Abstract

We theoretically explore an all-optical method for generating tunable diffractive Fresnel lenses in coherent media based on electromagnetically induced transparency. In this method, intensity-modulated images in coupling light fields can pattern the coherent media to induce the desired modulo-2π quadratic phase profiles for the lenses to diffract probe light fields. We characterize the focusing and imaging properties of the induced lenses. In particular, we show that the images in coupling fields can flexibly control the images in probe fields by diffraction, where large focal length tunability from 1 m to infinity and high output (∼ 88% diffraction efficiency) can be achieved. Additionally, we also find that the induced Fresnel lenses can be rapidly modulated with megahertz refresh rates using image-bearing square pulse trains in coupling fields. Our proposed lenses may find a wide range of applications for multimode all-optical signal processing in both the classical and quantum regimes.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. S. Patel, and K. Rastani, "Electrically controlled polarization-independent liquid-crystal Fresnel lens arrays," Opt. Lett. 16, 532-534 (1991).
    [CrossRef] [PubMed]
  2. Y.-H. Fan, H. Ren, and S.-T. Wu, "Switchable Fresnel lens using polymer-stabilized liquid crystals," Opt. Express 11, 3080-3086 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-23-3080.
    [CrossRef] [PubMed]
  3. L.-C. Lin, H.-C. Jau, T.-H. Lin, and A. Y.-G. Fuh, "Highly efficient and polarization-independent Fresnel lens based on dye-doped liquid crystal," Opt. Express 15, 2900-2906 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-6-2900.
    [CrossRef] [PubMed]
  4. M. Ferstl, and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
    [CrossRef]
  5. G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
    [CrossRef] [PubMed]
  6. P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, "Tunable-focus flat liquid-crystal diffractive lens," Opt. Lett. 35, 336-338 (2010).
    [CrossRef] [PubMed]
  7. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005).
    [CrossRef]
  8. M. D. Lukin, "Colloquium: Trapping and manipulating photon states in atomic ensembles," Rev. Mod. Phys. 75, 457-472 (2003).
    [CrossRef]
  9. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing," Phys. Rev. Lett. 74, 670-673 (1995).
    [CrossRef] [PubMed]
  10. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Electromagnetically-induced focusing," Phys. Rev. A 53, 408-415 (1996).
    [CrossRef] [PubMed]
  11. M. Mitsunaga, M. Yamashita, and H. Inoue, "Absorption imaging of electromagnetically induced transparency in cold sodium atoms," Phys. Rev. A 62, 013817 (2000).
    [CrossRef]
  12. L. Zhao, T. Wang, and S. F. Yelin, "Two-dimensional all-optical spatial light modulation with high speed in coherent media," Opt. Lett. 34, 1930-1932 (2009).
    [CrossRef] [PubMed]
  13. M. Fleischhauer, and M. O. Scully, "Quantum sensitivity limits of an optical magnetometer based on atomic phase coherence," Phys. Rev. A 49, 1973-1986 (1994).
    [CrossRef] [PubMed]
  14. J. Gea-Banacloche, Y.-Q. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576-584 (1995).
    [CrossRef] [PubMed]
  15. R. P. Feynman, and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
  16. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  17. Y.-Q. Ling, and M. Xiao, "Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms," Phys. Rev. A 51, R2703-R2706 (1995).
    [CrossRef]
  18. D. A. Steck, "Rubidium 87 D Line Data," available online at http://steck.us/alkalidata (revision 2.1.2, 12 August 2009).
  19. M. Born, and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).
  20. T. Stone, and N. George, "Hybrid diffractive-refractive lenses and achromats," Appl. Opt. 27, 2960-2971 (1988).
    [CrossRef] [PubMed]
  21. V. K. Ingle, and J. G. Proakis, Digital Signal Processing Using MATLAB V.4 (PWS Publishing Company, Boston, MA, 1997).
  22. S. E. Harris, and Z.-F. Luo, "Preparation energy for electromagnetically induced transparency," Phys. Rev. A 52, R928-R931 (1995).
    [CrossRef] [PubMed]
  23. H. Schmidt, and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
    [CrossRef]
  24. M. Fleischhauer, and A. S. Manka, "Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture," Phys. Rev. A 54, 794-803 (1996).
    [CrossRef] [PubMed]
  25. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
    [CrossRef]
  26. S. Knappe, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
    [CrossRef] [PubMed]
  27. A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
    [CrossRef]
  28. Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
    [CrossRef]
  29. S. J. Seltzera, and M. V. Romalis, "High-temperature alkali vapor cells with antirelaxation surface coatings," J. Appl. Phys. 106, 114905 (2009).
    [CrossRef]
  30. M. Meucci, E. Mariotti, P. Bicchi, C. Marinelli, and L. Moi, "Light-Induced Atom Desorption," Europhys. Lett. 25, 639-643 (1994).
    [CrossRef]
  31. A. Bogi, C. Marinelli, A. Burchianti, E. Mariotti, L. Moi, S. Gozzini, L. Marmugi, and A. Lucchesini, "Full control of sodium vapor density in siloxane-coated cells using blue LED light-induced atomic desorption," Opt. Lett. 34, 2643-2645 (2009).
    [CrossRef] [PubMed]
  32. W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, "High densities of cold atoms in a dark spontaneous-force optical trap," Phys. Rev. Lett. 70, 2253-2256 (1993).
    [CrossRef] [PubMed]
  33. I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, "Compensation of ac Stark shifts in optical magnetometry," Phys. Rev. A 63, 063802 (2001).
    [CrossRef]
  34. R. Drampyan, S. Pustelny, and W. Gawlik, "Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization," Phys. Rev. A 80, 033815 (2009).
    [CrossRef]

