Optimal Frames for Polarization State Reconstruction

Physical Review Letters
Matthew R ForemanAndrea Aiello

Abstract

Complete determination of the polarization state of light requires at least four distinct projective measurements of the associated Stokes vector. Stability of state reconstruction, however, hinges on the condition number κ of the corresponding instrument matrix. Optimization of redundant measurement frames with an arbitrary number of analysis states, m, is considered in this Letter in the sense of minimization of κ. The minimum achievable κ is analytically found and shown to be independent of m, except for m=5 where this minimum is unachievable. Distribution of the optimal analysis states over the Poincaré sphere is found to be described by spherical 2 designs, including the Platonic solids as special cases. Higher order polarization properties also play a key role in nonlinear, stochastic, and quantum processes. Optimal measurement schemes for nonlinear measurands of degree t are hence also considered and found to correspond to spherical 2t designs, thereby constituting a generalization of the concept of mutually unbiased bases.

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Citations

Sep 30, 2016·Scientific Reports·Junxiao ZhouShuangchun Wen
Apr 8, 2017·Nano Letters·Alba Espinosa-SoriaAlejandro Martínez
Sep 11, 2019·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Jun Dai, François Goudail
Sep 15, 2018·Science·Kai WangAndrey A Sukhorukov
Sep 11, 2019·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Jun Dai, François Goudail
Apr 27, 2016·Nanotechnology·Wei Ting ChenDin Ping Tsai
Jul 7, 2020·Optics Letters·Xiaobo LiFrançois Goudail
Sep 9, 2016·Optics Letters·James G TitchenerAndrey A Sukhorukov
Dec 17, 2020·Optics Letters·R Gutiérrez-Cuevas, M A Alonso
Oct 16, 2020·Optics Letters·Kai Ling C SeowMatthew R Foreman
Sep 24, 2021·Light, Science & Applications·Chao HeMartin J Booth

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