Gaussian Beam Waist Research Articles

Analysis of finite energy fresnel bessel beams scintillation level in turbulent communication links

Scintillation indices of Finite Energy Fresnel-Bessel Beams (FEFBBs) propagating for 6 Km in a turbulent atmosphere are analyzed. In this context, the effects of beam order and Gaussian beam waist on the reduction of scintillation level are evaluated. Both the point-like scintillation and the power scintillation indices are examined. The obtained results show that beam order does not have a significant impact on the scintillation levels. FEFBBs are able to reduce the power scintillation levels, then improve the system performance better than fundamental Gaussian beams. Thus, the provided results are significant for not only the performance improvement of the free-space optical (FSO) communication systems but also for the applications that require line of sight alignment namely directed infrared countermeasure (DIRCM).

Research on the tilt-to-length coupling noise suppression method inside the gravitational wave detection telescope.

As an integral component of the laser interferometry measurement system, the tilt-to-length (TTL) coupling noise inside the telescope stands out as a critical noise factor that requires meticulous consideration. In the TianQin project, the non-geometric TTL-coupled noise inside the telescope should be less than 0.22 pm/Hz1/2. Additionally, the wavefront aberration RMS at the small pupil of the telescope needs to be better than 0.0065 λ. These requirements set for the telescope are exceptionally stringent. To address this challenge, this study aims to relax the wavefront aberration requirements by mitigating non-geometric TTL coupling noise, while ensuring the non-geometric TTL coupling noise remains below 0.22 pm/Hz1/2. By controlling the coupling aberration proportion, the wavefront aberration RMS at the small pupil of the telescope can be relaxed to 0.014 λ. Alternatively, optimizing the Gaussian beam waist radius can relax the wavefront aberration RMS to 0.016 λ. By simultaneously utilizing two optimization methods, the wavefront aberration at the small pupil of the telescope can be reduced to 0.033 λ, resulting in an impressive success rate of 91.15% in meeting the noise requirements.

Propagation of Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beam in uniaxial crystal

The evolution behavior of the intensity profile, beam spreading, and spectral degree of coherence of the Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beam propagating in uniaxial crystal are studied. The expression of the cross spectral density of the beam in uniaxial crystal is obtained based on Huygens-Fresnel integration, and the expressions of spectral coherence and root mean square (rms) beam width are derived. The beam spot is circular or elliptical while the ordinary and extraordinary refractive indices of the crystal are equal or unequal, respectively. The ellipticity of the light spot is affected by the Lorentz parameters. The larger the ratio of ordinary to extraordinary refractive index in uniaxial crystal is, the larger the spectral coherence of beam and rms beam waist width is. The spectral coherence increases with the increase of the Gaussian beam waist and the decrease of the Lorentz parameters. The rms beam width of the beam increases with the increase of the Gaussian beam width and Lorentz partial parameters. With the increase of the transmission distance, the influence of the light source parameters on the rms beam width gradually weakens. The total number of terms of multi-Gaussian correlated Schell-Model (MGSM) source and the spatial coherence lengths add additional degree of freedom for adjusting the spot pattern inside crystal.

Optimizing geometrical parameters of coherent beam combining in the near and far-field distance

Determining the characteristics of the laser array to improve the performance of a laser system based on coherent beam combination (CBC) has continuously garnered interest. To this end, the parameters of the Gaussian beam waist, array shape, and distance between adjacent beams were studied and numerically investigated in this study. Consequently, the combined beam quality was compared for hexagonal, circular, and square arrays. The observing plane’s location was fixed at 10 km and varied from 0.25 to 10 km to investigate the effect of beam waist on combined beam quality in two modes (near and far field) using the power in the 5 cm bucket metric (PIB5cm). Furthermore, the average PIB5cm was investigated to determine all observing plane distances. The simulation results in two states of fixed and variable observing plane distances demonstrated that the hexagonal array has an advantage in attaining PIB5cm and higher combined beam quality. In addition, the quality of the combined beam degrades as the space between the beams increases. Moreover, the optimal beam waist and aperture diameter are independent of the array geometry and the vacancy between adjacent beams.

Self-focusing effect analysis of a perfect optical vortex beam in atmospheric turbulence.

