Cylinder gauge measurement using a position sensitive detector

A position sensitive detector (PSD) has been used to determine the diameter of cylindrical pins based on the shift in a laser beam's centroid. The centroid of the light beam is defined here as the weighted average of position by the local intensity. A shift can be observed in the centroid of an otherwise axially symmetric light beam, which is partially obstructed. Additionally, the maximum shift in the centroid is a unique function of the obstructing cylinder diameter. Thus to determine the cylinder diameter, one only needs to detect this maximum shift as the cylinder is swept across the beam.     

Extinction paradox and actual power scattered in light beam scattering: a two-dimensional study

The extinction paradox is examined by applying partial-wave analysis to a two-dimensional light beam interacting with a long transverse cylinder without absorption, assuming always short wavelengths. We show that the (conventional) power scattered, Psca, except for a very narrow beam hitting a transparent cylinder on axis, is always double the power directly intercepted by the scatterer, Pitc, including a zero result for Psca when the incident beam is basically off the material surface. This contradicts the interpretation that attributes one half of Psca to edge diffraction by the scatterer. Furthermore, we identify the shadow-forming wave (SFW) from the partial-wave sum in the forward direction and show that the actual power scattered or, equivalently, the power depleted from the incident beam is equal to one unit of Pitc for a narrow beam, gets larger for a broader beam, and approaches 2Pitc for a very broad beam. The larger value in the latter cases is due to the extent of divergence of the SFW beam out of the incident beam at distances well beyond the Rayleigh range.     

Taper array in silica glass for beam splitting

We proposed taper array in silica glass for beam splitting which was fabricated by water-assisted femtosecond laser direct writing technology and the subsequent heat treatment. We divided the array into many fabricating cells which were executed automatically in sequences as specified by the program that contained the information for the three-dimensional stage movements. Each cell could fabricated a rectangular cylinder. The size and distribution of the rectangular cylinder could be controlled by adjusting the position of the fabricating cells. Then the heat treatment should be used to reshape the rectangular cylinders into taper array. The experimental results show that the taper periodic microstructures in silica glass are uniform and smooth, and the tapers can divide the incident light into beam array. The results demonstrated that the combination of the water-assisted femtosecond laser direct writing technology and the heat treatment is accessible and practical for the high quality micro-optical elements. These micro-optical elements will have potential applications in fluorescence detection and beam splitter.     

Calculating the pressure force of the non-paraxial cylindrical Gaussian beam exerted upon a homogeneous circular-shaped cylinder

Forces exerted upon a dielectric cylinder of infinite length and arbitrary, or circular, cross-section by the non-paraxial cylindrical Gaussian beam are considered. The projections of the vector of the light force pressure exerted upon a dielectric cylinder of arbitrary and circular cross-section are expressed analytically. In particular, the pressure force is expressed through the coefficients of decomposition of the non-paraxial Gaussian beam into the cylindrical functions. Using numerical examples, a possibility to optically trap a circular-shaped cylinder in two oppositely directed Gaussian beams or a single non-paraxial Gaussian beam is demonstrated.     

Three-dimensional diffraction of a thin metallic cylinder illuminated in conical incidence: application to diameter estimation

We present a model to determine the far-field diffraction pattern of a metallic cylinder of infinite length when it is illuminated in oblique incidence. This model is based on the Helmholtz-Kirchhoff integral using the Beckmann conditions for reflection. It considers the three-dimensional nature of the diffracting object as well as the material of which the cylinder is made. This model shows that the diffraction orders are placed in a cone of light. The amplitude at the far field can be divided into three terms: the first term accounts for Babinet's principle, that is, the contribution of the cylinder projection; the second term accounts for the three dimensionality of the cylinder; and the third term accounts for the material of which the cylinder is made. This model is applied to the diameter estimation of the cylinder. Since the amplitude of the Babinet contribution is much larger than the light reflected by the surface, the cylinder diameter can be obtained in a simple way. With this approximation, the locations of the diffraction minima do not vary when the cylinder is inclined. On the other hand, when the reflected light is considered the location of the minima and, hence, the estimation of the diameter, varies. Also, a modification of the diffraction minima is produced by the material of which the cylinder is made. Experimental results are also obtained that corroborate the theoretical approach.     

Fluorescence reabsorption calculation and influence on solid-state optical cooling

The calculation model of fluorescence reabsorption and reemission with consideration of reflection on the boundary and material size using Monte Carlo method is proposed. To validate this stochastic model, experiments were conducted, and the calculated steady state spectra showed a good agreement with measurements. Using the absorption and fluorescence spectra of Yb-doped phosphate glass by careful measurements and corrections, we calculated the redshift in the observed fluorescence spectra and external quantum efficiency caused by fluorescence reabsorption and re-emission for the samples with the geometries of cylinder and cuboid. The calculation results show that the fluorescence reabsorption and re-emission have significant influence on the cooling efficiency. The calculation results also show that the cylinder with small waist beam incident (the incident light beam diameter is much less than the size of the sample, and goes through the center of the sample) is suitable for optical cooling.     

