Abstract

We present a method to create a blazed atomic diffraction grating by use of a periodical optical potential. Like its optical counterpart, the blazed atomic diffraction grating distributes intensity into a specific nonzero diffraction order. Total internal reflection of a laser beam coupled to the nanostructured surface of a prism results in transverse modulation of the intensity responsible for atomic diffraction. For specific illumination parameters and periodicity of the pattern, the long-range potential interacting with the atoms has an asymmetric sawtooth shape. Analytic and numerical calculations show that population diffracted in the +1 order can be optimized to approximately 55%, with almost no population into the 1 order.

© 2005 Optical Society of America

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  1. C. Davisson and L. H. Germer, "Diffraction of electrons by a crystal of nickel," Phys. Rev. 30, 705-740 (1927).
    [CrossRef]
  2. J. Baudon, R. Mathevet, and J. Robert, "Atomic interferometry," J. Phys. B 32, R173-R195 (1999).
    [CrossRef]
  3. P.R.Berman, ed., Atomic Interferometry (Academic, 1997).
  4. D. W. Keith, Ch. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, "An interferometer for atoms," Phys. Rev. Lett. 66, 2693-2696 (1988).
    [CrossRef]
  5. V. P. Chebotayev, B. Y. Dubetsky, A. P. Kasantsev, and V. P. Yakovlev, "Interference of atoms in separated optical fields," J. Opt. Soc. Am. B 2, 1791-1798 (1985).
    [CrossRef]
  6. T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, "Magneto-optical beam splitter for atoms," Phys. Rev. Lett. 71, 3427-3430 (1993).
    [CrossRef] [PubMed]
  7. R. Grimm, J. Söding, and Yu. B. Ovchinnikov, "Coherent beam splitter for atoms based on a bichromatic standing light wave," Opt. Lett. 19, 658-660 (1994).
    [CrossRef] [PubMed]
  8. K. S. Johnson, A. Chu, T. W. Lynn, K. K. Berggren, M. S. Shahriar, and M. Prentiss, "Demonstration of a nonmagnetic blazed-grating atomic beam splitter," Opt. Lett. 20, 1310-1312 (1995).
    [CrossRef] [PubMed]
  9. B. Rohwedder, "Atom optic elements based on nearfield grating sequences," Fortschr. Phys. 47, 883-911 (1999).
    [CrossRef]
  10. R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
    [CrossRef]
  11. A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
    [CrossRef] [PubMed]
  12. P. Szriftgiser, D. Guéry-Odelin, M. Arndt, and J. Dalibard, "Atomic wave diffraction and interference using temporal slits," Phys. Rev. Lett. 77, 4-7 (1996).
    [CrossRef] [PubMed]
  13. R. Folman, P. Krüger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002).
    [CrossRef]
  14. G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
    [CrossRef]
  15. G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
    [CrossRef]
  16. J. Dalibard and C. Cohen-Tannoudji, "Dressed-atom approach to atomic motion in laser light: the dipole force revisited," J. Opt. Soc. Am. B 2, 1707-1720 (1985).
    [CrossRef]
  17. C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
    [CrossRef]
  18. G. Lévêque, "Manipulation d'atomes froids par champs optiques confinés: théorie et simulation numérique," Ph. D. thesis (Université Paul Sabatier, Toulouse, France, 2003).
  19. Jµ2(phiv)=J-µ2(phiv): M. Abramowitz and L. A. Stegun, Handbook of Mathematical Functions, Applied Mathematics Series (National Bureau of Standards1964).
  20. R. Petit, M. Cadilhac, D. Maystre, P. Vincent, and M. Nevière, Electromagnetic Theory of Gratings Vol. 22 of Topics in Current Physics (Springer-Verlag, 1980).
    [CrossRef]
  21. See also J. C. Weeber, "Diffraction en champ proche optique. Analyse des images de microscopie à effet tunnel photonique," Ph.D. thesis (Université de Bourgogne, Dijon, France, 1996).
  22. R. C. Mowrey and D. J. Kouri, "Close-coupling wave packet approach to numerically exact molecule-surface scattering calculations," J. Chem. Phys. 84, 6466-6473 (1986).
    [CrossRef]