2010 (1)

2009 (4)

R. Drampyan, S. Pustelny, and W. Gawlik, "Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization," Phys. Rev. A 80, 033815 (2009).
[CrossRef]

L. Zhao, T. Wang, and S. F. Yelin, "Two-dimensional all-optical spatial light modulation with high speed in coherent media," Opt. Lett. 34, 1930-1932 (2009).
[CrossRef] [PubMed]

A. Bogi, C. Marinelli, A. Burchianti, E. Mariotti, L. Moi, S. Gozzini, L. Marmugi, and A. Lucchesini, "Full control of sodium vapor density in siloxane-coated cells using blue LED light-induced atomic desorption," Opt. Lett. 34, 2643-2645 (2009).
[CrossRef] [PubMed]

S. J. Seltzera, and M. V. Romalis, "High-temperature alkali vapor cells with antirelaxation surface coatings," J. Appl. Phys. 106, 114905 (2009).
[CrossRef]

2008 (1)

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

2007 (1)

2006 (2)

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

2004 (1)

2003 (2)

2001 (1)

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, "Compensation of ac Stark shifts in optical magnetometry," Phys. Rev. A 63, 063802 (2001).
[CrossRef]

2000 (2)

M. Mitsunaga, M. Yamashita, and H. Inoue, "Absorption imaging of electromagnetically induced transparency in cold sodium atoms," Phys. Rev. A 62, 013817 (2000).
[CrossRef]

H. Schmidt, and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
[CrossRef]

1996 (4)

M. Fleischhauer, and A. S. Manka, "Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture," Phys. Rev. A 54, 794-803 (1996).
[CrossRef] [PubMed]

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

M. Ferstl, and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Electromagnetically-induced focusing," Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

1995 (4)

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing," Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

J. Gea-Banacloche, Y.-Q. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

Y.-Q. Ling, and M. Xiao, "Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms," Phys. Rev. A 51, R2703-R2706 (1995).
[CrossRef]

S. E. Harris, and Z.-F. Luo, "Preparation energy for electromagnetically induced transparency," Phys. Rev. A 52, R928-R931 (1995).
[CrossRef] [PubMed]

1994 (2)

M. Meucci, E. Mariotti, P. Bicchi, C. Marinelli, and L. Moi, "Light-Induced Atom Desorption," Europhys. Lett. 25, 639-643 (1994).
[CrossRef]

M. Fleischhauer, and M. O. Scully, "Quantum sensitivity limits of an optical magnetometer based on atomic phase coherence," Phys. Rev. A 49, 1973-1986 (1994).
[CrossRef] [PubMed]

1993 (1)

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, "High densities of cold atoms in a dark spontaneous-force optical trap," Phys. Rev. Lett. 70, 2253-2256 (1993).
[CrossRef] [PubMed]

1991 (1)

1988 (1)

Äyräs, P.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Bicchi, P.

M. Meucci, E. Mariotti, P. Bicchi, C. Marinelli, and L. Moi, "Light-Induced Atom Desorption," Europhys. Lett. 25, 639-643 (1994).
[CrossRef]

Bogi, A.

