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.     

Output power optimisation of slab-waveguide laser with Gaussian output mirror

We present an approximate analysis of the nonlinear operation of the hollow slab-waveguide laser with Gaussian reflectivity profile output mirror, including gain saturation and longitudinal as well as transverse field distribution of the laser mode. The model presented is general and can be applied to the study of arbitrary configuration of the slab-waveguide laser. In particular, the laser characteristics obtained reveal the influence of the position of the output mirror and the Gaussian mirror parameter on the power efficiency of the laser system. Received: 6 January 2000 / Published online: 8 November 2000     

激光束光强分布对材料激光加热的影响

 对激光强度空间均匀分布光束、高斯、超高斯以及平顶高斯光束进行了分析比较,在激光功率与光斑半径相同条件下,计算了各种光束的峰值光强和光束填充因子与光束阶次的关系,给出了光强分布的表达式。并将不同空间分布的光束作为热源,耦合到材料热传导方程中,以数值计算说明了各种光束辐照下,2mm厚30CrMnSiA钢材料靶面不同的热效应。     

Global rate equation description of a laser

The global integro-differential rate equations describing a multimode laser are analyzed. Expressions for the relaxation oscillation frequencies and their damping rates in the single-mode and two-mode regimes are obtained without specifying either the cavity geometry or the longitudinal pump profile. On the same level of generality, we prove the existence of universal relations relating the peaks of the power spectra in the two-mode regime. For a Fabry-Perot with arbitrary longitudinal pump profile, series expansions of all the physical functions are derived in powers of the pump moments. These moments are averages of the pump profile over cavity modes at linear combinations of the lasing frequencies and their harmonics. These results apply to end-pumped and/or partially filled lasers. For a single mode Fabry-Perot laser, we prove that the contribution to the steady state intensity from the lasing mode varies from 75% close to the lasing threshold to zero at high intensity. The remainder comes from the harmonics of the lasing mode. Analyzing the steady state single mode intensity equation in terms of the pump gratings, we prove that close to the lasing threshold only the space average of the pump and its grating oscillating at twice the lasing wave number do not vanish. This provides a hint towards the justification of the usual modal rate equations which retain only these two functions in the dynamical evolution of a laser. For a Fabry-Perot with constant pump profile, an exact expression for the upper boundary of the stable single mode regime is derived. In that two-mode regime, we prove that there is a critical value of the pump at which the ratio of the two relaxation oscillation frequencies is 2, leading to an internal resonance.     

Dynamic pulsed-beam shaping using a TAG lens in the near UV

The ability to dynamically shape the spatial intensity profile of an incident laser beam enables new ways to modify and structure surfaces through pulsed laser processing. Here we describe a method to generate doughnut-shaped beams from an input Gaussian source using a tunable acoustic gradient index (TAG) lens. The TAG lens is capable of modulating between focused beams and annular rings of variable size, using sinusoidal driving frequencies. Laser micromachining is accomplished by synchronizing the TAG lens to a 355 nm pulsed nanosecond laser. Results in polyimide demonstrate the ability to generate adjacent surface features with different shapes and sizes.     

Arbitrary direction incident Gaussian beam scattering by multispheres

Based on spherical vector wave functions and their coordinate rotation theory,the field of a Gaussian beam in terms of the spherical vector wave functions in an arbitrary unparallel Cartesian coordinate system is expanded.The beam shape coefficient and its convergence property are discussed in detail.Scattering of an arbitrary direction Gaussian beam by multiple homogeneous isotropic spheres is investigated.The effects of beam waist width,sphere separation distance,sphere number,beam centre positioning,and incident angle for a Gaussian beam with two polarization modes incident on various shaped sphere clusters are numerically studied.Moreover,the scattering characteristics of two kinds of shaped red blood cells illuminated by an arbitrary direction incident Gaussian beam with two polarization modes are investigated.Our results are expected to provide useful insights into particle sizing and the measurement of the scattering characteristics of blood corpuscle particles with laser diagnostic techniques.     

