Measurement of nonlinear absorption coefficients of organic materials by mode-mismatched Z-scan thermal lensing technique

We evaluate a new pump-probe mode-mismatched thermal lens (TL) scheme for the measurement of nonlinear absorption in nitrobenzene, benzene, and chloroform. In this new scheme the pump beam is focused in the presence of a collimated probe beam. Values of the nonlinear absorption coefficients of the materials studied for the wavelength of 532 nm are reported, and we compare the proposed technique with the well-known open Z-scan method.     

Continuous-wave power transmission and thermal lensing of a saturable absorber subject to excited-state absorption

Rate-equation analysis has been used in an investigation of the role of saturation and excited-state absorption in the power transmission characteristics and thermal lensing of an absorber. Use of an iterative approach gives explicit analytical results for power transmission and thermal focal length in the presence of excited-state absorption. Sample calculations indicate that pump absorption can increase or decrease with increasing incident pump power, depending on the relative strength of the excited-state absorption cross section with respect to the ground-state absorption cross section. In the case of thermal lensing, results further indicate that saturation and excited-state absorption act as two competing effects, the former reducing the strength of the thermal lens and the latter causing the opposite effect. The analytical formulas derived in this analysis should prove useful to experimentalists in determination of ground-state and excited-state absorption cross sections from experimental power transmission and lensing data.     

Analytical approach to thermal lensing in end-pumped Yb:YAG thin-disk laser

Thermal lensing in the thin-disk laser influences the output beam quality and optical efficiency significantly. In this paper, an analytical approach is taken to study the production mechanisms, features, and influences of thermal lensing in the end-pumped thin-disk laser. We calculate the distributions of temperature, stress, strain, and expansion in the disk and the curvature of the crystal using an analytic method. The expressions of the thermal lens focal length depending on the radius are presented. The optical path difference, a major cause of thermal lensing, is induced by the thermo-optical effect, the photoelastic effect, and inhomogeneous distribution of thermal expansion and the excited population. Thermal lensing is found to be aspheric with undesired aberrations and birefringence effects. Furthermore, a convex mirror due to the axial temperature gradient occurs in a free disk, and the convex mirror is found to be spherical in the center region of the disk. Based on the results of our analysis, the aspect ratio and size of the laser mode of the gain region may be adjusted to limit the damaging effects of thermal lensing.     

Sensitivity analysis and shape optimization in nonlinear solid mechanics

The objective of this paper is twofold. First, it presents a boundary element formulation for sensitivity analysis for solid mechanics problems involving both material and geometric nonlinearities. The second focus is on the use of such sensitivities to obtain optimal design for problems of this class. Numerical examples include sensitivity analysis for small (material nonlinearities only) and large deformation problems. These numerical results are in good agreement with direct integration results. Further, by using these sensitivities, a shape optimization problem has been solved for a plate with a cutout involving only material nonlinearities. The difference between the optimal shapes of solids, undergoing purely elastic or elasto-viscoplastic deformation is shown clearly in this example.     

Light control through a nonlinear lensing effect in a colloid of biosynthesized gold nanoparticles

Biosynthesis of four samples of colloidal suspensions of gold nanoparticles is achieved using hydroalcoholic extract and three different separated compounds of the plant Bacopa procumbens. The nonlinear optical properties of each sample are characterized with the Z-scan technique. In all cases, the Z-scan curves indicate a negative or self-defocusing response, which is mainly attributed to thermal effects. Among the four samples, the hydroalcoholic extract was noted to have the highest nonlinear optical response and was selected to demonstrate the formation of self-collimated beams (SCBs). This kind of beams are obtained when a convergent CW laser, with only few tens of milliwatts of optical power, is introduced into the sample and induces a negative-lens effect that shifts the focal spot forward. As a result, the otherwise highly focused beam propagate with little divergence over lengths of up to 10?mm. Moreover, an SCB is capable of controlling and steering a weak probe beam of a different wavelength, since the probe experiences the lensing induced by the pump. Noteworthy, the response time of the material was found to be less than 0.07?s, which makes it a plausible candidate for photonic applications.     

Flexural analysis of cross-ply laminated plates subjected to nonlinear thermal and mechanical loadings

The objective of this paper is to present an equivalent single-layer shear deformation theory for evaluation of displacements and stresses of cross-ply laminated plates subjected to uniformly distributed nonlinear thermo-mechanical load. A trigonometric shear deformation theory is used. The in-plane displacement field uses a sinusoidal function in terms of the thickness coordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of a shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to uniformly distributed nonlinear thermo-mechanical load are obtained. Numerical results of the present theory for displacement and thermal stresses are compared with those of classical, first-order and higher-order shear deformation plate theories.     

