Maximal polarization order of random optical beams: reversible and irreversible polarization variations

Definition of a second-order degree of polarization in terms of the complex degree of coherence

The classical theory of random electric fields and polarization formalism has been formulated considering the Stokes parameters' auto-correlations. However, in this work, the need to consider the Stokes parameters' cross-correlations to obtain a complete description of the polarization dynamics of a light source is explained. We propose a general expression for the Stokes parameters' degree of correlation using both auto-correlations and cross-correlations, which we derive from the application of Kent's distribution in the statistical study of Stokes parameter dynamics on Poincaré's sphere. Additionally, from the proposed degree of correlation, we obtain a new expression for the degree of polarization (DOP) in terms of the complex degree of coherence, which is a generalization of the well-known Wolf's DOP. The new DOP is tested using a depolarization experiment in which partially coherent light sources propagate through a liquid crystal variable retarder. The experimental results show that our generalization for the DOP improves the theoretical description of a new depolarization phenomenon that Wolf's DOP cannot describe.

Temporal modes of stationary and pulsed quasistationary electromagnetic beams

We present a novel time-domain coherent-mode representation for random, stationary electromagnetic beams. We subsequently introduce random, quasistationary pulsed electromagnetic beams and develop an analogous (pseudo) mode decomposition for them as well. The former decomposition is valid provided the time window in which the field is considered is much longer than the coherence time, while the latter requires the field to vanish outside the window. For stationary beams, the theory is demonstrated by an example illustrating the role of polarization in the representation. In both cases, the data needed for the construction of the mode decomposition are straightforward to measure. The formalisms enable us to treat random vector-light beams in the time domain in terms of deterministic fields. We expect that the modal representations will find a wide range of applications in problems involving spatiotemporal propagation of temporally partially coherent light in optical systems.

Electromagnetic theory of optical coherence [Invited]

The coherence theory of random, vector-valued optical fields has been of great research interest in recent years. In this work we formulate the foundations of electromagnetic coherence theory both in the space-time and space-frequency domains, with particular emphasis on various types of optical interferometry. Analyzing statistically stationary, two-component (paraxial) electric fields in the classical and quantum-optical contexts we show fundamental connections between the conventional (polarization) Stokes parameters and the associated two-point (coherence) Stokes parameters. Measurement of the coherence and polarization properties of random vector beams by nanoparticle scattering and two-photon absorption is also addressed.

Connection of electromagnetic degrees of coherence in space-time and space-frequency domains

We study the relationship between the electromagnetic degrees of coherence of stationary random fields in the space-time and space-frequency domains. In contrast to a known result on scalar fields, it appears that, due to the structure of the electromagnetic degree of coherence, no general closed-form relationship exists for the electromagnetic degrees in the two domains. However, relations that illustrate the similarities and differences between the two quantities can be established by specific considerations covering quasi-monochromatic and broadband situations of electromagnetic Gaussian Schell-model beams and blackbody radiation.

Polarization changes in temporal imaging with pulses of random light

We consider polarization changes of randomly fluctuating electromagnetic pulsed light in temporal imaging. The polarization properties of pulses formed by the time lens are formulated in terms of the Stokes parameters. For Gaussian Schell-model pulses we show that the degree and state of polarization of the time-imaged pulse can be tailored in versatile ways, depending on the temporal polarization and coherence of the input pulse and the system parameters. In particular, weakly polarized central region of the pulse may become fully polarized without energy absorption. The results have potential applications in optical communication, micromachining, and light-matter interactions.