Diffraction Focusing Research Articles

Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality

In order to study the effect of diffraction focusing characteristics of microlens arrays on the parallel laser direct writing quality, we use nonparaxial approximation to analyze the diffraction focus characteristic of a single microlens, take into consideration the cross-talk effect of a number of microlenses on the diffraction focusing characteristics of an array, and establish a theoretical focusing intensity model of a microlens array to describe the influence of a change in F-number and/or center distance on the diffraction focusing characteristics of a parallel laser direct writing system while incident writing laser is normal. Numerical simulation results indicate that there is a cross-talk effect among microlenses which increases as the F-number increases when the center distance is the same as the smaller aperture, and parallel writing quality can be improved by reducing or totally eliminating the cross-talk effect by reducing F-number and/or increasing center distance.

Modeling focusing characteristics of low Fnumber diffractive optical elements with continuous relief fabricated by laser direct writing

A theoretical model is established using Rayleigh-Sommerfeld diffraction theory to describe the diffraction focusing characteristics of low F-number diffractive optical elements with continuous relief fabricated by laser direct writing, and continuous-relief diffractive optical elements with a design wavelength of 441.6nm and a F-number of F/4 are fabricated and measured to verify the validity of the diffraction focusing model. The measurements made indicate that the spot size is 1.75mum and the diffraction efficiency is 70.7% at the design wavelength, which coincide well with the theoretical results: a spot size of 1.66mum and a diffraction efficiency of 71.2%.

Propagation properties of a hard-edged diffracted beam generated by a Gaussian mirror resonator

Based on the scalar diffraction theory, the propagation and focusing properties of a hard-edged diffracted beam generated by a Gaussian mirror resonator were investigated. Explicit expressions for the field distribution of the truncated beam that propagates through a paraxial optical ABCD system were derived in detail. Numerical examples are given to illustrate our analytical results.

X-ray diffraction in single crystals under the influence of temperature gradient

In Bragg condition and Laue geometry specific interest are presented coherent processes in optics of x-ray when external influences are applied to the monocrystal. As an example of such coherent processes may serve total pumping x-rays from the direction of propagation to the reflection direction [1], diffraction focusing and defocusing of x-rays under temperature gradient [2], the phenomenon of transparency of the crystal under influence of ultrasound [3], etc. The Laue diffraction of narrow collimated (collimation angle ≈3′′) polychromatic X-ray radiation in single quartz and KDP crystals under the influence of temperature gradient is studied in present work. It is shown, that the deformation field distribution in the crystal stimulated by the external fields can be determined from the polychromatic beam spectral distribution. Due to the relative layout of diffraction g and temperature gradient B vectors the geometrical focusing B ↑↓ g and defocusing B↑↑ g of the reflected beams is obtained. A principle of the new type of x-ray spectrometry is considered for which a linear and angular dispersion depends on the magnitude of temperature gradient.

Birefringence in multiple X-ray scatterings deduced from the alternative theory of Pendelloesung beat

The study of the inner structure of the weak-absorbing noncrystalline materials as well as the biological objects is carried out by the method of the X-ray phase contrast which at present is substantially in progress. In the present work the possibility of reconstructing the inner structure of the one-dimensional phase objects under the diffraction focusing of the X-ray spherical wave is reported.The fact that with the incidence of the monochromatic X-ray spherical wave on the crystal in Laue geometry the diffracted radiation is focused inside the crystal is used. The focal line is perpendicular to the diffraction plane. Before entering the crystal the radiation is supposed to pass through the phase object where the inhomogeneities have one-dimensional distribution along the perpendicular diffraction plane.With the wave transmission trough the phase object the conditions of the focusing are broken: because of the refraction on the inhomogeneities the X-rays change their directions and the wave front is deformed. The intensity distribution analysis in the image diffracted from a strong-absorbing wedge-like crystal with rib parallel to the diffraction vector shows that the focusing is possible for every point of the phase object if one compensates the deviation from Bragg condition along the diffraction vector and the wave front deformation along the perpendicular diffraction plane. The focusing is possible if the source-crystal distance is smaller than the ratio of the inhomogeneity size and the difference of the index of refraction from the unit. m35.p03

