ABSTRACT
In the previous chapters we have concerned ourselves with the fundamental properties of polarized light. In this chapter, we now turn our attention to the study of the interaction of polarized light with elements which can change the state of polarization and see that the matrix representation of the Stokes parameters leads to a very powerful mathematical tool for treating this interaction. In Figure 6.1, we show an incident beam, an interaction with a polarizing element, and the emerging beam. The incident beam is characterized by its Stokes parameters Si, where i = 0, 1, 2, 3. The incident polarized beam interacts with the polarizing medium, and the emerging beam is characterized by a new set of Stokes parameters ′Si . We now assume that ′Si can be expressed as a linear combination of the four Stokes parameters of the incident beam by the relations
′ = + + +S m S m S m S m S0 00 0 01 1 02 2 03 3, (6.1)
′ = + + +S m S m S m S m S1 10 0 11 1 12 2 13 3, (6.2)
′ = + + +S m S m S m S m S2 20 0 21 1 22 2 23 3, (6.3)
′ = + + +S m S m S m S m S3 30 0 31 1 32 2 33 3. (6.4)
In matrix form, these equations are written as
′ ′ ′ ′
=
S
S
S
S
m m m m
m m 0
10 11 m m
m m m m
m m m m
S
S
S
S
(6.5)
or
′ = ⋅S M S, (6.6)
where S and S′ are the Stokes vectors and M is the 4 × 4 matrix known as the Mueller matrix. It was introduced by Hans Mueller during the early 1940s [1]. While Mueller appears to have based his 4 × 4 matrix on a paper by Perrin [2] and a still earlier paper by Soleillet [3], his name is firmly attached to it in the optical literature. Mueller’s important contribution was that he was apparently the first to describe polarizing components in terms of his Mueller matrices. Remarkably, Mueller never published his work on his matrices. Their appearance in the optical literature was due to
others, such as Park [4], a graduate student of Mueller’s who published Mueller’s ideas along with his own contributions and others shortly after the end of the Second World War.
