Abstract

We demonstrate the generation of non-diffracting heralded single photons, i.e. which are characterized by a single-photon transverse intensity distribution which remains essentially unchanged over a significant propagation distance. For this purpose we have relied on the process of spontaneous parametric downconversion (SPDC) for the generation of signal and idler photon pairs, where our SPDC crystal is pumped by a Bessel-Gauss (BG) beam. Our experiment shows that the well-understood non-diffracting behavior of a BG beam may be directly mapped to the signal-mode, single photons heralded by the detection of a single idler photon. In our experiment, the heralded single photon is thus arranged to be non-diffracting without the need for projecting its single-photon transverse amplitude, post-generation, in any manner.

© 2012 Optical Society of America

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References

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  1. J. Durnin, J.J. Micely, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  2. J. Turunen and A. Friberg, “Propagation-invariant optical fields,” Progress in Optics 54, 2–81 (2009).
  3. J. C. Gutierrez-Vega and M. A. Bandres, “Helmholtz–Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).
  4. D.C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
    [Crossref]
  5. see for example: J.P. Torres, K. Banaszek, and I.A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. in Opt. 56227–331 (2011)
    [Crossref]
  6. A.B. U’Ren, K Banaszek, and I.A. Walmsley, “Photon engineering for quantum information processing,” Quant. Inf. and Comp. J. 3480–502 (2003)
  7. S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribero, “Spatial correlations in parametric down-conversion.” Phys. Rep. 495, 87–139 (2010).
    [Crossref]
  8. A. Valencia, A. Cer, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007)
    [Crossref]
  9. see for example: G. Molina-Terriza, J.P. Torres, and L. Torner, “Twisted photons,” Nature Physics 3305–310 (2007)
    [Crossref]
  10. C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
    [Crossref]
  11. G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
    [Crossref]
  12. J. Lekki, Q.V. Nguyen, M. Seibert, K. Weiland, and J. Williams, “Single-photon non-diffracting Bessel beams,” Proc SPIE5531(2004)
  13. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Comm. 151, 207–211 (1998).
    [Crossref]
  14. G. Gbur and O. Korotkova, “Angular spectrum representation for the propagation of arbitrary coherent and partially coherent beams through atmospheric turbulence,” J. Opt. Soc. Am. A 24, 745–752 (2007)
    [Crossref]
  15. R.J. Noriega-Manez and J.C. Gutirrez-Vega, “Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere,” Opt. Express 15, 16328–16341 (2007)
    [Crossref] [PubMed]
  16. R. Ramirez-Alarcon, H. Cruz-Ramirez, and A.B. U’Ren, “Crystal length effects on the angular spectrum of spontaneous parametric downconversion photon pairs,” submitted
  17. R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
    [Crossref]
  18. H. Di Lorenzo Pires, C.H. Monken, and M.P. van Exter, “Near-field correlations in the two-photon field,” Phys. Rev. A 80, 022307 (2009).
    [Crossref]

2011 (1)

see for example: J.P. Torres, K. Banaszek, and I.A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. in Opt. 56227–331 (2011)
[Crossref]

2010 (1)

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribero, “Spatial correlations in parametric down-conversion.” Phys. Rep. 495, 87–139 (2010).
[Crossref]

2009 (2)

J. Turunen and A. Friberg, “Propagation-invariant optical fields,” Progress in Optics 54, 2–81 (2009).

H. Di Lorenzo Pires, C.H. Monken, and M.P. van Exter, “Near-field correlations in the two-photon field,” Phys. Rev. A 80, 022307 (2009).
[Crossref]

2007 (4)

G. Gbur and O. Korotkova, “Angular spectrum representation for the propagation of arbitrary coherent and partially coherent beams through atmospheric turbulence,” J. Opt. Soc. Am. A 24, 745–752 (2007)
[Crossref]

R.J. Noriega-Manez and J.C. Gutirrez-Vega, “Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere,” Opt. Express 15, 16328–16341 (2007)
[Crossref] [PubMed]

A. Valencia, A. Cer, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007)
[Crossref]

see for example: G. Molina-Terriza, J.P. Torres, and L. Torner, “Twisted photons,” Nature Physics 3305–310 (2007)
[Crossref]

2006 (1)

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

2005 (2)

J. C. Gutierrez-Vega and M. A. Bandres, “Helmholtz–Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
[Crossref]

2004 (1)

J. Lekki, Q.V. Nguyen, M. Seibert, K. Weiland, and J. Williams, “Single-photon non-diffracting Bessel beams,” Proc SPIE5531(2004)

2003 (1)

A.B. U’Ren, K Banaszek, and I.A. Walmsley, “Photon engineering for quantum information processing,” Quant. Inf. and Comp. J. 3480–502 (2003)

1998 (2)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Comm. 151, 207–211 (1998).
[Crossref]

C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

1987 (1)

J. Durnin, J.J. Micely, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

1970 (1)

D.C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Banaszek, K

A.B. U’Ren, K Banaszek, and I.A. Walmsley, “Photon engineering for quantum information processing,” Quant. Inf. and Comp. J. 3480–502 (2003)

Banaszek, K.

see for example: J.P. Torres, K. Banaszek, and I.A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. in Opt. 56227–331 (2011)
[Crossref]

Bandres, M. A.

