Diffraction losses and selection of transverse modes in complex resonators

Diffraction losses are estimated for TEM₀₀, TEM₀₁, and TEM₁₀ modes which can be generated in complex resonators. Dependences of the output power of the laser operating in the regime of transverse oscillation suppression on the transmission of the mirror are obtained. Optimal relationships between the field stop aperture area and the optical beam cross section are determined as functions of the gain of the active medium.     

Investigation in the far field characteristics of TM polarized Gaussian beam from the vectorial structure

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of TM polarized Gaussian beam, the rigorous solution of Maxwell's equations for a confocal resonator, have been presented in the far field. Then in terms of the vectorial structure, TM polarized Gaussian beam is compared with Gaussian TEM₀₀ mode. The TE term is located at the y-axis, and the TM term the x-axis. At the non-paraxial case, the whole beam spot is elliptical, and the long axis is located at the y-axis. Moreover, the whole beam spot of TM polarized Gaussian beam is smaller than that of Gaussian TEM₀₀ mode. At the paraxial case, the whole beam spot is circular, and TM polarized Gaussian beam reduces to be Gaussian TEM₀₀ mode.     

一种CCD辅助测量基模(TEM00)激光光斑尺寸的方法

激光光束是一种振幅和等相位面都在变化的高斯球面光波,其最小光斑的位置和大小不易确定,本文在实践的基础上提出一种测量基模(TEM₀₀)激光光斑尺寸的方法,解决了这一问题.     

单口径相干合成系统激光光束的M2因子研究

单口径相干合成系统激光光束的光束质量是一个亟待解决的重要问题.基于二阶矩定义, 文中给出了单口径TEM₀₀, TEM₀₁及TEM₁₀两两相干光束M²因子的解析表达式, 并比较分析了束腰宽度、传输距离、振幅之比,以及源场位置矢量对相干光束M²因子的影响, 得到了诸如源场位置参量d₁<100λ时,各相干光束M²因子恒定,反之, 其随位置参量d₁的增大而增大等一些结论.最后,文章对两TEM₀₀模相干光束M²因子的 部分理论进行了实验验证.     

Competition effects on spatial coherence in a CO2 laser

The degree of spatial coherence between two points separated by 6 mm in a radiation beam is almost unity, when two competing transitions lines which differ below 100 cm^-1 oscillate with a TEM₀₀ mode, while it varies greatly when a single line occurs on competing TEM₀₀ and TEM₁₀ modes.     

Tailored TEMp0 beams for large size 3-D laser prototyping

The Laser-Lithography technique allows the fabrication of complex objects having microsizes by selectively solidifying polymeric materials layer by layer upon exposure to a focused Gaussian laser beam having a beam propagation factor M²=1. We can expect that extension of this technique to large sizes 3-D prototyping comes up against a large increase in the design time. A possible solution is the increase in the focused spot size, but unfortunately at the price of a great reduction in the longitudinal resolution due to the resulting increase in the depth of focus. To overcome these difficulties, we propose the use of a rectified TEM_p0 beam allowing the obtaining of a Gaussian beam intensity profile in the focus plane of a lens. The reshaped TEM_p0 beam has a beam propagation factor M²≈(2p+1), and this yields to a relative improvement of the longitudinal resolution although the spot size is increased for reducing the processing time.     

Amplitude and phase clipping: Strehl ratio versus divergence

We consider the transverse characteristics of a Gaussian laser beam subject to a phase or amplitude clipping due to a pupil which is a π-plate or an opaque disc (stop). In particular, we consider the correlation between two features, the Strehl ratio and divergence angle, usually used for characterising the focusability of a diffracted beam. It is demonstrated that the Strehl ratio does not give systematically a global view, from a divergence point of view, on the transverse properties of a Gaussian beam suffering amplitude or phase diffraction. In addition, we consider the case of self-diffraction of a Gaussian beam upon a Gaussian phase aberration of same width, and it is found that the on-axis intensity describes correctly the whole diffracted beam cross-section, from a divergence point of view, only if the central phase shift is smaller than π. Another example showing that the focusability of a pure high-order Laguerre–Gauss TEM_p0 beam, free from any clipping, cannot be correctly described by Strehl ratio is also considered.     

Second-harmonic power of KTiOPO4 with double refraction

Second harmonic (SH) power of the type-II phase matching in KTiOPO₄ (KTP) is calculated for the fundamental beams of TEM₀₀ mode within the near field approximation (parallel Gaussian beam) taking the beam walk-off effect among the two fundamental and the SH beams into account. The slit intensity and the total SH power are calculated as functions of the beam radius and the crystal length. Two approximations are made for the SH power calculation at tight beam focusing condition. The measurements of the SH power in KTP are carried out for three crystals of 6, 3, and 1.5 mm thickness. The effective nonlinear coefficient for Nd: YAG incident radiation is estimated to be 4.3 pm/V with 10% uncertainty, taking the enhancement factor due to the multimode structure of the laser beam into account.     

