Abstract

We elucidate the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric downconversion in different noncollinear geometries in which the entangled photons counterpropagate. We find, in particular, the orbital angular momentum of entangled pairs generated in transverse-emitting configurations, in which none of the known rules for selecting orbital angular momentum holds.

© 2004 Optical Society of America

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2004 (1)

2003 (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, Opt. Commun. 228, 155 (2003).
[CrossRef]

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

2002 (3)

A. De Rossi and V. Berger, Phys. Rev. Lett. 88, 043901 (2002).
[CrossRef]

M. C. Booth, M. Atature, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 66, 023815 (2002).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

C. Weiss, G. Torosyan, Y. Avetisyan, and R. Beigang, Opt. Lett. 26, 563 (2001).
[CrossRef]

2000 (2)

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

C. K. Law, I. A. Walmsley, and J. E. Eberly, Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

1997 (2)

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

1994 (1)

1988 (1)

J. B. Khurgin, Phys. Rev. B 38, 4056 (1988).
[CrossRef]

1979 (1)

1969 (1)

D. N. Klyshko, Sov. Phys. JETP 28, 522 (1969).

Abouraddy, A. F.

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Alexandrescu, A.

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. 39, pp. 291–372.
[CrossRef]

Atature, M.

M. C. Booth, M. Atature, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 66, 023815 (2002).
[CrossRef]

Avetisyan, Y.

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. 39, pp. 291–372.
[CrossRef]

Beigang, R.

Berger, V.

A. De Rossi and V. Berger, Phys. Rev. Lett. 88, 043901 (2002).
[CrossRef]

Booth, M. C.

M. C. Booth, M. Atature, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 66, 023815 (2002).
[CrossRef]

Burns, W. K.

Carrasco, S.

Chatenoud, F.

De Rossi, A.

A. De Rossi and V. Berger, Phys. Rev. Lett. 88, 043901 (2002).
[CrossRef]

Deyanova, Y.

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

Di Giuseppe, G.

M. C. Booth, M. Atature, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 66, 023815 (2002).
[CrossRef]

Ding, Y. J.

Eberly, J. E.

C. K. Law, I. A. Walmsley, and J. E. Eberly, Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Janz, S.

Kang, J. U.

Khurgin, J. B.

J. B. Khurgin, Phys. Rev. B 38, 4056 (1988).
[CrossRef]

Klyshko, D. N.

D. N. Klyshko, Sov. Phys. JETP 28, 522 (1969).

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Law, C. K.

C. K. Law, I. A. Walmsley, and J. E. Eberly, Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Melinger, J. S.

Migdall, A.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Opt. Commun. 228, 155 (2003).
[CrossRef]

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

Normadin, R.

Normandin, R.

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. 39, pp. 291–372.
[CrossRef]

Saleh, B. E. A.

M. C. Booth, M. Atature, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 66, 023815 (2002).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Sergienko, A. V.

M. C. Booth, M. Atature, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 66, 023815 (2002).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Stegeman, G. I.

Teich, M. C.

M. C. Booth, M. Atature, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 66, 023815 (2002).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Torner, L.

J. P. Torres, A. Alexandrescu, S. Carrasco, and L. Torner, Opt. Lett. 29, 376 (2004).
[CrossRef] [PubMed]

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Opt. Commun. 228, 155 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

Torosyan, G.

Torres, J. P.

J. P. Torres, A. Alexandrescu, S. Carrasco, and L. Torner, Opt. Lett. 29, 376 (2004).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, Opt. Commun. 228, 155 (2003).
[CrossRef]

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Walmsley, I. A.

C. K. Law, I. A. Walmsley, and J. E. Eberly, Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Weiss, C.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Opt. Commun. 228, 155 (2003).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (3)

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 62, 043816 (2000).
[CrossRef]

J. P. Torres, Y. Deyanova, L. Torner, and G. Molina-Terriza, Phys. Rev. A 67, 052313 (2003).
[CrossRef]

M. C. Booth, M. Atature, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. A 66, 023815 (2002).
[CrossRef]

Phys. Rev. B (1)

J. B. Khurgin, Phys. Rev. B 38, 4056 (1988).
[CrossRef]

Phys. Rev. Lett. (4)

A. De Rossi and V. Berger, Phys. Rev. Lett. 88, 043901 (2002).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

C. K. Law, I. A. Walmsley, and J. E. Eberly, Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

D. N. Klyshko, Sov. Phys. JETP 28, 522 (1969).

Other (2)

D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information (Springer-Verlag, Berlin, 2000).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. 39, pp. 291–372.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Several noncollinear geometric configurations for SPDC. In (a) we show the usual collinear configurations for the sake of comparison. In (d) we show the angles φ1 and φ2.

Fig. 2
Fig. 2

Spatial shape and OAM decomposition of the mode function of the signal photon. (a), (b) φ1=φ2=0°; (c), (d) φ1=-φ2=90°; (e), (f) φ1=φ2=180°. Parameters: l0=1, w0=300 µm, and L=1 mm. The idler photon is projected into a Gaussian mode (l2=0) with a mode width of w1=300 µm. The momentum px,py is normalized to a beam width of w=100 µm.

Fig. 3
Fig. 3

OAM decomposition of the spatial mode function of the signal photon for φ1=-φ2=90°. (a) l0=0, w0=100 µm; (b) l0=0, w0=50 µm; (c) l0=1, w0=100 µm; (d) l0=1, w0=50 µm. The crystal length is L=1 mm. In all cases the idler photon is projected into a Gaussian mode (l2=0) with a mode width of w1=300 µm. Insets, spatial shape of the mode function. The momentum px,py is normalized to a beam width of w=100 µm.

Equations (2)

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Es-x,z,tdωsdpexp-ip·x1-iksz1+iωst×as+ωs,p,
l0=s1l1+s2l2

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