The formation of the X-ray phase contrast under the diffraction focusing of the spherical wave

The study of the inner structure of the weak-absorbing noncrystalline materials as well as the biological objects is carried out by the method of the X-ray phase contrast which at present is substantially in progress. In the present work the possibility of reconstructing the inner structure of the one-dimensional phase objects under the diffraction focusing of the X-ray spherical wave is reported.The fact that with the incidence of the monochromatic X-ray spherical wave on the crystal in Laue geometry the diffracted radiation is focused inside the crystal is used. The focal line is perpendicular to the diffraction plane. Before entering the crystal the radiation is supposed to pass through the phase object where the inhomogeneities have one-dimensional distribution along the perpendicular diffraction plane. With the wave transmission trough the phase object the conditions of the focusing are broken: because of the refraction on the inhomogeneities the X-rays change their directions and the wave front is deformed. The intensity distribution analysis in the image diffracted from a strong-absorbing wedge-like crystal with rib parallel to the diffraction vector shows that the focusing is possible for every point of the phase object if one compensates the deviation from Bragg condition along the diffraction vector and the wave front deformation along the perpendicular diffraction plane. The focusing is possible if the source-crystal distance is smaller than the ratio of the inhomogeneity size and the difference of the index of refraction from the unit.

Axially symmetric focusing as a cuspoid diffraction catastrophe: Scalar and vector cases and comparison with the theory of Mie

An analytical description of arbitrary strongly aberrated axially symmetric focusing is developed. This is done by matching the solution of geometrical optics with a wave pattern which is universal for the underlying ray structure. The corresponding canonical integral is the Bessoid integral, which is a three-dimensional generalization of the Pearcey integral that approximates the field near an arbitrary two-dimensional cusp. We first develop the description for scalar fields and then generalize it to the vector case. As a practical example the formalism is applied to the focusing of light by transparent dielectric spheres with a few wavelengths in diameter. The results demonstrate good agreement with the Mie theory down to Mie parameters of about 30. Compact analytical expressions are derived for the intensity on the axis and the position of the diffraction focus both for the general case and for the focusing by microspheres. The high intensity region is narrower than for an ideal lens of the same aperture at the expense of longitudinal localization and has a polarization dependent fine structure, which can be explained quantitatively. The results are relevant for aerosol and colloid science where natural light focusing occurs and can be used in laser micro- and nano-processing of materials.

All-optical atom surface traps implemented with one-dimensional planar diffractive microstructures

We characterize the loading, containment and optical properties of all-optical atom traps implemented by diffractive focusing with one-dimensional (1D) microstructures milled on gold films. These on-chip Fresnel lenses with focal lengths of the order of a few hundred microns produce optical-gradient-dipole traps. Cold atoms are loaded from a mirror magneto-optical trap (MMOT) centered a few hundred microns above the gold mirror surface. Details of loading optimization are reported and perspectives for future development of these structures are discussed.

Apodized multilevel diffractive lenses that produce desired diffraction-limited focal spots

An apodized, multilevel diffractive lens that can produce a desired diffraction-limited focal spot is proposed for many applications, such as focusing, imaging, optical storage, and optical trapping. The three key points for the design are the innovative idea of complex conjugate subzones, the use of Babinet's principle, and the equivalent-pupil (or aperture) function theory of diffractive focusing elements composed of concentric transparent rings. As a concrete example, we numerically design a mixed multilevel diffractive lens (the highest phase level is 8) to produce a diffraction-limited Gaussian focal spot. Some related problems, such as the validity range and the combination with high-numerical-aperture refractive lenses, are also discussed.

Diffraction focusing of the sound field of a vertical antenna array in a range-dependent shallow sea

Using the adiabatic approximation for the mode representation of the sound field, it is shown that the efficiency of the diffraction focusing grows when the thickness of the isovelocity water layer increases with distance.

