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In this paper, we analytically demonstrate the propagation of a useful structured light laser beam;namely, the vortex Laguerre-Gaussian beam, the latter is an eigenmode of free space propagation,which is invariant under propagation in lossless systems. Through some numerical simulations, weshow the main spatial features of such interesting beams.

In this work, we present a detailed study of the on-axis intensitydistribution of the Laguerre-Gaussian beam with no azimuthal index,diffracted by an opaque disk, by means of numerical simulation ofFresnel-Kirchhoff diffraction integral. We investigate the effect of theopaque disk size, the beam order, the beam waist, and the focal length.The results show that different focal phenomena may occur includingthe focal shift, focal split, and focal switch.

Accelerating beams, of which the Airy beam is an important representative, are characterized by intensity maxima that propagate along curved trajectories. In this work we present a simple approach to directly generate accelerating beams with controllable trajectories by means of binary phase structures that consist of only a π phase step modulation in comparison to previous studies where two-dimensional cubic phase modulations for example are required, and which have practical limitations due to their challenging fabrication with phase plates or diffractive optical elements (DOEs), or the spatially extended system needed for their generation at the Fourier plane. In our approach, two intensity maxima are formed that propagate along root parabolic trajectories in contrast to Airy and higher order caustic beams that propagate along a parabolic curve, hence we call these beams Dual Projectile Beams (DPBs). By tailoring a step or slit phase patterns with additional Fresnel lenses, we either generate hollow-core or abruptly focusing beams and control their curvatures. Moreover, using DPBs as a simpler complement to complex structured light fields, we demonstrate their versatility at the example of their interaction with nonlinear matter, namely the formation of a spatial soliton in a photorefractive material. We show that the formed solitary state propagates almost unchanged for a distance of several Rayleigh lengths. This light matter interaction can be regarded as a light beam deceleration. The simplicity of this approach makes these beams suitable for integrated optics and high-power laser applications using DOEs or meta-surfaces.

The present paper investigates the spatial proprieties of a novel beam introduced recently known as Airyprime beam, its on-axis and transverse intensities are studied numerically. It is shown that the focused Airyprime beam exhibits two focuses corresponding to two intensities maxima limiting an Optical Bottle Beam (OBB), the latter is characterized by its length where numerical examples show that we can adjust and change it by changing the scale parameter w 0 x which is related directly to the input width of the Airyprime beam. The spatial proprieties of the truncated Airyprime beam are also studied; by acting on the aperture diameter one can modify the on-axis intensity to choose between a mono focus beam and dual focus beam. Depending on the aperture diameter the Airyprime beam is transformed into other interesting laser beam patterns such as, a flattop beam, Gaussian beam, and tune Optical Bottle Beam. The Airyprime beam could be interesting tool of trapping and guiding microparticles.

This publisher’s note corrects the Fig. 6 caption in J. Opt. Soc. Am. A 37, C1 (2020)JOAOD60740-323210.1364/JOSAA.385913.

It has been known for some time that Bessel–Gaussian beams and their associated families self-heal after encountering obstacles. Recently, it has been shown theoretically and experimentally that radial mode Laguerre–Gaussian (LG) beams would likewise self-heal. In this work, we show that the self-healing occurs after opaque disks but not after circular apertures. We put forward arguments to explain this and perform key experiments, assessing the impact of obstructions on the usual intensity reconstruction, as well as the focal shift effect and the beam propagation factor, $$M^2$$ . In addition, these results are supported by a physical interpretation based on the Abbe experiment of spatial frequency filtering, highlighting that the self-healing process requires a high-spatial frequency component to the field, i.e., LG beams self-heal when modulated by a low spatial frequency filter (opaque disk) but not when modulated by a high-spatial frequency filter (circular aperture). We believe that this work will contribute significantly to the field of laser beam propagation through obstacles.

In this paper, we propose a predictor or indicator of the self-healing ability of coherent structured light beams: the field's modal content. Specifically, the fidelity between the obstructed and unobstructed beams' modal spectrum serves as a useful measure of the degree to which the beam will likely self-heal after an arbitrary obstacle. Since any optical field can be decomposed in terms of any chosen orthonormal basis, this analysis is, therefore, less restrictive than other methods for determining self-healing ability. Furthermore, since modal content is propagation invariant, this allows beam self-reconstruction to be studied in this way at any available transverse plane. As a case study, we present convincing experimental evidence for the superiority of the self-healing properties of Laguerre-Gaussian over Bessel-Gaussian beams, analysis that is facilitated primarily by the proposed measure.