Bennink, R. S.

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Comm. 151, 207–211 (1998).
[Crossref]

Burnham, D.C.

D.C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Cer, A.

A. Valencia, A. Cer, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007)
[Crossref]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Comm. 151, 207–211 (1998).
[Crossref]

Cruz-Ramirez, H.

R. Ramirez-Alarcon, H. Cruz-Ramirez, and A.B. U’Ren, “Crystal length effects on the angular spectrum of spontaneous parametric downconversion photon pairs,” submitted

Deyanova, Y.

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
[Crossref]

Di Lorenzo Pires, H.

H. Di Lorenzo Pires, C.H. Monken, and M.P. van Exter, “Near-field correlations in the two-photon field,” Phys. Rev. A 80, 022307 (2009).
[Crossref]

Durnin, J.

J. Durnin, J.J. Micely, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Earl, D. D.

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

Eberly, J. H.

J. Durnin, J.J. Micely, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Friberg, A.

J. Turunen and A. Friberg, “Propagation-invariant optical fields,” Progress in Optics 54, 2–81 (2009).

Gbur, G.

Grice, W. P.

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

Gutierrez-Vega, J. C.

Gutirrez-Vega, J.C.

Hendrych, M.

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
[Crossref]

Korotkova, O.

Lekki, J.

J. Lekki, Q.V. Nguyen, M. Seibert, K. Weiland, and J. Williams, “Single-photon non-diffracting Bessel beams,” Proc SPIE5531(2004)

Liu, Y.

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

Micely, J.J.

J. Durnin, J.J. Micely, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Minardi, S.

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
[Crossref]

Molina-Terriza, G.

see for example: G. Molina-Terriza, J.P. Torres, and L. Torner, “Twisted photons,” Nature Physics 3305–310 (2007)
[Crossref]

A. Valencia, A. Cer, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007)
[Crossref]

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
[Crossref]

Monken, C. H.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribero, “Spatial correlations in parametric down-conversion.” Phys. Rep. 495, 87–139 (2010).
[Crossref]

C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

Monken, C.H.

H. Di Lorenzo Pires, C.H. Monken, and M.P. van Exter, “Near-field correlations in the two-photon field,” Phys. Rev. A 80, 022307 (2009).
[Crossref]

Nguyen, Q.V.

J. Lekki, Q.V. Nguyen, M. Seibert, K. Weiland, and J. Williams, “Single-photon non-diffracting Bessel beams,” Proc SPIE5531(2004)

Noriega-Manez, R.J.

Osorio, C. I.

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
[Crossref]

Pádua, S.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribero, “Spatial correlations in parametric down-conversion.” Phys. Rep. 495, 87–139 (2010).
[Crossref]

C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

Ramirez-Alarcon, R.

R. Ramirez-Alarcon, H. Cruz-Ramirez, and A.B. U’Ren, “Crystal length effects on the angular spectrum of spontaneous parametric downconversion photon pairs,” submitted

Seibert, M.

J. Lekki, Q.V. Nguyen, M. Seibert, K. Weiland, and J. Williams, “Single-photon non-diffracting Bessel beams,” Proc SPIE5531(2004)

Shi, X.

A. Valencia, A. Cer, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007)
[Crossref]

Souto Ribeiro, P. H.

C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

Souto Ribero, P. H.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribero, “Spatial correlations in parametric down-conversion.” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Torner, L.

see for example: G. Molina-Terriza, J.P. Torres, and L. Torner, “Twisted photons,” Nature Physics 3305–310 (2007)
[Crossref]

Torres, J. P.

A. Valencia, A. Cer, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007)
[Crossref]

Torres, J.P.

see for example: J.P. Torres, K. Banaszek, and I.A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. in Opt. 56227–331 (2011)
[Crossref]

see for example: G. Molina-Terriza, J.P. Torres, and L. Torner, “Twisted photons,” Nature Physics 3305–310 (2007)
[Crossref]

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
[Crossref]

Turunen, J.

J. Turunen and A. Friberg, “Propagation-invariant optical fields,” Progress in Optics 54, 2–81 (2009).

U’Ren, A.B.

