Generation of flattened Gaussian beam profiles in a Nd:YAG laser with a Gaussian mirror resonator

We report the experimental generation of a family of flattened Gaussian beams with bell-shaped, flattened, and annular intensity profiles in an electro-optically Q-switched Nd:YAG laser with a variable reflectivity mirror of a Gaussian reflectivity profile as an output coupler. The laser beams of different profiles were generated by modifying the resonator magnification. The propagation characteristics of the experimentally generated flat Gaussian beams were found to be in agreement with theory. To the best of our knowledge this is the first time such a family of flattened Gaussian beams is experimentally generated intracavity using a single variable reflectivity mirror.     

Gaussian content as a laser beam quality parameter

We propose the Gaussian content (GC) as an optional quality parameter for the characterization of laser beams. It is defined as the overlap integral of a given field with an optimally defined Gaussian. The definition is especially suited for applications where coherence properties are targeted. Mathematical definitions and basic calculation procedures are given along with results for basic beam profiles. The coherent combination of an array of laser beams and the optimal coupling between a diode laser and a single-mode fiber are elaborated as application examples. The measurement of the GC and its conservation upon propagation are experimentally confirmed.     

Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium

Log-amplitude and phase-correlation and structure functions of higher-order annular laser beams in a turbulent atmosphere are derived. A higher-order annular beam source is defined as the superposition of two different higher-order Hermite-Gaussian beams. A special case of such an excitation is the annular Gaussian beam in which two beams operate at fundamental modes of different Gaussian beam sizes, yielding a doughnut-shaped (annular) beam when the second beam is subtracted from the first beam. Our formulation utilizes Rytov approximation, which makes it applicable in the weak-turbulence regime, especially for log-amplitude fluctuations. Limiting cases of our formulations correctly match with known higher-order-mode solutions that in turn reduce to the Gaussian-beam-wave (TEM00-mode) results. Our results can be applied to determine the scintillation index and the phase fluctuations in free-space optics links under higher-order annular laser beam excitation. Except for the numerical evaluation of a specific example covering an annular Gaussian beam, the results in general are left in integral form and need to be numerically evaluated in detail to obtain quantitative results.     

Rotating shutters: a mechanical way of flattening gaussian beam profiles in time average

A mechanical method of flattening the Gaussian intensity distribution of laser beams in time average is presented. Specially shaped rotating shutters are the key feature of this method, which has been applied to achieve homogeneous submicrometer patterning of macroscopically large samples by laser interference exposure. This method represents a simple yet useful alternative to applying beam broadening or degaussing plates (apodizing filters).     

Complex Gaussian functions expansion method applied to truncated Gaussian beams

An analytical expression for the beam propagation factor (M ² factor) of truncated Gaussian beams was derived by using the complex Gaussian functions expansion method. The reasonability of the approximation of complex Gaussian functions expansion method is studied, and a comparison of this method with the generalised truncated second-order moments method and the asymptotic analysis method is also made. In general, an easy analytical expression for the M ² factor of truncated laser beams can be derived by using the complex Gaussian functions expansion method. The M ² factor obtained by using the complex Gaussian functions expansion method is more consistent with that in practice than that obtained by using two other methods. The analytical results obtained by using the complex Gaussian functions expansion method can be reduced to that for the non-truncated case when the truncation parameter is sufficiently large. Therefore, the complex Gaussian functions expansion method is a suitable approximation method for studying the M ² factor of truncated laser beams.     

An intuitive model for on-axis pulse evolution of ultrashort pulsed Gaussian beams diffracted from a circular aperture

The diffraction of ultrashort pulsed Gaussian beams from a circular aperture is studied by means of Fresnel diffraction integral and Fourier transform method. A uniform analytical expression is derived for temporal pulse form of ultrashort pulsed Gaussian beams in two cases, i.e. with constant beam waist and with constant diffraction length. It is shown that the on-axis pulse can be formulated as a superposition of an unapertured pulse and an aperture-induced pulse. The superposition of these two pulses leads to an enhanced pulse intensity for small truncation parameters at certain distances in the near field. Our results may find applications in high-intensity laser waveform control.     

Characterizing output beams for lasers that use high-magnification unstable resonators.

