Z-scan analysis of high-order nonlinear refraction effect induced by using elliptic Gaussian beam

The irradiance of an elliptic Gaussian beam that is high enough to excite high-order nonlinear refraction effect is used to calculate the normalized on-axis transmittance function in the z-scan technique by introducing complex beam parameters which make the calculation simpler. The transmittance formula is applied to the first-, first two-, and first three-order nonlinearities. Numerical evaluation shows that the symmetry no longer holds when using an elliptic Gaussian beam instead of a circular Gaussian beam. A distortion is observed in the central part of the curve, which decreases as ellipticity increases. Moreover, the variation of the normalized peak-valley difference decreases as ellipticity decreases.     

Scattering of Cluster Spheres Located on Axis by a Gaussian Beam in Millimeter Waves

Multi-spheres scattering has been fully discussed, but almost all kinds of these researches are in plane wave. The special case of an incident shaped beam is introduced in this paper. While some numerical results for cluster spheres illuminated on the axis of a shaped beam in millimeter waves are presented. Finally, results of numerical computations illuminated by a shape beam in different beam waist radius are compared with those for a plane wave illumination.     

Far-field structural property of a Gaussian beam diffracted by a phase aperture

Based on the angular spectrum representation of an arbitrary electromagnetic beam and the method of stationary phase, an analytically vectorial structure of a Gaussian beam diffracted by a phase aperture has been derived in the far-field. Moreover, the derivation is performed without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured Gaussian beam are also presented in the far-field, respectively. The influence of the phase delay on the energy flux distributions of the TE term, the TM term, and the apertured Gaussian beam is discussed in the far-field.     

Time-dependent thermal lensing and Kerr nonlinearity in CS2 with CO2-laser radiation

We report on optical limiting and z-scan in CS₂ as a function of the pulse duration of 10 µm TEA CO₂-laser radiation. We present a comprehensive and simple model for the shape of a laser pulse transmitted through this limiting device. For the first time, we propose the use of an optical limiting device for beam shaping.     

Gradient force evolution of Gaussian beam induced by a phase plate

The evolution of gradient force pattern induced by an annular phase distribution plate is numerically investigated in this paper. The phase plate, which may alter the wavefront phase of incident Gaussian beam with tunable topological charge, consists of two concentric portions, one center circle portion and one annular portion. Numerical simulations show that the proposed plate can induce the tunable gradient force on the particles in the focal region. By adjusting the geometrical parameters or changing the topological charge of the phase-shifting plate, some novel trap patterns may occur, such as triangle shape trap, quadrangle shape trap, pentagon shape trap, hexagon shape trap, and the shapes of optical traps change very considerably. Therefore, the phase plate may be very advantageous for constructing tunable optical traps. The method is more versatile in that it allows precise control of the parameters and has the possibility of generating specific patterns of optical vortices. The gradient force pattern focal of intensity distribution depends on both the annular width and the topological charge.     

Small Gaussian laser beam diameter measurement using a quadrant photodiode

A method that uses the quadrant photodiode has been shown to be relatively inexpensive and robust in measuring Gaussian laser beam diameters in two axes. This approach requires neither component rotation nor precision alignment, and it facilitates integration of Gaussian laser beam diameter measurement with laser beam tracking in instruments. The physical gap between sensors in the quadrant photodiode, however, limits laser beam diameter measurements to those in the millimeter range. Here, we describe a modified approach to measure Gaussian laser beam diameters that are significantly smaller.     

Propagation Characteristics of a Partially Coherent Gaussian Schell-model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

This work investigates the joint effects of jet engine exhaust-induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell-model Array (GSMA) vortex beam. Using the two-process propagation method, analytical formulae are derived for the cross-spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high-strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.     

赝火花脉冲电子束传输中束斑分析

通过赝火花强流脉冲电子束对酸敏变色片和单晶硅的轰击试验，结合束流自箍缩效应进行理论计算，对赝火花脉冲电子束传输中束斑的变形进行了研究与分析. 结果表明椭圆形轰击束斑是由通过旁路电容的瞬态电流产生的方位角磁场所引起的，并且提出了解决束斑变形的有效方法. 关键词： 脉冲电子束 赝火花放电 束斑 自箍缩效应     

Z-scan technique for elliptic Gaussian beams

A novel z-scan technique suitable for elliptic Gaussian beams is proposed. It is based on the direct measurement of the beams semiaxes in the far field instead of the irradiance transmitted through an aperture, as in the case of circular beams. This technique overcomes, for the first time, the insurmountable obstacles encountered when a z-scan technique based on transmittance measurements is used in the case of elliptic beams. The experimental procedure of this technique is realized using a CCD camera connected to a laser beam profiler, and has the advantage of being insensitive to beam pointing instability and energy fluctuations. It also reveals the different influence of the optical non-linearities on the two principal semiaxes of the elliptic beam. PACS 42.65.-k; 42.65.An; 42.65.Jx     

Propagation of high-order Bessel–Gaussian beam through a misaligned first-order optical system

The generalized diffraction integralis used to derive a generalized formula for high-order Bessel–Gaussian beams (HBGBs) through a misaligned first-order ABCD optical system. It is found that, when a HBGB propagates through a misaligned optical system, the beam shape of the output beam is unchanged. However, the center of the output beam is deviated from the optical axis, forming a decentered HBGB. The position of the output beam may be controlled by adjusting the misaligned parameters. Based on the derived formula, the diffraction patterns of HBGBs propagating through a simple misaligned lens system have been calculated numerically. These results may be useful in the application of laser beams for trapping and manipulating a wide variety of particles.     