A.B. U’Ren, K Banaszek, and I.A. Walmsley, “Photon engineering for quantum information processing,” Quant. Inf. and Comp. J. 3480–502 (2003)

R. Ramirez-Alarcon, H. Cruz-Ramirez, and A.B. U’Ren, “Crystal length effects on the angular spectrum of spontaneous parametric downconversion photon pairs,” submitted

Valencia, A.

A. Valencia, A. Cer, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007)
[Crossref]

van Exter, M.P.

H. Di Lorenzo Pires, C.H. Monken, and M.P. van Exter, “Near-field correlations in the two-photon field,” Phys. Rev. A 80, 022307 (2009).
[Crossref]

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Comm. 151, 207–211 (1998).
[Crossref]

Walborn, S. P.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribero, “Spatial correlations in parametric down-conversion.” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Walmsley, I.A.

see for example: J.P. Torres, K. Banaszek, and I.A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. in Opt. 56227–331 (2011)
[Crossref]

A.B. U’Ren, K Banaszek, and I.A. Walmsley, “Photon engineering for quantum information processing,” Quant. Inf. and Comp. J. 3480–502 (2003)

Weiland, K.

J. Lekki, Q.V. Nguyen, M. Seibert, K. Weiland, and J. Williams, “Single-photon non-diffracting Bessel beams,” Proc SPIE5531(2004)

Weinberg, D. L.

D.C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Williams, J.

J. Lekki, Q.V. Nguyen, M. Seibert, K. Weiland, and J. Williams, “Single-photon non-diffracting Bessel beams,” Proc SPIE5531(2004)

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

Nature Physics (1)

see for example: G. Molina-Terriza, J.P. Torres, and L. Torner, “Twisted photons,” Nature Physics 3305–310 (2007)
[Crossref]

Opt. Comm. (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Comm. 151, 207–211 (1998).
[Crossref]

Opt. Express (1)

Phys. Rep. (1)

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. Souto Ribero, “Spatial correlations in parametric down-conversion.” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Phys. Rev. A (4)

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

H. Di Lorenzo Pires, C.H. Monken, and M.P. van Exter, “Near-field correlations in the two-photon field,” Phys. Rev. A 80, 022307 (2009).
[Crossref]

C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J.P. Torres, “Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion,” Phys. Rev. A 72, 065802 (2005).
[Crossref]

Phys. Rev. Lett. (3)

A. Valencia, A. Cer, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping the waveform of entangled photons,” Phys. Rev. Lett. 99, 243601 (2007)
[Crossref]

J. Durnin, J.J. Micely, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

D.C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Proc SPIE (1)

J. Lekki, Q.V. Nguyen, M. Seibert, K. Weiland, and J. Williams, “Single-photon non-diffracting Bessel beams,” Proc SPIE5531(2004)

Prog. in Opt. (1)

see for example: J.P. Torres, K. Banaszek, and I.A. Walmsley, “Engineering nonlinear optic sources of photonic entanglement,” Prog. in Opt. 56227–331 (2011)
[Crossref]

Progress in Optics (1)

J. Turunen and A. Friberg, “Propagation-invariant optical fields,” Progress in Optics 54, 2–81 (2009).

Quant. Inf. and Comp. J. (1)

A.B. U’Ren, K Banaszek, and I.A. Walmsley, “Photon engineering for quantum information processing,” Quant. Inf. and Comp. J. 3480–502 (2003)

Other (1)

R. Ramirez-Alarcon, H. Cruz-Ramirez, and A.B. U’Ren, “Crystal length effects on the angular spectrum of spontaneous parametric downconversion photon pairs,” submitted

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Figures (4)

Fig. 1
Fig. 1 Experimental setup for the generation of non-diffracting single photons.

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Fig. 2
Fig. 2 BG pump properties: a) Measured transverse intensity, b) measured angular spectrum, and c) measured transverse intensity vs coordinate y, measured under propagation along coordinate z.

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Fig. 3
Fig. 3 a) Measured angular spectrum of SPDC photon pairs. b) Measured conditional angular spectrum of signal-mode heralded single photons. c) measured transverse intensity of signal-mode heralded single photons.

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Fig. 4
Fig. 4 a) Measured heralded single-photon intensity, as a function of y, under propagation along z. b) Similar to a) except showing single-channel signal counts. c) Maximum counts Rc for each curve in a). d) Maximum counts Rs for each curve in b).

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Equations (3)

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

| Ψ 〉 s = ∫ d k s ⊥ S p ( k s ⊥ + k ˜ i ⊥ ) | ω p − ω ˜ i , k s ⊥ 〉 ,
S p ( k ⊥ ) = A exp ( − w 0 2 4 | k ⊥ | 2 ) I 0 ( k t w 0 2 | k ⊥ | 2 ) ,
A p ( ρ ) = A ′ 1 μ exp { − 1 μ ( i k t 2 z 2 k p + | ρ | 2 w 0 2 ) } J 0 ( k t | ρ | μ ) ,

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