https://doi.org/10.1140/epjd/e2012-30035-3
Regular Article
Spatial Schmidt modes generated in parametric down-conversion
1 SUPA and Department of Physics,
University of Strathclyde, G4 0NG
Glasgow, Scotland,
UK
2 Huygens Laboratory, Leiden
University, P.O. Box
9504, 2300 RA
Leiden, The
Netherlands
a e-mail: filippo.miatto@strath.ac.uk
Received:
14
January
2012
Received in final form:
10
May
2012
Published online:
18
October
2012
This paper presents the general spatial Schmidt decomposition of two-photon fields generated in spontaneous parametric down-conversion (SPDC). It discusses in particular the separation of the radial and azimuthal degrees of freedom, the role of projection in modal analysis, and the benefits of collinear phase mismatch. The paper is written in a review style and presents a wealth of numerical results. It aims at emphasising the physics beyond the mathematics, through discussions and graphical representations of key results. The two main conclusions of the paper are the finding of a better law to describe the effective dimensionality of the spatial part of the total Hilbert space and a possible novel feature of the radial Schmidt modes.
Key words: Topical issue: High Dimensional Quantum Entanglement. Guest editors: Sonja Franke-Arnold, Alessandra Gatti and Nicolas Treps
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2012