Burchianti, A.

Clark, N. A.

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Davis, K. B.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, "High densities of cold atoms in a dark spontaneous-force optical trap," Phys. Rev. Lett. 70, 2253-2256 (1993).
[CrossRef] [PubMed]

Dodge, M. R.

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Drampyan, R.

R. Drampyan, S. Pustelny, and W. Gawlik, "Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization," Phys. Rev. A 80, 033815 (2009).
[CrossRef]

Dunn, M. H.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Electromagnetically-induced focusing," Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing," Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Fan, Y.-H.

Ferstl, M.

M. Ferstl, and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

M. Fleischhauer, and A. S. Manka, "Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture," Phys. Rev. A 54, 794-803 (1996).
[CrossRef] [PubMed]

M. Fleischhauer, and M. O. Scully, "Quantum sensitivity limits of an optical magnetometer based on atomic phase coherence," Phys. Rev. A 49, 1973-1986 (1994).
[CrossRef] [PubMed]

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Frisch, A.-M.

M. Ferstl, and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
[CrossRef]

Fuh, A. Y.-G.

Fulton, D. J.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Electromagnetically-induced focusing," Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing," Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Gawlik, W.

R. Drampyan, S. Pustelny, and W. Gawlik, "Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization," Phys. Rev. A 80, 033815 (2009).
[CrossRef]

Gea-Banacloche, J.

J. Gea-Banacloche, Y.-Q. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

George, N.

Giridhar, M. S.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Gozzini, S.

Haddock, J. N.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris, and Z.-F. Luo, "Preparation energy for electromagnetically induced transparency," Phys. Rev. A 52, R928-R931 (1995).
[CrossRef] [PubMed]

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Hollberg, L.

Holz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Honkanen, S.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

Inoue, H.

M. Mitsunaga, M. Yamashita, and H. Inoue, "Absorption imaging of electromagnetically induced transparency in cold sodium atoms," Phys. Rev. A 62, 013817 (2000).
[CrossRef]

Jau, H.-C.

Jin, S.

J. Gea-Banacloche, Y.-Q. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

Joffe, M. A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, "High densities of cold atoms in a dark spontaneous-force optical trap," Phys. Rev. Lett. 70, 2253-2256 (1993).
[CrossRef] [PubMed]

Jones, C. D.

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

Ketterle, W.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, "High densities of cold atoms in a dark spontaneous-force optical trap," Phys. Rev. Lett. 70, 2253-2256 (1993).
[CrossRef] [PubMed]

Kippelen, B.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Kitching, J.

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

S. Knappe, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
[CrossRef] [PubMed]

Knappe, S.

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

S. Knappe, L. Hollberg, and J. Kitching, "Dark-line atomic resonances in submillimeter structures," Opt. Lett. 29, 388-390 (2004).
[CrossRef] [PubMed]

Li, G.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Li, Y.-Q.

J. Gea-Banacloche, Y.-Q. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

Lieberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Lin, L.-C.

Lin, T.-H.

Ling, Y.-Q.

Y.-Q. Ling, and M. Xiao, "Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms," Phys. Rev. A 51, R2703-R2706 (1995).
[CrossRef]

Lucchesini, A.

Lukin, M. D.

M. D. Lukin, "Colloquium: Trapping and manipulating photon states in atomic ensembles," Rev. Mod. Phys. 75, 457-472 (2003).
[CrossRef]

Luo, Z.-F.

S. E. Harris, and Z.-F. Luo, "Preparation energy for electromagnetically induced transparency," Phys. Rev. A 52, R928-R931 (1995).
[CrossRef] [PubMed]

MacLennan, J. E.

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

Manka, A. S.

M. Fleischhauer, and A. S. Manka, "Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture," Phys. Rev. A 54, 794-803 (1996).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

Marinelli, C.

Mariotti, E.

Marmugi, L.

Martin, A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, "High densities of cold atoms in a dark spontaneous-force optical trap," Phys. Rev. Lett. 70, 2253-2256 (1993).
[CrossRef] [PubMed]

Mathine, D. L.

P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, "Tunable-focus flat liquid-crystal diffractive lens," Opt. Lett. 35, 336-338 (2010).
[CrossRef] [PubMed]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Matsko, A. B.