2002 (3)

R. Folman, P. Krüger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002).
[CrossRef]

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
[CrossRef]

1999 (3)

B. Rohwedder, "Atom optic elements based on nearfield grating sequences," Fortschr. Phys. 47, 883-911 (1999).
[CrossRef]

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

J. Baudon, R. Mathevet, and J. Robert, "Atomic interferometry," J. Phys. B 32, R173-R195 (1999).
[CrossRef]

1996 (3)

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
[CrossRef] [PubMed]

P. Szriftgiser, D. Guéry-Odelin, M. Arndt, and J. Dalibard, "Atomic wave diffraction and interference using temporal slits," Phys. Rev. Lett. 77, 4-7 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

1993 (1)

T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, "Magneto-optical beam splitter for atoms," Phys. Rev. Lett. 71, 3427-3430 (1993).
[CrossRef] [PubMed]

1988 (1)

D. W. Keith, Ch. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, "An interferometer for atoms," Phys. Rev. Lett. 66, 2693-2696 (1988).
[CrossRef]

1986 (1)

R. C. Mowrey and D. J. Kouri, "Close-coupling wave packet approach to numerically exact molecule-surface scattering calculations," J. Chem. Phys. 84, 6466-6473 (1986).
[CrossRef]

1985 (2)

1927 (1)

C. Davisson and L. H. Germer, "Diffraction of electrons by a crystal of nickel," Phys. Rev. 30, 705-740 (1927).
[CrossRef]

Abramowitz, M.

Jµ2(phiv)=J-µ2(phiv): M. Abramowitz and L. A. Stegun, Handbook of Mathematical Functions, Applied Mathematics Series (National Bureau of Standards1964).

Adams, C. S.

T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, "Magneto-optical beam splitter for atoms," Phys. Rev. Lett. 71, 3427-3430 (1993).
[CrossRef] [PubMed]

Arndt, M.

P. Szriftgiser, D. Guéry-Odelin, M. Arndt, and J. Dalibard, "Atomic wave diffraction and interference using temporal slits," Phys. Rev. Lett. 77, 4-7 (1996).
[CrossRef] [PubMed]

Asimov, R.

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

Aspect, A.

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
[CrossRef] [PubMed]

Baudon, J.

J. Baudon, R. Mathevet, and J. Robert, "Atomic interferometry," J. Phys. B 32, R173-R195 (1999).
[CrossRef]

Berggren, K. K.

Brouri, R.

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

Cadilhac, M.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, and M. Nevière, Electromagnetic Theory of Gratings Vol. 22 of Topics in Current Physics (Springer-Verlag, 1980).
[CrossRef]

Chebotayev, V. P.

Chu, A.

Cohen-Tannoudji, C.

Courtois, J. Y.

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
[CrossRef] [PubMed]

Dalibard, J.

P. Szriftgiser, D. Guéry-Odelin, M. Arndt, and J. Dalibard, "Atomic wave diffraction and interference using temporal slits," Phys. Rev. Lett. 77, 4-7 (1996).
[CrossRef] [PubMed]

J. Dalibard and C. Cohen-Tannoudji, "Dressed-atom approach to atomic motion in laser light: the dipole force revisited," J. Opt. Soc. Am. B 2, 1707-1720 (1985).
[CrossRef]

Davisson, C.

C. Davisson and L. H. Germer, "Diffraction of electrons by a crystal of nickel," Phys. Rev. 30, 705-740 (1927).
[CrossRef]

Denschlag, J.

R. Folman, P. Krüger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002).
[CrossRef]

Dubetsky, B. Y.

Ekstrom, Ch. R.

