Abstract

The generation and numerical and optical characterization of a single-beam, ponderomotive-optical trap are discussed. A novel segmented wave-plate technique is described, and experimental results of the trap formation are presented. Several methods to tune the traps are discussed, including techniques to realize a bright trap for dark-seeking electrons. The effects of non-Gaussian incident beams and beams with phase aberrations on trap formation are also described.

© 2000 Optical Society of America

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  1. H. A. H. Boot and R. B. R.-S. Harvie, “Charged particles in a non-uniform radio-frequency field,” Nature 180, 1187 (1957).
    [Crossref]
  2. E. S. Sarachik and G. T. Schappert, “Classical theory of the scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
    [Crossref]
  3. J. H. Eberly, “Interaction of very intense light with free electrons,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1969), Vol. 7, pp. 359–415.
  4. V. Gapanov and M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” J. Exp. Theor. Phys. 34, 242–243 (1958).
  5. N. J. Phillips and J. J. Sanderson, “Trapping of electrons in a spatially inhomogeneous laser beam,” Phys. Lett. 21, 533–534 (1966).
    [Crossref]
  6. U. Mohideen, H. W. K. Tom, R. R. Freeman, J. Bokor, and P. H. Bucksbaum, “Interaction of free electrons with an intense focused laser pulse in Gaussian and conical axicon geometries,” J. Opt. Soc. Am. B 9, 2190–2195 (1992).
    [Crossref]
  7. C. I. Moore, “Confinement of electrons to the center of a laser focus via the ponderomotive potential,” J. Mod. Opt. 39, 2171–2178 (1992).
    [Crossref]
  8. J. L. Chaloupka, Y. Fisher, T. J. Kessler, and D. D. Meyerhofer, “Single-beam, ponderomotive-optical trap for free electrons and neutral atoms,” Opt. Lett. 22, 1021–1023 (1997).
    [Crossref] [PubMed]
  9. H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman cooling of atoms in an optical dipole trap,” Phys. Rev. Lett. 76, 2658–2661 (1996).
    [Crossref] [PubMed]
  10. P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N. P. Bigelow, “All-optical dynamical dark trap for neutral atoms,” submitted to Phys. Rev. Lett.
  11. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
    [Crossref]
  12. J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fibre,” Opt. Commun. 152, 421–428 (1998).
    [Crossref]
  13. Yu. B. Ovchinnikov, I. Manek, A. I. Sidorov, G. Wasik, and R. Grimm, “Gravito-optical atom trap based on a conical hollow beam,” Europhys. Lett. 43, 510–515 (1998).
    [Crossref]
  14. R. Ozeri, L. Khayovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
    [Crossref]
  15. J. L. Chaloupka and D. D. Meyerhofer, “Observation of electron trapping in an intense laser beam,” Phys. Rev. Lett. 83, 4538–4541 (1999).
    [Crossref]
  16. P. W. Milonni and J. H. Eberly, “Laser resonators,” in Lasers (Wiley, New York, 1975), pp. 484–490.
  17. Ref. 16, pp. 511–514.
  18. L. W. Casperson, “Spatial modulation of Gaussian laser beams,” Opt. Quantum Electron. 10, 483–493 (1978).
    [Crossref]
  19. J. Ojeda-Castañeda and G. Ramírez, “Zone plates for zero axial irradiance,” Opt. Lett. 18, 87–89 (1993).
    [Crossref] [PubMed]
  20. S. B. Viñas, Z. Jaroszewicz, A. Kolodziejczyk, and M. Sypek, “Zone plates with black focal spots,” Appl. Opt. 31, 192–198 (1992).
    [Crossref] [PubMed]
  21. G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
    [Crossref]
  22. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [Crossref]
  23. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
    [Crossref]
  24. Y.-H. Chuang, D. D. Meyerhofer, S. Augst, H. Chen, J. Peatross, and S. Uchida, “Suppression of the pedestal in a chirped-pulse-amplification laser,” J. Opt. Soc. Am. B 8, 1226–1235 (1991).
    [Crossref]
  25. Vachaspati, “Harmonics in the scattering of light by free electrons,” Phys. Rev. 128, 664–666 (1962).
    [Crossref]
  26. S.-Y. Chen, A. Maksimchuk, and D. Umstadter, “Experimental observation of relativistic nonlinear Thomson scattering,” Nature 396, 653–655 (1998).
    [Crossref]
  27. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
    [Crossref] [PubMed]
  28. R. S. Longhurst, Geometrical and Physical Optics (Wiley, New York, 1967), pp. 365–366.
  29. C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
    [Crossref] [PubMed]