Laser beams generated from high-magnification on-axis unstable resonators by use of hard-edged optics typically have a doughnut-shaped distribution in the near field (i.e., a flat-top profile with a hole in the middle for an axially coupled beam). We derive analytical expressions describing this distribution by using the flattened Gaussian beams concept. The superposition of two flattened Gaussian beams whose flatness and steepness of edges are controlled by defined parameters (i.e., the beam width and the order) is used to analyze the output beam intensity along the propagation axis. Finally, experimental measurements of beam propagation from a copper-vapor laser fitted with a high-magnification unstable resonator show excellent agreement with theoretical predictions.     

Electrical control of shape of laser beam using axially symmetric liquid crystal cells

This work demonstrates the electrical tuning of laser beam shape using an axially symmetric dye-dope liquid crystal (ASDDLC) device that is fabricated using a photo-alignment method. Various beam shapes can be obtained by linearly polarized Gaussian laser beams through an ASDDLC device under various applied voltages. The far-field intensity patterns generated by laser beams of selected shapes under various applied voltages are simulated, and the results are consistent with experiment. A rotatable petal-shaped beam is obtained by controlling the polarization of the output donut-shaped beam. The tenability of beam shape of light with a wavelength of 1064 nm, which is commonly used in biomedical applications, is also demonstrated.     

Atmospheric optical communication with a Gaussian Schell beam

We consider a wireless optical communication link in which the laser source is a Gaussian Schell beam. The effects of atmospheric turbulence strength and degree of source spatial coherence on aperture averaging and average bit error rate are examined. To accomplish this, we have derived analytic expressions for the spatial covariance of irradiance fluctuations and log-intensity variance for a Gaussian beam of any degree of coherence in the weak fluctuation regime. When spatial coherence of the transmitted source beam is reduced, intensity fluctuations (scintillations) decrease, leading to a significant reduction in the bit error rate of the optical communication link. We have also identified an enhanced aperture-averaging effect that occurs in tightly focused coherent Gaussian beams and in collimated and slightly divergent partially coherent beams. The expressions derived provide a useful design tool for selecting the optimal transmitter beam size, receiver aperture size, beam spatial coherence, transmitter focusing, etc., for the anticipated atmospheric channel conditions.     

Beam-divergence control of excimers with plane-parallel Gaussian cavities

Plane-parallel cavities with Gaussian-reflectivity-profile mirrors as full reflectors were applied to a XeCl laser, and the near- and the far-field characteristics of the laser radiation were analyzed. It is shown that excimer lasers fitted with plane-parallel Gaussian cavities deliver laser radiation with a beam-quality factor M(2) that is more than 50% smaller than that of laser beams delivered by conventional plane-parallel cavities. The effect of the Gaussian mirror spot size on M(2) was also investigated, and it is shown that the narrowing of the Gaussian mirror spot size reduces the beam-quality-factor value.     

Reconstruction dynamics of recorded holograms in photochromic glass

We have investigated the dynamics of the record-erase process of holograms in photochromic glass using continuum Nd:YVO? laser radiation (λ=532 nm). A bidimensional microgrid pattern was formed and visualized in photochromic glass, and its diffraction efficiency decay versus time (during reconstruction step) gave us information (D, Δn) about the diffusion process inside the material. The recording and reconstruction processes were carried out in an off-axis setup, and the images of the reconstructed object were recorded by a CCD camera. Measurements realized on reconstructed object images using holograms recorded at a different incident power laser have shown a two-stage process involved in silver atom kinetics.     

Effect of crossed beams on Stokes gain and interaction length in stimulated Raman gain spectroscopy

We have numerically calculated the change in spatial resolution and Stokes gain for stimulated Raman gain experiments that use two crossed laser beams. The laser beams are modeled as diffraction-limited, Gaussian TEM(00) beams. Results for interaction length and relative Stokes gain are presented for crossing angles of 0-15°, focusing ?/#'s 2-250, and mismatches in the positions of the focal points of the two beams. The numerical results for spatial resolution and gain are compared with geometric approximations that have been previously published. These numerical simulations show where the approximations are valid and also extend into regions where the approximations are invalid. PACS: 42.65 Dr.     

Effect of reconstruction beam polarization on the kinetics of anisotropic gratings in bacteriorhodopsin

Anisotropic gratings are recorded on bacteriorhodopsin films by two parallelly polarized beams, and the effect of the polarization orientation of the reconstructing beam on the diffraction efficiency kinetics is studied. A theoretical model for the diffraction efficiency kinetics of the anisotropic grating is developed by combining Jones-matrix and photochromic two-state theory. It is found that the polarization azimuth of the reconstructing beam produces a cosine modulation on the kinetics of the diffraction efficiency, being positive at the peak efficiency and negative for steady state. By adding auxiliary violet light during grating formation, the saturation of the grating can be restrained. As a result, the negative cosine modulation for the steady-state diffraction efficiency changes to a positive one. In addition, the steady-state diffraction efficiency is increased appreciably for all reconstructing polarization orientations.     

Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence

The spreading of partially coherent beams propagating through atmospheric turbulence is studied by use of the coherent-mode representation of the beams. Specifically, we consider partially coherent Gaussian Schell-model beams entering the atmosphere, and we examine the spreading of each coherent mode, represented by a Hermite-Gaussian function, on propagation. We find that in atmospheric turbulence the relative spreading of higher-order modes is smaller than that of lower-order modes, whereas the relative spreading of all order modes is the same as in free space. This modal behavior successfully explains why under certain circumstances partially coherent beams are less affected by atmospheric turbulence than are fully spatially coherent laser beams.     

Generalized beam-propagation factor of partially coherent beams propagating through hard-edged apertures

The second-order intensity moments and beam-propagation factor (M2 factor) of partially coherent beams have been generalized to include the case of hard-edged diffraction. A laser beam with amplitude modulation and phase fluctuation and a Gaussian Schell-model beam are taken as two typical examples of partially coherent beams. Analytical expressions for the generalized M2 factor are derived.     

环状光束通过球差透镜的聚焦特性

利用偏心高斯光束相干叠加的方法,建立了柱坐标系下环状光束的新模型.从广义衍射积分理论出发,经过大量数值计算分析,详细研究了环状光束通过球差透镜的聚焦特性,定量分析了环状光束的阶数L,M、偏心高斯光束的束腰宽度w0以及球差系数C4对聚焦光场实际焦点(轴上最大光强)位置以及轴上最大光强的影响.研究结果表明,本文提出的模型可统-描述基模高斯光束和环状光束.在透镜焦距和入射光束波长一定的情况下,环状光束通过球差透镜的聚焦特性不仅与透镜的球差系数C4有关,而且还与环状光束的阶数L,M以及偏心高斯光束的束腰宽度w0有关.     

Optimization of the arrangement of fiber laser array in beam coherent combining

Based on the expanding of the fundamental mode of a step-index fiber in terms of Laguerre–Gaussian modes, the accurate expression for the beam propagation of a fiber laser in free space is obtained. Thereby, the coherent combining beam of three fiber laser arrays including circular arrangement, square arrangement, and diamond arrangement are numerically analyzed. The study shows that all the beams gradually concentrate centrally on the propagation axis and the highest far-field peak intensity can be obtained by using the circular arrangement. Meanwhile, the far-field intensity of the circular arrangement by using the Laguerre–Gaussian approximation is also compared with that by using the pure Gaussian approximation, which indicates that the pure Gaussian approximation will induce much error in the far-field intensity. Finally, the influence of the radius of a circular fiber laser array on the far-field intensity is studied, of which the result shows that the far-field intensity decreases with increasing radius. Therefore, the fiber laser elements are suggested to be placed as close as possible.     

星地量子密钥分配中单光子捕获理论分析

基于TEM10模拉盖尔-高斯光束,推导了自由空间量子密钥分配的单光子捕获概率表达式,分析了低轨卫星-地面站间链路的单光子捕获问题。结果表明,采用TEM10模拉盖尔-高斯型高度衰减激光脉冲作为单光子源,单光子捕获采用前驱波参考脉冲设置时间窗口的方法,可使得卫星上接收机以最大概率捕获光子。单光子捕获概率一般在10-1~10-3量级。与基模高斯光束相比,采用TEM10模拉盖尔-高斯光束的优点是,不会由于卫星运动而产生单光子捕获概率的损耗。通过考虑大气湍流的影响,对单光子捕获概率的表达式进行了修正。     

Fractional Fourier transform of a higher-order cosh–Gaussian beam

A higher-order cosh–Gaussian beam is an appropriate model to describe the flattened laser beam. The fractional Fourier transform (FRFT) is applied to treat the propagation of higher-order cosh–Gaussian beams. An analytical expression for a higher-order cosh–Gaussian beam passing through a FRFT system has been derived. By using the derived expression, the properties of a higher-order cosh–Gaussian beam in the FRFT plane are graphically illustrated with numerical examples.