Two-dimensional Gaussian Beam Research Articles

Extending orbital angular momentum multiplexing to radially high orders for massive mode channels in fiber transmission.

Orbital angular momentum (OAM) beams with different angular indices l have the potential to greatly increase communication capacity. However, the finite aperture of optical systems limits the value of the angular index. In order to fully use the orthogonal mode channels supported in the fiber for high-capacity communications, we propose extending the radial indices p of OAM modes as an additional multiplexing dimension. In this paper, we introduce spatially discrete multiple phase planes to multiplex the angular and radial OAM modes simultaneously. Due to the orthogonal property of the central symmetric OAM modes, a two-dimensional (2D) input Gaussian beams array can be converted to coaxial OAM modes through Cartesian to log-polar coordinate transformation by inverse design. For a proof-of-concept demonstration, a 10-mode multiplexer for high-order radial OAM modes was designed using five phase planes. The fabricated multiplexer generated high-quality multiplexed OAM modes with a loss of less than 5.4 dB. The multiplexed OAM modes were coupled into a specially designed ring-core fiber by mode-field matching, achieving stable mode transmission in 2 km fiber. The approach provides a scalable technology to increase the number of transmission channels and could lead to the practical applications of OAM multiplexing in communication.

Optimal Focusing Conditions for Two-Dimensional Gaussian Light Beams with Arbitrary Input Polarization in a Strontium–Barium Niobate Photorefractive Crystal

Optimal Focusing Conditions for Two-Dimensional Gaussian Light Beams with Arbitrary Input Polarization in a Strontium–Barium Niobate Photorefractive Crystal

OPTIMAL FOCUSING CONDITIONS FOR TWO-DIMENSIONAL GAUSSIAN LIGHT BEAMS WITH ARBITRARY INPUT POLARIZATION IN A PHOTOREFRACTIVE BARIUM-STRONTIUM NIOBATE CRYSTAL

Calculating nonlinear optical phenomena in a barium-strontium niobate photorefractive crystal we constructed a mathematical model of the two-dimensional linearly polarized Gaussian light beams propagation taking into account all components of the linear electrooptic tensor. We investigated the dependence of the light beam intensity on the polarization azimuth at the entrance of the crystal and on the direction of the external electric field applied to a photorefractive crystal. We determined the conditions under which the focusing of two-dimensional Gaussian light beams at the exit of the crystal is maximal.

Mechanism of two-dimensional finite airy gaussian array beams through curved slab systems

Combining the ABCD transfer matrix and the generalised Huygens-Fresnel integral equation method, the closed-form expression of a finite Airy Gaussian array beam (FAGAB) threading through a paraxial optical system was established in a space domain. We systematically investigated the evolution of the FAGAB's properties travelling through a curved slab system based on previously derived formula. The wave's characteristics through the flat slab system were the special cases of the main findings. We also assess the influence of the truncation factor and adjustment parameter on the FAGAB's intensity distribution on the slab system model's input and output cross-sections.

Diffraction-free beams in fractional Schrödinger equation.

We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories z = ±2(x − x0), which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.

Definition of the waist plane for general astigmatic Gaussian beams.

We propose a possible generalization of the waist plane for a two-dimensional astigmatic Gaussian beam as a plane of minimal spot area of the beam during propagation. It is shown that the defocusing component of the beam phase vanishes in this plane. Some examples of astigmatic Gaussian beams and corresponding area waist planes are presented and discussed.

Physics of elliptical reflectors at large reflection and divergence angles II: Analysis of optical beam distortions in integrated ultra-large-angle elliptical curved reflectors

In this work, we study the behavior of elliptical reflectors in nanophotonic integrated circuits in the context of two-dimensional multimode Gaussian beam. We show that the transformation of the beam profile at the input/output waveguide mouths, and the transformation of the beam profile at the reflector can be described in terms of 2D Hermite-Gaussian (HG) beam modes under first order approximation (FOA), referred to as HG-FOA. Due to the wavelength-scale waveguides in nanophotonic integrated circuits, the beams incident on the elliptical reflector have large diffraction angle which will result in asymmetric amplitude distortion upon non-normal reflection even for ideal elliptical reflecting surfaces. The amplitude distortion can be illustrated in the oscillation of the peaks of the reflected beam profiles around the propagation axis of the reflected beam. The amplitude distortion can also be shown by the deterioration in the coupling efficiency from the input waveguide to the output waveguide due to the excitation of higher order HG modes during the reflection. These two observations can both be explained by the HG-FOA method and are verified with Finite-Difference Time-Domain (FDTD) method. Moreover, we show that the coupling loss from the input waveguide to the output waveguide due to the higher order modes excited can be eliminated via insertion of a second reflector. Two specific arrangement of the second reflector are discussed and verified by the FDTD simulation.

