Spatial Schmidt modes generated in parametric down-conversion

Miatto, F. M. and Pires, H. Di Lorenzo and Barnett, S. M. and van Exter, M. P. (2012) Spatial Schmidt modes generated in parametric down-conversion. European Physical Journal D: Atomic, Molecular, Optical and Plasma Physics, 66 (10). 263. ISSN 1434-6060

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Abstract

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.