Polarizing optical devices - Jones formalism and applications

The study of the electric field generated by luminous flux and its propagation in optical devices is commonly referred to as "light polarization". This very important field of optics is omnipresent in our daily lives, from the observation of the different colors present on insects, such as the iridescence of butterflies, beetles and, more particularly, the Indonesian beetle. It is even supposed that our Viking ancestors used the polarization revealed by the "Sun Stone" to orient themselves. More recently, cutting-edge technology is exploiting polarization, for example in the manufacture of high-quality polarizing filters, or in the visualization of three-dimensional films.

The aim of this article is to set out a practical formalism that can be used for technical studies, but also as a pragmatic aid in the teaching of optics, and more specifically of polarization. The modern mathematical formalism of polarization was invented by Irish physicist George Gabriel Stokes in 1852 and completed by Swiss physicist Hans Mueller in 1943, proposing a four-dimensional vector algebra based on calculations of light intensity. Another two-dimensional vector mathematical formalism was invented by American physicist Robert Clark Jones in 1941, with the advantage of including diffraction and interference phenomena, but also the disadvantage of applying only to totally polarized light. Nevertheless, in this article, Jones' formalism is presented considering only that partially polarized light is the superposition of depolarized natural light and totally polarized light.

The first part of this article focuses on the two-dimensional Jones vector formalism, starting with the definition of Jones vectors deduced from the complex representation of the electric field. Next, the search for Jones vector expressions for classical polarization states is described. Jones matrices are in turn defined and calculated for a number of polarizing devices commonly used in practice. This section concludes with the study of partial polarization by reflection and transmission, also described using Jones matrices.

A second, more applicative section describes a number of devices made up of several polarizing components, such as the optical isolator or the Laurent polarimeter. This section concludes with an illustration of color polarimetry using the polychromatic polarizing microscope (PPM).

A number of illustrations, numerical examples and summary tables are provided throughout the article to facilitate understanding.

At the end of the article, readers will find a glossary and a table of symbols used.