Unraveling beam self-healing

Power transfer efficiency for obstructed wireless links using Bessel beams

The power transfer efficiency of a partially obstructed wireless link operating in the Fresnel region is studied in this work. The wireless link consists of two equal apertures, axially aligned, radiating weakly-diffractive beams (truncated Bessel beams). A metallic obstacle is considered along the propagation path of the radiated beam to analyze its impact on the power transfer efficiency with respect to a clear line of sight link. The power transfer efficiency in the obstructed case is derived by resorting to a scattered field formulation. In the proposed approach, the distance between the apertures is considered larger than their radius, which is also bigger than the operating wavelength. A paraxial approximation is then applied to the formulation. Numerical results validate the proposed approach. It appears that the transverse propagation constant of the Bessel Beam and resulting non-diffractive range strongly affects the distance of operation of the wireless link in both the clear and obstructed cases. In addition, we observe how the self-healing property of Bessel beams preserves the efficiency of the partially obstructed link by establishing a resilient link under defined conditions for the propagating beam and size of the obstruction.

Universal understanding of self-healing and transformation of complex structured beams based on eigenmode superposition

The self-healing property of laser beams with special spatial structures is of great interest. We take the Hermite-Gaussian (HG) eigenmode as an example, theoretically and experimentally investigating the self-healing and transformation characteristics of complex structured beams composed of incoherent or coherent superposition of multiple eigenmodes. It is found that a partially blocked single HG mode can recover the original structure or transfer to a lower order distribution in the far field. When the obstacle retains one pair of edged bright spots of the HG mode in each direction of two symmetry axes, the beam structure information (number of knot lines) along each axis can be restored. Otherwise, it will transfer to the corresponding low-order mode or multi-interference fringes in the far field, according to the interval of the two most-edged remaining spots. It is proved that the above effect is induced by the diffraction and interference results of the partially retained light field. This principle is also applicable to other scale-invariant structured beams such as Laguerre-Gauss (LG) beams. The self-healing and transformation characteristics of multi-eigenmode composed beams with specially customized structures can be intuitively investigated based on eigenmode superposition theory. It is found that the HG mode incoherently composed structured beams have a stronger ability to recover themselves in the far field after occlusion. These investigations can expand the applications of optical lattice structures of laser communication, atom optical capture, and optical imaging.

Manipulation of curved beams using beam-domain optimization

An efficient scheme for the design of aperture fields (distributed sources) that radiate arbitrary trajectory curved (accelerating) beams, with enhanced controllability of various beam features, is presented. The scheme utilizes a frame-based phase-space representation of aperture fields to overcome the main hurdles in the design for large apertures: First, it uses the a-priory localization of caustic beams to significantly reduce the optimization problem's variable space, to that of few Gaussian window coefficients accurately capturing those beams. Then, the optimization problem is solved in the reduced (local) spectral domain. We adopt a linearization approach that enables the solution by sequential application of conventional convex optimization tools, which are naturally compatible with the proposed phase-space representation. The localized nature of the Gaussian windows' radiation is used also for fast field evaluation at a greatly reduced number of optimization constraint points. The significant enhancement in the controllability over the various beam parameters is demonstrated through a range of examples.

What are the traveling waves composing the Hermite-Gauss beams that make them structured wavefields?

To the best of our knowledge, at the present time there is no answer to the fundamental question stated in the title that provides a complete and satisfactory physical description of the structured nature of Hermite-Gauss beams. The purpose of this manuscript is to provide proper answers supported by a rigorous mathematical-physics framework that is physically consistent with the observed propagation of these beams under different circumstances. In the process we identify that the paraxial approximation introduces spurious effects in the solutions that are unphysical. By removing them and using the property of self-healing, that is characteristic to structured beams, we demonstrate that Hermite-Gaussian beams are constituted by the superposition of four traveling waves.

Elegant Gaussian beams: nondiffracting nature and self-healing property

Alongside the well-known solutions of standard beams, elegant Gaussian beams (eGBs) have been presented as alternative solutions to the paraxial wave equation. In this work, we show that the eGBs in cartesian (elegant Hermite-Gauss) and cylindrical (elegant Laguerre-Gauss) coordinates are asymptotically equivalent to pseudo-nondiffracting beams (pNDBs) in the same coordinates (cosine-Gauss and Bessel-Gauss, respectively). A theoretical comparison of their intensity distributions at different planes without and with obstruction is given, allowing to revisit and discuss the diffraction-free nature and self-healing property. The obtained results demonstrate that both families of beams are indistinguishable and have similar propagation features, which means that the eGBs class can be used as an alternative to pNDBs.

