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.     

Vector propagation of radially polarized Gaussian beams diffracted by an axicon

On the basis of the vectorial Rayleigh diffraction integrals and stationary-phase method, the analytic expression describing the vectorial field distribution of radially polarized Gaussian beams diffracted by an axicon is derived. The theoretical analysis and simulation calculation show that the radial component of the diffraction field is the propagation-invariant first-order Bessel beam when the radially polarized Gaussian beam illuminates the axicon. However, the longitudinal component possesses no such behavior because of its intrinsic r dependence, and its central intensity is the maximum. The longitudinal component is related to the open angle and index of the axicon, which has to be considered when the open angle and index are large. For a small open angle and index, the longitudinal component can be neglected, and the scalar approximation is valid.     

Diffraction of conic and Gaussian beams by a spiral phase plate

An analytical expression for the spatial spectrum of the conic wave diffracted by a spiral phase plate (SPP) with arbitrary integer singularity of order n is obtained. Conic wave diffraction by the SPP is equivalent to plane-wave diffraction by a helical axicon. A comparison of the conic wave and Gaussian beam diffraction on a SPP is made. It is shown that in both cases a light ring is formed, with the intensity function growing in proportion to rho(2n) at small values of radial variable rho and decreasing as n(2)rho(-4) at large rho. By use of direct e-beam writing on the resist, a 32 level SPP of the 2nd order and diameter 5 mm is manufactured. By use of this SPP, a He-Ne laser beam is transformed into a beam with phase singularity and ringlike intensity distribution. A four-order binary diffractive optical element (DOE) with its transmittance proportional to a linear superposition of four angular harmonics is also manufactured. With this DOE, simultaneous optical trapping of several polystyrene beads of diameter 5 microm is performed.     

Diffraction characteristics of spatial and temporal Gaussian-shaped femtosecond laser pulse by rectangle reflection grating

The exact intensity distribution expression for the spatial and temporal Gaussian-shaped femtosecond laser pulse diffracted by a rectangle reflection grating is derived. The spatial and temporal diffraction characteristics are theoretically investigated in detail, and a criterion for judging whether or not the diffraction pulse is just split into two independent pulses in the temporal domain is obtained. The results show that the diffraction intensity in the temporal domain consists of three parts: the intensity diffracted by the upper reflection surface of the grating, the intensity diffracted by the nether reflection surface, and their temporal coherent intensity. The temporal coherent intensity becomes weaker, even is zero, for the higher height from the nether surface to the upper surface of the grating. The principal maximum becomes more sharply bright for the bigger waist width of the femtosecond laser pulse in the spatial domain.     

Observation of self-diffraction effect in acid blue 7 dye soaked gelatin films

Abstract

Permanent self-diffraction gratings are formed in red sensitive Acid blue 7 dye soaked gelatin films under illumination of an interference pattern by two linearly polarized beams from a He-Ne laser at 632.8 nm. Growth of the self-diffraction grating is monitored by measuring intensities of various diffraction orders. Systematic studies are carried out to investigate the influence of various parameters involved in diffraction efficiency of the grating such as time of exposure, concentration of dye in the gelatin-coated plate, intensity of interfering beams and intensity ratio of interfering beams. Efficient gratings with ten diffracted orders are formed. Several interesting observations are made by blocking one of the writing beams and an attempt is made to analyse these results.     

Influences of twist phenomenon of partially coherent field with uniform-intensity diffractive axicons

The effects of twist phenomenon (beam rotation) of a partially coherent field are studied on the operation of two classes of uniform-intensity diffractive axicons. A general theory of axicon image formation is developed, discussed, and examined. We show that the intensity of the diffracted field is a multiple Bessel field, and only the energy of the zero-order Bessel field diffracts along the propagation axes. We also show that, at any twist strength in all correlation levels, the images can be evaluated by using the stationary-phase method. The three-dimensional stationary-phase formula of axicon images is derived. Such formula may be used in fast image evaluation, for designing diffractive axicons that perform a uniform axial intensity in a twisted partially coherent field.     

Gradient-index axicon lenses: a quasi-geometrical study

Unconventional imaging and focusing properties are obtained when odd powers of the radial coordinate are present in a radial gradient-index profile. We calculate the transmittance function for this kind of medium under a paraxial approximation by a quasi-geometrical approach. Likewise, we analyze the pupil effect; that is, we evaluate the intensity distribution diffracted by a gradient-index axicon at the image plane.     

