Unpolarized Light

Unpolarized light is electromagnetic radiation in which the orientation of the electric field vector changes so rapidly and randomly over time that there is no statistically preferred direction of polarization. In other words, over any sufficiently long observation period, all polarization directions are equally likely, and the light exhibits no net polarization. Consequently, when unpolarized light passes through a polarizer, its transmission is not dependent on the polarizer’s orientation.

Note that the absence of orientation dependence with a polarizer is not by itself sufficient to establish that light is unpolarized. For example, circularly polarized light also passes through a linear polarizer with constant transmission but is still completely polarized, just not linearly. Similarly, the mixture of two orthogonally polarized laser beams with equal optical powers but differing wavelengths exhibit orientation independence in transmission, but this might not be called truly unpolarized light.

Interestingly, strictly monochromatic light cannot be unpolarized, as it cannot have random fluctuations. Pseudo-monochromatic light with a small optical bandwidth can be unpolarized, but with a relatively long correlation time.

There are also cases where light may be locally polarized — meaning at each point in the beam, the polarization is well-defined — but with the polarization direction varying randomly across space (e.g., across a transverse profile of a light beam. However, such spatial variation still allows orientation-dependent effects through a polarizer, hence the light is not unpolarized.

In a practical context, light is often called unpolarized already if it substantially behaves like truly unpolarized light.

Light is not limited to just the two extremes of fully polarized or fully unpolarized; real beams often display partial polarization. The degree of polarization quantifies where the light lies between these two limits.

Most textbook equations for light waves describe ideal, perfectly polarized fields, typically with linear, circular or elliptical polarization. To model unpolarized or partially polarized light, statistical optics methods are necessary, as random fluctuations play a central role. For light to qualify as unpolarized, the timescale over which the electric field direction decorrelates (the correlation time) must be much shorter than that of the relevant physical measurement or observation.

Unpolarized light is mathematically characterized using statistical descriptors like the coherency matrix (or coherence matrix, polarization matrix), which is a 2×2 Hermitian matrix capturing intensity and polarization correlations across orthogonal field components. Another widely used tool is the set of Stokes parameters — four real-valued quantities that describe the polarization state. The three parameters associated with the Stokes vector (S1, S2, S3) define a point on the Poincaré sphere:

• Fully polarized light is represented by points on the surface.
• Unpolarized light corresponds to the origin.
• Partially polarized light leads to a point inside the sphere (but not the origin).

The normalized length of the Stokes vector (relative to the total intensity) determines the above mentioned degree of polarization.

Note that the coherency matrix and the Stokes parameters do not involve the correlation time of polarization, as they involve only field correlations at the same time. Extended concepts are needed to fully characterize temporal correlations.

Typical sources of unpolarized light are based on thermal emission (blackbody radiation), such as the Sun, flames and incandescent lamps (including halogen lamps). Here, many atoms emit in an uncoordinated manner; this emission is thus completely random, with no preference for any direction of polarization.

The same holds for fluorescence, as e.g. obtained from fluorescent lamps, and normally also for other kinds of luminescence, such as electroluminescence and bioluminescence.

By contrast, lasers generally emit light which is polarized to a substantial degree. In some cases, they have an undefined polarization, but that does not necessarily mean unpolarized emission; rather, it could be polarized emission with an unstable polarization direction, but not with a low correlation time. For reliably obtaining unpolarized light, laser light usually needs to be subjected to additional treatment as explained in the following section.

Transforming polarized light into truly unpolarized light is nontrivial, as it requires not just manipulating the polarization direction, but also introducing randomness over time sufficient to destroy correlations. Simple optical elements like prisms or waveplates can only rotate or mix polarization; they cannot create the required stochastic variation. However, there are various types of depolarizers, which can at least provide some pseudo-unpolarized light, with the effectiveness often depending on the circumstances, e.g. on the optical bandwidth of the light. In some cases, one obtains spatially unpolarized light, which may be locally polarized, but with spatial variations which are averaged out over a sufficiently large area. In other cases, monochromatic light remains fully polarized, but the polarization properties become strongly wavelength-dependent, leading to averaging out within the optical bandwidth of the processed light.

Better results can be achieved with electro-optic modulators as polarization scramblers, driven with (pseudo-)random signals. Here, the light can become unpolarized at any location and for any spectral component. Another approach is based on random light scattering — which, however, also tends to destroy beam quality.

Passing unpolarized light through a polarizer yields a polarized output beam, while typically discarding about half the optical power, or sending that power to another output port. It is impossible to transform all of the optical power from an unpolarized source into a single, perfectly polarized beam without some loss of beam quality or power. This limitation is fundamentally due to statistical thermodynamics: Unpolarized light carries higher entropy, reflecting greater disorder, which cannot be fully eliminated by passive optical elements.