Classical and quantum properties of cylindrically polarized states of light

doi:10.1364/OE.19.009714

Classical and quantum properties of cylindrically polarized states of light

Annemarie Holleczek, Andrea Aiello, Christian Gabriel, Christoph Marquardt, and Gerd Leuchs »View Author Affiliations

Optics Express, Vol. 19, Issue 10, pp. 9714-9736 (2011)
http://dx.doi.org/10.1364/OE.19.009714

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Abstract

We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electromagnetic field, calculate their total angular momentum and highlight the subtleties of their structure. Furthermore, a hybrid spatio-polarization description for such modes is introduced and developed. In particular, two independent Poincaré spheres have been introduced to represent simultaneously the polarization and spatial degree of freedom of CPMs. Possible mode-to-mode transformations accomplishable with the help of Bconventional polarization and spatial phase retarders are shown within this representation. Moreover, the importance of these CPMs in the quantum optics domain due to their classical features is highlighted.

OCIS Codes
(260.0260) Physical optics : Physical optics
(260.5430) Physical optics : Polarization
(270.0270) Quantum optics : Quantum optics

ToC Category:
Physical Optics

History
Original Manuscript: December 20, 2010
Revised Manuscript: February 18, 2011
Manuscript Accepted: February 22, 2011
Published: May 4, 2011

Citation
Annemarie Holleczek, Andrea Aiello, Christian Gabriel, Christoph Marquardt, and Gerd Leuchs, "Classical and quantum properties of cylindrically polarized states of light," Opt. Express 19, 9714-9736 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9714

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References

A. E. Siegman, Lasers (University Science Books, 1986).
R. Martinez-Herrero, P. M. Mejías, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer, 2009). [CrossRef]
C. J. R. Sheppard, “Polarization of almost-plane waves,” J. Opt. Soc. Am. A 17, 335 (2000). [CrossRef]
C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” N. J. Phys. 9, 78 (2007). [CrossRef]
S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Comm. 179, 1 – 7 (2000). [CrossRef]
R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003). [CrossRef] [PubMed]
N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6, 273–276 (2001). [CrossRef] [PubMed]
M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, and G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007). [CrossRef]
M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2006). [CrossRef]
P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express 18(10), 10905–10923 (2010). [CrossRef] [PubMed]
M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous variable entanglement and squeezing of orbital angular momentum states,” Phys. Rev. Lett. 102(16), 163602 (2009). [CrossRef] [PubMed]
C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106(6), 060502 (2011). [CrossRef] [PubMed]
J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105(3), 030407 (2010). [CrossRef] [PubMed]
R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).
M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999). [CrossRef]
A. Peres, Quantum Theory: Concept and Methods (Kluwer Academic, Boston, 1995).
M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009). [CrossRef]
A. Aiello, N. Lindlein, Ch. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009). [CrossRef] [PubMed]
J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons: The relativistic Field Theory of Charged Particles with Spin one-half (Addison-Wesley Publishing Company, 1955).
R. M. A. Azzam and N. Bashra, Ellipsometry and Polarized Light (North Holland Personal Library, 1988).
L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]
H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68(1), 012323 (2003). [CrossRef]
M. T. L. Hsu, W. P. Bowen, and P. K. Lam, “Spatial-state stokes-operator squeezing and entanglement for optical beams,” Phys. Rev. A 79(4), 043825 (2009). [CrossRef]
N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and Ch. Silberhorn, “Polarization squeezing and continuous-variable polarization entanglement,” Phys. Rev. A 65(5), 052306 (2002). [CrossRef]
J. N. Damask, Polarization Optics in Telecommunication (Springer, 2005).
W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, “Experimental investigation of criteria for continuous variable entanglement,” Phys. Rev. Lett. 90(4), 043601 (2003). [CrossRef] [PubMed]
M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, 2000).
C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82(3), 033833 (2010). [CrossRef]