Simple and rigorous analytical expression of the propagating field behind an axicon illuminated by an azimuthally polarized beam

A simple and rigorous analytical expression of the propagating field behind an axicon illuminated by an azimuthally polarized beam has been deduced by use of the vector interference theory. This analytical expression can easily be used to calculate accurately the propagation field distribution of azimuthally polarized beams throughout the whole space behind an axicon with any size base angle, not just restricted inside the geometric focal region as does the Fresnel diffraction integral. The numerical results show that the pattern of the beam produced by the azimuthally polarized Gaussian beam that passes through an axicon is a multiring, almost-equal-intensity, and propagation-invariant interference beam in the geometric focal region. The number of bright rings increases with the propagation distance, reaching its maximum at half of the geometric focal length and then decreasing. The intensity of bright rings gradually decreases with the propagation distance in the geometric focal region. However, in the far-field (noninterference) region, only one single-ring pattern is produced and the dark spot size expands rapidly with propagation distance.     

Uniformization of the axial intensity of diffraction axicons by polychromatic illumination

The axial intensity of axicons illuminated by a coherent wave usually exhibits rapid oscillations from diffraction on the sharp edges of the aperture of the element. These oscillations can be suppressed when the diffractive version of the axicon is illuminated from a polychromatic source. This possibility is examined based on the example of the annular-aperture logarithmic axicon. The estimate for the wavelength interval of the illuminating source required for uniformization is obtained with the help of the stationary-phase method. Furthermore the shape of the radial intensity distribution can be maintained almost unchanged. These findings are confirmed by numerical evaluation of the Fresnel diffraction integral.     

Computer Reconstruction of a Random Rough Surface in the Presence of Higher Diffraction Orders

Abstract

The profile of a random rough surface (RRS), whose mean roughness R_a is greater than the light wavelength, is visualized by computer processing. The surface is presented as a sum of sinusoidal gratings. The light diffracted from this surface field is registered by a photodiode array. The second and third diffraction orders from each grating are taken into account in computer processing of the diffracted field and the mixing field–the field obtained at the mixing of the reference and the diffraction fields. The criterion for taking into account higher diffraction orders is the asymmetry of the diffraction pattern to the left and to the right relative to the central peak (the field of zero diffraction orders obtained from each grating) The number of the diffraction orders higher than the first is defined from the average intensity distribution between the central peak and the diffraction orders to the left and to the right at arbitrary light wavelength. The surface profile is reconstructed by a computer program and the mean roughness R_a is calculated. The obtained value of R_a is in satisfactory agreement with that measured by the contact pin method.     

Mechanical and structural studies of low density polyethylene

During uniaxial orientation of low density polyethylene (LDPE) at 90 to 95°C some unusual structural changes occur, as revealed by wide and low angle X-ray diffraction. Quantitative measurements of diffracted intensity distributions have been made. At low draw ratios a novel 6-point low angle pattern appears which persists to extensions of over 300%. Cone distributions are present in all the crystal axis orientations, and these are superimposed on transverse components to give complex wide angle diffracted intensity profiles. A spherulite deformation model is proposed to explain these observations. At high draw ratios uniaxial crystal alignment obtains, but we find that the lamellar orientations differ between specimens annealed after drawing at room temperature and those drawn directly at the higher temperature. The implications of this observation are considered.     

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.     

Optical monitoring of the end point in thin film plasma etching

An in-process optical technique is described for accurately monitoring the end point in plasma etching processes. A grating pattern is lithographed somewhere in the film to be etched. The grating modulation decreases as the film is etched out and the process may be monitored by measuring the diffraction of a low power He-Ne laser beam aimed at the grating. The etching end point is accurately detected by the disappearance of all diffracted orders. The laser beam does not need to be directed at normal incidence and so any available plasma etching equipment is suitable. The detection is carried out with low cost photovoltaic detectors but simple visual inspection is satisfactory also.Comparative experimental results are presented.     

Image structure from mirrors with print-through undulations: theoretical analysis

The image structure produced by a periodic hexagonal pattern of mirror surface undulations has been analyzed. Such undulations form a two-dimensional phase grating that can result from the polishing of honeycomb mirrors or, for example, meniscus mirrors with a hexagonal pattern of axial supports. For monochromatic light of wavelength lambda, undulations having uniform peak-to-valley amplitude H ? lambda and period L cause a decrease in the central intensity of the point spread function (PSF), and a fraction, ~13(H/lambda)(2), of the total power is diffracted into an infinite hexagonal array of satellite images. These have angular separations of 2lambda/ radical3L and intensity profiles in the form of perfect diffraction limited PSF's, but with intensities decreasing with increasing diffraction order. The six innermost (first-order) satellites each have central intensities approximately 2(H/lambda)(2) times that of the central image. If the amplitudes of the surface bumps are of random size with a normal frequency distribution, then the intensity of the diffracted orders decreases, and an additional weak structure appears over the image plane; the positions and heights of the peaks in this grasslike structure depend on the particular two-dimensional distribution of the random bumps. When the input is polychromatic, the diffracted orders other than zero give images that are elongated radially and decrease outward in intensity with a 1/lambda(4) dependence.     

