Kirchhoff Diffraction Theory Research Articles

The Generation of Equal-Intensity and Multi-Focus Optical Vortices by a Composite Spiral Zone Plate

We propose a new vortex lens for producing multiple focused coaxial vortices with approximately equal intensities along the optical axis, termed equal-intensity multi-focus composite spiral zone plates (EMCSZPs). In this typical methodology, two concentric conventional spiral zone plates (SZPs) of different focal lengths were composited together and the alternate transparent and opaque zones were arranged with specific m-bonacci sequence. Based on the Fresnel–Kirchhoff diffraction theory, the focusing properties of the EMCSZPs were calculated in detail and the corresponding demonstration experiment was been carried out to verify our proposal. The investigations indicate that the EMCSZPs indeed exhibit superior performance, which accords well with our physical design. In addition, the topological charges (TCs) of the multi-focus vortices can be flexibly selected and controlled by optimizing the parameters of the zone plates. These findings which were demonstrated by the performed experiment may open new avenues towards improving the performance of biomedical imaging, quantum computation and optical manipulation.

SOME REMARKS ABOUT THE OBLIQUITY FACTOR USING IN THE KIRCHHOFF DIFFRACTION THEORY

In the framework of the work the description of sphere wave filed in the far observation region is discussed. The consideration is based on the decomposition of the wave field over the longitudinal and transverse spatial parameters of the problem in the direction of observation. It is shown that the approximation of a sphere wave by the flat field is correct only if the consideration is conducted in the limit of solid angle. The magnitude of the solid angle, which includes the area of flatness of the spherical wave, is determined using the so-called wave parameters corresponding to the observation area and the illuminated point. The wave field created by a small flat area is defined as a limit case of a superposition field generated by a system of point sources. It is shown that in an observation point the wave field of a small flat area can be characterized by the angle between the area normal and the vector indicting from the given area the observation point. The problem of description of a wave filed in the framework of a small flat aria is also discussed. A new method for deriving of the well-known obliquity factor of the Kirchhoff diffraction theory is suggested.

Performance analysis of single-focus phase singularity based on elliptical reflective annulus quadrangle-element coded spiral zone plates

Optical vortices generated by the conventional vortex lens are usually disturbed by the undesired higher-order foci, which may lead to additional artifacts and thus degrade the contrast sensitivity. In this work, we propose an efficient methodology to combine the merit of elliptical reflective zone plates (ERZPs) and the advantage of spiral zone plates (SZPs) in establishing a specific single optical element, termed elliptical reflective annulus quadrangle-element coded spiral zone plates (ERAQSZPs) to generate single-focus phase singularity. Differing from the abrupt reflectance of the ERZPs, a series of randomly distributed nanometer apertures are adopted to realize the sinusoidal reflectance. Typically, according to our physical design, the ERAQSZPs are fabricated on a bulk substrate; therefore, the new idea can significantly reduce the difficulty in the fabrication process. Based on the Kirchhoff diffraction theory and convolution theorem, the focusing performance of ERAQSZPs is calculated. The results reveal that apart from the capability of generating optical vortices, ERAQSZPs can also integrate the function of focusing, energy selection, higher-order foci elimination, as well as high spectral resolution together. In addition, the focusing properties can be further improved by appropriately adjusting the parameters, such as zone number and the size of the consisted primitives. These findings are expected to direct a new direction toward improving the performance of optical capture, x-ray fluorescence spectra, and forbidden transition.

Fraunhofer diffraction pattern of a Gaussian beam passing through a photorefractive crystal Bi12GeO20

In this theoretical–experimental study, we use the Fresnel–Kirchhoff diffraction theory to simulate the formation of the far-field diffraction pattern of a divergent Gaussian beam propagated through a photorefractive crystal Bi12GeO20 (BGO). We show that for the BGO, in addition to the wavefront curvature and change in the refractive index of the medium due to light intensity, there is a third contribution affecting the medium-induced nonlinear phase shift; the latter is related to the additional change in the refractive index produced by the photorefractive nature effect. We consider that this work contributes to the characterization of photorefractive materials using diffraction patterns.