Optical Bistability,Instability and Optical Computing

The formation of a cone-type light beam structure in an amplifying medium exhibiting the Kerr-type non-linearity and two-photon absorption is considered. The dependences of the relative diameter, contrast, and the position of the origin of a filamentary light region (that formed on the beam axis) on the active medium parameters are investigated. The effects of additional factors, such as a dielectric tube covering the active medium cylinder, the inhomogeneity of the medium amplification in the cross-section, and a saturable absorber mixed with the active medium on the light propagation pattern, are also discussed. Here, it is shown that a cone-type light beam structure is highly stable under the influence of such factors. It is noted that picosecond and sub-picosecond spectroscopy, including the study of multiphoton transitions and the measurement of the Kerr-type non-linearity constant in a medium on observation of a cone-type light beam structure, are possible.     

Acousto-optic interaction of a Gaussian laser beam with an ultrasonic wave of cylindrical symmetry

We present experimental studies of the interaction between a narrow Gaussian laser beam and a standing cylindrical ultrasonic wave. As a theoretical approach, a Fourier-optics-based successive diffraction model is used. Depending on the ratio of the Gaussian laser beam diameter to the first nodal diameter of the cylindrical ultrasound, light refraction or diffraction is observed. We experimentally investigate the time-averaged light intensity as well as the modulation of light in the far field of light refraction-diffraction by a cylindrical ultrasound. It is revealed that significant focusing appears if the phase front of the incident light is curved. The focusing effects of the acousto-optic system depend on the width of the laser beam and curvature of the phase front. Finally, possible applications are discussed.     

椭圆柱透镜组准直半导体激光束的优化设计

采用光线矢量法设计了两个相互垂直的椭圆截面柱透镜组来准直半导体激光束。利用多目标优化中的加权和法进行优化计算，并提出自适应加权系数优化法。此方法能根据计算结果自动调整加权系数，从而达到最佳的优化结果。计算结果表明，该准直系统可达到45μrad左右的发散角，远远优于其它截面柱透镜组（毫弧度数量级）的准直效果。同时两柱透镜间距取适当值，还可在远场形成圆形光宽。     

Effect of beam size parameters on internal fields in an infinite cylinder irradiated by an elliptical Gaussian beam

The scattered and internal fields of an infinite, homogeneous cylinder illuminated by a linearly polarized beam depend on the following parameters: the object size parameter of the cylinder (ka, where k=2pi/lambda, lambda is the wavelength of the incident beam in the surrounding medium, and a is the radius of cylinder), the complex relative refractive index of the object, the beam size parameters (komega(1) and komega(2), where omega(1), omega(2) are the representative beam dimensions), the angle between the cylinder axis and the Poynting vector of the incident wave, and the angle between the plane of polarization and the plane of incidence. Only when the dimensions of the beam are much greater than the cylinder diameter, and hence the portion of the beam interacting with the cylinder is essentially uniform, can the plane-wave solution be used in computing the scattered and internal fields. Hence a rigorous electromagnetic approach like the generalized Lorenz-Mie theory for spheres is used to study the effect of beam size parameters on the internal fields in an infinite cylinder irradiated by elliptical Gaussian beams. The significant effects of beam size parameters on the internal fields in an infinite cylinder are presented using specific cases of (1) resonance effects in a glass cylinder (ka=45.726, transverse-electric mode 53,3) and (2) a cylindrical microchannel (ka approximately 760) irradiated by a 632.8 nm laser beam.     

Observation of enhanced backscattering from a plane mirror viewed through polymer-film-dispersed liquid crystals

We report experimental results on enhanced backscattering from a plane mirror that is viewed through polymer-film-dispersed nematic liquid crystals. The distribution of the averaged intensity of the light reflected from the mirror placed behind the polymer film is investigated with an image-processing system when a Gaussian beam wave is incident. The enhanced light peak is observed in an incident beam direction, the result of which is predicted by a theory based on the circular Gaussian statistic random-phase-screen model. We pay attention to the enhancement dependence on parameters such as the distance between the polymer film and the flat mirror. The observed result is similar to a previous study by Jakeman et al. in which a random diffusive glass plate was used as a random-phase screen [J. Phys. D 21, 32 (1988)].     