Generation of electromagnetic waves in the terahertz frequency range by optical rectification of a Gaussian laser pulse in a plasma in presence of an externally applied static electric field

We propose a theoretical model for the generation of electromagnetic waves in the terahertz (THz) frequency range by the optical rectification of a Gaussian laser pulse in a plasma with an applied static electric field transverse to the direction of propagation. A Gaussian laser pulse can exert a transverse component of the quasi‐static ponderomotive force on the electrons at a frequency in the THz range by a suitable choice of the laser pulse width. This nonlinear force is responsible for the density oscillation. The coupling of this oscillation with the drift velocity acquired by electrons due to the applied static electric field leads to the generation of a nonlinear current density. A spatial Gaussian intensity profile of the laser beam enhances the generated THz yield by many folds as compared to a uniform spatial intensity profile.     

Emittance measurement & optimization for the photocathode RF gun with laser profile shaping

The Laser Undulator Compact X-ray source(LUCX) is a test bench for a compact high brightness X-ray generator,based on inverse Compton Scattering at KEK,which requires high intensity multi-bunch trains with low transverse emittance.A photocathode RF gun with emittance compensation solenoid is used as an electron source.Much endeavor has been made to increase the beam intensity in the multi-bunch trains.The cavity of the RF gun is tuned into an unbalanced field in order to reduce space charge effects,so that the field gradient on the cathode surface is relatively higher when the forward RF power into gun cavity is not high enough.A laser profile shaper is employed to convert the driving laser profile from Gaussian into uniform.In this research we seek to find the optimized operational conditions for the decrease of the transverse emittance.With the uniform driving laser and the unbalanced RF gun,the RMS transverse emittance of a 1 nC bunch has been improved effectively from 5.46 πmm.mrad to 3.66 πmm.mrad.     

Experimental and theoretical waveforms of Rayleigh waves generated by a thermoelastic laser line source

An analytical model has been developed for the generation of surface acoustic (Rayleigh) waves in an isotropic solid by a thermoelastic laser line source. For a Gaussian light intensity profile, this model leads to an expression in closed form for the normal surface displacement of the Rayleigh wave either in the near field or in the far field domain. Quantitative agreement has been found for experiments carried out with an interferometric optical probe on a duraluminum plate.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity: Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity:Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated.An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field,with linear absorption and due to saturation effects for arbitrary large intensity.The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters.Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode.Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence.The beam is more focussed at lower intensity in both cases viz.extraordinary and ordinary mode.     

Propagation aspects of Mathieu–Gaussian beams in turbulence

Based on our recent source plane formulation, the propagation characteristics of Mathieu–Gaussian beams in turbulent atmosphere are investigated. In this connection, the average receiver plane intensity expression is deduced using the Huygens–Fresnel integral. Our results offered in the form of graphical illustrations reveal that, for some settings of source and propagation parameters, the center of the source beam is evacuated after propagation, while the initially smaller side lobes begin to grow. In a parallel development, the angular distribution of the beam also changes. At small Gaussian source sizes and transverse components of the wave vector, the source beam profile remains almost invariant throughout the propagation. The larger refractive index structure constant values cause the final Gaussian beam profile to be attained at earlier propagation distances. Smaller refractive index structure constants, on the other hand, do not change the beam profile substantially from that of free space.     

光强非均匀分布对波前曲率传感器的影响

为了将波前曲率传感器用于涉及激光波前的领域,理论分析了非均匀光强入射条件下的曲率传感器测量信号。用菲涅耳衍射公式,数值计算了相位分布为前10阶泽尼克多项式,光强为高斯分布和正态随机分布闪烁的曲率传感器信号,并和相同相位分布,光强均匀情况下的传感器信号比较。分析表明光强非均匀分布给波前曲率传感器测量信号带来了一定的误差。光强高斯分布对散焦相差的曲率信号影响较大,信号百分比误差达到25%,对其他相差的曲率信号影响很小;对于有正态随机分布闪烁的光强分布,信号百分比误差与正态随机分布的均方差成线性关系。在一定条件下,波前曲率传感器也能够用于光强非均匀分布的领域。     

Suppression for the Low spatial frequency Rings and Ripples of Laser Near field Intensity Distribution in the Spatial Filter Used in ICF Laser DriveSupported by the key project of the National Science Foundation, National Hi Tech Foundation.

