A transport model for broadening of a linearly polarized, coherent beam due to inhomogeneities in a turbulent atmosphere

Transport Model for the Propagation of Partially-Coherent, Polarization-Gradient Vector Beams

“…In short, we are leveraging the relationship between polarization anisotropy and a non-uniform Patcharatnam-Berry phase as noted in [37], however rather than using the medium as the source of the anisotropy (as in [37]), anisotropy can be imparted at the aperture, for example, using spatial light modulators as in [1]. Finally, we note that in the case of diffraction only, the model (59) recovers the known beam path for both the Gaussian beam [26])…”

“…The components of ì v( ì 𝑥, 𝑧, 𝜔) in Eq. ( 22) are referred to as "velocities" as they were noted in the coherent case to govern the change in optical path in the transverse direction per unit change in the direction of propagation [1,26]. We present a basic derivation supporting this interpretation in Appendix (A).…”

“…However, no mechanism exists in (59) to cause this to occur upon propagation. While it is known that the atmosphere can serve as a depolarizing element, under the MA model such an effect can only be observed by retaining higher-order spatial variations in the refractive index (stemming ultimately from retaining the electric field divergence term in the wave equation) [11,26]. In both of the cited works retention of such terms has almost no influence on beam propagation but for very long distances.…”

Parametric Signal Estimation Using the Cumulative Distribution Transform

“…Indeed, Eqn. ( 1) is simply a Lagrangian restatement of the continuity equation from continuum mechanics where the function g p (t) transforms the independent variable according to the problem physics (see e.g., [10,11]).…”

“…( 1) is seen to operate on the squared magnitude of a wavefunction or an electric field (see e.g., Schrodinger equation [12] or paraxial wave equation [13,14]). For example, if s(t) represents the time-varying optical intensity of a beam propagating through a lossless medium, g p (t) captures the influence of the medium to yield the modified intensity s g (t) [11]. Similar physics can be observed in phase modulated acoustic signals of finite duration (i.e., "pulses") propagating through linear elastic solids [15].…”