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, "Compensation of ac Stark shifts in optical magnetometry," Phys. Rev. A 63, 063802 (2001).
[CrossRef]

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Meredith, G. R.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Meucci, M.

M. Meucci, E. Mariotti, P. Bicchi, C. Marinelli, and L. Moi, "Light-Induced Atom Desorption," Europhys. Lett. 25, 639-643 (1994).
[CrossRef]

Mitsunaga, M.

M. Mitsunaga, M. Yamashita, and H. Inoue, "Absorption imaging of electromagnetically induced transparency in cold sodium atoms," Phys. Rev. A 62, 013817 (2000).
[CrossRef]

Moi, L.

Moseley, R. R.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Electromagnetically-induced focusing," Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing," Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Novikova, I.

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, "Compensation of ac Stark shifts in optical magnetometry," Phys. Rev. A 63, 063802 (2001).
[CrossRef]

Papoyan, A.

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

Patel, J. S.

Peyghambarian, N.

P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, "Tunable-focus flat liquid-crystal diffractive lens," Opt. Lett. 35, 336-338 (2010).
[CrossRef] [PubMed]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Peyman, G.

Pritchard, D. E.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, "High densities of cold atoms in a dark spontaneous-force optical trap," Phys. Rev. Lett. 70, 2253-2256 (1993).
[CrossRef] [PubMed]

Pustelny, S.

R. Drampyan, S. Pustelny, and W. Gawlik, "Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization," Phys. Rev. A 80, 033815 (2009).
[CrossRef]

Ram, R. J.

H. Schmidt, and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
[CrossRef]

Rastani, K.

Ren, H.

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Robinson, H. G.

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

Romalis, M. V.

S. J. Seltzera, and M. V. Romalis, "High-temperature alkali vapor cells with antirelaxation surface coatings," J. Appl. Phys. 106, 114905 (2009).
[CrossRef]

Sargsyan, A.

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

Sarkisyan, D.

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

Schmidt, H.

H. Schmidt, and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
[CrossRef]

Schwiegerling, J.

P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, "Tunable-focus flat liquid-crystal diffractive lens," Opt. Lett. 35, 336-338 (2010).
[CrossRef] [PubMed]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Scully, M. O.

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, "Compensation of ac Stark shifts in optical magnetometry," Phys. Rev. A 63, 063802 (2001).
[CrossRef]

M. Fleischhauer, and M. O. Scully, "Quantum sensitivity limits of an optical magnetometer based on atomic phase coherence," Phys. Rev. A 49, 1973-1986 (1994).
[CrossRef] [PubMed]

Seltzera, S. J.

S. J. Seltzera, and M. V. Romalis, "High-temperature alkali vapor cells with antirelaxation surface coatings," J. Appl. Phys. 106, 114905 (2009).
[CrossRef]

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Shepherd, S.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Electromagnetically-induced focusing," Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing," Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Sinclair, B. D.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Electromagnetically-induced focusing," Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing," Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Stone, T.

Valley, P.

P. Valley, D. L. Mathine, M. R. Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, "Tunable-focus flat liquid-crystal diffractive lens," Opt. Lett. 35, 336-338 (2010).
[CrossRef] [PubMed]

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Velichansky, V. L.

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, "Compensation of ac Stark shifts in optical magnetometry," Phys. Rev. A 63, 063802 (2001).
[CrossRef]

Wang, T.

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Welch, G. R.

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, "Compensation of ac Stark shifts in optical magnetometry," Phys. Rev. A 63, 063802 (2001).
[CrossRef]

Williby, G.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Wu, S.-T.

Xiao, M.

Y.-Q. Ling, and M. Xiao, "Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms," Phys. Rev. A 51, R2703-R2706 (1995).
[CrossRef]

J. Gea-Banacloche, Y.-Q. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

Yamashita, M.

M. Mitsunaga, M. Yamashita, and H. Inoue, "Absorption imaging of electromagnetically induced transparency in cold sodium atoms," Phys. Rev. A 62, 013817 (2000).
[CrossRef]

Yelin, S. F.

Yi, Y. W.

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

Zhao, L.

Zhu, C.