Reduction methods for nonlinear steady-state thermal analysis

Hybrid analysis techniques based on the combined use of finite elements and the classical Bubnov–Galerkin approximation are presented for predicting nonlinear steady-state temperature distributions in structures and solids. In these hybrid techniques the modelling versatility of the finite element method is preserved and a substantial reduction in the number of degrees-of-freedom is achieved by expressing the vector of nodal temperatures as a linear combination of a small number of global-temperature modes, or basis vectors. The Bubnov–Galerkin technique is then used to compute the coefficients of the linear combination (i.e. the amplitudes of the global–temperature modes). The basis vectors chosen are the path derivatives commonly used in perturbation techniques, namely, the derivatives of the nodal–temperature vector with respect to a preselected control (or path) parameter(s). The vectors are generated by using the finite element model of the initial discretization. Also, the performance of alternate sets of basis vectors is investigated. In the alternate sets, only a few path derivatives are generated, and they are augmented by a constant vector representing a uniform temperature rise (or drop), and by reciprocal vectors with nonzero components equal to the reciprocals of the nonzero components of the path derivatives. A problem-adaptive computational algorithm is presented for efficient evaluation of global approximation vectors and generation of the reduced system of equations and for monitoring the accuracy of the reduced system of equations. The potential of the proposed reduction methods for the solution of large-scale, nonlinear steady-state thermal problems is also discussed. The effectiveness of these methods is demonstrated by means of four numerical examples, including conduction, convection and radiation modes of heat transfer. This study shows that the use of the uniform-temperature mode and the path derivatives as global approximation vectors significantly increases the accuracy of the solutions obtained by reduction methods, thereby enhancing the effectiveness of these methods for the solution of large-scale, nonlinear thermal problems.     

星载抛物面天线热变形敏感性分析

热变形是影响星载天线精度的主要因素,分析影响星载天线在轨热变形因素的敏感性是控制其变形的基础.基于经典薄壳变形理论,采用一种曲线坐标系下的样条壳体单元,研究了不同太阳辐射角度下抛物面天线热变形均方根(RMS)对正交各向热传导系数的敏感性.为确定计算参数对抛物面天线在运行中变形RMS的影响,以运行一周中最大RMS(MRMS)为目标,基于正交试验方法分析了正交各向热传导系数、热膨胀系数、弹性模量和比热容对MRMS的敏感性.结果表明,在其所取水平条件下,热膨胀系数影响最大,热传导系数次之,弹性模量的影响较小,比热容最小.优化获得的参数为星载抛物面天线的复合材料铺层设计提供参考.     

A simple optical analysis of gravitational lensing

We analysed the influence of a static gravitational field on the vacuum and discussed the concept of an inhomogeneous vacuum. According to the corresponding Fermat's principle in general relativity, we derived a graded refractive index of vacuum in a static gravitational field. We found that the light deflection in a gravitational field can be calculated correctly with the use of this refractive index and therefore the gravitational lensing can be treated conveniently with the optical method. For illustration, we simulated the imaging of gravitational lensing, figured out the time delay between the two images and calculated the lens mass in a conventional optical way.     

Sensitivity analysis of nonlinear vibration of AFM piezoelectric microcantilever in liquid

In this paper sensitivity analysis of nonlinear vibrating motion of atomic force microscope (AFM) piezoelectric microcantilever (MC) is performed in liquid environment. With respect to the importance of resonance amplitude and system nonlinearity in AFM application, sensitivity analysis of nonlinear vibrating motion is performed on these two parameters. The sensitivity analysis is carried out based on the Sobol statistical method. Piezoelectric MC has geometrical discontinuities due to presence of piezoelectric layer and tip. Regarding these discontinuities, non-uniform beam model is chosen for the dynamic modeling. Vibrating motion of the MC is modeled in AFM non-contact mode. The sensitivity analysis is performed to study how the effective parameters affect nonlinear vibrating motion in liquid. The sensitivity analysis of piezoelectric MC in liquid was compared with the one performed in air to better specify the effect of liquid environment on motion. The obtained results show that sensitivity of piezoelectric MC to nonlinearity of interaction force in air is greater than liquid and the sensitivity decreases with the increase of liquid density. With respect to the sensitivity analysis results, it can be concluded that the most effective geometrical parameters on nonlinearity in both air and liquid environments are thickness and length of piezoelectric layer and length of tip. The results of sensitivity analysis also show that the length of probe in liquid has a considerable effect on amplitude, whereas it has less effect on amplitude in air.     

