Abstract

Three-dimensional focusing of evanescent waves by specially configured surface arrays of nanoparticles emulating near-field optical holograms of dipole sources (located close to the surface) is suggested and analyzed. The idea is to place chains of nanoparticles along bright fringes of calculated (holographic) interference patterns so that the local nanoparticle density along these chains would be proportional to the local intensity contrast in the interference patterns. Three different configurations are considered: a holographic scheme with totally internally reflected reference and reconstructing waves, a modified scheme with the reconstructing wave being represented by a suitable surface plasmon polariton (SPP) plane wave, and a SPP holographic scheme with reference and reconstructing waves both being (phase-conjugated) laterally-confined (Gaussian) SPP beams. Our numerical approach is based on the Green’s function technique with the point-dipole approximation for radiation scattering by nanoparticles. We demonstrate that a nanoparticle array configured in accordance with the intensity interference pattern formed by a dipole field and a reference wave allows one to efficiently focus the (phase-conjugated) reconstructing wave (via its scattering by the nanoparticle array) at the site of the dipole. Influence of the polarization and wavelength of the reconstructing wave on the resulting intensity distribution is also considered. Fabrication of suitable nanoparticle arrays is discussed along with their potential applications.

© 2008 Optical Society of America

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References

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  1. V. I. Balykin, V. V. Klimov, and V. S. Letokhov, "Atom nanooptics based on photon dots and photon holes," JETP Lett. 78, 8-12 (2003).
    [CrossRef]
  2. P. J. Reece, V. Garcés-Chávez, and K. Dholakia, "Near-field optical micromanipulation with cavity enhanced evanescent waves," Appl. Phys. Lett. 88, 221116 (2006).
    [CrossRef]
  3. R. Merlin, "Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).
    [CrossRef] [PubMed]
  4. S. I. Bozhevolnyi and B. Vohnsen, "Phase conjugation of optical near field by a surface hologram," Opt. Commun. 135, 19-23 (1997).
    [CrossRef]
  5. B. Vohnsen and S. I. Bozhevolnyi, "Holographic approach to phase conjugation of optical near fields," J. Opt. Soc. Am. A 14, 1491-1499 (1997).
    [CrossRef]
  6. L. C. Thomson, G. Whyte, M. Mazilu, and J. Courtial, "Simulated holographic three-dimensional intensity shaping of evanescent-wave fields," J. Opt. Soc. Am. B 25, 849-853 (2008).
    [CrossRef]
  7. S. I. Bozhevolnyi and B. Vohnsen, "Near-field optical holography," Phys. Rev. Lett. 77, 3351-3354 (1996).
    [CrossRef] [PubMed]
  8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  9. A. B. Evlyukhin and S. I. Bozhevolnyi, "Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations," Phys. Rev. B 71, 134303 (2005).
    [CrossRef]
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    [CrossRef]
  12. L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
    [CrossRef]
  13. O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74,526-529 (1995).
    [CrossRef] [PubMed]
  14. O. Keller, "Attached and radiated electromagnetic fields of an electric point dipole," J. Opt. Soc. Am. B 16, 835-847 (1999).
    [CrossRef]
  15. T. Søndergaard and S. I. Bozhevolnyi, "Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study," Phys. Rev. B 69,045422 (2004).
    [CrossRef]
  16. M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Greens tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
    [CrossRef]
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    [CrossRef]
  19. A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
    [CrossRef]
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    [CrossRef]

2008 (1)

2007 (1)

R. Merlin, "Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).
[CrossRef] [PubMed]

2006 (1)

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, "Near-field optical micromanipulation with cavity enhanced evanescent waves," Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

2005 (2)

A. B. Evlyukhin and S. I. Bozhevolnyi, "Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations," Phys. Rev. B 71, 134303 (2005).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Theoretical analysis of finite-size surface plasmon polariton band-gap structures," Phys. Rev. B 71, 125429 (2005).
[CrossRef]

2004 (1)

T. Søndergaard and S. I. Bozhevolnyi, "Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study," Phys. Rev. B 69,045422 (2004).
[CrossRef]

