Beam Propagation In Free Space Research Articles

Twist phase and classical entanglement of partially coherent light.

We demonstrate that the presence of a twist phase in a random light beam leads to classical entanglement between phase space degrees of freedom of the beam. We find analytically the bi-orthogonal decomposition of the Wigner function of a twisted Gaussian Schell-model (TGSM) source and quantify its entanglement by evaluating the Schmidt number of the decomposition. We show that (i) classical entanglement of a TGSM source vanishes concurrently with the twist in the fully coherent limit and (ii) entanglement dramatically increases as the source coherence level decreases. We also show that the discovered type of classical entanglement of a Gaussian Wigner function does not degrade on beam propagation in free space.

Focusing characteristics of Bessel-Gaussian beam passing through Cassegrain antenna system in weak turbulence

The transmission characteristics of the Bessel-Gaussian (BG) beam propagation in free space and turbulence atmosphere after passing through the Cassegrain antenna system are researched in this paper. The research results show that the half-cone angles of the beam and parameters of the optical system can be used to control the propagation trajectory and the cross-talk among different orbital angular momentum (OAM) modes of the BG beam. The BG beam has a focusing property when propagating in free space after passing through the collimating optical system. The trend of cross-talk among different OAM modes is different for focused BG beam and non-focused beam, and the focusing beam can potentially reduce cross-talk among different OAM modes at the receiver plane.

Propagation of a Hermite-cos-Gaussian correlated Schell-model beam in non-Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle, the cross-spectral density of a Hermite-cos-Gaussian correlated Schell-model (HcGCSM) beam propagating in non-Kolmogorov turbulence is derived in theory, and the intensity distribution and coherence properties of a HcGCSM beam propagation in atmospheric turbulence and free space are studied and compared by using numerical simulations. It is found that multiple beam spots of a HcGCSM beam propagation in atmospheric turbulence will combine with each other at the long distance, and the combination properties of multiple beam spots are related with initial beam parameters and strength of atmospheric turbulence. It is also found that spectral degree of coherence of a HcGCSM beam propagation in atmospheric turbulence will decrease faster than the beam propagation in free space as |r2−r1| increases

A Hankel transform distribution algorithm for paraxial wavefields with an application to free-space optical beam propagation

We propose an alternative method for evaluating numerically the complete set of integer order Hankel transforms that constitute a free-space paraxial wave. This algorithm consists only of fast Fourier transforms and one-dimensional interpolations, making it fast and efficient. To prove its reliability we compare the reconstruction it provides with the analyzed wavefield for a wide variety of profiles. Additionally, we make use of this set of Hankel transforms to construct an alternative free-space beam propagation scheme which, based on the evidence presented, we can conclude hinders the aliasing effect inside a finite region of space.

Propagation of a fundamental laser mode and its numerical simulation by the angular spectrum technique

This research aims to make a comparison between the analytical and numerical methods of simulation of the Gaussian beam propagation in free space. This comparison brings evaluation of the accuracy and applicability limitations of the angular spectrum diffraction algorithm. In this approach, planar harmonic waves are assumed as basic components of a propagating wave, so the algorithm combines the angular spectrum technique and the 2D fast Fourier transformation procedures. It means a quite different approach than the well-established Huygens–Sommerfeld one, based on spherical waves. The Gaussian beam is a rare case of the exact analytical 3D solution of a specific wave diffraction problem, in paraxial scalar approximation. Gaussian beam form has been chosen here as an evaluation reference. It allows to avoid comparisons between two numerical procedures, both of which may suffer from imperfections. In this comparison, the respective 2D cross-sections of calculated 3D complex valued wave fields distributions are presented. Also values of specific Gaussian beam parameters like full phase and Gouy phase shift and wave-front curvature radius are presented. The comparison between that form and the results of the angular spectrum algorithm brings information about the performance quality of that algorithm.