Theoretical simulation on Fraunhofer diffraction of arbitrarily shaped aperture

The diffraction refers to the phenomenon that when light encounters an obstacle during propagation, it will deviate from the original propagation path and propagate behind the obstacle. In the study of diffraction and the relevant, we often encounter the questions about the prediction or estimation on the diffraction patterns of apertures with various shapes. Yet the specially designed optical experiment is very time consuming and laborious for this simple purpose. In this paper, the laser far-field diffraction is studied based on Kirchhoff diffraction theory. The intensity distribution is described by using a two-dimensional matrix and then the mathematical representations of the diffraction pattern of arbitrary aperture are provided. Visualization of calculated data is achieved by computer programming, and high-precision diffraction patterns are obtained. The above theoretical analysis method presented in this paper has higher universality. When the calculation infinitesimals are small enough and the computer graphics display function is sufficient, the diffraction pattern with high resolution can be obtained efficiently compared with the experiment.

Absorption Enhancement in a Quantum Dot Thz Detector with a Metal-Semiconductor-Metal Structure

The low absorptivity of quantum dot nano-structures cannot meet the requirements for high-performance next-generation Thz detectors which can be used for environmental pollution detection. In this study, a novel metal-semiconductor-metal (MSM) cavity structure with a square hole array instead of a traditional planar metal electrode was developed to improve and enhance the absorptivity of a quantum dot Thz detector. The possible modes and loss problems in the metal resonant cavity were analyzed using the finite-element transmission matrix, the eigenvector method, and Kirchhoff diffraction theory. The results demonstrate that the MSM cavity structure introduced in the detector can enhance absorption up to 8.666 times higher than that of the conventional counterpart.

Recent Developments of Noise Attenuation Using Acoustic Barriers for a Specific Edge Geometry

The aim of this research is to provide a better prediction for noise attenuation using thin rigid barriers. In particular, the paper presents an analysis on four methods of computing the noise attenuation using acoustic barriers: Maekawa-Tatge formulation, Kurze and Anderson algorithm, Menounou formulation, and the general prediction method (GPM-ISO 9613). Accordingly, to improve the GPM, the prediction computation of noise attenuation was optimized for an acoustic barrier by considering new effects, such as attenuation due to geometrical divergence, ground absorption-reflections, and atmospheric absorption. The new method, modified GPM (MGPM), was tested for the optimization of an y-shape edge geometry of the noise barrier and a closed agreement with the experimental data was found in the published literature. The specific y-shape edge geometry of the noise barrier contributes to the attenuation due to the diffraction phenomena. This aspect is based on the Kirchhoff diffraction theory that contains the Huygens-Fresnel theory, which is applied to a semi-infinite acoustic barrier. The new method MGPM of predicting the noise attenuation using acoustic barriers takes into consideration the next phenomena: The effect of the relative position of the receiver, the effect of the proximity of the source or receiver to the midplane of the barrier, the effect of the proximity of the receiver to the shadow boundary, the effect of ground absorption-reflections, the effect of atmospheric absorption, and the meteorological effect due to downwind. The conclusion of the paper reveals the optimization of the method for computing the noise attenuation using acoustic barriers, including the necessary corrections for ISO-9613 and the Sound PLAN software, as well as the optimization on a case study of a specific geometry of the edge barrier.

A Retroreflection Reduction Technique Based on the Wavefront Coded Imaging System

A novel anti-cat-eye effect imaging technique based on wavefront coding is proposed as a solution to the problem of previous anti-cat-eye effect imaging techniques where imaging quality was sacrificed to reduce the retroreflection from the photoelectric imaging equipment. With the application of the Fresnel–Kirchhoff diffraction theory, and the definition of generalized pupil function combining both phase modulation and defocus factors, the cat-eye echo formation of the wavefront coded imaging system is theoretically modeled. Based on the physical model, the diffracted spot profile distribution and the light intensity distribution on the observation plane are further simulated with the changes in the defocus parameter and the phase modulation coefficient. A verification test on the cat-eye laser echo power of the wavefront coded imaging system and that of the conventional imaging system at a 20 m distance are conducted, respectively. Simulations and experiment results show that compared with conventional imaging systems, the wavefront coding imaging system can reduce the retroreflection echo by two orders of magnitude while maintaining better imaging quality through defocusing.