D. W. Keith, Ch. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, "An interferometer for atoms," Phys. Rev. Lett. 66, 2693-2696 (1988).
[CrossRef]

Ertmer, W.

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

Féron, S.

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

Folman, R.

R. Folman, P. Krüger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002).
[CrossRef]

Germer, L. H.

C. Davisson and L. H. Germer, "Diffraction of electrons by a crystal of nickel," Phys. Rev. 30, 705-740 (1927).
[CrossRef]

Girard, C.

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
[CrossRef]

Gorlicki, M.

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

Grimm, R.

Guéry-Odelin, D.

P. Szriftgiser, D. Guéry-Odelin, M. Arndt, and J. Dalibard, "Atomic wave diffraction and interference using temporal slits," Phys. Rev. Lett. 77, 4-7 (1996).
[CrossRef] [PubMed]

Haberland, H.

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

Henkel, C.

R. Folman, P. Krüger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002).
[CrossRef]

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

Johnson, K. S.

Kasantsev, A. P.

Keith, D. W.

D. W. Keith, Ch. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, "An interferometer for atoms," Phys. Rev. Lett. 66, 2693-2696 (1988).
[CrossRef]

Kouri, D. J.

R. C. Mowrey and D. J. Kouri, "Close-coupling wave packet approach to numerically exact molecule-surface scattering calculations," J. Chem. Phys. 84, 6466-6473 (1986).
[CrossRef]

Krüger, P.

R. Folman, P. Krüger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002).
[CrossRef]

Kurtsiefer, Ch.

T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, "Magneto-optical beam splitter for atoms," Phys. Rev. Lett. 71, 3427-3430 (1993).
[CrossRef] [PubMed]

Labeyrie, G.

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
[CrossRef] [PubMed]

Landragin, A.

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
[CrossRef] [PubMed]

Lévêque, G.

G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
[CrossRef]

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

G. Lévêque, "Manipulation d'atomes froids par champs optiques confinés: théorie et simulation numérique," Ph. D. thesis (Université Paul Sabatier, Toulouse, France, 2003).

Lorent, V.

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

Lynn, T. W.

Mathevet, R.

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
[CrossRef]

J. Baudon, R. Mathevet, and J. Robert, "Atomic interferometry," J. Phys. B 32, R173-R195 (1999).
[CrossRef]

Maystre, D.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, and M. Nevière, Electromagnetic Theory of Gratings Vol. 22 of Topics in Current Physics (Springer-Verlag, 1980).
[CrossRef]

Meier, C.

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
[CrossRef]

Mlynek, J.

T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, "Magneto-optical beam splitter for atoms," Phys. Rev. Lett. 71, 3427-3430 (1993).
[CrossRef] [PubMed]

Mowrey, R. C.

R. C. Mowrey and D. J. Kouri, "Close-coupling wave packet approach to numerically exact molecule-surface scattering calculations," J. Chem. Phys. 84, 6466-6473 (1986).
[CrossRef]

Nevière, M.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, and M. Nevière, Electromagnetic Theory of Gratings Vol. 22 of Topics in Current Physics (Springer-Verlag, 1980).
[CrossRef]

Ovchinnikov, Yu. B.

Petit, R.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, and M. Nevière, Electromagnetic Theory of Gratings Vol. 22 of Topics in Current Physics (Springer-Verlag, 1980).
[CrossRef]

Pfau, T.

T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, "Magneto-optical beam splitter for atoms," Phys. Rev. Lett. 71, 3427-3430 (1993).
[CrossRef] [PubMed]

Prentiss, M.

Pritchard, D. E.

D. W. Keith, Ch. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, "An interferometer for atoms," Phys. Rev. Lett. 66, 2693-2696 (1988).
[CrossRef]

Reinhardt, J.

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

Robert, J.

J. Baudon, R. Mathevet, and J. Robert, "Atomic interferometry," J. Phys. B 32, R173-R195 (1999).
[CrossRef]

Robilliard, C.