1999 (2)

R. Ozeri, L. Khayovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[Crossref]

J. L. Chaloupka and D. D. Meyerhofer, “Observation of electron trapping in an intense laser beam,” Phys. Rev. Lett. 83, 4538–4541 (1999).
[Crossref]

1998 (3)

J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fibre,” Opt. Commun. 152, 421–428 (1998).
[Crossref]

Yu. B. Ovchinnikov, I. Manek, A. I. Sidorov, G. Wasik, and R. Grimm, “Gravito-optical atom trap based on a conical hollow beam,” Europhys. Lett. 43, 510–515 (1998).
[Crossref]

S.-Y. Chen, A. Maksimchuk, and D. Umstadter, “Experimental observation of relativistic nonlinear Thomson scattering,” Nature 396, 653–655 (1998).
[Crossref]

1997 (2)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

J. L. Chaloupka, Y. Fisher, T. J. Kessler, and D. D. Meyerhofer, “Single-beam, ponderomotive-optical trap for free electrons and neutral atoms,” Opt. Lett. 22, 1021–1023 (1997).
[Crossref] [PubMed]

1996 (2)

H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman cooling of atoms in an optical dipole trap,” Phys. Rev. Lett. 76, 2658–2661 (1996).
[Crossref] [PubMed]

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

1995 (2)

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

1993 (1)

1992 (3)

1991 (1)

1986 (1)

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

1978 (1)

L. W. Casperson, “Spatial modulation of Gaussian laser beams,” Opt. Quantum Electron. 10, 483–493 (1978).
[Crossref]

1970 (1)

E. S. Sarachik and G. T. Schappert, “Classical theory of the scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
[Crossref]

1966 (1)

N. J. Phillips and J. J. Sanderson, “Trapping of electrons in a spatially inhomogeneous laser beam,” Phys. Lett. 21, 533–534 (1966).
[Crossref]

1962 (1)

Vachaspati, “Harmonics in the scattering of light by free electrons,” Phys. Rev. 128, 664–666 (1962).
[Crossref]

1958 (1)

V. Gapanov and M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” J. Exp. Theor. Phys. 34, 242–243 (1958).

1957 (1)

H. A. H. Boot and R. B. R.-S. Harvie, “Charged particles in a non-uniform radio-frequency field,” Nature 180, 1187 (1957).
[Crossref]

Adams, C. S.

H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman cooling of atoms in an optical dipole trap,” Phys. Rev. Lett. 76, 2658–2661 (1996).
[Crossref] [PubMed]

Allen, L.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

Ashkin, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

Augst, S.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Bigelow, N. P.

P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N. P. Bigelow, “All-optical dynamical dark trap for neutral atoms,” submitted to Phys. Rev. Lett.

Bjorkholm, J. E.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

Bokor, J.

Boot, H. A. H.

H. A. H. Boot and R. B. R.-S. Harvie, “Charged particles in a non-uniform radio-frequency field,” Nature 180, 1187 (1957).
[Crossref]

Bucksbaum, P. H.

Cable, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

Casperson, L. W.

L. W. Casperson, “Spatial modulation of Gaussian laser beams,” Opt. Quantum Electron. 10, 483–493 (1978).
[Crossref]

Chaloupka, J. L.

J. L. Chaloupka and D. D. Meyerhofer, “Observation of electron trapping in an intense laser beam,” Phys. Rev. Lett. 83, 4538–4541 (1999).
[Crossref]

J. L. Chaloupka, Y. Fisher, T. J. Kessler, and D. D. Meyerhofer, “Single-beam, ponderomotive-optical trap for free electrons and neutral atoms,” Opt. Lett. 22, 1021–1023 (1997).
[Crossref] [PubMed]

Chen, H.

Chen, S.-Y.