2003 (3)

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

V. I. Balykin, V. V. Klimov, and V. S. Letokhov, "Atom nanooptics based on photon dots and photon holes," JETP Lett. 78, 8-12 (2003).
[CrossRef]

2000 (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Greens tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

1999 (1)

1997 (3)

L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
[CrossRef]

S. I. Bozhevolnyi and B. Vohnsen, "Phase conjugation of optical near field by a surface hologram," Opt. Commun. 135, 19-23 (1997).
[CrossRef]

B. Vohnsen and S. I. Bozhevolnyi, "Holographic approach to phase conjugation of optical near fields," J. Opt. Soc. Am. A 14, 1491-1499 (1997).
[CrossRef]

1996 (1)

S. I. Bozhevolnyi and B. Vohnsen, "Near-field optical holography," Phys. Rev. Lett. 77, 3351-3354 (1996).
[CrossRef] [PubMed]

1995 (1)

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74,526-529 (1995).
[CrossRef] [PubMed]

1993 (2)

O. Keller, M. Xiao, and S. Bozhevolnyi, "Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach," Surf. Sci. 280, 217-230 (1993).
[CrossRef]

D. Van Labeke and D. Barchiesi, "Probes for scanning tunneling optical microscopy: a theoretical comparison," J. Opt. Soc. Am. A 10, 2193-2201 (1993).
[CrossRef]

1977 (1)

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4579 (1972).
[CrossRef]

Balykin, V. I.

V. I. Balykin, V. V. Klimov, and V. S. Letokhov, "Atom nanooptics based on photon dots and photon holes," JETP Lett. 78, 8-12 (2003).
[CrossRef]

Barchiesi, D.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Bozhevolnyi, S.

O. Keller, M. Xiao, and S. Bozhevolnyi, "Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach," Surf. Sci. 280, 217-230 (1993).
[CrossRef]

Bozhevolnyi, S. I.

A. B. Evlyukhin and S. I. Bozhevolnyi, "Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations," Phys. Rev. B 71, 134303 (2005).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Theoretical analysis of finite-size surface plasmon polariton band-gap structures," Phys. Rev. B 71, 125429 (2005).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study," Phys. Rev. B 69,045422 (2004).
[CrossRef]

B. Vohnsen and S. I. Bozhevolnyi, "Holographic approach to phase conjugation of optical near fields," J. Opt. Soc. Am. A 14, 1491-1499 (1997).
[CrossRef]

S. I. Bozhevolnyi and B. Vohnsen, "Phase conjugation of optical near field by a surface hologram," Opt. Commun. 135, 19-23 (1997).
[CrossRef]

S. I. Bozhevolnyi and B. Vohnsen, "Near-field optical holography," Phys. Rev. Lett. 77, 3351-3354 (1996).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4579 (1972).
[CrossRef]

Courtial, J.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74,526-529 (1995).
[CrossRef] [PubMed]

Dholakia, K.

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, "Near-field optical micromanipulation with cavity enhanced evanescent waves," Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Evlyukhin, A. B.

A. B. Evlyukhin and S. I. Bozhevolnyi, "Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations," Phys. Rev. B 71, 134303 (2005).
[CrossRef]

Garcés-Chávez, V.

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, "Near-field optical micromanipulation with cavity enhanced evanescent waves," Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Greens tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

Girard, C.

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74,526-529 (1995).
[CrossRef] [PubMed]

Hecht, B.

L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4579 (1972).
[CrossRef]

Keller, O.

O. Keller, "Attached and radiated electromagnetic fields of an electric point dipole," J. Opt. Soc. Am. B 16, 835-847 (1999).
[CrossRef]

O. Keller, M. Xiao, and S. Bozhevolnyi, "Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach," Surf. Sci. 280, 217-230 (1993).
[CrossRef]

Klimov, V. V.

V. I. Balykin, V. V. Klimov, and V. S. Letokhov, "Atom nanooptics based on photon dots and photon holes," JETP Lett. 78, 8-12 (2003).
[CrossRef]

Kunz, R. E.

Letokhov, V. S.