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

Rohwedder, B.

B. Rohwedder, "Atom optic elements based on nearfield grating sequences," Fortschr. Phys. 47, 883-911 (1999).
[CrossRef]

Schmiedmayer, J.

R. Folman, P. Krüger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002).
[CrossRef]

Sengstock, K.

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

Shahriar, M. S.

Sigel, M.

T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, "Magneto-optical beam splitter for atoms," Phys. Rev. Lett. 71, 3427-3430 (1993).
[CrossRef] [PubMed]

Söding, J.

Stegun, L. A.

Jµ2(phiv)=J-µ2(phiv): M. Abramowitz and L. A. Stegun, Handbook of Mathematical Functions, Applied Mathematics Series (National Bureau of Standards1964).

Szriftgiser, P.

P. Szriftgiser, D. Guéry-Odelin, M. Arndt, and J. Dalibard, "Atomic wave diffraction and interference using temporal slits," Phys. Rev. Lett. 77, 4-7 (1996).
[CrossRef] [PubMed]

Turchette, Q. A.

D. W. Keith, Ch. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, "An interferometer for atoms," Phys. Rev. Lett. 66, 2693-2696 (1988).
[CrossRef]

Vansteenkiste, N.

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
[CrossRef] [PubMed]

Viaris, B.

G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
[CrossRef]

Vincent, P.

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, and M. Nevière, Electromagnetic Theory of Gratings Vol. 22 of Topics in Current Physics (Springer-Verlag, 1980).
[CrossRef]

Wallis, H.

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

Weeber, J. C.

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

See also J. C. Weeber, "Diffraction en champ proche optique. Analyse des images de microscopie à effet tunnel photonique," Ph.D. thesis (Université de Bourgogne, Dijon, France, 1996).

Weiner, J.

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
[CrossRef]

Westbrook, C. I.

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
[CrossRef] [PubMed]

Westbrook, N.

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

Yakovlev, V. P.

Adv. At. Mol. Opt. Phys. (1)

R. Folman, P. Krüger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002).
[CrossRef]

Appl. Phys. B (1)

C. Henkel, H. Wallis, N. Westbrook, C. I. Westbrook, A. Aspect, K. Sengstock, and W. Ertmer, "Theory of atomic diffraction from evanescent waves," Appl. Phys. B 69, 277-289 (1999).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

G. Lévêque, C. Meier, R. Mathevet, B. Viaris, J. Weiner, and C. Girard, "Designing experiments for the study of atom diffraction from nanostructured optical potentials," Eur. Phys. J. Appl. Phys. 20, 219-226 (2002).
[CrossRef]

Fortschr. Phys. (1)

B. Rohwedder, "Atom optic elements based on nearfield grating sequences," Fortschr. Phys. 47, 883-911 (1999).
[CrossRef]

J. Chem. Phys. (1)

R. C. Mowrey and D. J. Kouri, "Close-coupling wave packet approach to numerically exact molecule-surface scattering calculations," J. Chem. Phys. 84, 6466-6473 (1986).
[CrossRef]

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

J. Phys. B (1)

J. Baudon, R. Mathevet, and J. Robert, "Atomic interferometry," J. Phys. B 32, R173-R195 (1999).
[CrossRef]

Opt. Commun. (1)

R. Brouri, R. Asimov, M. Gorlicki, S. Féron, J. Reinhardt, V. Lorent, and H. Haberland, "Thermal atom beam splitting by an evanescent standing wave," Opt. Commun. 124, 448-451 (1996).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

C. Davisson and L. H. Germer, "Diffraction of electrons by a crystal of nickel," Phys. Rev. 30, 705-740 (1927).
[CrossRef]

Phys. Rev. A (1)