Creation of a sharper focus by using a rectified TEMp0 beam

The superresolution technique is usually used in optical imaging for its ability to make the central diffractive spot smaller than the Airy spot. In this paper, we apply the superresolution technique for transforming a symmetrical TEM_p0 Laguerre-Gauss beam into a Gaussian intensity distribution in the plane of a converging lens. The beam shaping is achieved by an annular binary Diffractive Optical Element having a transmittance, alternatively equal to −1 or + 1, modelled on the p light rings of the incident beam. It is observed that the rectified TEM₃₀ beam at focus has a focal volume 170 times smaller than that of a Gaussian beam.     

Trapping Rayleigh particles using highly focused higher-order radially polarized beams

The optical trapping characteristics of highly focused higher-order radially polarized beams (R-TEM_p1*) acting on a Rayleigh particle are studied theoretically. Numerical results show that as the order p of beam increases and the numerical aperture NA_o of the objective decreases, the axial trap distance increases but the trap depth and maximum restoring force decreases. In a limit of NA_o = 1, three higher-order R-TEM_p1* beams of p = 1, 2, 3, like the fundamental lowest-order radially polarized beam of p = 0, can three-dimensionally trap a particle to the focus but the axial trap stiffness decreases with the increase of p. When NA_o = 0.95, the focus is still a stable trap point for the two beams of p = 0 and 1 but it becomes an unstable trap point for the two beams of p = 2 and 3. The trap stability is also discussed for higher-order radially polarized beam illumination.     

Frequency splitting phenomenon of dual transverse modes in a Nd:YAG laser

We observed frequency splitting phenomenon of dual transverse modes (TEM_00q and TEM_01q) in a Nd:YAG microchip standing wave laser utilizing intracavity stress birefringence effects. Four resonance frequencies (ν_00qe, ν_00qo, ν_01qe, and ν_01qo, respectively) were produced and tuned by changing the diametral compression force applied on the laser crystal. The transverse mode frequency spacing for the same longitudinal mode number (Δν_trans) was 1.16 GHz, and the magnitude of frequency splitting (Δν) ranged from 0 MHz to 1.16 GHz. Based on this phenomenon, a four-mode differential standing wave laser, whose signal characteristics were a little like those of a four-mode differential travelling wave laser gyro however with a much larger frequency splitting range, was produced. The theoretical analysis is in good agreement with the experimental results. This phenomenon not only can be used to make lasers with two or more frequency differences, but also can be used to make high-resolution self-sensing laser sensors (e.g. laser force sensors and laser accelerometers).     

Cross focusing of two coaxial spatial modes of a single frequency of a laser beam in a nonlinear dielectric

The cross-focusing of two co-axial transverse modes of a laser beam viz. TEM₀₀ and TEM₀₁ modes of the same frequency in a non-linear dielectric has been studied. When the TEM₀₀ mode is stronger than the TEM₀₁ mode, both modes focus on the axis. In the opposite case, defocusing occurs at the axis and energy concentrates in a ring.     

Generation and detection of optical vortices using all fiber-optic system

We demonstrate simultaneous generation, propagation and detection of optical vortices using all fiber-optic system. A fiber-optic Y-coupler was used for generating spherical and doughnut beams, simultaneously. Gaussian (TEM₀₀) beam emitted from CW red He-Ne laser is coupled into the fiber coupler and is converted into vortex beam via second arm of fiber which propagates with azimuthal phase dependence having well defined orbital angular momentum. The phase structure of vortex beam was detected by interfering both the beams using simple fiber-optic interferometer. The present all fiber-optic system might find application for detecting, sensing physical parameters and is simple and cost effective for generating and detecting optical vortices.     

Laser Mode-Dependent Size of Plasma Zones Induced by Femtosecond Laser Pulses in Fused Silica

We carry out the numerical simulations of femtosecond laser propagation with TEMoo mode, TEM10 mode and a beam combining both the modes in fused silica. It is found that the transverse size of plasma zones induced by laser pulses with the TEM10 mode is smaller than that induced by the TEM00 mode, while the longitudinal size is almost the same, and the saturated plasma density is higher. The transverse size, the longitudinal size and the ratio of the longitudinal to transverse size, for the beam combining both the modes, all could be reduced at the same time in comparison with the TEM00 mode under the same focusing conditions.     

平衡零拍平移测量实验研究

利用平衡零拍探测方法对TEM00模相干光激光束的微小平移进行一维测量的实验研究,实验装置最小可测平移量为0.3nm.实验验证了平移与倾斜这两个物理量之间的共轭关系.最后用模式重叠的概念分析了本底光偏离标准的TEM10模对测量结果的影响.实验结果与理论基本符合.     

