Kinoform design with an optimal-rotation-angle method

Kinoforms (i.e., computer-generated phase holograms) are designed with a new algorithm, the optimalrotation- angle method, in the paraxial domain. This is a direct Fourier method (i.e., no inverse transform is performed) in which the height of the kinoform relief in each discrete point is chosen so that the diffraction efficiency is increased. The optimal-rotation-angle algorithm has a straightforward geometrical interpretation. It yields excellent results close to, or better than, those obtained with other state-of-the-art methods. The optimal-rotation-angle algorithm can easily be modified to take different restraints into account; as an example, phase-swing-restricted kinoforms, which distribute the light into a number of equally bright spots (so called fan-outs), were designed. The phase-swing restriction lowers the efficiency, but the uniformity can still be made almost perfect.     

Homogeneous and evanescent contributions in scalar near-field diffraction

The contributions of homogeneous and evanescent waves to two-dimensional near-field diffraction patterns of scalar optical fields are examined in detail. The total plane-integrated intensities of the two contributions are introduced as convenient measures of their relative importance. As an example, the diffraction of a plane wave by a slit is considered.     

Description of the propagation of a radially polarized beam with the scalar Kirchhoff diffraction

Since radially polarized beams have only one magnetic field component, the azimuthal component, a scalar Kirchhoff diffraction integral can be used to describe the propagation of the magnetic field. In the far-field zone, this diffraction formula gives an analytic expression for the magnetic field from which the electric field component expressions are derived by the Faraday relation. Numerical results from these expressions correctly reflect the properties of a radially polarized beam.     

Exact analysis of the effects of sampling of the scalar diffraction field

If the sampled diffraction pattern due to a planar object is used to reconstruct the object pattern by backpropagation, the obtained pattern is no longer the same as the original. The effect of such sampling on the reconstruction is analyzed. The formulation uses the plane-wave expansion, and therefore the provided solution is exact for wave propagation in media where scalar wave propagation is valid. In contrast to the sampling effects under the Fresnel approximation, the exact solution indicates that there are no modulated replicas of the original object in the reconstructed pattern. Rather, the distortion is in the form of modulated, translated, and dispersed versions of the original.     

Computer simulation of the scatter plate interferometer by scalar diffraction theory

Detailed computer simulations of the scatter plate interferometer with random scatterers in the scatter plate are performed, for the first time to our knowledge, by use of the scalar diffraction theory in the paraxial domain. It is shown that the computer simulations produce output image patterns of the expected qualitative characteristics. A qualitative comparison of the computed pattern with the experimentally observed pattern is presented. The effects of translation of the scatter plate and distortion and tilting of the test object are also successfully simulated by the computer.     

High-aperture diffraction of a scalar, off-axis Gaussian beam

A scalar treatment for Gaussian beams offset from the optic axis and then focused by a high-numerical-aperture lens is presented. Such a theory is required for describing certain types of Doppler microscopes, i.e., when the measurement is simultaneously performed by more than a single beam axially offset and then focused by a lens. Analytic expressions for the intensity in the focal region of the high-aperture lens are derived. From these expressions we calculate the intensity in the focal region with parameters of beam size, beam offset, and the numerical aperture of the lens. The relative location and variation of the intensity around the focal region are discussed in detail. We show that for small-diameter Gaussian beams the Strehl ratio increases above unity as the beam is offset from the optic axis. This is explained by the increase in the effective numerical aperture of the offset beam compared with the one collinear with the optic axis. From examining the focal distribution, we conclude that it rotates for small beam size and that increasing beam diameter causes the focused distribution to rotate and shear, i.e., to distort. We also show that the distortion of the distribution increases with increasing numerical aperture.     

Interlacing technique approach for the synthesis of kinoforms

An interlacing technique algorithm is proposed for the synthesis of kinoforms. The conventional iterative methods are quite powerful for optimizing kinoforms, but there is still a large reconstruction error for a quantized kinoform. We suggest the use of a number of subkinoforms interlaced together to synthesize a multikinoform for reconstructing the desired image. The idea of our interlacing technique is to increase the size of a kinoform to reduce the reconstruction error. The first subkinoform is generated from the desired image. Other subkinoforms are generated from the error images between the desired image and the image reconstructed from the previous subkinoforms. A theoretical analysis shows that the reconstruction error will be reduced as the number of subkinoforms is increased. Simulation results show that our interlacing method can reduce the reconstruction error more than do the conventional iterative methods and that the reconstructed image can be improved.     

Diffracted radiance: a fundamental quantity in nonparaxial scalar diffraction theory

Most authors include a paraxial (small-angle) limitation in their discussion of diffracted wave fields. This paraxial limitation severely limits the conditions under which diffraction behavior is adequately described. A linear systems approach to modeling nonparaxial scalar diffraction theory is developed by normalization of the spatial variables by the wavelength of light and by recognition that the reciprocal variables in Fourier transform space are the direction cosines of the propagation vectors of the resulting angular spectrum of plane waves. It is then shown that wide-angle scalar diffraction phenomena are shift invariant with respect to changes in the incident angle only in direction cosine space. Furthermore, it is the diffracted radiance (not the intensity or the irradiance) that is shift invariant in direction cosine space. This realization greatly extends the range of parameters over which simple Fourier techniques can be used to make accurate calculations concerning wide-angle diffraction phenomena. Diffraction-grating behavior and surface-scattering effects are two diffraction phenomena that are not limited to the paraxial region and benefit greatly from this new development.     