Fraunhofer diffraction of a slit aperture between a knife-edge and a metal cylinder

The Fraunhofer diffraction pattern of a slit aperture formed between a reference knife-edge and a metal-cylinder surface is different from that of an ideal slit aperture. This pattern should include reflected light coming from both the front and rear sides of a cylinder surface. To investigate the influence of light reflected from the cylinder surface, we discuss the theoretical consideration based on the simple model of the reflected light on the surface. The experimental setup is designed and constructed to measure the actual diffraction pattern produced by the slit between the knife-edge and the cylinder surface. As a result it is obvious that the reflection of diffracted light on the rear side is dominant in both the simulation and the experiment.     

Scattering of a gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results

We present numerical results concerning the properties of the electromagnetic field scattered by an infinite circular cylinder illuminated by a circular Gaussian beam. The cylinder is arbitrarily located and arbitrarily oriented with respect to the illuminating Gaussian beam. Numerical evaluations are provided within the framework of a rigorous electromagnetic theory, the generalized Lorenz-Mie theory, for infinite cylinders. This theory provides new insights that could not be obtained from older formulations, i.e., geometrical optics and plane-wave scattering. In particular, some emphasis is laid on the waveguiding effect and on the rainbow phenomenon whose fine structure is hardly predictable by use of geometrical optics.     

Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system

The trajectory of the polarization state of a monochromatic light beam after it passes through a fixed linear polarizer and a rotating linear retarder of arbitrary retardance delta is determined on the Poincaré sphere. The three-dimensional figure-8 contour is shown to be the line of intersection of a right-circular cylinder with the sphere. The cylinder is parallel to the polar (S3) axis, touches the sphere at the equator (at the point that represents the linear polarization transmitted by the fixed polarizer), and has a radius r = sin2(delta/2). Projections of the trajectory in the coordinate planes of the normalized Stokes parameter space (s1, s2, S3) are also determined.     

Optical imaging with a directional detector

We demonstrate a new optical imaging technique based on a directional detector that measures the intensity of light waves that propagate only in a narrow angular window around a specific direction. Light waves that propagate in other directions do not significantly affect the detector output. The directional detector is obtained by illuminating the interrogated object with a high-coherence light source and measuring the interference between the light wave reflected from the object and a reference wave. By measuring the intensity of the interference pattern with an optical detector that has a finite width and moving the object by use of a rotation stage, one can obtain the angular directionality of the filter. The use of coherent detection in the directional detector makes it possible to increase the sensitivity of the system. The directional detector was analyzed theoretically and demonstrated experimentally for a Gaussian beam scattered from a conducting cylinder. The interference enabled us to theoretically increase the angular resolution by a factor of approximately 10 and experimentally by a factor of 8.5. A configuration for using a directional detector array to reconstruct a two-dimensional object is suggested. Since the directional detector makes it possible to reduce the effect of diffraction and scattering, reconstruction techniques based on nondiffracting sources, as implemented in x-ray tomography, may be used.     

Continuous phase plate for laser beam smoothing

We discuss the beam smoothing principle of a continuous phase plate (CPP) while the input light is varying. The analysis model of the process in which the laser beam with random phase noise propagates through a CPP has been established. With this model the beam smoothing mechanism of the CPP for the laser beam with a different phase aberrations can be described. A method to optimize the smoothing result is introduced.     

Numerical Analysis of Parameters in a Laminated Beam Model by Radial Basis Functions

In this paper we investigate a thermal driven Micro-Electrical-Mechanical system which was originally designed for inkjet printer to precisely deliver small ink droplets onto paper. In the model, a tiny free-ended beam of metal bends and projects ink onto paper. The model is solved by using the recently developed radial basis functions method. We establish the accuracy of the proposed approach by comparing the numerical results with reported experimental data. Numerical simulations indicate that a light (low composite mass) beam is more stable as it does not oscillate much. A soft (low rigidity) beam results in a higher rate of deflection, when compared to a high rigidity one. Effects caused by the values of physical parameters are also studied. Finally, we give a prediction on the optimal time for the second current pulse which results in maximum rate of second deflection of the beam.     

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.     

Modulation depth of Michelson interferometer with Gaussian beam

Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.     

Optical response of a single spherical particle in a tightly focused light beam: application to the spatial modulation spectroscopy technique

We develop a new and numerically efficient formalism to describe the general problem of the scattering and absorption of light by a spherical metal or dielectric particle illuminated by a tightly focused beam. The theory is based on (i) the generalized Mie theory equations, (ii) the plane-wave decomposition of the converging light beam, and (iii) the expansion of a plane wave in terms of vector spherical harmonics. The predictions of the model are illustrated in the case of silver nanoparticles. The results are compared with the Mie theory in the local approximation. Finally, some effects related to the convergence of the beam are analyzed in the context of experiments based on the spatial modulation spectroscopy technique.