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. Schmidt, and R. J. Ram, "All-optical wavelength converter and switch based on electromagnetically induced transparency," Appl. Phys. Lett. 76, 3173-3175 (2000).
[CrossRef]

Europhys. Lett. (1)

M. Meucci, E. Mariotti, P. Bicchi, C. Marinelli, and L. Moi, "Light-Induced Atom Desorption," Europhys. Lett. 25, 639-643 (1994).
[CrossRef]

J. Appl. Phys. (2)

Y. W. Yi, H. G. Robinson, S. Knappe, J. E. MacLennan, C. D. Jones, C. Zhu, N. A. Clark, and J. Kitching, "Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells," J. Appl. Phys. 104, 023534 (2008).
[CrossRef]

S. J. Seltzera, and M. V. Romalis, "High-temperature alkali vapor cells with antirelaxation surface coatings," J. Appl. Phys. 106, 114905 (2009).
[CrossRef]

J. Mod. Opt. (1)

M. Ferstl, and A.-M. Frisch, "Static and dynamic Fresnel zone lenses for optical interconnections," J. Mod. Opt. 43, 1451-1462 (1996).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (10)

A. Sargsyan, D. Sarkisyan, and A. Papoyan, "Dark-line atomic resonances in a submicron-thin Rb vapor layer," Phys. Rev. A 73, 033803 (2006).
[CrossRef]

I. Novikova, A. B. Matsko, V. L. Velichansky, M. O. Scully, and G. R. Welch, "Compensation of ac Stark shifts in optical magnetometry," Phys. Rev. A 63, 063802 (2001).
[CrossRef]

R. Drampyan, S. Pustelny, and W. Gawlik, "Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization," Phys. Rev. A 80, 033815 (2009).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Electromagnetically-induced focusing," Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

M. Mitsunaga, M. Yamashita, and H. Inoue, "Absorption imaging of electromagnetically induced transparency in cold sodium atoms," Phys. Rev. A 62, 013817 (2000).
[CrossRef]

M. Fleischhauer, and M. O. Scully, "Quantum sensitivity limits of an optical magnetometer based on atomic phase coherence," Phys. Rev. A 49, 1973-1986 (1994).
[CrossRef] [PubMed]

J. Gea-Banacloche, Y.-Q. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

M. Fleischhauer, and A. S. Manka, "Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture," Phys. Rev. A 54, 794-803 (1996).
[CrossRef] [PubMed]

S. E. Harris, and Z.-F. Luo, "Preparation energy for electromagnetically induced transparency," Phys. Rev. A 52, R928-R931 (1995).
[CrossRef] [PubMed]

Y.-Q. Ling, and M. Xiao, "Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms," Phys. Rev. A 51, R2703-R2706 (1995).
[CrossRef]

Phys. Rev. Lett. (2)

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, "Spatial Consequences of Electromagnetically Induced Transparency: Observation of Electromagnetically Induced Focusing," Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, "High densities of cold atoms in a dark spontaneous-force optical trap," Phys. Rev. Lett. 70, 2253-2256 (1993).
[CrossRef] [PubMed]

Proc. IEEE (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Lieberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, "Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications," Proc. Natl. Acad. Sci. U.S.A. 103, 6100-6104 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

M. D. Lukin, "Colloquium: Trapping and manipulating photon states in atomic ensembles," Rev. Mod. Phys. 75, 457-472 (2003).
[CrossRef]

Other (5)

R. P. Feynman, and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

D. A. Steck, "Rubidium 87 D Line Data," available online at http://steck.us/alkalidata (revision 2.1.2, 12 August 2009).

M. Born, and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

V. K. Ingle, and J. G. Proakis, Digital Signal Processing Using MATLAB V.4 (PWS Publishing Company, Boston, MA, 1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(Color online) (a) Modulo-2π quadratic phase profile for generating a Fresnel lens to focus and image incident light fields by diffraction. For simplicity, we only draw four zones in the phase profile. (b) Energy-level scheme of a Λ-type EIT system with two copropagating light fields interacting with three atomic energy levels. Intensity-modulated images can be adopted in the strong coupling field to pattern the EIT system and modulate the probe field.

Fig. 2
Fig. 2

(Color online) (a) Numerical illustration of the intensity profile of the image in the coupling field based on Eq. (6), where the image gives four zones (i.e., M = 4) and their outer radiuses are r1 = 1.26 mm, r2 = 1.78 mm, r3 = 2.18 mm, and r4 = 2.52 mm, respectively. For example, in the first zone, we have Ic(0) = 1.58 W/cm2 and Ic(r → r1) = 6.33 W/cm2. (b) The induced r-dependent susceptibility χ′ (solid curve) and χ″ (dotted curve). Therefore, both phase and amplitude modulation can be induced for the probe field. (c) High transmission rate (T > 96%) of the probe field, which suggests that the amplitude modulation should be weak.

