Determination of the characteristic directions of lossless linear optical elements

Details Determination of the characteristic directions of lossless linear optical elements Determination of the characteristic directions of lossless linear optical elements

2004-08-14

arxiv.org/abs/physics/0408069v2

Journal of Modern Optics, Vol. 52, No. 11, 20 July 2005, 1597 - 1610

Physics

Optics

Replaced with extended version as published in JMO

Scientific paper

10.1080/09500340500058199

We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of the optical device. This formulation makes any actual computation of the characteristic directions amenable to pre-implemented numerical routines, thereby facilitating the decomposition of the transfer matrix into equivalent linear retarders and rotators according to the related Poincare equivalence theorem. The method is expected to be useful whenever the inverse problem of reconstruction of the internal state of a transparent medium from optical data obtained by tomographical methods is an issue.

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