S.-Y. Chen, A. Maksimchuk, and D. Umstadter, “Experimental observation of relativistic nonlinear Thomson scattering,” Nature 396, 653–655 (1998).
[Crossref]

Chu, S.

H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman cooling of atoms in an optical dipole trap,” Phys. Rev. Lett. 76, 2658–2661 (1996).
[Crossref] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

Chuang, Y.-H.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Davidson, N.

R. Ozeri, L. Khayovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[Crossref]

Eberly, J. H.

P. W. Milonni and J. H. Eberly, “Laser resonators,” in Lasers (Wiley, New York, 1975), pp. 484–490.

J. H. Eberly, “Interaction of very intense light with free electrons,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1969), Vol. 7, pp. 359–415.

Ejnisman, R.

P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N. P. Bigelow, “All-optical dynamical dark trap for neutral atoms,” submitted to Phys. Rev. Lett.

Fisher, Y.

Freeman, R. R.

Gapanov, V.

V. Gapanov and M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” J. Exp. Theor. Phys. 34, 242–243 (1958).

Grimm, R.

Yu. B. Ovchinnikov, I. Manek, A. I. Sidorov, G. Wasik, and R. Grimm, “Gravito-optical atom trap based on a conical hollow beam,” Europhys. Lett. 43, 510–515 (1998).
[Crossref]

Harvie, R. B. R.-S.

H. A. H. Boot and R. B. R.-S. Harvie, “Charged particles in a non-uniform radio-frequency field,” Nature 180, 1187 (1957).
[Crossref]

He, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

Heckenberg, N. R.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Jaroszewicz, Z.

Kasevich, M.

H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman cooling of atoms in an optical dipole trap,” Phys. Rev. Lett. 76, 2658–2661 (1996).
[Crossref] [PubMed]

Kessler, T. J.

Khayovich, L.

R. Ozeri, L. Khayovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[Crossref]

Knauer, J. P.

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

Kolodziejczyk, A.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Lee, H. J.

H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman cooling of atoms in an optical dipole trap,” Phys. Rev. Lett. 76, 2658–2661 (1996).
[Crossref] [PubMed]

Lee, S.

P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N. P. Bigelow, “All-optical dynamical dark trap for neutral atoms,” submitted to Phys. Rev. Lett.

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (Wiley, New York, 1967), pp. 365–366.

Maksimchuk, A.

S.-Y. Chen, A. Maksimchuk, and D. Umstadter, “Experimental observation of relativistic nonlinear Thomson scattering,” Nature 396, 653–655 (1998).
[Crossref]

Manek, I.

Yu. B. Ovchinnikov, I. Manek, A. I. Sidorov, G. Wasik, and R. Grimm, “Gravito-optical atom trap based on a conical hollow beam,” Europhys. Lett. 43, 510–515 (1998).
[Crossref]

Meyerhofer, D. D.

J. L. Chaloupka and D. D. Meyerhofer, “Observation of electron trapping in an intense laser beam,” Phys. Rev. Lett. 83, 4538–4541 (1999).
[Crossref]

J. L. Chaloupka, Y. Fisher, T. J. Kessler, and D. D. Meyerhofer, “Single-beam, ponderomotive-optical trap for free electrons and neutral atoms,” Opt. Lett. 22, 1021–1023 (1997).
[Crossref] [PubMed]

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

Y.-H. Chuang, D. D. Meyerhofer, S. Augst, H. Chen, J. Peatross, and S. Uchida, “Suppression of the pedestal in a chirped-pulse-amplification laser,” J. Opt. Soc. Am. B 8, 1226–1235 (1991).
[Crossref]

Miller, M. A.

V. Gapanov and M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” J. Exp. Theor. Phys. 34, 242–243 (1958).

Milonni, P. W.

P. W. Milonni and J. H. Eberly, “Laser resonators,” in Lasers (Wiley, New York, 1975), pp. 484–490.

Mohideen, U.

Moore, C. I.

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

C. I. Moore, “Confinement of electrons to the center of a laser focus via the ponderomotive potential,” J. Mod. Opt. 39, 2171–2178 (1992).
[Crossref]

Ojeda-Castañeda, J.