Diagnostics of hypersonic plasma by method of intrinsic electromagnetic oscillations of open resonator with non-uniform inclusions

For various areas of radiophysics, plasma physics, studies of spectral and diffraction characteristics of open resonators containing various inhomogeneous inclusions within themselves are of great interest, the material parameters of which depend on spatial coordinates or on frequency parameters of the structure. Approximate models of optical resonators are based on integral equations, the nuclei of which are answered by non-self-conjugated completely continuous operators in some functional spaces (Hilbert or Banach spaces). The rationale for these equations does not seem mathematically correct enough. These equations are derived from the scalar formulation of the mathematically inconsistent Kirchhoff diffraction theory. Therefore, the relationship of these equations with the strict electrodynamic setting of the spectral problem is unclear and, therefore, the applicability of the corresponding models of optical resonators is unclear. The task set forth in the article is to build a strict mathematically justified and effective solution of edge problems about free and forced electromagnetic oscillations for one class of two-dimensional optical resonators with dielectric inclusions. The mirrors of this optical resonator are modeled by a final system of perfectly conductive open circular cylindrical surfaces, and the inclusions by a final system of circular cylindrical regions filled with dielectric medium. The wavelength, geometric parameters of the mirrors of the optical resonators, their mutual location, as well as the dimensions of the inclusions of a priori restrictions are not imposed. The main results obtained are also true for the case of an empty optical resonator that does not contain dielectric inclusions.

Theoretical study of high order and saturable Kerr media nonlinearities in Z-scan

Based on Fresnel–Kirchhoff diffraction theory, the effect of high order nonlinearities and saturable Kerr media in Z-scan experiments are theoretically investigated. Analytical expressions were obtained for the Z-scan curve, which can be strongly affected by the pump intensity. Moreover, empirical relationships were found to describe the intensity dependence of the peak-valley distance and the transmittance difference, allowing an accurate determination of parameters such as high-order nonlinearities, the saturation intensity and the confocal parameter.

A Microlens Super-Surface Film with Regular Graded Circular Hole-Like Subwavelength Structures for Highly Focusing Strength

Using the fact that a sub-wavelength structure exhibits the same thermal expansion coefficient as a micro-lens array, we design a micro-lens super-surface film with regular circular hole-like subwavelength structures to realize the high performances of central highly focusing strength and short focal length. In addition, based on the Fresnel—Kirchhoff diffraction theory, the influences of subwavelength structural period and height on the focusing performance of a micro-lens are analyzed. Furthermore, the finite-difference time-domain method is utilized to optimize the structural parameters. Via direct laser writing and an inductively coupled plasma process, we fabricated a square micro-lens array consisting of a 1000 × 1000 micro-lens unit with a sub-wavelength structure, and the optical focusing performance was measured in the visible light band. Finally, the experimental results indicate that the focal length is decreased to 15 μm, the focal spot central energy is increased by 7.3%, and the light transmission, enhanced via inserting sub-wavelength structures, corresponds to 3%. This proves that the designed micro-lens array with a regular-graded circular hole-like subwavelength structure can achieve central high focusing and a short focal length. This has applications in several fields of wavefront detection and light field imaging systems.

Anti-cat-eye effect imaging technique based on the light-field imaging technique

Based on previous anti-cat-eye effect imaging techniques sacrificing too much imaging quality to achieve substantial retroreflection reduction, an anti-cat-eye effect imaging technique based on light-field imaging is proposed. Relevant studies have been carried out regarding the mechanism and effectiveness of both antilaser reconnaissance and blinding for this technique. By applying the Fresnel–Kirchhoff diffraction theory and defining the microlens array as a superposition of a series of microlens units, the retroreflection formation of the light-field imaging system is theoretically modeled. Based on the physical model, the influences of defocusing on the intensity distributions of spots on both the light-field detector and observation planes are further studied. The results show that, compared with a conventional system with the defocus invariant and flexible reconstruction properties, the light-field imaging system not only increases the interference and blinding thresholds by nearly one order of magnitude but also reduces both the retroreflection maximum intensity and the echo-detector receiving power by more than one order of magnitude, which sufficiently manifests the superior antilaser reconnaissance and blinding performances of the light-field imaging system.