In this paper, we demonstrate the shaping of an incident Gaussian beam into a tunable hyperbolic Airy-like beam, using an acoustooptics cell. The latter contains a transparent liquid (water), where an ultrasound wave propagating and creating a sinusoidal refractive index variation (giving rise to a sinusoidal phase transmittance). By adding an aperture, this sinusoidal phase transmittance becomes equivalent to a cubic phase ( sin(x) ≈ x − x 3 / 3 ! for x 0 . 2 λ a , λ a is the ultrasound wavelength), which allows the generation of a tunable Airy-like beam. Using the Fresnel-Kirchhoff diffraction integral, we derive analytical expressions for the diffracted Gaussian beam by the acoustooptics cell in two cases; (a) with and (b) without the aperture. For the first case, the algebra is straightforward and the field has a closed analytical expression, however for the second case, the diffraction integral has no analytical expression, thus, we expand the aperture into a weighted sum of Gaussian functions, to overcome such problem. Based on the obtained mathematical expressions, we study the effect of each parameter of the acoustooptics interaction, on the propagation behavior of the generated Airy-like beam. We believe that the results of this paper could be useful for many interesting applications, involving Airy beams, such as particle manipulation, optical tweezing, and optical communication.

We have investigated the potential of using the E-field induced birefringence for improving the sensitivity of uniaxial anisotropic slab waveguide sensor based on evanescent wave interactions. LiNbO3 waveguide core was used as an example. We have calculated the sensor sensitivity formulas for the two kinds of modes propagating simultaneously in the waveguide sensor. In our study, we have distinguished between two different cases. The first case when the electric field is applied along the optic axis (+c) of the LiNbO3 wave guiding film (positive electric field); the second case when the electric field is applied opposite to the optic axis (−c) of such uniaxial crystal (negative electric field). The obtained results showed that, for positive electric field, increasing the electric field induces an increasing of the total anisotropy which causes decreasing on sensor sensitivity. However, for negative electric field, the increase of absolute values of negative electric field induces a decrease of the total anisotropy, the latter increases the sensor sensitivity. On the other hand, the study of the physical parameters on the sensor sensitivity showed that, to maximize the sensor sensitivity, it is advisable to use isotropic substrate that has a refractive index as closer as possible to the measurand index.

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.

We demonstrate theoretically the generation of a variety of dynamic 2D Airy beams. We generate single, 2D dual-, and quad-Airy-like beams using a dynamic optical phase, obtained by the propagation of two crossed standing ultrasonic waves (UWs) in a liquid medium (water). These UWs create sinusoidal variation of the liquid medium refractive index in two dimensions. Using the asymptotic behavior of the sine function near zero, the 2D sinusoidal phase created by the piezoelectric transducer is reduced to a 2D periodic cubic phase. As it is known, the latter converts an input plane wave (Gaussian beam) into an Airy (Airy-like) beam in the far field. By acting on the dynamic optical phase parameters, one can change the characteristics of the obtained Airy beam (trajectory and acceleration). Using combined Gaussian beams, we clearly demonstrate the existence of a variety of combined dynamic Airy beams, such as Airy, dual-Airy, symmetric-Airy, anti-symmetric-Airy, and quad-Airy beams. We believe that the present work is of significant interest in the fields of dynamic focusing, curved manipulation, and transportation of microparticles.

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.

The circular Airyprime (CiAiP) beam is introduced in this paper. The spatial proprieties are well discussed and compared to the first order radial Laguerre–Gaussian beam LG10. The width, the divergence and the beam propagation factor are calculated based on the second order moments method, the latter is equal to M2 = 3.08. The free propagating CiAiP beam exhibits an unexpected non-diffracting character, it doesn’t spread through propagation. The on-axis intensity of the focused circular Airyprime beam is also explored, it exhibits a dual focus corresponding to two on-axis intensity maxima, it could be modified under diffraction using a hard circular aperture. The latter presents a cheap beam shaper, it is shown that a hard aperture could transform an input circular Airyprime beam into perfect ringed beam, a perfect Gaussian beam and a top hat beam. By combining the axial and the transversal behavior of a truncated circular Airyprime beam for a particular aperture diameter a perfect cylindrical optical bottle beam is obtained. The present work could be of big interest in the field of structured light.

Profile shaping of a Gaussian laser beam by an acoustic wave is well described using Collins integral and ABCD matrix formalism. It is shown by a numerical simulation that the relative width of the laser beam to the ultrasonic wavelength and the acoustic pressure inside the acoustooptic cell act on the light intensity diffraction pattern. Obtained results show that the output intensity profile differs from the incident Gaussian beam shape, and it is more broadened with an increase in the acoustic pressure. The intensity of a focused laser beam is transformed in a flat form in the central region if the acoustic pressure is proprely controlled. On the other hand the intensity longitudinal range (ILR) of the flat shape is discussed along the propagation axes, we have found the ILR is about 2 mm for a focal length distance f =100 mm.

The superresolution technique is usually used in optical imaging for its ability to make the central diffractive spot smaller than the Airy spot. In this paper, we apply the superresolution technique for transforming a symmetrical TEM p0 Laguerre–Gauss beam into a Gaussian intensity distribution in the plane of a converging lens. The beam shaping is achieved by an annular binary Diffractive Optical Element having a transmittance, alternatively equal to −1 or + 1, modelled on the p light rings of the incident beam. It is observed that the rectified TEM 30 beam at focus has a focal volume 170 times smaller than that of a Gaussian beam.