Holographic femtosecond laser processing using optimal-rotation-angle method with compensation of spatial frequency response of liquid crystal spatial light modulator

Holographic femtosecond laser processing performs high-speed parallel processing using a computer-generated hologram (CGH) displayed on a liquid crystal spatial light modulator. A critical issue is to precisely control the intensities of the diffraction peaks of the CGH. We propose a method of compensating for the spatial frequency response in the design of CGH using the optimal-rotation-angle method. By applying the proposed method, the uniformity of the diffraction peaks was improved. We demonstrate holographic femtosecond laser processing with two-dimensional and three-dimensional parallelism.     

Direct inclusion of the proximity effect in the calculation of kinoforms

Within the direct inclusion method the proximity effect is already taken care of when one calculates the kinoform relief, whereas conventionally the proximity effect is compensated for after one has calculated the relief. In particular, when proximity effects are considerable, that is, for small structures, the direct inclusion method is shown to give significantly better results than the conventional two-step method. Provided that the proximity effect is correctly modeled, it is shown that for an 8 × 8 array illuminator nearly perfect uniformity can be achieved even for a kinoform with very small structures.     

Analysis of diffraction gratings by using an edge element method

Typically the grating problem is formulated for TE and TM polarizations by using, respectively, the electric and magnetic fields aligned with the grating wall and perpendicular to the plane of incidence, and this leads to a one-field-component problem. For some grating profiles such as metallic gratings with a triangular profile, the prediction of TM polarization by using a standard finite-element method experiences a slower convergence rate, and this reduces the accuracy of the computed results and also introduces a numerical polarization effect. This discrepancy cannot be seen as a simple numerical issue, since it has been observed for different types of numerical methods based on the classical formulation. Hence an alternative formulation is proposed, where the grating problem is modeled by taking the electric field as unknown for TM polarization. The application of this idea to both TE and TM polarizations leads to a two-field-component problem. The purpose of the paper is to propose an edge finite-element method to solve this wave problem. A comparison of the results of the proposed formulation and the classical formulation shows improvement and robustness in the new approach.     

Analysis of the influence of the passive facet of blazed transmission gratings in the intermediate diffraction regime

Blazed diffraction gratings are of enormous practical importance for imaging and analyzing hybrid optical systems. The intermediate diffraction regime is characterized by the transition from the scalar to the rigorous electromagnetic theory. An effect known as shadowing occurs and reduces the diffraction efficiency. Based on rigorous calculations for optimized sawtooth-shaped and binary-multilevel blaze profiles, we deduce a semianalytical model describing the shadowing phenomenon for the general case of oblique incidence. We discuss illumination both from air and from the substrate. Though a multilevel blaze possesses a discrete substructure, our shadowing model remains valid, if substructural effects are neglected. We find that electromagnetic effects due to the passive blaze facet lead to the efficiency reduction, and the blazing efficiency shows a linear dependence on the ratio of blaze wavelength to grating period. Our shadowing model is applied to predict the performance of a Littrow-like blazing condition in transmission geometry as, e.g., for a diffractive solid immersion lens.     

Experimental characterization of subwavelength diffraction gratings by an inverse-scattering neural method

Characterization of gratings with small period-to-wavelength ratios is difficult to perform but is very helpful in improving the fabrication process. We experimentally tested an inverse-scattering method using a neural network on silicon etched gratings. We also characterized the gratings by using two popular microscopic methods. The validity of each method was determined by comparing measured diffracted intensities with calculated ones obtained from measured profiles. An estimation of accuracy and repeatability was deduced from a scan along a grating sample. This method was thus well validated for nondestructive and noninvasive measurements under experimental conditions that were close conditions of actual usage. This method is easy to implement and requires the measurement of only a few diffracted intensities.     

Error of the diffraction method of measuring microholes with local defects

Translated from Izmeritel'naya Tekhnika, No. 11, pp. 19–21, November, 1988.     

Measuring and modeling the proximity effect in direct-write electron-beam lithography kinoforms

The proximity effect in successively developed direct-write electron-beam lithography gratings is measured. The grating relief shapes are obtained from the measured power in several of the gratings' diffraction orders. Describing the proximity effect by a convolution with a double Gaussian point-spread function, we determine the parameters of the point-spread function. The writing part of the point-spread function is found to increase significantly with increasing development time, the background part much less.     

An integral equation method for the diffraction of oblique waves by an infinite cylinder

A hybrid integral equation method is formulated to study the diffraction of oblique waves by an infinite cylinder. The water depth and the geometry of the floating cylinder are assumed to be uniform in the y-direction (one of the horizontal axes). Numerical discretization and integrations are performed in the vertical plane. Analytical solutions are used in far fields such that radiation boundary conditions are satisfied. Numerical results are obtained for the case of wave scattering by a floating rectangular cylinder in a constant water depth. The accuracy and efficiency of present method are compared with those obtained by other numerical techniques.