The field of values of Jones matrices: classification and special cases

Author:

Gutiérrez-Vega Julio C.1ORCID

Affiliation:

1. Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey 64849, México

Abstract

The concept of field of values (FoV), also known as the numerical range, is applied to the 2 × 2 Jones matrices used in polarization optics. We discover the relevant interplay between the geometric properties of the FoV, the algebraic properties of the Jones matrices and the representation of polarization states on the Poincaré sphere. The properties of the FoV reveal hidden symmetries in the relationships between the eigenvectors and eigenvalues of the Jones matrices. We determine the main mathematical properties of the FoV, discuss the special cases that are relevant to polarization optics, and describe its application to calculate the Pancharatnam-Berry phase introduced by an optical system to the input state.

Funder

Consejo Nacional de Ciencia y Tecnología

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

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