The Laser-Lithography technique allows the fabrication of complex objects having microsizes by selectively solidifying polymeric materials layer by layer upon exposure to a focused Gaussian laser beam having a beam propagation factor M 2 =1. We can expect that extension of this technique to large sizes 3-D prototyping comes up against a large increase in the design time. A possible solution is the increase in the focused spot size, but unfortunately at the price of a great reduction in the longitudinal resolution due to the resulting increase in the depth of focus. To overcome these difficulties, we propose the use of a rectified TEM p 0 beam allowing the obtaining of a Gaussian beam intensity profile in the focus plane of a lens. The reshaped TEM p 0 beam has a beam propagation factor M 2 ≈(2 p +1), and this yields to a relative improvement of the longitudinal resolution although the spot size is increased for reducing the processing time.

It is shown that the work entitled “Conversion of Laguerre-Gaussian beams into Gaussian beams of reduced focal spot by use of a circular echelon” repoted by S.Cherif et al. (Optik 127 (2016) 3134–3137), follows the same procedures as presented in the papers of the authors ([A. Hasnaoui, A.Bencheikh and K.ait ameur, Opt. Lasers Eng. 49 (2011) 248–251], [A. Hasnaoui, A. Bencheikh, M. Fromager, E. Cagniot, K. Ait-Ameur, Creation of a sharper focus by using a rectified TEMp0beam, Opt. Commun. 284 (2011) 1331–1334]), but concludes that their results are substantially different from the results of the authors. We find that there is no new result in the whole work, in addition there are big mistakes that we look to clarify and to correct.

In the present work, we have readjusted some empirical parameters obtained by Kumar et al. in their work which contains some numerical errors.

A quantitative form of the linear correlation between the high-frequency and static dielectric constants in ANB8-N (N = 2, 3) tetrahedrally coordinated semiconductor materials, and also in I-VII group alkali halides was studied. So, a quasi-linear relationship was found between the high-frequency and the static dielectric constants for some selected II-VI (ZnS, ZnSe, ZnTe and CdTe) and III-V (AlP, AlAs, AlSb,….etc) cubic zincblende type materials, in the other side a weak uphill linear relationship has been found in the case of I-VII (LiF, NaF, LiCl,….etc) group alkali halides compounds. In the case of II-VI and III-V cubic zincblende semiconductors, the linear regression is established with a correlation coefficient ( ) of about 0.98. The significance of the linear regression is given as the probability P

Spatial characteristics of diffracted beams produced by an acousto-optic cell from an incident Gaussian beam are studied theoretically. The complex amplitude distribution of a diffracted beam is described using Collins integral and ABCD matrix formalism. Obtained results show that the output intensity profile differs from the incident Gaussian beam shape and takes a form of doughnut beam for a specific values of the acoustic pressure inside the acousto-optic cell and the truncature parameter, defined as the ratio of the acoustic wavelength and the laser beam width.

In recent years, considerable attention has been devoted to laser beams with specific intensity profile, i.e., non-Gaussian. In this work, we present a novel technique to generate high-radial-order Laguerre-Gaussian beams LG(p0) based on the use of a binary phase diffractive optical element (BPDOE). The latter is a phase plate made up of annular zones introducing alternatively a phase shift equal to 0 or π modeled on positions which do not coincide with the position of the zeros of the desired LG(p0) beam. The LG(p0) beams are obtained by transforming a fundamental Gaussian beam through an appropriate BPDOE. The design of the latter is based on the calculation of the Fresnel-Kirchhoff integral, and the diffracted intensity at the focus plane of a lens has been modeled analytically for the first time. The numerical simulations and experiment demonstrate a good beam quality transformation. Obtained LG(p0) are suitable for atom trap and pumping solid state laser applications.

The cosine Gaussian beam (CGB) resulting from the coherent coaxial superposition of two Gaussian beams having the same width W and opposite radii of curvature R and − R is a ringed beam characterized by an M2 factor which can be very high, and adjustable by changing R. According to the paper by Hasnaoui et al(2011 Opt. Commun.284 1331–4) we expect that the CGB after ‘rectification’ by a binary diffractive optical element could be a good candidate for focal volume reduction, so useful to many laser applications. Unfortunately, this is not the case, and the physical factors responsible for this unexpected behaviour have been analysed. In particular, we have demonstrated that the three features (M2 factor, divergence and on-axis intensity) do not hold the same information about the spatial characteristics of rectified or unrectified CGBs.

a Laboratoire d'Electronique Quantique, Faculte de Physique, Universite des Sciences et de la Technologie Houari Boumediene, B.P. n°32, El Alia, 16111 Algiers, Algeria b Laboratoire d'Optique Appliquee, Universite de Setif, Cite Maâbouda, 19000 Setif, Algeria c Centre de Recherche sur les Ions, les Materiaux et la Photonique, UMR 6252-CEA-CNRS-ENSICAEN-Universite de Caen, ENSICAEN, 6 Boulevard Marechal Juin, F14050 Caen, France