Unpolarized light
Unpolarized light is
Unpolarized light can be produced from the incoherent combination of vertical and horizontal linearly polarized light, or right- and left-handed circularly polarized light.[1] Conversely, the two constituent linearly polarized states of unpolarized light cannot form an
A so-called depolarizer acts on a polarized beam to create one in which the polarization varies so rapidly across the beam that it may be ignored in the intended applications. Conversely, a polarizer acts on an unpolarized beam or arbitrarily polarized beam to create one which is polarized.
Unpolarized light can be described as a mixture of two independent oppositely polarized streams, each with half the intensity.
Motivation
The transmission of plane waves through a homogeneous medium are fully described in terms of Jones vectors and 2×2 Jones matrices. However, in practice there are cases in which all of the light cannot be viewed in such a simple manner due to spatial inhomogeneities or the presence of mutually incoherent waves. So-called depolarization, for instance, cannot be described using Jones matrices. For these cases it is usual instead to use a 4×4 matrix that acts upon the Stokes 4-vector. Such matrices were first used by Paul Soleillet in 1929, although they have come to be known as
Coherency matrix
The Jones vector perfectly describes the state of polarization and phase of a single monochromatic wave, representing a pure state of polarization as described above. However any mixture of waves of different polarizations (or even of different frequencies) do not correspond to a Jones vector. In so-called partially polarized radiation the fields are
: 137–142where angular brackets denote averaging over many wave cycles. Several variants of the coherency matrix have been proposed: the Wiener coherency matrix and the spectral coherency matrix of Richard Barakat measure the coherence of a spectral decomposition of the signal, while the Wolf coherency matrix averages over all time/frequencies.
The coherency matrix contains all second order statistical information about the polarization. This matrix can be decomposed into the sum of two
Stokes parameters
The coherency matrix is not easy to visualize, and it is therefore common to describe incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. An alternative and mathematically convenient description is given by the
Here Ip, 2ψ and 2χ are the
The four Stokes parameters are enough to describe 2D polarization of a paraxial wave, but not the 3D polarization of a general non-paraxial wave or an evanescent field.[8][9]
Poincaré sphere
Neglecting the first Stokes parameter S0 (or I), the three other Stokes parameters can be plotted directly in three-dimensional Cartesian coordinates. For a given power in the polarized component given by
the set of all polarization states are then mapped to points on the surface of the so-called Poincaré sphere (but of radius P), as shown in the accompanying diagram. In quantum mechanics and computing, a related concept is the Bloch sphere.
Often the total beam power is not of interest, in which case a normalized Stokes vector is used by dividing the Stokes vector by the total intensity S0:
The normalized Stokes vector then has unity power () and the three significant Stokes parameters plotted in three dimensions will lie on the unity-radius Poincaré sphere for pure polarization states (where ). Partially polarized states will lie inside the Poincaré sphere at a distance of from the origin. When the non-polarized component is not of interest, the Stokes vector can be further normalized to obtain
When plotted, that point will lie on the surface of the unity-radius Poincaré sphere and indicate the state of polarization of the polarized component.
Any two antipodal points on the Poincaré sphere refer to orthogonal polarization states. The
See also
References
- ISBN 978-1-4987-0057-3. Retrieved 2023-01-20.
- ISBN 978-0-08-046391-9. Retrieved 2023-01-20.
- .
- ^ Chandrasekhar, Subrahmanyan (2013). Radiative transfer. Courier. p. 30.
- ^ ISBN 0-8053-8566-5.
- ISBN 0-262-52047-8.
- ISBN 978-0-486-43578-7.
- S2CID 215238513.
- ISSN 2643-1564.