V. I. Balykin, V. V. Klimov, and V. S. Letokhov, "Atom nanooptics based on photon dots and photon holes," JETP Lett. 78, 8-12 (2003).
[CrossRef]

Lukosz, W.

Martin, O. J. F.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Greens tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74,526-529 (1995).
[CrossRef] [PubMed]

Mazilu, M.

Merlin, R.

R. Merlin, "Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).
[CrossRef] [PubMed]

Novotny, L.

L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
[CrossRef]

Paulus, M.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Greens tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

Pohl, D. W.

L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
[CrossRef]

Reece, P. J.

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, "Near-field optical micromanipulation with cavity enhanced evanescent waves," Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

Søndergaard, T.

T. Søndergaard and S. I. Bozhevolnyi, "Theoretical analysis of finite-size surface plasmon polariton band-gap structures," Phys. Rev. B 71, 125429 (2005).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study," Phys. Rev. B 69,045422 (2004).
[CrossRef]

Thomson, L. C.

Van Labeke, D.

Vohnsen, B.

S. I. Bozhevolnyi and B. Vohnsen, "Phase conjugation of optical near field by a surface hologram," Opt. Commun. 135, 19-23 (1997).
[CrossRef]

B. Vohnsen and S. I. Bozhevolnyi, "Holographic approach to phase conjugation of optical near fields," J. Opt. Soc. Am. A 14, 1491-1499 (1997).
[CrossRef]

S. I. Bozhevolnyi and B. Vohnsen, "Near-field optical holography," Phys. Rev. Lett. 77, 3351-3354 (1996).
[CrossRef] [PubMed]

Whyte, G.

Xiao, M.

O. Keller, M. Xiao, and S. Bozhevolnyi, "Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach," Surf. Sci. 280, 217-230 (1993).
[CrossRef]

Zayats, A. V.

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, "Near-field optical micromanipulation with cavity enhanced evanescent waves," Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

J. Appl. Phys. (1)

L. Novotny, B. Hecht, and D. W. Pohl, "Interference of locally excited surface plasmons," J. Appl. Phys. 81, 1798-1806 (1997).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

A. V. Zayats and I. I. Smolyaninov, "Near-field photonics: surface plasmon polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

JETP Lett. (1)

V. I. Balykin, V. V. Klimov, and V. S. Letokhov, "Atom nanooptics based on photon dots and photon holes," JETP Lett. 78, 8-12 (2003).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. I. Bozhevolnyi and B. Vohnsen, "Phase conjugation of optical near field by a surface hologram," Opt. Commun. 135, 19-23 (1997).
[CrossRef]

Phys. Rev. B (4)

A. B. Evlyukhin and S. I. Bozhevolnyi, "Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations," Phys. Rev. B 71, 134303 (2005).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study," Phys. Rev. B 69,045422 (2004).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Theoretical analysis of finite-size surface plasmon polariton band-gap structures," Phys. Rev. B 71, 125429 (2005).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4579 (1972).
[CrossRef]

Phys. Rev. E (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Greens tensor for stratified media," Phys. Rev. E 62, 5797-5807 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement," Phys. Rev. Lett. 74,526-529 (1995).
[CrossRef] [PubMed]

S. I. Bozhevolnyi and B. Vohnsen, "Near-field optical holography," Phys. Rev. Lett. 77, 3351-3354 (1996).
[CrossRef] [PubMed]

Science (1)

R. Merlin, "Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).
[CrossRef] [PubMed]

Surf. Sci. (1)

O. Keller, M. Xiao, and S. Bozhevolnyi, "Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach," Surf. Sci. 280, 217-230 (1993).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Schematic side view of the holographic technique (a) with TIR reference wave and (b) with SPP Gaussian beam as the reference wave.

Fig. 2.
Fig. 2.

Interference on the plane with zob =50 nm [Fig. 1(a)] between the field of dipole situated at zd =800 nm above the substrate and the reference evanescent wave being the result of the TIR for an optical plane wave with wavelength 800 nm (the TIR configuration). (a) Linear color representation. (b) Contour-representation of the interference, the black small circles indicate the positions of the nanoparticles recording the hologram.