Aiello, A.
Allen, L.
Andersen, U. L.
Azzam, R. M. A.
Banzer, P.
Barreiro, J. T.
Bashra, N.
Beijersbergen, M. W.
Bernet, S.
Berry, M. V.
Borges, C. V. S.
Bowen, W. P.
Chuang, I. L.
Courtial, J.
Damask, J. N.
Dorn, R.
Eberler, M.
Elser, D.
Euser, T. G.
Feurer, T.
Förtsch, M.
Fürhapter, S.
Gabriel, C.
Glöckl, O.
Hell, S. W.
Hor-Meyll, M.
Hsu, M. T. L.
Huguenin, J. A. O.
Huse, N.
Jauch, J. M.
Jesacher, A.
Joly, N. Y.
Khoury, A. Z.
Konermann, H.
Korolkova, N.
Kwiat, P. G.
Lam, P. K.
Lassen, M.
Leuchs, G.
Lindlein, N.
Loudon, R.
Maiwald, R.
Marquardt, Ch.
Martinez-Herrero, R.
Maurer, C.
Meier, M.
Mejías, P. M.
Nielsen, M. A.
Okamoto, M.
Padgett, M. J.
Peres, A.
Peschel, U.
Piquero, G.
Quabis, S.
Ralph, T. C.
Ritsch-Marte, M.
Rohrlich, F.
Romano, V.
Russell, P. St. J.
Sasada, H.
Schnabel, R.
Schönle, A.
Sheppard, C. J. R.
Siegman, A. E.
Silberhorn, Ch.
Sondermann, M.
Spreeuw, R. J. C.
Wei, T.-C.
Woerdman, J. P.
Zhong, W.

Appl. Phys. A

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2006). [CrossRef]

Appl. Phys. B

M. Sondermann, R. Maiwald, H. Konermann, N. Lindlein, U. Peschel, and G. Leuchs, “Design of a mode converter for efficient light-atom coupling in free space,” Appl. Phys. B 89, 489–492 (2007). [CrossRef]

J. Biomed. Opt.

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt. 6, 273–276 (2001). [CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt.

M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009). [CrossRef]

J. Opt. Soc. Am. A

C. J. R. Sheppard, “Polarization of almost-plane waves,” J. Opt. Soc. Am. A 17, 335 (2000). [CrossRef]

N. J. Phys.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” N. J. Phys. 9, 78 (2007). [CrossRef]

Opt. Comm.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Comm. 179, 1 – 7 (2000). [CrossRef]

Opt. Express

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express 18(10), 10905–10923 (2010). [CrossRef] [PubMed]

Opt. Lett.

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999). [CrossRef]

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]
H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68(1), 012323 (2003). [CrossRef]
M. T. L. Hsu, W. P. Bowen, and P. K. Lam, “Spatial-state stokes-operator squeezing and entanglement for optical beams,” Phys. Rev. A 79(4), 043825 (2009). [CrossRef]
N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and Ch. Silberhorn, “Polarization squeezing and continuous-variable polarization entanglement,” Phys. Rev. A 65(5), 052306 (2002). [CrossRef]
C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82(3), 033833 (2010). [CrossRef]

Phys. Rev. Lett.

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, “Experimental investigation of criteria for continuous variable entanglement,” Phys. Rev. Lett. 90(4), 043601 (2003). [CrossRef] [PubMed]
M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous variable entanglement and squeezing of orbital angular momentum states,” Phys. Rev. Lett. 102(16), 163602 (2009). [CrossRef] [PubMed]
C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russell, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett. 106(6), 060502 (2011). [CrossRef] [PubMed]
J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105(3), 030407 (2010). [CrossRef] [PubMed]
A. Aiello, N. Lindlein, Ch. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009). [CrossRef] [PubMed]
R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003). [CrossRef] [PubMed]

Other

A. E. Siegman, Lasers (University Science Books, 1986).
R. Martinez-Herrero, P. M. Mejías, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer, 2009). [CrossRef]
J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons: The relativistic Field Theory of Charged Particles with Spin one-half (Addison-Wesley Publishing Company, 1955).
R. M. A. Azzam and N. Bashra, Ellipsometry and Polarized Light (North Holland Personal Library, 1988).
R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).
M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, 2000).
A. Peres, Quantum Theory: Concept and Methods (Kluwer Academic, Boston, 1995).
J. N. Damask, Polarization Optics in Telecommunication (Springer, 2005).

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