Ovchinnikov, Yu. B.

Yu. B. Ovchinnikov, I. Manek, A. I. Sidorov, G. Wasik, and R. Grimm, “Gravito-optical atom trap based on a conical hollow beam,” Europhys. Lett. 43, 510–515 (1998).
[Crossref]

Ozeri, R.

R. Ozeri, L. Khayovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).
[Crossref]

Padgett, M. J.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

Peatross, J.

Phillips, N. J.

N. J. Phillips and J. J. Sanderson, “Trapping of electrons in a spatially inhomogeneous laser beam,” Phys. Lett. 21, 533–534 (1966).
[Crossref]

Rahman, A.

P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N. P. Bigelow, “All-optical dynamical dark trap for neutral atoms,” submitted to Phys. Rev. Lett.

Ramírez, G.

Robertson, D. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

Rudy, P.

P. Rudy, R. Ejnisman, A. Rahman, S. Lee, and N. P. Bigelow, “All-optical dynamical dark trap for neutral atoms,” submitted to Phys. Rev. Lett.

Sanderson, J. J.

N. J. Phillips and J. J. Sanderson, “Trapping of electrons in a spatially inhomogeneous laser beam,” Phys. Lett. 21, 533–534 (1966).
[Crossref]

Sarachik, E. S.

E. S. Sarachik and G. T. Schappert, “Classical theory of the scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
[Crossref]

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Schappert, G. T.

E. S. Sarachik and G. T. Schappert, “Classical theory of the scattering of intense laser radiation by free electrons,” Phys. Rev. D 1, 2738–2753 (1970).
[Crossref]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Sidorov, A. I.

Yu. B. Ovchinnikov, I. Manek, A. I. Sidorov, G. Wasik, and R. Grimm, “Gravito-optical atom trap based on a conical hollow beam,” Europhys. Lett. 43, 510–515 (1998).
[Crossref]

Smith, G. M.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

Sypek, M.

Tom, H. W. K.

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Turnbull, G. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127, 183–188 (1996).
[Crossref]

Uchida, S.

Umstadter, D.

S.-Y. Chen, A. Maksimchuk, and D. Umstadter, “Experimental observation of relativistic nonlinear Thomson scattering,” Nature 396, 653–655 (1998).
[Crossref]

Vachaspati,

Vachaspati, “Harmonics in the scattering of light by free electrons,” Phys. Rev. 128, 664–666 (1962).
[Crossref]

Viñas, S. B.

Wasik, G.

Yu. B. Ovchinnikov, I. Manek, A. I. Sidorov, G. Wasik, and R. Grimm, “Gravito-optical atom trap based on a conical hollow beam,” Europhys. Lett. 43, 510–515 (1998).
[Crossref]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Yin, J.

J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fibre,” Opt. Commun. 152, 421–428 (1998).
[Crossref]

Zhu, Y.

J. Yin and Y. Zhu, “Dark-hollow-beam gravito-optical atom trap above an apex of a hollow optical fibre,” Opt. Commun. 152, 421–428 (1998).
[Crossref]

Appl. Opt. (1)

Europhys. Lett. (1)

Yu. B. Ovchinnikov, I. Manek, A. I. Sidorov, G. Wasik, and R. Grimm, “Gravito-optical atom trap based on a conical hollow beam,” Europhys. Lett. 43, 510–515 (1998).
[Crossref]

J. Exp. Theor. Phys. (1)

V. Gapanov and M. A. Miller, “Potential wells for charged particles in a high-frequency electromagnetic field,” J. Exp. Theor. Phys. 34, 242–243 (1958).

J. Mod. Opt. (2)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

C. I. Moore, “Confinement of electrons to the center of a laser focus via the ponderomotive potential,” J. Mod. Opt. 39, 2171–2178 (1992).
[Crossref]

J. Opt. Soc. Am. B (2)

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Figures (18)

Fig. 1
Fig. 1

A focused Gaussian beam forms a well-behaved, centrally peaked focal region. The first gray-scale image (a) shows the near-field intensity distribution. The second image (b) shows the intensity distribution as a function of z and x (y=0); the center of the image corresponds to the best focus: z=0,r=0). The third image (c) shows the focal plane image at z=0. The radii (at the 1/e2 point in intensity) of the incident beam (w) and the focal spot (w0) are shown, along with the Rayleigh range (z0). In these and all subsequent images, the darkest shades represent the regions of highest fields.