Propagation of a fundamental laser mode and its numerical simulation by the angular spectrum technique

This research aims to make a comparison between the analytical and numerical methods of simulation of the Gaussian beam propagation in free space. This comparison brings evaluation of the accuracy and applicability limitations of the angular spectrum diffraction algorithm. In this approach, planar harmonic waves are assumed as basic components of a propagating wave, so the algorithm combines the angular spectrum technique and the 2D fast Fourier transformation procedures. It means a quite different approach than the well-established Huygens–Fresnel–Rayleigh–Sommerfeld one, based on spherical waves. The Gaussian beam is a rare case of the exact analytical 3D solution of a specific wave diffraction problem, in paraxial scalar approximation. Gaussian beam form has been chosen here as an evaluation reference. It allows to avoid comparisons between two numerical procedures, both of which may suffer from imperfections. In this comparison, the respective 2D cross-sections of calculated 3D complex valued wave fields distributions are presented. Also values of specific Gaussian beam parameters like full phase and Gouy phase shift and wave-front curvature radius are presented. The comparison between that form and the results of the angular spectrum algorithm brings information about the performance quality of that algorithm.

Rotation of the polarization direction and reversal of helicity of ultrashort pulsed beams propagating in free space.

We unveil the origin of the recently revealed polarization-state changes of polarization-shaped few-cycle pulses induced by free-space beam propagation. Simple rules are formulated to show how the orientation and ellipticity of the instantaneous polarization ellipse of the source and propagated pulses relate to each other. We demonstrate our findings with examples that clearly display the relationships found and highlight their relevance. We show, for example, that pulses often used in high-harmonic generation or attosecond pulse production rotate as a whole during free-space beam propagation or upon focusing. A pulse that may reverse its ellipticity from right-handed to left-handed during propagation is also introduced. It is shown that these effects are independent of the beam size and/or focal length. We also present how these instantaneous polarization-state changes could be noticed in classical measurements of light polarization using polarizers, phase retarders, and time-integrating detectors.

Suppression of small-scale self-focusing of high-intensity femtosecond radiation

An original method for suppressing small-scale self-focusing in laser beams with the intensity of several TW/cm2 has been proposed, justified theoretically and verified in experiment. The idea underlying the method is to filter spatial perturbations during beam propagation in free space.

Spatially induced Airy-Bessel light bullets

Based on wave equation, we theoretically study the effect of spatially induced group velocity dispersion (SIGVD) of pulsed Bessel light beam propagation in free space. The results show that the third-order SIGVD can make pulsed Bessel beam gradually evolve into temporally Airy distribution. Airy-Bessel wave packet is such an exotic localized optical wave packet that it can possibly serve versatile tool in the research of light-matter interactions and has extensive applications. Hence we demonstrate the realization scheme of Airy-Bessel light bullets in free space by compensating the second-order SIGVD through utilizing dispersion management technique. To analyze the spatiotemporal propagation properties, we numerically simulate this light bullet propagation in a dispersion medium. The results show that it can retain spatial diffraction-free and temporal dispersion-free propagation in medium.

Fabrication and optical characterisation of planar silica lens pair

The fabrication and experimental results on the performance of a planar silica lens pair that facilitates low-loss optical beam propagation in free space between opposing planar silica waveguides/singlemode fibres are presented. Each lens uses the parabolic graded refractive index vertically and the convex curvature horizontally to focus the optical beam in free space. The lens pair, designed for 200 mu m of free space propagation distance with ideal zero loss, is fabricated and measured for net loss of 1.6 dB which is 12.4 dB less than the coupling loss without a lens pair at 633 nm wavelength.

Arbitrary laser beam propagation in free space

The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.

