We propose a generalized model for the creation of vector Bessel-Gauss (BG) beams having state of polarization (SoP) varying along the propagation direction. By engineering longitudinally varying Pancharatnam-Berry (PB) phases of two constituent components with orthogonal polarizations, we create zeroth- and higher-order vector BG beams having (i) uniform polarizations in the transverse plane that change along z following either the equator or meridian of the Poincare sphere and (ii) inhomogeneous polarizations in the transverse plane that rotate during propagation along z. Moreover, we evaluate the self-healing capability of these vector BG beams after two disparate obstacles. The self-healing capability of spatial SoP information may enrich the application of BG beams in light-matter interaction, polarization metrology and microscopy.

Generation and self-healing of vector Bessel-Gauss beams with variant state of polarizations upon propagation.

Bessel beams’ great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.

Wave-optics description of self-healing mechanism in Bessel beams

Self-reconstruction of Bessel beams in inhomogeneous media is beneficial in light-sheet based microscopy. Although the beam’s ring system enables propagation stability, the resulting image contrast is reduced. Here, we show that by a combination of two self-reconstructing beams with different orbital angular momenta it is possible to inhibit fluorescence from the ring system by using stimulated emission depletion (STED) even in strongly scattering media. Our theoretical study shows that the remaining fluorescence γ depends non-linearly on the beams’ relative radial and orbital angular momenta. For various scattering media we demonstrate that γ remains remarkably stable over long beam propagation distances.

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Light-sheet generation in inhomogeneous media using self-reconstructing beams and the STED-principle.

We show that, contrary to popular belief, diffraction-free beams may not only reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon Shack-Hartmann wave front reconstruction. We believe that these results can open new avenues in this field.

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Unraveling beam self-healing.

We study theoretically and experimentally the influence of the obstacle position separation from the source on the self-healing capacity of partially coherent beams using Hermite-Gaussian correlated Schell-model beams as a case in point. We establish that the shorter the distance between the obstacle and the source plane and the longer the distance between the obstacle and the observation (receiver) plane, the better the self-healing capacity of the beams. In addition, a similarity degree between the reconstructed and original beams is introduced to quantify the self-healing capacity of partially coherent beams. The derived interesting results may find applications in optical information processing, image transmission, and recovery.

Self-healing properties of Hermite-Gaussian correlated Schell-model beams

Quantitative description of the self-healing ability of a beam is very important for studying or comparing the self-healing ability of different beams. As describing the similarity by using the angle of two infinite-dimensional complex vectors in Hilbert space, the angle of two intensity profiles is proposed to quantitatively describe the self-healing ability of different beams. As a special case, quantitative description of the self-healing ability of a Bessel-Gaussian beam is studied. Results show that the angle of two intensity profiles can be used to describe the self-healing ability of arbitrary beams as the reconstruction distance for quantitatively describing the self-healing ability of Bessel beam. It offers a new method for studying or comparing the self-healing ability of different beams.

Xiuxiang Chu

Papers

Quantitative description of the self-healing ability of a beam.