Terahertz generation by an amplitude-modulated Gaussian laser beam in a rippled density plasma column

The nonlinear interaction of amplitude-modulated two-dimensional and three-dimensional laser beams with a cylindrical plasma column and the generation of terahertz (THz) radiation are studied. The plasma column could be formed by a cylindrically symmetric laser pre-pulse impinging on a gas jet target. A two-dimensional Gaussian laser beam propagating through the plasma exerts a ponderomotive force on electrons, imparting on them a resonant transverse velocity at the modulation frequency, Ω, when , where ωp is the plasma frequency of the column. The current produces THz radiation. In the case of a cylindrically symmetric Gaussian laser beam, the electron response to ponderomotive force misses the resonance, yet the phase matching introduced by a density ripple could efficiently produce THz radiation. The power conversion efficiency of the order of the ratio of THz radiation frequency to laser frequency can be achieved at a laser intensity of ≈1015 W cm−2 at 1 μm wavelength.

Propagation properties of Gaussian beams through the anamorphic fractional Fourier transform system with an eccentric circular aperture

As known, it is important for the propagation of Gaussian beams in optics. In this paper, based on the expanding a hard-edge circular aperture function as a finite sum of complex Gaussian functions and the scalar Rayleigh–Sommerfeld diffraction formula, an approximation analytical solution for Gaussian beams propagating through the anamorphic fractional Fourier transform system with an eccentric circular aperture is performed. Then, the detailed numerical calculation for the two-dimensional Gaussian beams in the above-mentioned optical system is presented. The simulation also shows that different location and size of aperture result in the change of diffracted field, including location, intensity and width. All these characteristics help us understand Gaussian beams propagation better.

Impedance-matched three-dimensional beam expander and compressor designs via transformation optics

Based on the coordinate transformation technique, a three-dimensional beam expander/compressor design is presented. Spatial coordinates in two orthogonal directions tangential to the device boundary are scaled at the same rate. The reflection and transmission coefficients are obtained in a closed form at the planar boundary for a plane wave illumination at an arbitrary incidence angle. The reflection and transmission characteristics under two-dimensional Gaussian beam illuminations are analyzed by constructing the incident, reflected, and transmitted waves as a superposition of plane wave components via Fourier transform. Numerical examples are provided to demonstrate the small amount of reflection compared with two-dimensional counterparts of the expander/compressor.

Gaussian beam scattering from a dielectric cylinder, including the evanescent region

The scattering of a two-dimensional Gaussian beam from a homogeneous dielectric cylinder is analyzed using a plane-wave spectrum. Special attention is given to the computation of the evanescent field of the beam and its effect in the scattering. A comparison is made between the evanescent field in Cartesian coordinates and in cylindrical coordinates as a sum of cylindrical waves. The field given by the cylindrical wave equation is found to converge spatially as we include more Bessel modes. The evanescent field incident on the dielectric cylinder is found to cause radiating waves to form and propagate outward.

Gaussian Beam Summation Representation of a Two-Dimensional Gaussian Beam Diffraction by a Half Plane

A Gaussian beam summation (GBS) representation for half plane diffraction of an incident two dimensional Gaussian beam (GB) that hits arbitrarily close to the edge is presented. The scattered field is expanded into an angular spectrum of GBs that emerge from the edge. We derive asymptotic expressions for the diffracted beams amplitudes, that are valid uniformly as a function of the distance of the incident beam from the edge and of the scattering beams angles. In the limiting cases when the incident GB hits far from the edge, these expressions reduce uniformly to a geometrical optics model plus a weak edge diffractions due to the off-axis beam field that hits the edge. Applications to GBS modeling of indoor propagation are discussed.

Effect of optical activity on propagation of two-dimensional spatial solitons in cubic photorefractive crystals

The self-focusing of two-dimensional Gaussian beams in cubic photorefractive optically active crystals of the (1̄1̄0) cut in the external electric field arbitrarily oriented in the cut plane is theoretically studied. The ranges of orientation of the external electric field are found in which the divergence of the light beam is smaller than the diffraction divergence. The dependences illustrating the existence of two-dimensional spatial solitons in a 15-mm-thick Bi12SiO20 crystal are constructed taking into account the optical activity or neglecting it. The shape of a light beam propagating in the crystal is determined.

