Effective beam parameters and the turbulent beam waist for convergent Gaussian beams

Expressions are developed for the location and the size of the beam waist for a convergent Gaussian beam in statistically homogeneous and isotropic atmospheric turbulence. Subsidiary expressions are presented that lead to the maximum distance from the transmitter at which the beam waist can be located under given optical turbulence conditions and the optimal initial radius of curvature required for placing the beam waist at a desired location. The free-space beam radius W of a Gaussian beam satisfies the relationship ?W/?z = - W/R, where z represents the path length and R is the phase-front radius of curvature at z. By enforcing this relation on the effective beam spot size in turbulence W(e), we can define an effective radius of curvature R(e). In addition to specifying the beam waist, R(e) leads to a pair of effective beam parameters θ(e) and Λ(e) that provide a natural extension to the complex amplitude plane. Within this context, general propagation characteristics may be described, including the coherence properties of a Gaussian beam in both weak and strong optical turbulence.     

Ray matrix for Gaussian beam propagation in a nonlinear medium: experimental results

The validity of a ray-matrix formulation of Gaussian beam propagation in a liquid nonlinear medium exhibiting self-defocusing is examined experimentally. By comparing the measured spot size of a Gaussian laser beam passing through the medium with the calculated spot size, it was found that the theory is consistent with the experimental results as long as the waist position of the input beam is not close to the exit surface of the medium.     

Determination of waist parameters of a Gaussian beam

A simple method is presented for determining the waist position and the waist size of a Gaussian beam from measured spot sizes. The method does not require any least-squares process, and substitution of measured spot sizes directly into the formulas gives the waist parameters. Only few data are required to determine the parameters accurately as long as measured spot sizes contain small errors.     

Optimized coupling of a Gaussian beam into an optical waveguide with a grating coupler: comparison of experimental and theoretical results

The coupling efficiency of grating couplers is derived for a Gaussian incident beam. Its optimum value depends on the beam waist and on the position of a light spot with respect to the coupler edge for given grating parameters. The characteristic coupling length has been experimentally determined for the grating coupler studied. Relative measurements of the coupling efficiency as a function of incident beam characteristics are in good agreement with the numerical results.     

Subwavelength-resolvable focused non-gaussian beam shaped with a binary diffractive optical element.

The diffraction-limited spot size limits the optical disk storage capacity and microscopic resolution. We describe a technique to shape a focused Gaussian beam into a superresolving beam by using a diffractive optical element fabricated by laser-assisted chemical etching. The focused shaped beam has a smaller width and a longer depth of focus than a similarly focused Gaussian beam. Using the diffraction-limited shaped beam along with threshold writing, we achieved a written pit size of less than 0.33 mum at a 695-nm laser wavelength, compared with a 0.7-mum focused Gaussian spot size (full width at e(-2) of the peak) with the same focusing lens. The energy conversion efficiency for the beam shaping was ~81%.     

激光测速仪定焦系统设计

为满足激光测速仪在米级距离的测速需要,设计了一种激光测速仪定焦系统.通过光束分析仪测量距离激光出射口不同位置处的光斑半径,利用函数拟合的方法得到激光束腰斑半径与腰斑位置.采用望远镜系统作为定焦系统的基本结构,通过MATLAB软件穷举定焦系统的各项参数,记录满足条件的参数.根据操作过程中的实际条件选择其中一种数据搭建定焦...     

On the Global Efficiency of the Laser Optical Excitation of a Fast Atomic Beam

Abstract

The interaction of a fast atomic beam and a laser beam that crosses at right angles has been considered. We have studied the competition between the Doppler effect, due to the angular divergence of the atomic beam and the effect of the laser light intensity distribution. For low laser power values, an optimum waist size can be determined. For higher laser power values, the conditions for a maximum global efficiency are outlined.     

Geometry of the fringe field formed in the intersection of two Gaussian beams

A general expression is obtained for the exact computation of the fringe field in the intersection volume of two paraxial Gaussian beams for arbitrary beam waist positions and sizes. The expression is then simplified to allow easy fringe field computation while retaining good accuracy. By relating the simplified expression to the system parameters relevant to dual-beam laser Doppler velocimeters, simple design equations are obtained. These equations permit rapid evaluation of the fringe field variation along the major and minor axes of the intersection volume and clearly identify the system parameters controlling this variation.     

Analysis of dark spot formation in absorbing liquid media

Abstract

A theoretical analysis based on coupled field-matter equations is given to describe the recently observed phenomenon of a central dark spot formation of a Gaussian beam transmitted through an absorbing defocusing liquid medium. We find that such a pattern formation, which is accompanied by normal defocusing rings in the far field, originates from interplay between the wave-front curvature of the Gaussian beam and strong spatial self-phase medulation arising from thermally induced refractive index change in the medium. Results of numerical analysis for a thin medium are shown to be in a good quantitative agreement with our experimental findings. Further, the dark spot formation is also predicted by using a focused Gaussian beam and self-focusing medium.     

Propagation properties of cylindrical sinc Gaussian beam

Abstract

We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.     

Acoustooptic 2-D profile shaping of a Gaussian laser beam

Acoustooptic 2-D profile shaping of a Gaussian laser beam has been achieved by two plane ultrasonic waves progressing in orthogonal directions. The spot size W of the Gaussian laser beam must be considerable less than the wavelength lambda of the ultrasonic wave at the acoustooptic interaction region. The ultrasonic cell is dealt with as a Raman-Nath 2-D phase grating but serves as a 2-D beam deflector in time for the interaction scheme of interest. The wave front of the Gaussian laser beam must be almost plane in the interaction region. The profile shaping condition is 0.15 < or = (W/lambda) < or = 0.30 only when the Raman-Nath parameter dependent on the ultrasonic power has values between v = 1.0 and 2.0.     