Coherence scanning and phase imaging optical interference microscopy at the lateral resolution limit.

To get physical insight into the 3D transfer characteristics of interference microscopy at high numerical apertures we study reflecting rectangular grating structures. In general, the height obtained from phase information seems to be reduced, whereas height values resulting from coherence scanning sometimes seem to be systematically overestimated. Increasing the numerical aperture of an interference microscope broadens the spectra of the resulting interference signals, thus offering a broad variety of wavelength contributions to be analyzed. If phase analysis of a measured far-field interference wavefront is performed at very short wavelengths the periodical profiles obtained from coherence scanning and phase shifting analysis differ only by the measured amplitude. However, at longer wavelength there is a 180° phase shift of the measured profiles obtained from phase analysis compared to coherence peak analysis. Increasing the evaluation wavelength improves the lateral resolution since the long wavelength contributions are related to electromagnetic waves of high angles of incidence. This behavior is to the best of our knowledge not documented in literature so far. It was first observed experimentally and could be confirmed by simulation results obtained from either Kirchhoff diffraction theory or an extended Richards-Wolf model developed in our group. Compared to original input profiles used for the simulation the profiles obtained from phase evaluation correspond quite well at longer wavelength, whereas the results obtained from coherence peak analysis are typically inverted with respect to height.

Diffractive focusing fan-out element for the parallel DNA sequencer

Various issues of creation of diffractive optical elements transforming one laser beam with small divergence to a matrix of converging beams with a diffraction size of focused spots in the plane of object illumination and their application for problems of DNA sequencing and microscopy are considered. The parameters of diffractive elements are calculated and optimized in the approximation of the Fresnel–Kirchhoff diffraction theory. Diffractive elements are fabricated by the method of direct laser writing on a photoresist by using a circular laser writing system. Experimental characteristics of a diffractive element creating a matrix consisting of 33 × 33 beams, which are focused in one plane at a distance of 210 mm, are presented. The degree of nonuniformity of beam intensities determined by the ratio of beam intensities in the central region to intensities of peripheral beams is 1/2.5, which is potentially sufficient to be used in DNA sequencing problems. The maximum distortions of spot positions in the entire focusing field is <0.15%.

Theoretical Research on the Thermal-Lens Effect of Magnetic Fluid by Using Brownian Dynamics Method

Magnetic fluid has not only rich optical properties, but also interesting thermal-lens effect. The thermal-lens effect of magnetic fluid was studied by using the Brownian dynamics method. The Theoretical simulation and analysis were taken to research the whole generation process of thermal-lens effect. The thermal-lens effect generation of water-based magnetic fluid irradiated by the laser of different optical powers was studied in microscopic view. Based on the model of the thermal-lens effect, Monte Carlo method and Kirchhoff diffraction theory were adopted to simulate and analyze the far-field diffraction ring pattern generated by a Gauss light beam passing through the magnetic fluid. Then, the influences of different central temperatures of the magnetic fluid to the ring numbers, width, and intensity distribution of far-field diffraction ring pattern were obtained. The results were verified with the published experimental results.

Light scattering by ice crystals of cirrus clouds: comparison of the physical optics methods

The physical optics approximations are derived from the Maxwell equations. The scattered field equations by Kirchhoff, Stratton-Chu, Kottler and Franz are compared and discussed. It is shown that in the case of faceted particles, these equations reduce to a sum of the diffraction integrals, where every diffraction integral is associated with one plane–parallel optical beam leaving a particle facet. In the far zone, these diffraction integrals correspond to the Fraunhofer diffraction patterns. The paper discusses the E-, M- and (E, M)-diffraction theories as applied to ice crystals of cirrus clouds. The comparison to the exact solution obtained by the discontinuous Galerkin time domain method shows that the Kirchhoff diffraction theory is preferable.