Fig. 2
Fig. 2

Amplitude masking of the center of a Gaussian beam results in only small amplitude modulations in the focal region. The images are presented as in Fig. 1: (a) the near field, (b) the xz slice of the focal region, and (c) the focal plane image. The scaling shown is for the unaltered beam (Fig. 1).

Fig. 3
Fig. 3

Masking a Gaussian beam in the near field with a simple binary phase plate results in a drastic change in the focal region. (a) The two-level phase plate used to alter the focal region. (b) The xz slice of the altered focal region (the yz slice is devoid of a field). (c) The focal-plane image. The scaling shown is for the unaltered beam (Fig. 1).

Fig. 4
Fig. 4

A Gaussian beam focused after passing through a helical phase plate forms a highly altered focal region. (a) The smoothly varying helical phase plate. (b) The xz slice of the focal region. (c) The focal-plane image similar in shape to the doughnut mode (TEM01*). The scaling shown is for the unaltered beam (Fig. 1).

Fig. 5
Fig. 5

A simple two-level phase plate alters the focal region primarily near best focus, creating a doughnut-shaped focal spot. (a) The two-level binary phase plate used to alter the focal region. (b) The xz slice of the focal region. (Because of the azimuthal symmetry of both the incident beam and the phase plate, the focal region is also azimuthally symmetric.) (c) The focal-plane image. The scaling shown is for the unaltered beam (Fig. 1).

Fig. 6
Fig. 6

Expanded view of the focal region generated by passage of a Gaussian beam (with 1/e2 in intensity radius equal to w) through a π-phase plate [with the diameter of the π region (dπ) equal to 1.65 w] as in Fig. 6. (a) Surface plot of the xz slice of the focal region. Because of the azimuthal symmetry, all rz slices are identical. (b) Contour plot of the trapping region. The contour lines represent the percent values of the peak intensity of the unaltered beam (i.e., in the absence of the phase mask). (c) Contour surface of the three-dimensional trapping region, corresponding to the 8.2% contour line.

Fig. 7
Fig. 7

Experimental setup for the segmented wave-plate technique for generating a trapped focal region. The annulus has an 80-mm outer diameter and a 41-mm inner diameter; the disk has a 39-mm diameter.

Fig. 8
Fig. 8

Focal-plane image and contour plots of the trapping focal region generated with a continuous-wave beam (the upcollimated output of a Nd:YLF oscillator) and the segmented wave plate. (a) The beam at best focus (z=0). The beam radius for the unaltered beam (w0 exp) is shown. (b) Image of the xz slice of the focal region (taken by scanning the camera through the focal region) with the corresponding contour plot. Dashed curves indicate intensity values of 7.5%, 8.0%, 8.5%, 9.0%, and 9.5% of the unaltered beam’s peak intensity. The solid curve corresponds to 10.0% of the unaltered beam’s peak intensity and surrounds the region of complete, three-dimensional trapping. (c) The yz slice.

Fig. 9
Fig. 9

Focal-plane images at z=0 taken with a single laser pulse (E40 mJ, τ∼2 ps, λ∼1 µm): (a) without the wave-plate arrangement in place, (b) with the wave-plate setup in place and set to 90°, (c) with the wave-plate setup in place and set to 0°, (d) with the wave-plate setup at 90° and E500 mJ.

Fig. 10
Fig. 10

Lineouts of the trapping focal region taken with a moderate-power, pulsed laser beam [as in Fig. 10(b)]. (a) Lineout in the x direction (at best focus: z=0). (b) Lineout in the y direction (z=0). (c) The intensity at r=0 as a function of z (the discrete points represent the camera position through the z scan). All axes are normalized to the experimentally determined values for the unaltered beam (spot size for the x and y positions, Rayleigh range for the z positions, and unaltered beam peak intensity for the intensity values).