Analytical calculation of the longitudinal electric field resulting from the tight focusing of an ultrafast transverse-magnetic laser beam

A purely time-domain approach is proposed for the propagation of vectorial ultrafast beams in free space beyond the paraxial and the slowly varying envelope approximations. As an example of application of this method, we describe in detail the vectorial properties of an ultrafast tightly focused transverse-magnetic (TM(01)) beam, where special attention is given to the longitudinal electric field component. We show that for spot sizes at the waist comparable to the wavelength, the beam diverges more rapidly than expected from paraxial theory. A consequence of this phenomenon is a faster decrease of the amplitude of the longitudinal field away from the waist and a faster evolution of the axial Gouy phase shift in the vicinity of the focus. It has been observed that the phase of the beam has an overall variation of 2pi from z=-infinity to infinity, independent of the beam spot size at the waist and pulse duration.     

Gaussian laser beam transformation into an optical vortex beam by helical lens

In this article, we investigate the Fresnel diffraction characteristics of the hybrid optical element which is a combination of a spiral phase plate (SPP) with topological charge p and a thin lens with focal length f, named the helical lens (HL). As incident a Gaussian laser beam is treated, having its waist a distance ζ from the HL plane and its axis passing through the centre of the HL. It is shown that the SPP introduces a phase singularity of pth order to the incident beam, while the lens transforms the beam characteristic parameters. The output light beam is analyzed in detail: its characteristic parameters and focusing properties, amplitude and intensity distributions and the vortex rings profiles, and radii, at any z distance behind the HL plane, as well as in the near and far field.     

Reducing the uncertainty in laser beam size measurement with a scanning edge method

A modification in the analysis of a conventional laser beam spot size measurement method has been developed. The new analysis significantly decreases the uncertainty in the estimation of the beam-spot size. A conventional beam scanning approach was used in the measurement, but instead of differentiating the data and fitting the result to a Gaussian function, the data were fit to an analytical approximation to the complementary error function. As a result, fitted parameters were obtained that were consistent with the standard differentiation approach, but with considerably smaller uncertainty.     

Laser-near-field-based Atomic Lens: Quantum Wave Optics Consideration

Abstract

This paper examines the focusing of an atomic beam by the near field of laser radiation diffracted by a small aperture. The wave properties of the atom are taken into consideration within the framework of an approximate Schrödinger equation. The possibility is demonstrated of focusing an atomic beam into a spot some 3 nm across, the atomic and laser beam characteristics being quite acceptable. The main contribution to the spot size is shown to be from spherical aberrations and diffraction effects, the chromatic aberrations of the atomic beam with a 5% velocity distribution broadening having a lesser effect.     

The rayleigh range of gaussian schell-model beams

Abstract

The concept of the Rayleigh range, well known in the theory of coherent beams, is generalized to a class of partially coherent beams. Curves are presented which show the dependence of the Rayleigh range on the spot size of the beam and on the spectral degree of coherence of the light in the plane of the waist.     

一种高灵敏度传感器：—四棱镜光点检测器

本文介绍一种用于激光准直高精度直线度测量的高灵敏度光电信号检测器,该检测器根据激光束腰处聚焦光斑点小的特点,采用一种四棱镜光点会聚式检测器来接收激光束信息,它的检测灵敏度比传统的四棱镜式四象限位敏传感器高出一个数量级以上;该检测器对激光束平行漂移与角漂移表现出不同的检出特征,因而尤适合于做为激光束漂移补偿检测和直线度误差检测;该检测器还具有结构简单、使用方便等优点。     

Estimation of electromagnetic scattering patterns from sinusoidalsurfaces using FFT

The scattering of electromagnetic waves from perfectly conducting sinusoidal surfaces as prototypes of periodic rough surfaces is studied. Physical optics and Fourier methods are used to calculate the scattered far field at a function of the observation angle. The patterns for several surface parameters are evaluated and plotted. The size of the illuminated surface area is varied. Homogeneous and Gaussian field amplitude perturbation of a laser beam in TEM₀₀-mode is considered. The results are compared with other methods and show a rather good agreement. Therefore, the method may be used for far-field computation if several criteria for the validity of the Kirchhoff approximation are not violated     

Propagation of Gaussian-Schell beam in turbulent atmosphere of three-layer altitude model

We propose a method that is used to derive the moment radius of intensity distribution in a turbulent atmosphere. From this study, we have found that the second moment radius is affected only by the first-order expansion coefficient of the wave structure function. If our attention is directed to a higher moment radius, a higher order approximation of the expansion needs to be used. As an example, the propagation of a Gaussian-Schell beam in a slant path has been studied based on the turbulent atmosphere of a three-layer model. The variation of some beam properties, such as the relative waist width, angular spread, and kurtosis parameter with the initial waist width, wavelength, and zenith angle, has been analyzed and discussed in detail. The study shows that there is little difference between the three-layer model and the Kolmogorov model in studying uplink propagation, and the difference is large for downlink propagation. The intensity profile of the Gaussian beam in turbulence does not keep a Gaussian shape unless the beam spreading due to turbulence is very large or very small.