Laser-machining experiment with an excimer laser and a kinoform

We have used a kinoform to increase the beam-power utilization in an excimer-laser-machining experiment. The kinoform creates the pattern to be machined. Thus less power is wasted on the blocking parts of a shadow mask. To achieve as smooth an intensity profile as possible, the kinoform was also used together with a microlens-array beam homogenizer. We discuss the intensity distributions of the patterns created by the kinoform with and without the beam homogenizer as well as the design of the kinoform and the homogenizer, with emphasis on the relation to the coherence properties of the laser beam.     

Optimization of kinoform lenses with the Monte Carlo method

For the optimization of non-Fourier-type computer-generated phase holograms (kinoform lenses), a method based on the Monte Carlo procedure is suggested. This method can be regarded as analogous to the iterative Fourier transform algorithm method that is widely used for the optimization of Fourier-type computer-generated phase holograms (kinoforms).     

Analysis and observation of finite beam Bragg diffraction by a thick planar phase grating

A numerical-impulse-response technique for studying the propagation and diffraction of finite-width beams in planar phase gratings is described. It can account for both symmetric and asymmetric diffractions. The grating-length-to-beam-width ratio is shown to govern the extent of beam-profile distortion and selectivity sidelobe suppression. Trade-offs between diffraction efficiency and beam profile have also been demonstrated. Theoretical results have been verified by experimental observations in a planar waveguide geometry of diffracted beams that change from a single diffraction peak to multiple peaks as the grating-length-to-beam-width ratio increases.     

Spectrum leveling by an iterative algorithm with a dummy area for synthesizing the kinoform

This paper describes a new iterative algorithm for synthesizing the kinoform so that the Fourier spectrum of an object is leveled by adjusting the information of a dummy area introduced into the object's domain, spatially isolated from the signal area. Theoretical consideration of the effect of the dummy area derives the required size of the dummy area, and computer simulations prove it to be valid, although restricted to an object composed of binary numbers. Also, it is shown that highly efficient use of the incident light is possible to achieve. Experimental results verify the proposed scheme.     

Speckle-noise reduction on kinoform reconstruction using a phase-only spatial light modulator

Random-phase distributions that are statistically independent individually are used for computing kinoforms. These uncorrelated kinoforms are recorded and read out sequentially by a phase-only liquid-crystal spatial light modulator, and reconstructed images with well-developed speckles are added. The fidelity of the resultant image to an original is improved as the number of additions increases. The dependence of the speckle contrast on the initial random phase and the influence of the liquid-crystal spatial light modulator's display performance on the image quality are discussed.     

Optically heterodyned 25-GHz true-time-delay lines on thick LD-3 polymer-based planar waveguides

Synthesis of the LD-3 electro-optic polymer has resulted in a highly reliable nonlinear organic material. Such a success has been impeded from further progress because the LD-3 films produced thus far are too thin (<0.5 mum) to form a waveguide. Further details of material synthesis have to be studied to solve this problem. We report the formation of thick LD-3 films ranging from 1.2 to 2.4 mum by introducing cyclopentanone as the new solvent in polymer synthesis. The formation of multimode planar waveguides on silicon with a waveguide loss of approximately 1.3 dB/cm at 1.3 mum is demonstrated. Preliminary studies aimed at forming true-time-delay lines are conducted by use of various waveguide lengths in conjunction with an optical heterodyne technique. Waveguide settings equivalent to different true-time-delay lines with a delay time of up to 0.27 ns and a base bandwidth of 25 GHz are demonstrated with a signal-to-noise ratio of 15 dB.     

Plastic zone in a thick layer with a disc-shaped crack

Summary The width of the annulus of plastic deformations for a layer of ideally elasto-plastic material with a very thin plastic zone has been discussed. The problem reduces to a Fredholm integral equation of the second kind, with the upper limit to be determined by a trial-and-error method from the condition of finiteness of the normal stress. The expression for the width of plastic zone has been found. The distribution of stresses is given in diagrams and its behavior discussed.