The correlation function and the detection probability of orbital angular momentum (OAM) of a perfect optical vortex beam (POVB) were obtained under atmospheric turbulence conditions and then used to estimate the POVB propagation model through atmospheric turbulence. The POVB propagation in a turbulence-free channel can be divided into anti-diffraction and self-focusing stages. The beam profile size can be well preserved in the anti-diffraction stage as the transmission distance increases. After shrinking and focusing the POVB in the self-focusing region, the beam profile size expands in the self-focusing stage. The influence of topological charge on the beam intensity and profile size differs depending on the propagation stage. The POVB degenerates into a Bessel-Gaussian beam (BGB)-like when the ratio of the ring radius to the Gaussian beam waist approaches 1. The unique self-focusing effect of the POVB enables higher received probability compared to the BGB when propagating over long distances in atmospheric turbulence. However, the property of the POVB that its initial beam profile size is not affected by topological charge does not contribute to the POVB achieving a higher received probability than the BGB in short-range transmission application scenarios. The BGB anti-diffraction is stronger than that of the POVB, assuming a similar initial beam profile size at short-range transmission.

Nonlinear focal shift due to the Kerr effect for a Gaussian beam focused by a lens.

When a low-power, monochromatic Gaussian beam is focused by a thin lens in air and the waist of the beam is in the plane of the lens, there is a shift of the focus position if the waist of the beam is much smaller than the size of the lens. The point of maximum intensity relative to the geometrical focal point shifts closer to the lens. We show that for ultra-intense light beams, when the Kerr effect is unavoidable, there is a nonlinear focal shift. The nonlinear focus position shifts closer to the lens for laser powers below the critical power. To avoid the nonlinear focal shift below the critical power, the correct combination of Gaussian beam waist and focal system has to be used in the experimental setup. It will be shown that as the Fresnel number N w associated with the Gaussian beam radius increases, the nonlinear focal shift first increases and then begins to decrease.

Measurement range expansion of single-beam Laser Doppler velocimeter based on a focusing transmitter

The own velocity of a ground vehicle with high precision provided by the single-beam Laser Doppler velocimeters (LDV) promotes the localization accuracy of vehicles efficiently. However, the present LDVs are unable to be mounted on air vehicles for the velocity measurement of vehicles so far because of the restricted working distance. In order to expand the measuring range, a mid-distance LDV is designed in this paper. An optical focusing transmitter that transforms the Gaussian beam waist to the pre-set distance with an appropriate radius is constructed through theoretical simulations. Further experiments show that the mid-distance velocimeter can measure the velocity of moving objects within 50 m and the signal quality of measurement holds at a high level. This improved single-beam LDV with a longer working distance has great potential in acquiring the high-precision velocity of low-altitude air vehicles and many other remote velocity measurement applications.

Sinusoidal Gaussian optical vortex as a superposition of two hypergeometric beams

We analyze the propagation of hypergeometric beams with a parabolic initial wavefront in a homogeneous medium. While hypergeomentric beams have a central amplitude singularity in the initial plane and are of infinite energy, superposition of two such beams has no singularity and is of finite energy. A particular case of such a superposition we study in detail is a sinusoidal Gaussian beam with a unit topological charge. This beam belongs to the class of elegant laser beams since it is described by the same complex-argument function both in the initial plane and in the Fresnel diffraction zone. The diameter of the first light ring of the sinusoidal Gaussian beam is almost independent of the Gaussian beam waist radius.

M2 factor of conically refracted Gaussian beams

Analytical expressions of second-order intensity moments and factors for a conically refracted (CR) Gaussian beam and its components are derived. for a CR beam is shown to depend on a single parameter, the ratio of the CR ray cylinder radius and the input Gaussian beam waist radius. In typical CR conditions when this ratio is much greater than one, is also much greater than one even though the divergence angle for a CR beam is the same as for the input Gaussian beam. The increased value results from the much larger size of CR beam in the focal plane compared with the waist size of input Gaussian beam. values derived from focal- and Fourier-plane intensity profiles agree with theoretically predicted ones. Second-order moments and factors of a CR beam and its components are compared with those of Gaussian, Laguerre–Gauss, and modified Bessel–Gauss beams.

Analysing the impact of non-parallelism in Fabry-Perot etalons through optical modelling.

Fabry-Perot (FP) etalons, composed of two parallel mirrors, are used widely as optical filters and sensors. In certain applications, however, such as when FP etalons with polymer cavities are used to detect ultrasound, the mirrors may not be perfectly parallel due to manufacturing limitations. As little is known about how the mirrors being non-parallel impacts upon FP etalon performance, it is challenging to optimize the design of such devices. To address this challenge, we developed a model of light propagation in non-parallel FP etalons. The model is valid for arbitrary monochromatic beams and calculates both the reflected and transmitted beams, assuming full-wave description of light. Wavelength resolved transmissivity simulations were computed to predict the effect that non-parallel mirrors have on the sensitivity, spectral bandwidth and peak transmissivity of FP etalons. Theoretical predictions show that the impact of the non-parallel mirrors increases with both mirror reflectivity and incident Gaussian beam waist. Guidelines regarding the maximum angle allowed between FP mirrors whilst maintaining the sensitivity and peak transmissivity of a parallel mirror FP etalon are provided as a function of mirror reflectivity, cavity thickness and Gaussian beam waist. This information, and the model, could be useful for guiding the design of FP etalons suffering a known degree of non-parallelism, for example, to optimize the sensitivity of polymer based FP ultrasound sensors.