Far-field modeling of obstructed Laguerre-Gauss beams

It was shown in the paper Opt. Lett.40, 3739 (2015)OPLEDP0146-959210.1364/OL.40.003739 that Laguerre-Gauss beams (LGB_n) of order n and Bessel beams (BB) are asymptotically equivalent for n≫1. Here we demonstrate that an LGB_n and a BB are equivalent just in the inner multiring parts of the two beams. However, the outer multiring parts are completely different, and this leads us to apply a truncation on the two beams to make them indistinguishable. Since the LGB_n could be approximated by a BB only in the inner multiring part, we suggest another beam that could replace its outer multiring part. By considering the LGB_n as a sum of n rings having different radii and widths, we model the LGB_n outer multiring part by a sum of what we call in this paper "ring shifted-Gaussian beams." The peer-to-peer comparison of the LGB_n with the two cited beams allowed us to provide a new analytical description of the obstructed LGB_n far field. These results will be very useful to study many aspects related to the LGB_n diffraction by apertures and stops. As an example, we show at the end of this paper how the self-healing ability of an obstructed LGB_n could be studied analytically.

Manipulation and control of 3-D caustic beams over an arbitrary trajectory

We present an algorithm for manipulating and controlling 3-D field patterns, with energy confined to the narrow vicinity of predefined 3-D trajectories in free-space, which are of arbitrary curvature and torsion. This is done by setting the aperture field's phase to form smooth caustic surfaces that include the desired trajectory. The aperture amplitude distribution is constructed to manipulate both the on-axis intensity profile and the off-axis beam-width, and is updated iteratively. Once the aperture distribution is calculated, the radiation from a finite sampled aperture is computed numerically using a Fast Fourier Transform-based scheme. This allows for both verification of the design and examination of its sensitivity to parameters of realistic discrete implementation. The algorithm is demonstrated for the cases of an Airy beam of a planar trajectory, as well as for helical and conical-helical trajectory beams.

Light sheet fluorescence microscopy using axi-symmetric binary phase filters

Light sheet fluorescence microscopy (LSFM) has become an indispensable tool in biomedical studies owing to its depth-sectioning capability and low photo-bleaching. The axial resolution in LSFM is determined mainly by the thickness of the illumination sheet, and a high numerical-aperture lens is thus preferred in the illumination to increase the axial resolution. However, a rapid divergence of the illumination beam limits the effective field-of-view (FoV), that provides high-resolution images. Several strategies have been demonstrated for FoV enhancement, which involve the use of Bessel or Airy beams, for example. However, the generation of these beams requires complicated optical setup or phase filters with continuous phase distributions, which are difficult to manufacture. In contrast, a binary phase filter (BPF) comprising concentric rings with 0 or π phases produces a response similar to its continuous original and is easy to realize. Here, we present a novel form of LSFM that integrates BPFs derived from two representative axi-symmetric aberrations, including phase axicon and spherical aberrations, to improve the imaging performance. We demonstrate that these BPFs significantly increase the FoV, and those derived from axicon generate self-reconstructing beams, which are highly desirable in imaging through scattering specimens. We validate its high-contrast imaging capability over extended FoV by presenting three-dimensional images of microspheres, imaginal disc of Drosophila larva, and Arabidopsis.

Hybrid refractive-diffractive axicons for Bessel-beam multiplexing and resolution improvement

Optical elements rely on refraction, diffraction, or reflection for light manipulation. Fusing diffractive and refractive functions in a single element provides an extra layer of control over the wave propagation, allowing complex beam shaping through self-aligned, monolithic and miniaturized optics. Using gray-scale lithography with high-current focused Xe ion-beams, we realized hybrid refractive-diffractive micro-axicons that feature diffractive gratings engraved on their conical surfaces. Furthermore, we fabricated these devices in lithium niobate, which is a challenging piezo/optoelectronic material for processing with an as-yet unexploited potential in optical applications. The curvilinear surfaces of fabricated micro-axicons with a 230-µm diameter were engraved with diffraction linear and circular gratings of various depths (<400 nm), and the optical performance of these components was characterized, showing excellent agreement with theoretical expectations. The fusing of diffractive elements with carrier refractive surfaces introduces additional or enhanced device functionalities, such as beam multiplexing and resolution improvement. The potential applications of such monolithic and miniaturized hybrid micro-optical components include beamshaping for fluorescence microscopy.

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

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.

Orbital angular momentum and informational entropy in perturbed vortex beams

We theoretically and experimentally investigated transformations of vortex beams subjected to sector perturbations in the form of a hard-edged aperture. The transformations of the vortex spectra, the orbital angular momentum (OAM), and the informational entropy of the perturbed beam were measured. We found that relatively small angular sector perturbations have almost no effect on the OAM, although the informational entropy is rapidly increasing due to the birth of new optical vortices caused by diffraction at the diaphragm edges. At large perturbation angles, the uncertainty principle between the angle and OAM involves vortices, with both positive and negative topological charges, so that the OAM decreases to almost zero, and the entropy increases sharply.

Are Bessel beams resilient to aberrations and turbulence?

It is understood from the conical wave picture that Bessel beams may self-heal after certain opaque obstructions, but the extrapolation to transparent phase screens is not self-evident. Here we consider the propagation of Bessel beams through aberrated obstacles and show that the self-healing is not guaranteed, but rather a function of the severity of the aberration. Paradoxically, we explain why strong aberrations may show self-healing while weak aberrations will not, and highlight the parameters that influence this. Finally, we combine aberrations to pass the Bessel beam through turbulence, and debunk the myth that Bessel beams are resilient to such perturbations.