Quantitative description of the self-healing ability of a beam

Modular Assembly of Metamaterials Using Light Gradients

This is a report on a pilot study that tests the feasibility of assembling photonic metamaterials (PMs) using light gradient forces. Following a strategy that works like modular construction, light gradient forces, produced by a tightly focused, 1D standing wave optical trap, time-multiplexed across a 2D lattice are used to assemble voxels consisting of prefabricated, monodispersed nanoparticles (NPs) with radii ranging from 30 to 500 nm into 3D structures on a hydrogel scaffold. Hundreds of NPs can be manipulated concurrently into a complex heterogeneous voxel this way, and then the process can be repeated by stitching together voxels to form a metamaterial of any size, shape, and constituency although imperfectly. Imperfections introduce random phase shifts and amplitude variations that can have an adverse effect on the band structure. Regardless, PMs are created this way using two different dielectric NPs, polystyrene and rutile, and then the near-infrared performance for each is analyzed with angle-, wavelength-, and polarization-dependent reflection spectroscopy. The cross-polarized spectra show evidence of a resonance peak. Interestingly, whereas the line shape from the polystyrene array is symmetric, the rutile array is not, which may be indicative of Fano resonance. So, even with the structural defects, reflection spectroscopy reveals a resonance.

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.

Generation and control of the circle Olver beams

The circle Olver beams (COBs) generated by modulation on the basis of a new type of Olver beam are presented numerically and experimentally. The zeroth order COB is the circle Airy beam. We demonstrate auto-focusing of the COBs with both inward and outward accelerations, where the odd order COBs display auto-defocusing while the even order COBs (ECOBs) tend to focus more abruptly. We also explore the effect of the decay factor and the scaling factor on the beams' focusing properties, such as the initial energy distribution, the focusing position, the focusing intensity and the focusing depth, by using the parity mode. In addition, we verify the self-healing property of the COBs. Finally, we set up an experimental platform to implement particle capture and manipulation with the ECOBs. Our results offer practical applications for particle manipulation, laser processing, etc.

Propagation properties of finite Airy beams on curved surfaces

Airy beams have provided exciting inspiration in the field of optical communication, particle manipulation, and imaging. We investigate the propagation properties of the exponential truncation Airy beams (ETABs) on constant Gaussian curvature surfaces (CGCSs) in this paper. The analytical expression of the electric field of ETABs propagating on the CGCSs is derived. It shows that the equivalent periodical accelerations of the trajectories of ETABs on the curved surface are always larger than the constant one on the flat surface because the CGCSs have a strong focusing ability. For the same reason, the non-diffraction propagation of ETABs is found when the focusing ability of the CGCSs is strong enough. Moreover, we investigate the self-healing length of ETABs on CGCSs and explore that the ability of self-healing is related to the geometry of CGCSs besides the width of the block and the size of the beam. The self-healing length gets larger with the increase of radius of CGCSs and finally consists with that on the flat surface. These propagation characteristics are different from those in the flat space and are useful for the future applications of ETABs in particle manipulation on waveguides, light-sheet fluorescence microscopy, curved nanophotonics, and so on.

Spatial properties and propagation dynamics of apodized Hermite-Gauss beams

Hermite-Gauss beams (HGBs), which have been presented as exact solutions to the paraxial wave equation in Cartesian coordinates, are natural resonating modes in stable laser resonators. In this work, we demonstrate that the apodized Hermite-Gauss beam (ApHGB), by a decaying exponential function exp⁡(γx) (γ is the decaying or apodization parameter), is equivalent, under certain circumstances, to the apodized Airy beam (ApAiB). Based on the asymptotic treatment of the Hermite polynomials, we provide analytical expressions to describe their propagation dynamics in free space, then we investigate their similarity as a function of the apodization parameter. Moreover, by combining symmetric ApHGBs, we build dual and quad ApHGBs. The obtained numerical simulations confirm our analytical predictions. We believe that the ApHGB could be used as an alternative to the Airy beam in many applications.

Entropy, purity and optical hysteresis in markovian optical modes

We describe the synthesis of optical modes whose axial structure follows a random tandem array of Bessel beams of integer order. The array follows fluctuations of Markov-chain type and the amplitude values for each beam are linked to a sequence of random vectors. As a prototype, we describe the synthesis of optical fields for Markov-chain type Ehrenfest. This process models the thermodynamic equilibrium and then it can be related to the evolution and stability of optical systems, in this way, it offers a similitude with partially coherent processes where the coherence degree is now distributed between all the compounds of the resulting random vector. The matrix representation for the stochastic process allows incorporating entropy properties and the calculus of the purity for the optical field. This constitutes the basis to describe the interference between markovian modes. When the set of markovian modes type Ehrenfest reaches a stable configuration they become indistinguishability non-conservative optical field having associated hysteresis features. Computer simulations are presented.

Self-healing property of focused circular Airy beams

We investigate the self-healing property of focused circular Airy beams (FCAB), and this property is associated with the transverse Poynting vector (energy flow) for a better interpretation. We both experimentally and numerically show the effect of the obstruction's position, size and shape on the self-healing property of FCAB. It is found that FCAB will heal if the obstruction is placed at the area between the two foci of FCAB, and it has the least influence on the FCAB when the obstruction is placed near the lens' rear focal plane, whereas FCAB cannot heal if the obstruction is out of the area between two foci. Our experimental results are in good agreement with numerical results.

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.

Cosine beam: diffraction-free propagation and self-healing

In this paper we revisit the nondiffracting properties of the cosine beam (CB). Since the CB is of infinite extension and not physically realizable, we use two apodization pupils to manage its transverse extent: the first one is a Gaussian apodized pupil, giving rise to the cosine-Gauss (CG) beam, and the second one is a window (aperture) apodized pupil, giving rise to the cosine-windowed beam. Based on the second-order intensity moments, we demonstrate analytical expressions for the CG beam width and its nondiffracting range as a function of some key parameters. By considering the CG beam a standing wave resulting from the superposition of two oppositely oblique traveling Gaussian beams, we extend the study to higher-order CG beams. The latter is generated by the superposition of two oppositely oblique Hermite-Gauss (HG_n) beams of order n, giving birth to a standing nondiffracting Hermite-cosine-Gauss (HCG_n) beam of order n. We also demonstrate the expressions of the higher-order CG beam width and its nondiffracting range z_max. After demonstrating the nondiffracting nature of the HCG beam family, we test their ability to self-heal and recover against obstacles, and we show the limit distance from which HCG_n beams self-heal as a function of obstruction size and CG parameter. The results of this paper are of big interest in fields involving structured light such as particle manipulation, imaging, and light sheet microscopy.

The non-diffracting nature of truncated Hermite-Gaussian beams

Using the asymptotic formula of the Hermite polynomials for higher-orders n≫1, an elegant mathematical expression that makes Hermite-Gaussian beams and cosine beams equivalent is obtained. Two factors of merit, the similarity and the power content ratio, are used to quantify the degree of equivalence between the two beams. These results yield a new nondiffracting Hermite-Gaussian beam in one dimension (1D) and that is easily extended to 2D.

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.

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.

Unraveling beam self-healing

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.

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

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 Poincaré 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.

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

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.

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

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.