Diffraction by a subwavelength-sized aperture in a metal plane.

We present an experimental study on the diffraction of light by an aperture small compared with the wavelength. The aperture is illuminated by laser light guided in a metal-clad tapered optical fiber. We investigate different orientations of the aperture in the plane: normal to the cleaved plane, oblique to the cleaved plane, and off-center. We measure the far-field, two-dimensional intensity distributions of the diffracted light as functions of angle coordinates theta and phi in a full half-space for various polarization states and analyze the patterns by using low-order multipole fields. We also examine the near- and far-field effects of placing small periodic corrugations near the aperture, focusing on the role of surface-wave excitations. We measure the near-field intensity distributions near the aperture with a near-field scanning optical microscope and discuss their relation to the far-field diffracted fields.     

Thermal efficiency of pulsed laser radiation increased by methods of multibeam acousto-optic diffraction

Bragg multibeam acousto-optic diffraction of pulsed laser radiation (with 150-ns pulse duration) has been studied under conditions of significant overlap between the neighboring beams. It is established that the initial beam with a Gaussian angular distribution of intensity can be transformed into diffracted radiation with a nearly rectangular profile of intensity provided that the laser pulse duration is much shorter than the period of interference beats in the overlapping regions. Using this circumstance, it is possible to increase the efficiency of high-power lasers in material processing (laser cutting, welding, engraving, etc.) with a threshold character of the radiation effect. This possibility was experimentally verified for a fiber laser operating at a 1.07 μm wavelength.     

X射线衍射增宽现象的旋转矢量法描述

在x射线衍射分析中,衍射增宽对x射线衍射强度的计算和粉末（多晶体）粒经的测量十分重要。通过描述波振动的旋转矢量,采用几何方法简捷、直观地解释了衍射的增宽现象。同时也用代数法和倒易点阵法对该现象进行了解释。     

Novelty filter that uses a bacteriorhodopsin film

We propose a new novelty optical filter that uses a bacteriorhodopsin film. This filter is based on the time-dependent nonlinear diffraction efficiency of real-time holograms recorded in the film. As soon as the signal beam carrying a pattern is diffracted by the polarization hologram recorded in the bacteriorhodopsin film, it begins to erase the hologram and suppresses the diffraction of the beam at the position of the stationary part of the pattern. This filter enhances only leading edges of moving patterns. In this system undesired scattered light, which is orthogonally polarized to the diffracted beam, is discriminated by a polarizer.     

高铬铸铁中残余奥氏体的X射线衍射定量分析

为了消除高铬铸铁中碳化物对残余奥氏体定量的影响,采用电解方法定量萃取高铬铸铁中的碳化物。经X射线衍射分析,碳化物为（Cr,Fe）7C3。选择碳化物的（411）晶面衍射强度作为标准,测量其它峰的相对衍射强度,得出马氏体与奥氏体（200）晶面的衍射强度校正因子分别为0．12和0．44。校正了碳化物对奥氏体定量分析的影响,可提高测量精度10％以上。     

Evanescent interferometric lithography

Simulation results are presented to illustrate the main features of what we believe is a new photolithographic technique, evanescent interferometric lithography (EIL). The technique exploits interference between resonantly enhanced, evanescently decaying diffracted orders to create a frequency-doubled intensity pattern in the near field of a metallic diffraction grating. It is shown that the intensity in a grating's near field can be enhanced significantly compared with conventional interferometric lithography. Contrast in the interference pattern is also increased, owing to a reduction in the zeroth-order transmission near resonance. The pattern's depth of field reduces as the wavelength is increased beyond cutoff of the first-order diffracted components, and results are presented showing the trade-offs that can be made between depth of field and intensity enhancement. Examples are given for a 270-nm-period grating embedded in material with refractive index n = 1.6 and illuminated with wavelengths near 450 nm. Under these conditions it is predicted that high-intensity, high-contrast patterns with 135-nm period can be formed in photoresists more than 50 nm thick.