Propagation-invariant laser beams with an array of phase singularities

In this work, we investigate multivortex beams with an infinite topological charge. Such optical vortices contain an array of an infinite, but countable, number of phase singularities (isolated intensity nulls), which typically have the unitary topological charge and are located either uniformly (or not uniformly) on a straight line (or on several crossing straight lines) in the beam transverse cross section. Such optical vortices are form invariant and their transverse intensity distribution is conserved on propagation, changing only in scale and rotation. The orbital angular momentum of such optical vortices is finite, since only a finite number of screw dislocations is located within the area of the notable intensity of the Gaussian beam, while the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to a parabolic growth of the orbital angular momentum of such beams.

Paraxial Propagation Properties of Radially Polarized Odd‐Pearcey Gaussian Beams in Free Space

AbstractA new type of radially polarized odd‐Pearcey Gaussian beam (RPOPGB) whose paraxial propagation in free space is studied analytically and numerically, is introduced. Intriguingly, the energy of RPOPGBs is found to auto‐focus several times with the Gaussian beam waist radius increasing to some certain extents. Furthermore, RPOPGBs exhibit a special transversal intensity distribution that has an optical trap in the center. During the propagation, at first the RPOPGBs' two main lobes auto‐focus toward the center with side lobes, and then the two main lobes separate after the end of auto‐focusing. The Poynting vectors prove that the energy variation of the lobes maintains excellent central symmetry throughout the propagation. In addition, the fractional vortices are observed from the angular momentum and phase. These findings will be of potential use to particle capture.

Optical vortex beams with the infinite topological charge

Up to now, Gaussian optical vortices (OVs) were investigated with the finite topological charge (TC). Here, we study an OV with the infinite TC. Such OVs have a countable number of phase singularities (isolated intensity nulls), which typically have the unitary TC and are located either equidistantly or not equidistantly on a straight line in the beam transverse cross section. Such OVs are structurally stable (form-invariant) and their transverse intensity is conserved on propagation, changing only in scale and rotation. Orbital angular momentum (OAM) of such OVs is finite, since only a finite number of screw dislocations are within the Gaussian beam in the area of notable intensity, whereas the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to the parabolic growth of the OAM of such beams. A unique feature of these beams is that their normalized OAM can be adjusted (both increased and decreased) by simple change of the waist radius of the Gaussian beam. In addition to the two form-invariant beams, we studied a Gaussian beam with a countable number of edge dislocations (zero-intensity lines), which is not form-invariant, but, after an astigmatic transform by a cylindrical lens, also becomes an infinite-topological-charge beam.

A 2D Gaussian beam launcher applied in parallel plate waveguide field mapping systems

Abstract3D Gaussian beam generation techniques have been studied by many researchers, while the problem of 2D Gaussian beam generations have not been addressed fully. However, 2D Gaussian beams are still useful in research and applications. This article presents the mechanism, design, simulation, and measurement of a 2D Gaussian beam launcher, which allows the easy control of the width and the location of Gaussian beam waist. The proposed Gaussian beam launcher consists of a radiator array fed with the designable excitation phase and magnitude to each radiator, so as to generate the necessary boundary condition that the Gaussian beam can be excited and propagate. Both simulation and measurement results are nearly identical with the profile of the lowest order 2D Gaussian beam mode. The proposed 2D Gaussian beam launcher is suitable as the excitation source of parallel plate waveguide measurement systems. By integrating tunable components, it can be easily extended in the future to control Gaussian beam parameters dynamically.

Weak measurements of the waist of an arbitrarily polarized beam via in-plane spin splitting

As an important parameter to determine the transmission characteristics of a Gaussian beam, the beam waist holds a huge impact in laser technology and imaging systems. Although it is necessary to clearly measure the specific value of the beam waist, the traditional measurement steps are complex and easily introduce error in the measurement process. In this work, we propose an effective method using the in-plane spin splitting (IPSS) generated by the photonic spin Hall effect (PSHE) to precisely estimate the beam waist. We establish a highly sensitive propagation model to describe the relationship between the IPSS shifts and the beam waist of an arbitrary linearly polarized light and then combine with the quantum weak measurement system to amplify the IPSS shifts. We reveal that the IPSS shifts are sensitive to the variation of beam waists when the beam is reflected near the Brewster angle. With the huge amplified IPSS shifts (maximum of 1500 microns), the variation of beam waist can be accurately detected, even by propagation amplification alone. Prospectively, our scheme may provide an effective method for accurately determining the Gaussian beam waist of arbitrary polarization.