Fig. 3.
Fig. 3.

Normalized intensity distribution of the total electric field being the result of the interaction between the reconstructing evanescent wave and nanoparticle structure recording the hologram of the dipole in the TIR configuration (Fig. 2). (a), (c), (e) TE-polarization of the reconstructing wave, (b), (d), (f) TM-polarization of the reconstructing wave. (a) and (b) cross section z=zd =800 nm, (c) and (d) cross section y=0, (e) and (f) cross sections x=0.

Fig. 4.
Fig. 4.

Normalized intensity of the different electric field components after the reconstruction process along cross section x=0, z=zd =800 nm. (a) TE-polarization of the reconstructing wave, (b) TM-polarization of the reconstructing wave.

Fig. 5.
Fig. 5.

Dependence of the reconstructed field upon nanoparticle structures. (a)–(e) nanoparticle structure and field intensity (arb. un.) after the reconstruction process along cross section z=zd =800 nm in the TIR configuration. TE-polarization of the reconstructing wave. The red small circles indicate the positions of the nanoparticles.

Fig. 6.
Fig. 6.

Normalized intensity distribution of the total electric field being the result of the interaction between the reconstructing SPP plane wave and nanoparticle structure recording the hologram of the dipole in the TIR configuration (Fig. 2). (a) cross section y=0, (b) cross sections x=0, (c) along the z-direction for x=0, y=0.

Fig. 7.
Fig. 7.

Interference on the plane with zob =50 nm (Fig. 1) between the field of dipole situated at zd =800 nm above the substrate and the reference SPP Gaussian beam (the waist W=2000 nm and light wavelength 642 nm) and corresponding nanoparticle array recording the hologram in the framework of the SPP configuration. (a) Dipole orientation is along the x-axis. (b) Dipole orientation is opposite to the z-axis. The black circles indicate the positions of the dipoles, the red small circles indicate the positions of the nanoparticles recording the hologram.

Fig. 8.
Fig. 8.

Cross sections [y=0 for (a), (b), (c) and x=0 for (d), (e), (f)] of the normalized intensity distribution of the total electric field being a result of the interaction between the reconstructing SPP Gaussian beam and nanoparticle structure in the SPP configuration (Fig. 7). (a) and (d) correspond the case in Fig. 7(a) (λ=642 nm), (b) and (e) correspond the case in Fig 7(b) (λ=642 nm), (c) and (f) the case when the reconstructing SPP Gaussian beam is corresponded to the light wavelength λ=705 nm, the nanoparticle structure from Fig. 7(b).

Equations (8)

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P = [ I ̂ k 0 2 ε 0 α ̂ G ̂ s ( r d , r d ) ] 1 α ̂ E 0 ( r d ) ,
α ̂ = 3 I ̂ V d ε 0 ε d 1 ε d + 2 .
E d ( r o b ) = k 0 2 ε 0 [ G ̂ 0 ( r ob , r d ) + G ̂ s ( r ob , r d ) ] p .
E r ( r ob ) = E t exp ( i k t r ob ) ,
p i = α ̂ E ct ( r i ) + k 0 2 ε 0 α ̂ G ̂ s ( r i , r i ) p i + k 0 2 ε 0 j i N α ̂ [ G ̂ 0 ( r i , r j ) + G ̂ s ( r i , r j ) ] p j , i = 1 , , N
E ( r ) = E ct ( r ) + k 0 2 ε 0 i = 1 N [ G ̂ 0 ( r , r i ) + G ̂ s ( r , r i ) ] p i .
E r ( r ob ) = exp ( i k SPP x ob + i k z z ob y ob 2 W 2 f ( x ob ) ) f ( x ob ) { z ̂ + y ̂ ( i 2 y ob k z ( k SPP W ) 2 f ( x ob ) )
+ x ̂ [ k z k SPP ( 1 + 1 ( k SPP W ) 2 f ( x ob ) 2 ( k SPP y ob ) 2 ( ( k SPP W ) 2 f ( x ob ) ) 2 ) ] } ,

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