Higher order annular Gaussian laser beam propagation in free space

Higher order annular Gaussian laser beam propagation in free space

Higher order annular Gaussian laser beam propagation in free space

Propagation of higher order annular Gaussian (HOAG) laser beams in free space is examined. HOAG beams are defined as the difference of two Hermite-Gaussian (HG) beams; thus, they can be produced by subtracting a smaller beam from a larger beam, that are cocentered and both possess HG mode field distributions. Such beams can be considered as a generalization of the well-known annular Gaussian beams. We formulate the source and receiver plane characteristics and kurtosis parameter of HOAG beams propagating in free space and evaluate them numerically. In comparison to HG beams, HOAG beams have a broader beam size with outer lobes of kidney shape. The amount of received power within the same receiver aperture size, that is, power in bucket, is generally lower for higher order beams. The convergence of the kurtosis parameter to an asymptotic value for higher order beams takes much longer propagation distances compared to zero-order beams.

Beam scattering of the Luneberg lens by a complex source point

The complex source point method and vector mode function expansion are used to calculate the electromagnetic beam scattering by the Luneberg lens. A six-layered medium with different radii is considered as a model of the Luneberg lens. A comparison between the well-known numerical result in the Cartesian coordinate system and the new numerical one in the vector mode function is made for the incident Gaussian beam propagation in free space. The propagation properties are in good agreement with each other. The total electric field distributions along the transversal and longitudinal axes are examined for scattering by the Luneberg lens, whose dimension is assumed to be comparable with the beam width. The focusing effect of the Gaussian beam is much lower than that of the plane wave. The spot size focused by the Luneberg lens almost equals the wavelength for the various beam parameters including the plane wave.

Spatial nonparaxial correction of the ultrashort pulsed beam propagation in free space.

In this paper, a family of integral solutions representing ultrashort pulsed beam propagation in free space is studied by using the comoving frame coordinates and the Fourier transformation for time variable in terms of well-known paraxial approximation. The pulsed Gaussian-like beam solution is obtained as a special case of the integral solution, where the pulsed Gaussian beam solution is included. Further, starting from the nonparaxial pulsed beam propagation equation in the temporal-frequency domain and making use of the spatial Fourier transform, the nonparaxial pulsed beam solution is derived based on the paraxial pulsed beam solution, where the nonparaxiality is evaluated by a series of expansions.

Ultrashort pulsed bessel beams and spatially induced group-velocity dispersion.

We find a new family of solutions of the nonparaxial wave equation that represents ultrashort pulsed light beam propagation in free space. The spatial and temporal parts of these pulsed beams are separable; the spatial transverse part is described by a Bessel function and remains unchanged during propagation, but the temporal profile can be arbitrary. Therefore the pulsed beam exhibits diffraction-free behavior with no transverse spreading, but the temporal part changes as if in a dispensive medium; the change is dominated by what we call spatially induced group-velocity dispersion. The analytical and numerical investigations show that the even- and odd-order spatially induced dispersions partially compensate for each other so as to give rise to pulse spreading, weakening, asymmetry, and center shift.

Approximate scalar finite-element beam-propagation method with perfectly matched layers for anisotropic optical waveguides

The perfectly matched layer boundary condition for arbitrary anisotropic media is incorporated into the approximate scalar beam propagation method. The procedure is based on a finite-element method for three-dimensional anisotropic optical waveguides with off-diagonal elements in a permittivity tensor. In order to treat a wide-angle beam propagation, the Pade approximant operator is employed. To show the validity and usefulness of this approach, numerical results are presented for Gaussian beam propagation in free space and Gaussian beam excitation on a three-dimensional anisotropic optical waveguide.

Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach

A fast and accurate numerical method for free-space beam propagation between arbitrarily oriented planes is developed. The only approximation made in the development of the method was that the vector nature of light was ignored. The method is based on evaluating the Rayleigh–Sommerfeld diffraction integral by use of the fast Fourier transform with a special transformation to handle tilts and offsets of planes. The fundamental aspects of a software package based on the developed method are presented. A numerical example realized with the software package is presented to establish the validity of the method.

Statistical Behavior of Paraxial Light Beam Propagation in Free Space and of Beam Quality Factor.

Statistical Behavior of Paraxial Light Beam Propagation in Free Space and of Beam Quality Factor.