<Emphasis Type="Italic">Z</Emphasis>-scan technique through beam radius measurements

A modification to the well-known z-scan technique for measuring optical non-linearities is introduced. It is based on directly measuring the beam radius in the far field instead of the transmittance of the irradiance through an aperture, as in the original version. It has the advantage of being insensitive to beam pointing instability and is almost insensitive to power fluctuations. Furthermore, the calculations required for the determination of the non-linear parameters are simplified. For demonstrating the advantages of the modified method, beam radius and transmittance measurements were simultaneously taken in the standard non-linear optical material CS₂. Separate fittings of these measurements gave almost the same values for the non-linearities, quite similar to those in the literature. A common fitting has been applied to both sets of measurements, enhancing the accuracy of the method. Received: 8 July 2002 / Revised version: 18 October 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. Fax: +30-2610/997470, E-mail: gianetas@physics.upatras.gr     

Transmitted characteristics for a Gaussian beam passing through a misaligned Fabry-Perot interferometer

After deriving the expression of the intensity of the transmitted beam for a Gaussian beam passing through a misaligned FPI, the influence of the nonparallelism in FPI mirrors alignment on the transmission of a Gaussian beam has been investigated numerically. The results show that the energy profile of the total transmitted beam appears multiple sub-peaks structure; with the increase of the nonparallelism in FPI mirrors alignment, the number of the sub-peaks raises, the peak intensity of the transmitted beam has a declining tendency, and the peak intensity position of the total transmitted beam is shifted.     

Design of a Quasi-Optical Mode Converter for a Frequency Step-Tunable Gyrotron

The quasi-optical mode converter for a frequency step-tunable gyrotron which consists of a dimpled-wall antenna (Denisov-type launcher) and a beam-forming mirror system has been optimized for 9 modes from TE_17,6 at 105 GHz to TE_23,8 at 143 GHz. The first mirror is a large quasi-elliptical focusing one; the second and third are phase-correcting mirrors with a non-quadratic shape of the surface. The results of calculations show that for these modes the Denisov-type launcher has a well-focused beam with low diffraction losses, and the radiation pattern presents an almost identical field shape for all modes considered. A multi-mode optimization of the phase-correcting mirrors with two different methods has been tested. The simulations show that the phase-correcting mirrors can be used for broadband operation in the frequency range from 105 GHz up to 143 GHz in the various design modes. This quasi-optical mode converter can achieve efficiencies of 94%-98% for converting the rotating high-order cylindrical cavity modes into the usable fundamental Gaussian mode.     

Diffraction of a Gaussian Beam by a Periodic Screen

Based on the plane wave analysis and the superposition of the plane waves, the diffraction of a Gaussian beam by a periodic screen with a dielectric plate is analyzed. The reflection power coefficient for different parameters of the beam and the screen is given. When the beam waist size is increased the results reaches that of the plane wave. It has been found that the power reflection coefficient is not sensitive to the beam waist size, however, it is sensitive to the period of the grating and polarization angle.     

Transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon

The transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon has been investigated. After deriving the expression of the intensity of the transmitted beam, several key characteristics of the transmitted beam have been specified. The results show that the peak intensity of the transmitted beam decreases with the increase of the input angle, the position of the peak intensity of the transmitted beam is shifted, and the spot size of the transmitted beam is changed.     

基于Z扫描理论的光限幅优化分析

基于Z扫描的基本理论,根据强光光束在非线性介质中的特殊传播规律,改变光路的几何排列及光阑孔径,计算了不同情况下光阑的归一化透过率,从而确定各个参数对限幅效果的影响,得出最佳的几何排布,以实现限幅器的优化设计.     

Hollow elliptical Gaussian beams generated by a triangular prism

Based on the tensor method, an analytical formula for hollow Gaussian beams (HGBs) generated by a triangular prism has been derived, and the propagation properties have been studied. It is shown that hollow elliptical Gaussian beams (HEGBs) can be obtained in the near field after the prism, and that the eccentricity of the output beam is affected by parameters such as the incidence angle, refractive index of the prism and the order of the HGB. It shows that by using a triangular prism one can conveniently obtain HEGBs.     

A review of the numerical investigation on the scattering of Gaussian beam by complex particles

The study of light scattering by various particles is an active and important subject of research with myriad practical applications. During the years the scattering of plane wave by various particles has been investigated extensively. In recent years, with the development of laser sources and the tremendous expansion of their application, there has been a growing interest in the study of light scattering by various particles illuminated by a focused Gaussian beam. Since the analytical methods are only suitable for the analysis of Gaussian beam scattering by some regular particles, for complex particles with arbitrary shape and structure, one has to resort to the numerical methods. In this article, we review the recent numerical investigation on the scattering of Gaussian beam by systems of complex particles, including arbitrarily shaped conducting particles, dielectric particles, composite particles with inclusions, as well as random discrete particles and fractal soot aggregates. The essential formulations of the proposed numerical methods are outlined and the numerical results for some complex particles are also presented. This review is expected to provide useful help for the study of the interaction between the laser beams and the complex particles.     

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.     

高斯光束在双层云中传输的蒙特卡罗模拟

基于辐射传输理论, 利用蒙特卡罗方法模拟了无限窄(冲击函数)准直光束入射到典型水云以及冰水双层云时的后向散射特性, 进而将得到的冲击响应与高斯光束卷积, 得到高斯光束在云层中传输的多次散射特性. 文中给出了两种波束入射时水云以及冰水双层云的反射函数随径向r和天顶角α的变化关系, 并给出了光强在云层内部的二维分布图. 计算结果表明, 高斯光束入射时, 云层反射函数的特点与无限窄准直光束入射时有较大区别. 因此在利用激光雷达进行云层探测时需要考虑激光的散斑, 文中的方法可以为此提供理论依据.