Self-focusing dynamics of polarization vortices in Kerr media

Abstract

We investigate numerically and experimentally the spatial collapse dynamics and polarization stability of radially and azimuthally polarized vortex beams in pure Kerr medium. These beams are unstable to azimuthal modulation instabilities and break up into distinct collapsing filaments. The polarization of the filaments is primarily linear with weak circular components at the filaments' boundaries. This unique hybrid linear-circular polarization collapse pattern persists to advanced stages of collapse and appears to be a general feature of beams with spatially variant linear polarization.

Critical power of collapsing vortices

“…In addition, the power of ψ AP and ψ RP is the sum of the power of ψ + and of ψ − . Hence, p RP cr = p AP cr = p cr (ψ + ) + p cr (ψ − ) = p cr (m = 1) ≈ 4.12p cr , in agreement with recent numerical simulations [16].…”

Taming the Collapse of Optical Fields

“…For the AV-HP-VF with the given m and , (i) the azimuthally-variant hybrid SoP distribution leads to the axial-symmetry breaking; (ii) the field undergoes the collapse to converge into the deterministic filaments; (iii) the number of filaments is 4 m depending solely on m ; (iv) the filaments are always located at the azimuthal positions , where their local SoPs are linearly polarized; (v) the collapsing pattern exhibits a 4 m -fold rotation ( C 4 m ) symmetry; and (vi) the collapsing patterns persist among simulations, with and without different random noise, implying that collapsing patterns are insensitive to noise. Meanwhile, for the AV-LP-VFs, (i) the purely ideal AV-LP-VF always remains in the axially symmetric ring, indicating that the purely ideal AV-LP-VF cannot converge to the deterministic multiple filaments; and (ii) the collapsing filaments produced by AV-LP-VF with the random noise has the uncertainty, similar with the collapses of optical vortices31 and polarization vortices34.…”

Bell-like inequality for the spin-orbit separability of a laser beam

“…In the space of spin-orbit modes of a classical beam, it plays a role analogous to a maximally entangled two-qubit state, and we shall refer to it as a maximally nonseparable mode (MNS). While the separable spin-orbit modes have a single polarization state over the beam wave front, the nonseparable modes exhibit a polarization gradient leading to a polarization-vortex behavior [15]. Let us take the arbitrary spin-orbit mode…”