Comparison between two models of absorption of matter waves by a thin time-dependent barrier

We report a quantitative, analytical and numerical, comparison between two models of the interaction of a non-relativistic quantum particle with a thin time-dependent absorbing barrier. The first model represents the barrier by a set of time-dependent discontinuous matching conditions, which are closely related to Kottler boundary conditions used in stationary wave optics as a mathematical basis for Kirchhoff diffraction theory. The second model mimics the absorbing barrier with an off-diagonal $\delta$-potential with a time-dependent amplitude. We show that the two models of absorption agree in their predictions in a semiclassical regime -- the regime readily accessible in modern experiments with ultracold atoms.

Heptad Phase Vortex Array in Extremely Deep Fresnel Diffraction Region Generated by Asymmetrical Metal Subwavelength Holes Film**Supported by the National Natural Science Foundation of China under Grant No 11574185, and the Science and Technology Development Program of Shandong Province under Grant No 2009GG10001005.

We report a heptad vortex array structure in the wave fields in an extremely deep Fresnel diffraction region by asymmetrical subwavelength holes in a metal film illuminated with linearly polarized light. A Mach–Zehnder interferometer with a microscopic objective is used to record the wave fields at different distances, and the phase maps are extracted by Fourier transform of the interference intensities. We study the evolutions of the heptad vortex array with distance from the sample to the object plane. To explain the formations and the evolutions of the vortex array, we calculate the diffracted wave fields with Kirchhoff's diffraction theory. The calculations are basically consistent with the experimental results, and the properties of the heptad vortex array structure are reasonably explained.

A software platform for phase contrast x-ray breast imaging research

PurposeTo present and validate a computer-based simulation platform dedicated for phase contrast x-ray breast imaging research. MethodsThe software platform, developed at the Technical University of Varna on the basis of a previously validated x-ray imaging software simulator, comprises modules for object creation and for x-ray image formation. These modules were updated to take into account the refractive index for phase contrast imaging as well as implementation of the Fresnel–Kirchhoff diffraction theory of the propagating x-ray waves. Projection images are generated in an in-line acquisition geometry. To test and validate the platform, several phantoms differing in their complexity were constructed and imaged at 25keV and 60keV at the beamline ID17 of the European Synchrotron Radiation Facility. The software platform was used to design computational phantoms that mimic those used in the experimental study and to generate x-ray images in absorption and phase contrast modes. ResultsThe visual and quantitative results of the validation process showed an overall good correlation between simulated and experimental images and show the potential of this platform for research in phase contrast x-ray imaging of the breast. The application of the platform is demonstrated in a feasibility study for phase contrast images of complex inhomogeneous and anthropomorphic breast phantoms, compared to x-ray images generated in absorption mode. ConclusionsThe improved visibility of mammographic structures suggests further investigation and optimisation of phase contrast x-ray breast imaging, especially when abnormalities are present. The software platform can be exploited also for educational purposes.

Qusia-random rectangular holes self-supporting transmission grating

Support-mesh structures of a self-supporting transmission grating may decrease the transmission area and diffraction efficiency, thus exert a ill effect on the original diffraction pattern of the grating and make it complicated to apply, especially in soft X-ray region. To solve this problem, we put forward a method to realize a kind of totally self-supporting transmission grating by arranging the rectangular transmission holes in a high Z foil quasi-randomly. Based on Fraunhofer's diffraction theory, we make a theoretical analysis on the diffraction pattern of this new kind of grating. We also calculate the diffraction pattern of this new kind of grating based on the Kirchhoff's diffraction theory. What's more, we fabricated a sample grating of 1000 lines/mm using focused ion beam (FIB) technology and then tested it on beam line 4B7B on the Beijing synchrotron radiation facility. Theatrical analysis and experimental result both proved that the diffraction of the transmission grating can get rid of the bad influence of the support-mesh structures by using this new designed method. Such a methodology can profit applications of this kind of X-ray dispersive element in a wide field.