Theoretical and Experimental Investigation of Gaussian Beam Transmission and Reflection by a Dielectric Slab at 110 GHz

Transmission and reflection properties of a Gaussian beam incident upon a dielectric slab are investigated by means the plane-wave spectrum method and compared with experimental results made at 110 GHz. The incident wave generated by a special circular horn antenna at 110 GHz is modeled as a two-dimensional Gaussian beam under the paraxial approximation and also as a simplified one-dimensional beam with a spreading factor. Measurement results are presented for the transmission and reflection of both the perpendicular and parallel polarizations. In particular, reflection measurements for a parallel-polarized beam incident at and near the Brewster angle are shown and compared to the theory. A small reflected two-lobe beam is observed even at the exact Brewster angle. Nonspecular phenomena in Gaussian beams are discussed and the relevance to a Brewster window for the output of a gyrotron is considered

Measurement and analysis of angle-resolved scatter from small particles in a cylindrical microchannel

Scatter of a two-dimensional Gaussian beam of a rectangular cross section by individual particles suspended in a fluid in a cylindrical channel is modeled by using a full-wave approach. First, the internal and scattered fields associated with the cylindrical channel and the two-dimensional Gaussian beam are computed. The spatial variations of the computed electromagnetic field inside the channel indicate that particles and cells of sizes relevant to flow cytometry are subjected to essentially plane-wave illumination, and hence Lorenz-Mie theory is applicable for spherical particles. Further, it is assumed that the perturbation of the electromagnetic field in the channel that is due to the presence of a particle is negligible, allowing us to ignore the interactive scatter of the particle and the channel (they are electromagnetically uncoupled). This approximation is valid when the particle intercepts a small fraction of the total energy inside the channel and when the particle or cell has a low relative refractive index. Measurements of scatter from the channel agree with the analytical model and are used to determine the location of detectors to measure scatter from particles in the channel. Experimental results of accumulated scatter from single latex spheres flowing in the channel show good agreement with computed results, thereby validating the internal field and uncoupled scatter models.

Waveguide lenses with multimode interference for low-loss slab propagation

It is shown that a nearly ideal two-dimensional focusing Gaussian beam can be synthesized by use of a linear combination of the two lowest-order even modes of an optical waveguide. This property can be used to couple laterally guided modes across slab waveguide regions with low loss. The technique is illustrated by use of a conventional multimode interference (MMI) geometry, in which the MMI coupler transforms the fundamental mode of an initial waveguide into a focusing Gaussian beam, which is then fed to a slab region. Two-dimensional beam propagation simulations show that the beam does not initially diverge in the slab region, but rather comes to a focus. A second MMI coupler then transforms the diverging beam back to the initial mode. A structure is designed that can couple the fundamental mode of a 9-microm-wide waveguide across an 88-microm-long slab region with only a 0.036-dB loss. This technique can be applied to improve the performance of small-angle waveguide crossings and integrated turning mirrors.

Halo formation at early stage of injection in high-intensity hadron rings.

Halo formation under a nonequilibrium state for a two-dimensional Gaussian beam in a FODO lattice, which is an array of magnets where F is focusing, D is defocusing, and O is the drift space between magnets, was examined in terms of a transition of time-varying nonlinear resonances. Nonlinear resonant-interactions between individual particles and intrinsic beam-core oscillations result in a beam halo. The location of the halo is analytically tractable using canonical equations derived from an isolated resonance Hamiltonian.

Interaction of a bounded ultrasonic beam with a thin inclusion inside a plate.

A theoretical study of the reflection of a two-dimensional Gaussian ultrasonic beam, incident at a Lamb angle of a plate containing a thin rectangular inclusion at an arbitrary position, is presented on the basis radiation mode theory. The inclusion is parallel to the plate surface and its thickness is assumed to be much smaller than the ultrasonic wavelength. It is shown that the amplitude and phase of the reflected beam profile can be used for accurate inclusion characterization. However, this only holds for certain internal positions of the inclusion and for material combinations that do not strongly perturb the excitation of Lamb waves in the plate. When these conditions are satisfied, it is possible to define the Lamb waves and the associated experimental conditions for which good estimates can be obtained of the position of the beginning point of the inclusion as well as of the length and the thickness of the inclusion.

Sound Field Calculations of Elliptical Pistons by theSuperposition of Two-Dimensional Gaussian Beams

We present an alternative approach to calculate the sound field ofultrasonic transducers. The distribution function of sources isexpanded into the superposition of a series of two-dimensional Gaussianfunctions. The corresponding radiated sound field is expressed as thesuperposition of these two-dimensional Gaussian beams and is thenreduced to the computation of these simple functions. This treatmentdoes not require the condition that the shape of the source is of circularaxial symmetry. A numerical example is presented for the uniformelliptical piston transducer and this is in good agreement with the resultsgiven by complicated computation.

Transversal optical vortex

A structure of wavefront edge dislocations and associated “transversal” optical vortices in an interference field of two two-dimensional Gaussian beams is analyzed. It was shown that the optical vortex rotation is directed toward the area of higher phase velocity in the interference field (the origin of the phase velocity variation is due to the Gouy effect). The conditions for the reversal of the sign of rotation were found as well as for annihilation of two edge dislocations. Topological reaction of “unfolding” of an edge dislocation, which happens when vortex collides with a phase saddle, is studied in details.