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Zusammenfassung Es wurde die Weite eines Ringes einer plastischen Veränderung in einer Schicht von idealem, elastisch-plastischem Material mit einer sehr dünnen plastischen Zone, untersucht. Das Problem verringerte sich zu einer Fredholm Integralgleichung zweiter Ordnung. Die obere Grenze wurde durch eine Versuchs- und Fehlermethode auf den Gebrauchszustand des normalen Druckes bestimmt. Die Formel für die Weite der plastischen Zone wurde gefunden. Die Verteilung der Drucke ist in einem Diagram gezeigt und ihr Verhalten wurde besprochen.

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Résumé Dans l'ouvrage on a discuté la largeur d'un anneau des déformations plastiques dans une couche d'un matériau élastoplastique avec une zone plastique très mince. Le problème est réduit à une equation intégrale de Fredholm de deuxième ordre, avee la limite supérieure déterminée par la méthode des essais successifs, appliquée sur la base d'une condition, que les contraintes normales ont des valeurs finies. Les formules pour la largeur de la zône plastique ont ététabliés et la répartition des contraintes est discutèe et prèsentée sur les graphiques.

     

基于拉伸振动精确化理论求解含孔厚板弹性波散射问题

针对采用弹性力学平面问题求解波动/振动时常产生较大误差的问题,基于厚板拉伸振动精确化方程,采用复变函数方法对含孔平板中弹性波散射与动应力集中问题进行了研究。利用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解。给出了含椭圆孔厚板拉压弹性波散射与动应力集中的数值结果。研究结果表明:动应力集中系数与分布取决于入射波数、平板厚度、椭圆偏心率等无量纲化参数。     

Modes of a planar waveguide with Fermi index profile

The wave equation of a planar waveguide with Fermi refractive-index profile is treated theoretically. An analytical solution has been obtained in terms of hypergeometric functions. It has been shown that the dispersion equation can be expressed as an infinite series of functions of modal index which converges rapidly. Highly accurate results can be obtained by taking the zero-order approximation only.     

Solid-state laser pumping with a planar compound parabolic concentrator

A novel solid-state laser-pumping scheme is proposed that combines a reflective lamp chamber and a compound parabolic concentrator (CPC) as a light guide. The CPC is made of a transparent material of high refractive index, and light is guided by the total internal reflection, with drastically reduced reflection losses. Material is chosen so that the absorption losses are minimized in the pumping wavelength range. The lamp chamber is designed with the principles of nonimaging optics, which ensures that the radiation is efficiently transferred from the lamp to the input aperture of the CPC. The pumping efficiency was first estimated theoretically, which gave us enough justification for the more accurate calculations with ray tracing. Single as well as multiple pumping cavities are discussed. New pumping geometry results in significantly increased pumping efficiency compared with conventional geometries. Also the lamp and the laser rod are separated, leading to reduced thermal load. We found that the proposed pumping method is also applicable to diode-pumped lasers.     

Stresses in a thick plate with a circular hole under axisymmetric loading

An exact theoretical solution is given for the stresses and displacements in an infinite plate of finite thickness having a circular hole and subjected to axisymmetric normal leading. The solution is given in the form of Fourier-Bessel series and integral. Numerical results are given for stresses in plates having different thickness to hole diameter ratios and loadings. The results are compared with the available approximate theoretical and experimental results.     

Axial and Extra-axial Responses in Aberrated Optical Systems with Apodizers. Optimization of the Strehl Ratio

Abstract

The effect of non-uniform transmission filters on the axial and extra-axial responses of aberrated optical systems is studied. The axial Strehl ratio (SR) is increased by varying the filter transmission function and the extra-axial SR by shifting the filter position along the axis of the optical system. It is shown that a filter which optimizes the axial SR can also improve the extra-axial SR. There are some positions of the filter for which the total results are improved. These positions are explained from the lack of radial symmetry of the wave aberration. The filters which improve the SR are also studied in terms of energy transmission.     

Light propagation in a planar dielectric waveguide with a gyrotropic layer

The nature of the magneto-optic Kerr effect in a planar dielectric waveguide geometry has been investigated by calculation of the Jones matrix for a planar waveguide structure with a gyrotropic magnetic material as one wall. The intensity of the component of the field that is in the polarization state orthogonal to the input was calculated as a function of length of the gyrotropic material and input polarization state. The degree of polarization rotation depends on the relative orientation of the magnetization in the magnetic material and the direction of propagation. It is found that there exists an optimal waveguide length and input polarization at which the output signal is maximized and that a significant enhancement in polarization rotation is available with respect to free-space reflection. These results indicate that a magnetic-film-bounded planar waveguide can be used for device applications such as magnetic field sensors or magneto-optic modulators.     