G. Lévêque, C. Meier, R. Mathevet, C. Robilliard, J. Weiner, C. Girard, and J. C. Weeber, "Atomic diffraction from nanostructured optical poentials," Phys. Rev. A 65, 053615 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, "Measurement of the van der Waals force in an atomic mirror," Phys. Rev. Lett. 77, 1464-1467 (1996).
[CrossRef] [PubMed]

P. Szriftgiser, D. Guéry-Odelin, M. Arndt, and J. Dalibard, "Atomic wave diffraction and interference using temporal slits," Phys. Rev. Lett. 77, 4-7 (1996).
[CrossRef] [PubMed]

T. Pfau, Ch. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, "Magneto-optical beam splitter for atoms," Phys. Rev. Lett. 71, 3427-3430 (1993).
[CrossRef] [PubMed]

D. W. Keith, Ch. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, "An interferometer for atoms," Phys. Rev. Lett. 66, 2693-2696 (1988).
[CrossRef]

Other (5)

P.R.Berman, ed., Atomic Interferometry (Academic, 1997).

G. Lévêque, "Manipulation d'atomes froids par champs optiques confinés: théorie et simulation numérique," Ph. D. thesis (Université Paul Sabatier, Toulouse, France, 2003).

Jµ2(phiv)=J-µ2(phiv): M. Abramowitz and L. A. Stegun, Handbook of Mathematical Functions, Applied Mathematics Series (National Bureau of Standards1964).

R. Petit, M. Cadilhac, D. Maystre, P. Vincent, and M. Nevière, Electromagnetic Theory of Gratings Vol. 22 of Topics in Current Physics (Springer-Verlag, 1980).
[CrossRef]

See also J. C. Weeber, "Diffraction en champ proche optique. Analyse des images de microscopie à effet tunnel photonique," Ph.D. thesis (Université de Bourgogne, Dijon, France, 1996).

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Figures (10)

Fig. 1
Fig. 1

Grating of parallel stripes of width a and period L. Illumination is made at incidence and azimuthal angles ( θ , φ ) , and light experiences total internal reflection into the prism. The near field above the prism is evanescent and modulated by the surface corrugation.

Fig. 2
Fig. 2

Graphical presentation of the dispersion relation, Eqs. (3). The figure is plotted for the following parameters: φ = 60 ° , λ = 850 nm , n = 1.46 , and L = 250 nm .

Fig. 3
Fig. 3

When L = λ 2 n sin θ , A is in the middle of the segment [ A 0 A 1 ] , and then κ 0 = κ 1 for φ = 0 . This situation gives the same field structure as a partial standing evanescent wave.

Fig. 4
Fig. 4

Analytic atomic diffraction spectrum, Eqs. (4), as a function of atomic incident normalized momentum P for a subwavelength grating. Only specular reflection ( μ = 0 ) and the first two channels ( μ = ± 1 , ± 2 ) are shown.

Fig. 5
Fig. 5

Schematic view of a dielectric blazed grating.

Fig. 6
Fig. 6

Left scale: potential transverse variation at the classical mean turning point V ( x , z r ) . Right scale: departure of the actual classical turning point from its mean value, Δ z = z ( x ) z r . It gives the section of an equivalent atomic hard mirror. Dotted line, an ideal sawtooth profile.

Fig. 7
Fig. 7

Graphical plot of the dispersion relation, Eqs. (3), for a blazed grating parameter set. If φ = 45 ° , all harmonics are evanescent. In contrast, the first, second, and third orders are radiative for φ = 0 ° .

Fig. 8
Fig. 8

First-order atomic diffraction path corresponding to the exchange of one quantum of momentum with the second harmonic of the potential (2) and one quantum in the opposite direction with the first harmonic of the potential (1). First-order atomic diffraction is the coherent sum of all such paths.