Fig. 3
Fig. 3

(Color online) (a) Intensity profiles in the focal plane with (solid curve) and without (dotted curve) the amplitude modulation in the induced lens. The amplitude modulation (i.e., absorption) only slightly lower the principal maximum to ≈ 98% (blue box, also shown in (b) for detailed information) and almost has no influence on the FWHM.

Fig. 4
Fig. 4

(Color online) (a) Two letters “TH” as the original object in the probe field. (b) Image in the coupling field to induce the four-zone Fresnel lens in the EIT system, where its intensity and diameter are numerically illustrated in Fig. 2(a). Note that, in our scheme, a glass lens is put right behind the EIT system to constitute a compound lens for imaging. Moreover, using the FFT algorithm, we can numerically calculate the image formation through the compound lens. (c) Image of the letters “TH” in the probe field generated by the compound lens and measured by the photodetector. The size of this picture (and all the following pictures of the images) is 9.5 × 9.5 mm2. (d) Image with a uniform intensity in the coupling field, which actually induces an aperture and leads to an infinite focal length for the EIT system. Consequently, a new compound lens can be produced for imaging. (e) Frauhofer diffraction pattern of the letters “TH” in the probe field generated by the new compound lens and measured by the photodetector. (f) Image in the coupling field to induce the three-zone Fresnel lens in the EIT system. (g) Corresponding fuzzy image received by the photodetector. The color bar on the right gives the normalized intensity of the probe images.

Fig. 5
Fig. 5

(Color online) (a)-(c) Coupling images with different aperture diameters, where the intensity distributions and the aperture diameters are numerically illustrated in Fig. 2(a). (d)-(f) Corresponding probe images measured by the photodetector. With the increase of the aperture diameters of the coupling images, the quality of the probe images can be improved. The color bar on the right gives the normalized intensity of the probe images.

Equations (17)

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

r m = 2 m f F λ , m = 1 , 2 , , M ,
χ = χ + i χ = K Δ Ω c 2 + i [ 2 Δ 2 Γ + γ ( Ω c 2 + Γ γ ) / 2 ] | Ω c 2 + Γ ( γ + i 2 Δ ) | 2 ,
Ω c { Γ , Δ } γ ,
χ = K Δ Ω c 2 and χ = K 2 Δ 2 Γ + γ Ω c 2 / 2 Ω c 4 ,
Ω c ( r ) = Γ [ ξ mod ( r 2 r 1 2 , 1 ) + ζ ] 1 / 2 ,
I c ( r ) = 1 2 ɛ 0 c E c 2 = ɛ 0 c h ¯ 2 Ω c 2 ( r ) 2 μ 23 2 = ɛ 0 c h ¯ 2 Γ 2 2 μ 23 2 ξ mod ( r 2 r 1 2 , 1 ) + ζ 1 ,
χ ( r ) = K Δ Γ 2 [ ξ mod ( r 2 r 1 2 , 1 ) + ζ ] .
[ χ ( r r m ) χ ( r = r m 1 ) ] d / 2 = λ p ,
χ ( r ) = 2 K Δ 2 Γ 3 [ ξ mod ( r 2 r 1 2 , 1 ) + ζ ] 2 + K γ 2 Γ 2 [ ξ mod ( r 2 r 1 2 , 1 ) + ζ ] ,
2 E p x 2 + 2 i k p E p z = k p 2 χ E p ,
E p z ( d ) = E p z ( 0 ) exp ( i 2 k p χ z d ) × 1 i λ p d x m 1 x m exp [ i k p 2 d ( x x ) 2 ] d x ,
N F = w m 2 4 λ p d 1 ,
1 i λ p d x m 1 x m exp [ i k p 2 d ( x x ) 2 ] d x 1
E p ( d ) = E p ( 0 ) exp ( i k p χ d / 2 ) ,
T p = exp ( α d ) ,
E f N ( r f ) = c 0 0 2 π 0 r 4 exp [ k p χ d / 2 i k p r r f cos ( ϕ ϕ f ) / f F ] d r d ϕ ,
η m = ( 1 R w m ) 2 ,

Metrics