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Calculation of the temperature and thermal expansion of a STM tip heated by a short laser pulse

A mathematical model for the calculation of the temperature field in a scanning tunneling microscope (STM) tip under laser illumination is developed. The duration of the laser pulse is a few nanoseconds or shorter. A Gaussian distribution of the laser light intensity in time and space is assumed. Two different mechanisms of tip heating are taken into account: 1. due to an enhanced electric field on the tip; 2. due to heating of the side surface of the tip by the focused spot of laser light. An average tip temperature is calculated using the heat conductivity equation. The enhanced electric field on the tip is calculated by the method of boundary integral equations. Received: 20 August 2002 / Revised version: 4 December 2002 / Published online: 19 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-2551/962-490, E-mail: sklein@fh-muenster.de     

Propagation characteristics of laser beams with amplitude modulations and phase fluctuations in apertured fractional Fourier transforming system

The apertured fractional Fourier transforming system is introduced and applied to treat the propagation of Gaussian beams with amplitude modulations and phase fluctuations. Based on the treatment that a rectangular function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, the analytical expressions for the mutual intensity distribution of laser beams with amplitude modulations and phase fluctuations passing through the apertured fractional Fourier transforming system are obtained. Some numerical simulations are illustrated for their propagation properties.     

节瘤缺陷对中红外高反射膜电场增强影响的数值分析

运用时域有限差分(FDTD)方法建立了薄膜中节瘤缺陷在高斯激光照射下电磁场响应模型，分析了节瘤的深度、起始颗粒大小和入射光角度对薄膜中电磁场的影响。结果表明：节瘤缺馅对薄膜中电场强度有显著的加强作用，其内部峰值场强是入射光的6倍，大而浅节瘤缺陷对倾斜入射p偏振态的激光具有最高的加强效应.     

Measuring temporal fluctuation on femtosecond scale in a random medium

We report an observation of femtosecond optical fluctuations of transmitted light when a coherent femtosecond pulse propagates through a random medium. They are a result of random interference among scattered waves coming from different trajectories in the time domain. Temporal fluctuations are measured by using cross-correlated frequency optical gating. It is shown that a femtosecond pulse will be broadened and distorted in pulse shape while it is propagating in random medium. The real and imaginary components of transmitted electric field are also distorted severely. The average of the fluctuated transmission pulses yields a smooth profile, probability functions show good agreement with Gaussian distribution.     

Propagation of partially coherent controllable dark hollow beams with various symmetries in turbulent atmosphere

Normalized intensity distribution, the complex degree of coherence and power in the bucket for partially coherent controllable dark hollow beams (DHBs) with various symmetries propagating in atmospheric turbulence are derived using tensor method and investigated in detail. Analytical results show that, after sufficient propagation distance, partially coherent DHBs with various symmetries eventually become circular Gaussian beam (without dark hollow) in turbulent atmosphere, which is different from its propagation properties in free space. The partially coherent DHBs return to a circular Gaussian beam rapidly for stronger turbulence, higher coherence, lower beam order, smaller p or smaller beam waist width. Another interesting observation is that the profile of the complex degree of coherence attains a similar profile to that of the average intensity of the related beam propagating in a turbulent atmosphere. Besides the laser power focusablity of DHBs are better than that of Gaussian beam propagating in turbulent atmosphere.     

The development of a portable line-shaping optical system for silicon surface treatment

This study proposes a beam shaper for converting a circle beam profile generated with a Gaussian intensity distribution by an 808 nm diode laser into a line beam profile for silicon surface treatment applications. To produce a hand-held and low-cost device with a large spot-size laser, this study uses a portable optical system consisting of a diode laser source, a collimator, a cylindrical lens, and a plano-convex lens to generate an approximately 40 × 3:5mm² line beam profile at a working distance of 200 mm. The silicon surface treated by the line-shaped laser beam has significantly reduced reflectance spectra. The proposed system is also suitable for the surface cleaning of materials.