基于拉盖尔-高斯光束的单光子捕获理论研究

基于TEM₁₀模拉盖尔-高斯光束,推导自由空间量子密钥分配中单光子捕获概率表达式。针对低轨卫星-地面站间激光链路进行单光子捕获分析。结果表明：采用可高度衰减激光脉冲的TEM₁₀模拉盖尔-高斯光束作为单光子源,单光子捕获采用前驱波参考脉冲设置时间窗口的方法,可使卫星上接收机以最大概率捕获光子。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增加单光子捕获概率的损耗。     

Operation of pulsed dye laser with an intracavity phase step

Effects of an intracavity phase step on the spectral and spatial characteristics of pulsed dye laser radiation are studied. In the broadband operation regime of the dye laser, the lasing spectrum was strongly, periodically modulated. In the narrowband regime, periodic alteration between TEM₀₀ and TEM₀₁-like beam profiles is observed on tuning the laser wavelength. Two different spectral periods of these effects are recognized. The shorter period corresponds to double passage and the longer one to apparent single passage of intracavity light through the phase step on a cavity round trip. Depending on the position of the phase step along the laser cavity, single-passage period, double-passage period, or a superposition of both periods appeared in the broadband emission spectrum and in the beam profile alteration sequence. These observations demonstrate several possibilities for the control of spectral, spatial, and phase characteristics of laser beams by simple intracavity phase elements.     

A study of the (00) LEED beam intensity at normal incidence from CdS(0001), Cu(001), Cu(111), and Ni(111)

A Faraday cage apparatus is used for the measurement of the (00) LEED beam intensity, I₍₀₀₎, and the total secondary emission coefficient, δ(E_k), for angles of incidence from 0° ± 2° to 8° ± 2°, with an energy resolution of ± 0.037 of the incident beam energy, in the energy range 1 to 200 eV. The data are normalized and expressed as a fraction of the incident beam intensity. The basic principle of operation is the separation of the incident and specularly diffracted beams in a uniform magnetic field. Monolayer, or in-plane, resonances associated with the emergence of nonspecular beams, as well as beam threshold minima, are observed in I₍₀₀₎ at normal incidence from clean CdS(0001), Cu(111), and Ni(111). Some major differences are observed in the I₍₀₀₎ profiles for the clean (111) surfaces of nickel and copper. All secondary Bragg peaks, except the 2$\text{2}\text{3}$ order, have greater intensities for Ni(111) in the energy range 50–150 eV, thus indicating that the atomic scattering cross-section for electrons in this energy range is larger for nickel than for copper. For the (111) surface of nickel, the (11) resonance is missing, but the (10) resonance and all $\text{1}\text{3}$ order secondary Bragg peaks between the second and fifth orders are observed. For Cu(111) both the (10) and (11) resonances are observed, but the $\text{1}\text{3}$, $\text{2}\text{3}$, 1$\text{2}\text{3}$, and 3$\text{1}\text{3}$ order secondary Bragg peaks are missing in this energy range. These data indicate that multiple scattering with evanescent intermediate waves, or “shadowing”, is predominate on the (111) surfaces on nickel and copper for energies above 30 eV, and that below 30 eV multiple scattering with propagating intermediate waves is predominate on Cu(111). Correlation of the (00) beam intensity profiles from clean Ni(111) at 0°, 2°, and 6° with the intensity profiles of the (10). (1&#x0304;0), and (11) non-specular beams is nearly one-to-one from 30 eV to 100 eV, thus supporting the dynamical theories of LEED in which peaks in the (00) beam are expected to occur at nearly the same energies as peaks in the non-specular beams.     

Performance of a zoom homogenizer for reshaping coherent laser beams

We have reshaped the TEM₀₀ beam emitted by a diode-pumped Nd-Yag laser by means of an optical homogenizer with zoom. The laser beam, first enlarged up to a size of (100 × 37.5) mm², is homogenized and resized to a final dimension continuously adjustable from (130 × 4.5) mm² up to (130 × 52) mm². We measured the plateau uniformity, the root mean square fluctuation and the edge steepness of the beam according to the ISO standard definitions, showing a poor reliability of the above parameter values due to the definitions themselves, and propose an amendment to overcome this problem. We obtained a very sharp edge steepness, but the spatial coherence of the laser beam put a lower limit to the high-frequency intensity fluctuations on the plateau region of the homogenized beam. Finally, we discuss the optimum homogenizer design for spatially coherent laser beams, including the depth of focus issue.     

Numerical investigation of relativistic self-focusing of intense laser beam with LG01 mode in plasmas

In this paper, we numerically investigate the relativistic self-focusing of laser beam with LG₀₁ mode in plasmas. An effective potential is introduced to identify the critical power. Numerical methods are employed to solve the governing equations. To verify the numerical procedures, we compare the known analytical solution of the relativistic critical power for TEM₀₀ mode with our numerical method. It is shown that there is a good agreement between our numerical results and the analytical solution. The critical power for relativistic self-focusing of a LG₀₁ laser beam is about 6 times of that for a TEM₀₀ laser beam.