Correction of birefringence and thermal lensing in nonreciprocal resonators by use of a dynamic imaging mirror

Enhanced correction of thermally induced birefringence in the presence of strong single-pass, azimuthally dependent bipolar focusing was achieved in single-rod laser oscillators by use of an adaptive optic rear mirror with image relay and aberration correction capabilities. Together with a Faraday rotator, the imaging variable radius mirror was successfully tested in stable and unstable Nd:Cr:GSGG power oscillators under variable pump power conditions from 0 to 800 W. Birefringence correction in the absence of ray retracing was achieved.     

Detection of separated analytes in subnanoliter volumes using coaxial thermal lensing

A collinear-beam thermal lens detector has been constructed and its properties were characterized. Its application to the high-performance liquid chromatography (HPLC) separation of a mixture of five anthraquinone dyes dissolved in water shows a linear response over 3.5 orders of magnitude and a detection limit that is subnanomolar in the dye concentrations. These results are compared with those obtained previously using cavity ring-down spectroscopy (CRDS) in a Brewster's angle flow cell (Bechtel, K. L.; Zare, R. N.; Kachanov, A. A.; Sanders, S. S.; Paldus, B. A. Anal. Chem. 2005, 77, 1177-1182). The peak-to-peak baseline noise of the thermal lensing detection is 3.5 x 10(-8) absorbance units (AU) with a path length of 200 microm, whereas the peak-to-peak baseline noise of CRDS detection is approximately 2 x 10(-7) AU with a path length of 300 microm. Both of these figures of merit should be compared to the peak-to-peak baseline noise of one of the best commercial UV-vis HPLC detection systems, which is approximately 5 x 10(-6) AU with a path length of 10 mm (1-s integration time). Therefore, the thermal lensing technique has a demonstrated sensitivity of subnanomolar detection that is approximately 140 times better than that of the best commercial UV-vis detector and approximately 5 times better than that of CRDS.     

Scattering and thermal lensing of 2.12- mum laser radiation in biological tissue

We studied light propagation of holmium:YAG laser radiation (lambda = 2.12 mum) by measuring the two-dimensional laser beam profile before and after propagation through a tissue sample with a modified fast-temperature-measurement technique. The comparison between water and cartilage tissue allowed us to differentiate between beam broadening caused by formation of a thermal lens and broadening due to light scattering. In water, beam propagation is influenced by formation of thermal lensing, whereas in cartilage the broadening was caused by a combination of light scattering and thermal lensing. Additionally, we discovered that the observed effects are subject to dynamic changes during the laser-tissue interaction.     

Control of the thermal lensing effect with different pump light distributions

We built a 32-laser-diode-formed virtual point source pumping system and achieved different pump light distributions from central intense to central uniform and central depressed. Continuous wave TEM(00) operations of a Nd:YAG laser were performed under these pump light distributions and their thermal lensing effects were estimated. Results show that the operation under central depressed pump light distribution has the lowest thermal lensing effect and can provide the highest output power, which agrees with the results derived from the theoretical calculation with the heat conduction equation.     

Sensitivity enhancement of a MEMS sensor in nonlinear regime

The aim of this study is to enhance the sensitivity of a micro electro mechanical Gyroscope in nonlinear regime. Sensitivity enhancement is achieved by applying appropriate Hoping voltages which pushes the micro-beam to the basin of attraction of a desired periodic attractor. The studied model is a silicon clamped–clamped micro beam actuated by an electrostatic voltage which is a combination of a constant DC and a harmonic AC voltage in the drive mode direction and a pure DC voltage in the direction of sense mode. The external angular velocity about the horizontal axis is used to create the Coriolis force along the sense mode. The governing differential equation of the motion is derived using Hamiltonian principle and discretized to two nonlinear Duffing type ODE’s using Galerkin method. Shooting method is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion. The stabilities of the periodic orbits are investigated by the Floquet theory. The results depict that the response of the system is highly affected by the applied DC and AC voltage; corresponding to a constant DC voltage, the more is the AC voltage, the more is the sensitivity. Based on the DC voltage the system exhibits both hardening and softening effects. The capacity of the capacitors is determined and the effects of the various applying Hoping voltages on capacity of them are investigated. The frequency response curve of the micro-beam for various quality factors are obtained and compared with the literature.     

北京正负电子对撞机重大改造工程超导腔恒温器静态热负荷分析

北京正负电子对撞机重大改造工程(BEPCII)采用了频率为500 MHz的单cell超导纯铌腔作为加速腔.通过有限元分析的方法对超导腔恒温器各部件进行热模拟和分析,并将模拟分析结果与超导腔的水平测试结果进行比较验证,确认数值分析结果为可信的,且得出对备用超导腔恒温器设计、加工和运行具有指导意义的结果.