Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane

Formulas are derived for the diffraction of a three-dimensional electromagnetic Gaussian beam by a perfectly conducting half-plane. The beam can be incident from any direction, and the main component of the electric field can point in any direction on the plane of the beam waist. The center of the beam waist is on the edge of the half-plane. The incident beam is constructed as a superposition of plane waves, and the total diffracted field is obtained from a superposition of the diffracted fields that are due to each plane wave. Physical constraints that limit the size and direction of the beam relative to the half-plane are described and incorporated into the theory. The scattered field in the far zone is obtained by asymptotic evaluation of the general formulas. Graphical results for the near-field as well as far-field patterns are presented and discussed.     

Second-harmonic diffraction from holographic volume grating

The full polarization property of holographic volume-grating enhanced second-harmonic diffraction (SHD) is investigated theoretically. The nonlinear coefficient is derived from a simple atomic model of the material. By using a simple volume-grating model, the SHD fields and Mueller matrices are first derived. The SHD phase-mismatching effect for a thick sample is analytically investigated. This theory is justified by fitting with published experimental SHD data of thin-film samples. The SHD of an existing polymethyl methacrylate (PMMA) holographic 2-mm-thick volume-grating sample is investigated. This sample has two strong coupling linear diffraction peaks and five SHD peaks. The splitting of SHD peaks is due to the phase-mismatching effect. The detector sensitivity and laser power needed to measure these peak signals are quantitatively estimated.     

Wavefront distortion of the reflected and diffracted beams produced by the thermoelastic deformation of a diffraction grating heated by a Gaussian laser beam

It may be advantageous in advanced gravitational-wave detectors to replace conventional beam splitters and Fabry-Perot input mirrors with diffractive elements. In each of these applications, the wavefront distortions produced by the absorption and subsequent heating of the grating can limit the maximum useful optical power. We present data on the wavefront distortions induced in a laser probe beam for both the reflected and diffracted beams from a grating that is heated by a Gaussian laser beam and compare these results to a simple theory of the wavefront distortions induced by thermoelastic deformations.     

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.     

Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Expressions describing the vortex beams that are generated by the process of Fresnel diffraction of a Gaussian beam incident out of waist on fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer diffraction by these gratings, are deduced. The common general transmission function of the gratings is defined and specialized for the cases of amplitude holograms, binary amplitude gratings, and their phase versions. Optical vortex beams, or carriers of phase singularity with charges mp and -mp, are the higher negative and positive diffraction-order beams. The radial part of their wave amplitudes is described by the product of the mpth-order Gauss-doughnut function and a Kummer function, or by the first-order Gauss-doughnut function and the difference of two modified Bessel functions whose orders do not match the singularity charge value. The wave amplitude and the intensity distributions are discussed for the near and far fields in the focal plane of a convergent lens, as well as the specialization of the results when the grating charge p=0; i.e., the grating turns from forked into rectilinear. The analytical expressions for the vortex radii are also discussed.     

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.     

Polarization-selective beam splitter based on a highly efficient simple binary diffraction grating

A polarization beam splitter (PBS) based on a giant-reflection to zero-order (GIRO) grating is presented. The GIRO grating is a simple binary diffraction grating with parameters chosen such that the excited optical modes in the grating interfere constructively and destructively at the respective interfaces. This interference results in high-zero-order reflection (>99%) with a high polarization-selective extinction ratio (+/-30 dB). The grating shows a low aspect ratio. The GIRO PBS is theoretically and experimentally shown to be an adequate PBS for use as an optical isolator in combination with a quarter-wave plate in a CO2-laser system.     

Modeling the reflection of a laser beam by a deformed highly reflective volume bragg grating

A model is presented for analyzing volume Bragg gratings having large diffractive strength that may become distorted upon the passage of high-power laser light. One result of this analysis is that very little distortion in a volume Bragg grating can greatly reduce the reflectivity. This is a critical issue in the design of systems in which these devices are used to combine high-power laser beams.     

Secondary diffraction of diffracted Gaussian beam of laser radiation

The diffraction of a narrow Gaussian beam of laser radiation on mutually perpendicular edges of crossed, superimposed sharp wedge-shaped blades (safety razors) has been studied. The diffraction pattern observed on a flat screen behind the blades comprises a very bright central spot, which exhibits the structure of a “light network” with rectangular cells, and four groups of narrow bright bands that expand from the central spot toward the periphery and form a rectangular cross. The spatial frequency of light-field modulation on the screen can be controlled by varying the distance from the blades to screen.     

Polarization-dependent diffraction efficiency of a photorefractive volume grating and suppression of this efficiency

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.     

Three-dimensional acoustic radiation force of a eukaryotic cell arbitrarily positioned in a Gaussian beam

Expressions are derived for calculating the three-dimensional acoustic radiation force(ARF) on a multilayer microsphere positioned arbitrarily in a Gaussian beam. A theoretical model of a three-layer microsphere with a cell membrane, cytoplasm, and nucleus is established to study how particle geometry and position affect the three-dimensional ARF, and its results agree well with finite-elemen numerical results.The microsphere can be moved relative to the beam axis by changing its structure and p...     

Sensing a wave front by use of a diffraction grating

A method is presented to sense the wave front at the exit of an optical surface. This method uses a set of diffracted rays generated when a He-Ne laser impinges on a rectangular diffraction grating. The grating was placed near the curvature center of the surface to be tested. After they are reflected in the test surface, the diffracted rays have the information of the slopes of the wave front, like in the Hartmann test. The Hartmann pattern was registered near the curvature center and captured with a CCD camera. The slopes for each ray are measured from the experimental pattern, and they are compared with the ideal ones simulated in a computer. The evaluation was carried out by use of Seidel polynomials to obtain the information of the aberrations of a mirror 53 cm in diameter.     

