reflected rays from a planet make an angle α at the objective of a telescope with focal length f and diameter D .

Fig. 2
Fig. 2

Line plots of the field amplitude through the center of vortex cores for values of topological charge, m = 1 4 . Solid curves are drawn to aid the eye. m = 0 corresponds to the Airy disk, which has a first minimum at r = R diff . Dotted curves, least-squares fits to a power-law curve proportional to r m .

Fig. 3
Fig. 3

Fraction of the total beam power transmitted through an aperture of radial size R ap located in the focal plane and centered on the vortex core. Dashed curves, predictions from a least-squares fit analysis for several values of the topological charge, m .

Fig. 4
Fig. 4

Combined vortex beams in the focal plane for two equally luminous sources subtending an angle α = θ diff . Topological charge m of both beams is identical. Each beam is transversely coherent, and the two beams are mutually (a) coherent and (b) incoherent. Crosses, location of the optical axis (which coincides with the vortex core of the primary beam).

Fig. 5
Fig. 5

Enhancement of the weak secondary signal over the strong primary signal for several values of angular aperture size θ ap , angular distance between sources α , and topological charge m . Data points are shown for m = 4 for θ ap / θ diff values of (a) 0.19, (b) 0.32, and (c) 0.65 and for m = 1 for θ ap / θ diff values of (d) 0.19, (e) 0.32, and (f) 0.65. Solid curves were drawn to aid the eye.

Equations (5)

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E r , ϕ , z ; t = A r , z exp im ϕ exp i ω t - kz ,
δ P / P tot 2 δ P / P tot 1 R ap , 2 / R ap , 1 1.44 + 1.82 m .
E = A s + A p exp ik x , p x exp i Φ exp i ω t - kz ,
FT EG = A s FT exp im ϕ + A p FT exp - ik α x × exp im ϕ exp i Φ ,
FT EG = A s ξ x , y + A p exp i Φ } ξ x - α f , y ,

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