Structural and dimensional synthesis of laser variosystems for setups and technological complexes with extended functionality

Structural–dimensional synthesis of laser variosystems (LVSs) for the formation of output Gaussian beam waist with smooth changes in its position and size according to a given law is considered. Synthesized variosystems can be used in setups and technological complexes with extended functionality: processing of materials, manufacturing of complex spatial configuration parts, moving micro-objects, etc. The method of automated dimensional synthesis of two-component LVSs on different operation principles with constraints on their parameters has been developed using the theory of laser optics. The method allows determining the best dimensional parameters of LVS, and in their absence, options of changing the initial data to obtain the solution of dimensional problem. Application of the method is demonstrated by examples of dimensional synthesis of LVSs of different types and extended functionality.

Simulation of the optical caustics associated with the primary rainbow for oblate spheroidal drops illuminated by a Gaussian beam.

A vector ray-tracing model (VRT) has been developed to compute the optical caustics associated with the primary rainbow for an oblate spheroidal water drop illuminated by a Gaussian beam. By comparing the optical caustic structures (in terms of limiting rainbow and hyperbolic umbilic fringes) for a water drop with a Gaussian beam (GB) illumination with that for the same drop, but with parallel beam (PB) illumination, the influence of the Gaussian beam on the optical caustics is investigated. For a water drop with GB illumination and different drop/beam ratios (i.e., the ratio between the drop equatorial radius and the Gaussian beam waist), the location of cusp points and the curvature of the limiting rainbow fringe are also studied. We anticipate that these results not only confirm the approach to compute optical caustics for oblate spheroidal drops illuminated by a shaped beam, but may also lead to a new method for measuring the aspect ratio of spheroidal drops.

Quasioptical System for Corneal Sensing at 220–330 GHz: Design, Evaluation, and Ex Vivo Cornea Parameter Extraction

The design, simulation, and characterization of a quasioptical system for submillimeter-wave quantification of corneal thickness and water content are presented. The optics operate in the 220-330 GHz band and are comprised of two, custom aspheric, biconvex lenses in a Gaussian beam telescope configuration. The design produces broadband wavefront curvature matching to 7.5 mm radius of curvature target surfaces thus emulating a plane-wave-on-planar-media condition and enabling application of stratified medium theory to data analysis. Aspheric lens coefficients were optimized with geometric ray tracing subject to optical path length penalties and physical-optics simulations showed aspheric designs achieved wavefront coupling to spherical surfaces, superior to equivalent, canonical hyperbolic lenses. The fabricated lens system was characterized in a planar near-field scanner system and demonstrated good agreement to physical-optics simulations. An average central corneal thickness of 652 μm and free water content volume of 47% were extracted from ex vivo sheep corneas via complex s-parameters and agree with literature values. Extracted contact lens thickness and water content agreed with independently validated values. Moreover, the quasioptical system enabled observation of dynamic changes in artificial tear-film, thickness, and water content. This work elucidates two major findings related to submillimeter-wave wavefront matching on spherical surfaces, with wavelength order radii of curvature: 1) An asphere whose sag coefficients are optimized via field phase variation on a spherical surface produces coupling superior to a plano-hyperbolic lens. 2) For most feasible apertures, the Gaussian beam waist is located in the aperture near field, suggesting consideration for operating in the beam near field.

Combined laser variosystems paraxial design for longitudinal movement of a Gaussian beam waist.

Optical variosystems that form the required diameter of the Gaussian beam waist and perform its smooth longitudinal movement with a constant diameter for laser technologies, processing materials, moving microobjects, etc., are considered. A combined method based on a movable tunable-focus lens for changing the optical characteristics of laser variosystems is proposed. The features and fundamental differences between the laws of transformation of Gaussian beams by optical systems of different structures for the dimensional synthesis of laser variosystems are discussed. Based on these laws and the theory of laser optics, a method for the dimensional synthesis of one- and two-component laser variosystems is developed, an algorithm for their automated synthesis, and an example of calculation are given.

Laser varifocal system synthesis for longitudinal Gaussian beam shifting.

This paper presents a modeling approach of a laser varifocal system for longitudinal Gaussian beam waist shifting. The developed approach is based on laser optics theory, which is considered to be classical optics generalized for coherent radiation. A basic optical system, consisting of two components, was developed using this theory. Components have fixed focal lengths and specific movements. An automated modeling algorithm was proposed, and an example was provided in text. Various systems shown in this paper form a Gaussian beam with required waist parameters and provide its longitudinal shifts, which exceed the length of the near-zone of a focused Gaussian beam. Such systems can be used in laser technologies, including micro- and nano-sized objects manipulation.