Diffraction of electromagnetic waves by a multielement diffraction grating

A rigorously posed electrodynamical problem of diffraction of a plane wave by a multielement diffraction grating that consists of cylindrical screens with arbitrary curvature is solved by the method of integral equations. We construct an integral representation of the Green function of the problem under consideration which gives a significant increase in the accuracy of calculations and investigate the phenomenon of resonance propagation of an electromagnetic wave along the axis of a two-layer grating irradiated with aE-polarized wave which propagates along the normal to the grating.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 2, pp. 87–98, March – April, 1995.     

Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition

We introduce a local signal decomposition method for the analysis of three-dimensional (3D) diffraction fields involving curved surfaces. We decompose a given field on a two-dimensional curved surface into a sum of properly shifted and modulated Gaussian-shaped elementary signals. Then we write the 3D diffraction field as a sum of Gaussian beams, each of which corresponds to a modulated Gaussian window function on the curved surface. The Gaussian beams are propagated according to a derived approximate expression that is based on the Rayleigh-Sommerfeld diffraction model. We assume that the given curved surface is smooth enough that the Gaussian window functions on it can be treated as written on planar patches. For the surfaces that satisfy this assumption, the simulation results show that the proposed method produces quite accurate 3D field solutions.     

Talbot effect by a photorefractive volume phase grating

In our proposal a light intensity distribution generated by an incoherently illuminated planar amplitude grating is projected into a photorefractive crystal. This 3D distribution is mapped as an index refractive perturbation via the photorefractive effect thereby generating a volume phase grating. The self-imaging phenomenon in the Fresnel field of this volume phase grating coherently illuminated is theoretically and experimentally analyzed. A model to simulate this volume grating that considers the 3D light intensity distribution formed in the crystal combined with the photorefractive grating formation theory is proposed. A path-integral approach to calculate the self-image patterns which account for the inhomogeneous propagation through the photorefractive grating is employed. The experimental and theoretical results show that the self-images location coincides with that of the self-images generated by planar phase grating of the same period. Moreover, the self-images visibility depends on three parameters: the exit pupil diameter of the incoherent recording optical system, the external electric field applied on the crystal, and the crystal thickness. To study the visibility behavior, a phase parameter which includes the three mentioned parameters is proposed. The self-images visibility shows the typical sinusoidal dependence found in planar phase grating. A good agreement between theoretical and experimental results is observed.     

Diffraction of a Gaussian beam by a logarithmic axicon

We derive an explicit analytical relationship to describe the axial light intensity when a Gaussian beam is diffracted by the logarithmic axicon (LA). An evaluation formula for the effective radius of the diffraction pattern that we deduce shows the said radius to be in inverse proportion to the LA "force" parameter. The finite-difference time-domain-based simulation has shown that using the LA makes it possible to go beyond the diffraction limit: in the LA vicinity, the FWHM of the light beam can be as small as one fifth of the illumination wavelength.     

Transducing mechanical force by use of a diffraction grating sensor

A novel means of transducing mechanical force by using a polymeric-based diffractive grating sensor is presented. The diffraction gratings are successfully fabricated upon poly(dimethyl siloxane) polymer substrates by holographic interference and micromolding. A micromaterial tensile test incorporated into the surface diffraction grating experiment showed that a relationship between the load and the observed diffraction-pattern shift could be obtained. The results show an excellent correlation between the optical measurement and load, with a sensitivity of 0.05 N.     

Analysis and design of a concave diffraction grating with total-internal-reflection facets by a hybrid diffraction method

A novel hybrid diffraction method is introduced to simulate the diffraction and imaging of a planar-integrated concave grating that has total internal reflection (TIR) facets. The Kirchhoff-Huygens diffraction formula is adopted to simulate the propagation of the lightwave field in the free-propagation region, and a rigorous coupled-wave analysis is used to calculate the polarization-dependent diffraction by the grating. The hybrid diffraction method can be used to analyze accurately the imaging properties as well as the polarization-dependent diffraction characteristics of a concave grating. The dependence of several merit parameters of a concave grating with TIR facets on its basic geometric parameters is studied. Compared with one with metallic echelle facets, a concave grating with TIR facets shows a much lower polarization-dependent loss. Since more performance specifications can be considered in the design of a concave grating than with the conventional scalar method, design error can be reduced greatly with the present hybrid diffraction method.     

Near-field anomalous spectral behavior in diffraction of a Gaussian pulsed beam from an annular aperture

Based on the Fresnel diffraction integral and by introducing a hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression for the near-field spectral intensity distribution of a space-time-dependent Gaussian pulsed beam passing through an annular aperture is derived, which permits us to study the on- and off-axis spectral anomalies that are near phase singularities of the diffracted Gaussian pulsed beam in the near-field. The expressions for a circular black screen and a circular aperture are given as special cases of the general results. The relative spectral shift of a space-time-dependent Gaussian pulsed beam versus the different values of the truncation parameters and the position parameters of observation points are also studied and illustrated with numerical calculations. It is shown that the spectral switch appears near phase singularities in the near-field, and the near-field spectral behavior depends on the truncation parameters, the pulse duration tau, and the position parameter. The results of this work have potential applications in free-space information encoding and transmission.