Simultaneous machining of parallel grooves in SnO(2) thin films using a Nd:YAG laser and a kinoform

A kinoform is used to split the beam of a Nd:YAG laser into six beams. The laser beams are, by means of optical fibers and collimating-focusing optics, transferred to the surface to be machined. Thus multiple grooves can be machined simultaneously. For demonstration, 100-μm-wide grooves are simultaneously machined into a SnO(2) thin film deposited on a glass substrate. The resulting grooves are well isolated. This result shows that the technique could be used, for example, in solar cell manufacturing to increase the efficiency of laser scribing.     

Optical design of a stigmatic extreme-ultraviolet spectroscopic system for emission and absorption studies of laser-produced plasmas

The design of a stigmatic spectroscopic system for diagnostics of laser-produced plasmas in the 2.5-40-nm region is presented. The system consists of a grazing-incidence toroidal mirror that focuses the radiation emitted by a laser-produced plasma onto the entrance slit of a spectrograph. The latter has a grazing-incidence spherical variable-line-spaced grating with flat-field properties coupled to a spherical focusing mirror that compensates for the astigmatism. The mirror is crossed with respect to the grating; i.e., it is mounted with its tangential plane coincident with the equatorial plane of the grating. The spectrum is acquired by an extreme-UV- (EUV-) enhanced CCD detector with high quantum efficiency. This stigmatic design also has spectral and spatial resolution capability for extended sources: The spectral resolution is also preserved for off-plane points, whereas the spatial resolution decreases for points far from the optical axis. The expected performance is presented and compared with that of a stigmatic design with a plane variable-line-spaced grating illuminated in converging light.     

M-type thick holograms in bacteriorhodopsin films with a high-divergence reference beam

The capacity to use differing read and write wavelengths for reconstructing volume holograms recorded in a shift-multiplexing geometry is analyzed and realized for M-type volume holograms recorded on bacteriorhodopsin films. The intensity distribution in the reconstructed wave is calculated as a function of the parameters of the recording and readout beams. Optimal recording and retrieving geometries, as well as a precise method for tuning the readout setup, are suggested.     

Synthesis of thick optical thin-film filters with a layer-peeling inverse-scattering algorithm

We present an efficient and accurate method for synthesis of optical thin-film structures. The method is based on a differential inverse-scattering algorithm and considers therefore both phase and amplitude reflectance data. We apply the algorithm to the synthesis of filters with arbitrary index layers and two-material filters consisting of only high- and low-index layers. The layered structure is approximated by a stack of discrete reflectors with equal distance between all reflectors. This mirror stack is in turn determined from the desired, complex reflection spectrum by a layer-peeling inverse-scattering algorithm. The complexity of the design algorithm is approximately the same as that of the forward problem of computing the spectrum from a known structure.     

Axisymmetric stress distribution in a transversely isotropic thick plate with a circular hole

Summary An exact solution for the stresses in a transversely isotropic infinite thick plate having a circular hole and subjected to axisymmetric uniformly distributed load on the plane surfaces has been given. The solution is in the form of Fourier-Bessel series and integrals. Numerical results for the stresses are given using the elastic constants for magnesium, and are compared with the isotropic case.

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Achsensymmetrische Spannungsverteilung in einer transversal isotropen, dicken Platte mit einem kreisförmigen Loch

Zusammenfassung Eine exakte Lösung für die Spannungen in einer transversal isotropen, unendlich ausgedehnten, dicken Platte mit einem kreisförmigen Loch, belastet durch eine achsensymmetrische, gleichmäßig verteilte Last an der ebenen Oberfläche, wird angegeben. Die Lösung ist in Form von Fourier-Bessel Reihen und Integralen dargestellt. Numerische Ergebnisse für die Spannungen werden unter Verwendung der elastischen Konstanten für Magnesium angegeben und mit dem isotropen Fall verglichen.

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With 4 Figures