Fig. 11
Fig. 11

The transverse lineouts of focal spots generated by three different phase plates show how the brightness at the center of the trap varies with the size of the inner π region. The solid curve shows an ideal dark trap generated with the half-field-shifted criterion (dπ=1.65w). The dotted curve shows a dark trap with a bright center (dπ=1.05w). Here, electrons will still be pushed into the region of the null field. The dashed curve shows an ideal bright trap (dπ=2.25w). Here, trapped electrons are forced to interact with the central region of high field.

Fig. 12
Fig. 12

Tuning the trap. The dashed–dotted curve represents the height of the trap wall (given in terms of the unaltered beam’s peak intensity), and the solid curve represents the minimum intensity within the trap. The distance between these lines is the trap depth. The short-dashed curve represents the trap volume in terms of a characteristic volume for the unaltered focus w02 z0). The arrows indicate the vertical axis for each curve. One can best realize the transmission from a dark to a bright trap by altering the size of the inner π region. As the trap brightens, it becomes shallower and smaller. One can duplicate this effect by placing the phase plate or the wave-plate arrangement at an appropriate distance behind the focusing lens.

Fig. 13
Fig. 13

One can generate a bright trap by rotating the outer annulus of the wave-plate arrangement (dinner=1.65w). Zero degrees corresponds to the ideal annulus orientation, where the o axis of the annulus lines up with the e axis of the disk and vice versa (performing in the same way as a π-phase plate). Ninety degrees corresponds to an ordinary half-wave plate. The curves in this plot are drawn as in Fig. 13.

Fig. 14
Fig. 14

Rotating the outer annulus (as in Fig. 14) and passing the beam through a polarizer can make the trap slightly brighter with the added benefit of only a single polarization in the beam. The curves in this plot are drawn as in Fig. 13.

Fig. 15
Fig. 15

By using a wave-plate arrangement with an oversized inner disk (dinner=2.00w) and passing the beam through a polarizer, one can tune the trap by rotating the inner disk to create a dark trap (corresponding to the negative angle values) or by rotating the outer annulus to create a bright trap (corresponding to the positive angle values). The curves in this plot are drawn as in Fig. 13.

Fig. 16
Fig. 16

Effects of spherical aberrations on the trap brightness, depth, and volume shown as a function of the number of waves of spherical aberration (Nsa) at the 1/e2 (in intensity) radius (w) of the incident beam. The thicker solid and dashed curves represent the minimum trap intensity and the height of the trap wall, respectively, normalized to the peak intensity of the nontrapping, nonaberrated beam. The thinner curves are normalized to the peak intensity of the nontrapping, aberrated beam. The short-dashed curve represents the trap volume normalized to the characteristic volume (w02 z0) of the nontrapping, nonaberrated beam. The short-dashed curve corresponds to the right vertical axis (volume), and all other curves correspond to the left vertical axis (intensity).

Fig. 17
Fig. 17

Effects of astigmatism on the trap brightness, depth, and volume shown as a function of the astigmatic focal-length difference (Δ f) divided by the Rayleigh range of the nonaberrated beam (z0). The curves in the plot are drawn as in Fig. 17.

Fig. 18
Fig. 18

Dark trapping focal regions generated by non-Gaussian beams: (a) a centrally blocked Gaussian in the near field and (b) a surface plot of the trapping region; (c) a Gaussian near field with an annular block and (d) a surface plot of the trapping region.

Equations (11)

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E(z, t)=iˆE0x cos(kz-ωt)+jˆE0y cos(kz-ωt+),
Einner(z, t)=iˆE0x cos(kz-ωt+ϕ)+jˆE0y cos(kz-ωt++ϕ+mπ)
=iˆE0x cos(kz-ωt+ϕ)-jˆE0y cos(kz-ωt++ϕ),
Eouter(z, t)=iˆE0x cos(kz-ωt+ϕ+mπ)+jˆE0y cos(kz-ωt++ϕ)
=-iˆE0x cos(kz-ωt+ϕ)+jˆE0y cos(kz-ωt++ϕ),
Φ(r)=k(f2-r2)1/2,
Φ(r)=kf(1-r2/2f2-r4/8f4-).
Φp(r)=-kr2/2 f.
Φs(r)=Φp(r)+A[Φ(r)-Φp(r)],
fx=f,
fy=f cos2 ϕlens.

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