Fig. 9
Fig. 9

Analytic atomic population, expression. (8), as a function of atomic-incident-reduced momentum P for an optimized blazed grating ( ϕ 0 = π 2 , Φ 1 = 1.84 , Φ 2 = 0.82 ). Only specular reflection ( μ = 0 , solid curve) and μ = ± 1 channels are shown ( μ = + 1 , long-dashed curve; μ = 1 , short-dashed curve).

Fig. 10
Fig. 10

Atomic diffraction population as a function of atomic-incident-reduced momentum P. Top panel, full numerical calculation; central panel, numerical calculation but with the potential spectrum artificially truncated to the zeroth, first, and second orders; lower panel, analytical calculation, expression (7). Only specular reflection ( μ = 0 , solid curve) and μ = ± 1 channels are shown ( μ = + 1 , long-dashed curve; μ = 1 , short-dashed curve).

Equations (25)

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V ( r ) = γ 2 8 δ I ( r ) I s .
E ( r ) = m E m exp ( i k m l ) exp ( κ m z ) .
k m = n k i + m 2 π L e x ,
κ m 2 = k m 2 k i 2 ,
V ( x , z ) V 0 exp ( 2 κ 0 z ) [ 1 + ϵ ̃ 1 ( z ) cos ( 2 π L x ) ] ,
ϵ ̃ 1 ( z ) = ϵ 1 exp [ ( κ 0 κ 1 ) z ] , ϵ 1 = 2 E 0 E 1 * E 0 2 .
P μ = J μ 2 [ ϵ ̃ 1 ( z r ) P B ̃ ( α 1 ) ] ,
α 1 = κ 1 κ 0 ,
P = p a κ 0 ,
z r = 1 2 κ 0 ln ( V 0 E k ) ,
B ̃ ( α 1 ) = 2 α 1 1 Γ ( α 1 + 1 2 ) 2 Γ ( α 1 + 1 ) ,
V ( x , z ) = V 0 exp ( 2 κ 0 z ) [ 1 + ϵ ̃ 1 ( z ) cos ( 2 π L x ) + ϵ ̃ 2 ( z ) cos ( 4 π L x + ϕ 0 ) ] ,
P μ = ν i ν exp ( i ν ϕ 0 ) J μ 2 ν [ ϵ ̃ 1 ( z r ) P B ̃ ( α 1 ) ] J ν [ ϵ ̃ 2 ( z r ) P B ̃ ( α 2 ) ] 2 .
P 1 J 0 ( Φ 2 ) J 1 ( Φ 1 ) + i exp ( i ϕ 0 ) J 1 ( Φ 2 ) J 1 ( Φ 1 ) 2 = J 1 ( Φ 1 ) [ J 0 ( Φ 2 ) i exp ( i ϕ 0 ) J 1 ( Φ 2 ) ] 2 .
P 1 opt J 1 ( Φ 1 ) [ J 0 ( Φ 2 ) + J 1 ( Φ 2 ) ] 2 .
P μ { ν J ν [ ϵ ̃ 2 ( z r ) P B ̃ ( α 2 ) ] J μ 2 ν [ ϵ ̃ 1 ( z r ) P B ̃ ( α 1 ) ] } 2 ,
m = 0 , 1 κ 0 = 86 nm ,
m = + 1 , 1 κ 1 = 139 nm ,
m = 2 , 1 κ 2 = 139 nm ,
m = 3 , 1 κ 3 = 86 nm ,
m = 1 , 1 κ 1 = 57 nm .
ϵ 1 = 1.3 × 10 2 , ϵ 2 = 5.8 × 10 3 , ϕ 0 68 ° .
θ diff ( P ) = λ dB L = Q k 0 .
2 κ 0 [ z ( x ) z r ] = 2 κ 0 Δ z ( x ) ϵ ̃ 1 ( z r ) cos ( Q x ) + ϵ ̃ 2 ( z r ) cos ( 2 Q x + ϕ 0 ) ,
θ ref ( P ) = 2 γ = 9 3 8 π Q κ 0 ϵ ̃ 1 [ z r ( P ) ] ,

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