Evolution properties of the radially polarized Laguerre–Gaussian-correlated Schell-model beams propagating in uniaxial crystals

Abstract

In this paper, we discuss, both analytically and numerically, the paraxial propagation of the radially polarized Laguerre–Gaussian-correlated Schell-model (LGCSM) beams orthogonal to the optical axis in uniaxial crystals. The analytical expression for the cross-spectral density function and the second-order moments of the radially polarized LGCSM beams are derived, and the evolution properties of the normalized intensity distribution, the spectral degree of the coherence (SDOC), and the spectral degree of the polarization (SDOP) in uniaxial crystals are elucidated by numerical examples. It is found that the intensity distribution of the radially polarized LGCSM beams evolves from a doughnut shape into a solid shape and finally converts into an elliptical symmetric hollow-ring profile in uniaxial crystals due to the combined effect of special correlation functions and the anisotropy effect of the uniaxial crystals. The evolution of the SDOC and SDOP for the radially polarized LGCSM beams is quite different from that of the radially polarized Gaussian–Schell-model beams. In addition, the propagation properties of the radially polarized LGCSM beams are closely related to the spatial coherence length, the mode order, and the ratio of extraordinary and ordinary reflective indices. The results show that the uniaxial crystals could modulate the evolution properties of the radially polarized LGCSM beams.

Vectorial light-matter interaction -- exploring spatially structured complex light fields

“…Crystals that naturally feature such an anisotropy are widely used to fabricate many kinds of polarization optics, including polarizers and wave retarders, and many publications describe the propagation of complex vector beams in anisotropic crystals. [60][61][62][63][64][65][66][67][68][69] Of particular importance for the manipulation of vector light fields are liquid crystals, which form the building blocks of SLMs and q-plates. The spatially varying birefringence of q-plates can be used as an interface to convert between spin and orbital states, for classical beams as well as for individual photons.…”

Propagation of Airyprime beam in uniaxial crystal orthogonal to propagation axis

“…Self imaging property of Laguerre and Bessel beam combination is discussed in [15]. Similarly, radially polarized Laguerre-Gaussian corraleted schell model beam turns into an elliptic shape after propagation [16]. As compared to Hermite-cosine Gauss beam at the source, output beam after crystal losses its symmetry as it is stated in [17].…”

Propagation of sine beam in uniaxial crystal orthogonal to optical axis

“…First‐order annular Bessel Gaussian beam becomes asymmetric while it is propagating in uniaxial crystal 6 . Doughnut‐like distribution of radially polarized Laguerre‐Gaussian‐correlated Schell‐model beam at the transverse source plane turns into hollow‐ring distribution 7 . Chirped finite Olver Gaussian beam has generally off‐axis intensity pattern 8 .…”

“…6 Doughnut-like distribution of radially polarized Laguerre-Gaussian-correlated Schellmodel beam at the transverse source plane turns into hollow-ring distribution. 7 Chirped finite Olver Gaussian beam has generally off-axis intensity pattern. 8 Off-axis hollow vortex Gaussian beam protects its vortex property along propagation.…”