Double focusing of hard x rays using combined multilayer and Bragg–Fresnel optics

A multilayer Bragg–Fresnel x-ray lens (MBFL) structure that combines diffraction and geometric focusing on a single device is presented. With the MBFL, the linear BFL focuses the x-ray beam vertically while the bent multilayer focuses x rays horizontally. This combination eliminates the need for a second mirror in the conventional Kirkpatrick–Baez-based microprobe, which will be advantageous in x-ray fluorescence microscopy as well as microdiffraction applications. The characterization of the MBFL was carried out at the European Synchrotron Radiation Facility and a 1.6 μm (vertical)×12 μm (horizontal) focus was obtained from a 250 μm (V)×200 μm (H) incident beam. With a binary Fresnel lens efficiency of about 35% this yields a gain of almost three orders of magnitude compared to obtaining the same spot size by a raw aperture.

Comprehensive focusing analysis of various Fresnel zone plates.

A series-form expression for the individual diffracted field of a general annular ring is derived from the Rayleigh-Sommerfeld diffraction integral. It can be used for the accurate and fast simulation of any diffractive focusing element composed of concentric transparent rings. We present a comprehensive analysis, based on the leading term and the linear superposition principle, of the focusing performances of various Fresnel zone plates. Many problems, such as the equivalent aperture function, the diffraction efficiency, the focal spot pattern, the suppression of higher orders and the appearance of "fractional orders," and the explanation for the appearance of Fraunhofer diffraction patterns, are analytically investigated in detail. Because of the great similarity between Fresnel zone plates and multilevel diffractive lenses, most of the obtained results are also applicable to multilevel diffractive lenses.

Diffraction focusing of acoustic fields in oceanic waveguides smoothly varying along the track

With the use of adiabatic and WKB approximations for the mode representation of an acoustic field excited by a tone source in an oceanic waveguide smoothly varying along the track, dependences of the characteristic spatial scales of the phenomenon of diffraction focusing are obtained. Conditions that should be satisfied for the formation of zones of diffraction focusing of the acoustic field in such a waveguide are formulated.

Diffraction theory and focusing of light by a slab of left-handed material

A diffraction theory in a system consisting of left- and right-handed materials is proposed. The theory is based upon the Huygens's principle and the Kirchhoff's integral and it is valid if the wavelength is smaller than any relevant length of the system. The theory is applied to the calculation of the smearing of the foci of the Veselago lens due to the finite wavelength. We show that the Veselago lens is a unique optical instrument for the 3D imaging, but it is not a “superlens” as it has been claimed recently.

Metal layer Bragg–Fresnel lenses for diffraction focusing of hard x-rays

A thin-film Bragg–Fresnel lens (BFL) was developed for diffractive focusing of hard x-rays into submicron to nanometer spots for scanning x-ray spectromicroscopy. The lens is made of metal-layer Fresnel zones deposited on an x-ray reflective substrate. The use of a high-density lens structure reduces the thickness of the lens and simplifies the fabrication process. Linear and elliptical lenses made of a 200-nm-thick Au film were fabricated using e-beam lithography and a metal deposition process. The focusing capabilities of the Au layer BFLs were demonstrated at the Advanced Photon Source.

The diffraction focusing of X-rays upon backscattering from a bent crystal covered with epitaxial film: Sensitivity with respect to the interplanar spacing mismatch between film and substrate

The diffraction focusing of an X-ray wave reflected from a thick bent crystal covered with an epitaxial film is theoretically studied in the case when the Bragg angle θB is close to π/2. It is shown that the X-ray wave focusing upon backscattering from this system is sensitive with respect to the relative interplanar spacing mismatch Δd/d between the epitaxial film and the thick crystal substrate. It is suggested that this effect can be employed for evaluating Δd/d with an accuracy on the order of 10−10.

Effect of the sound velocity stratification in the bottom sediment layer on the diffraction focusing of an acoustic field in a shallow sea

It is shown that an increase in the sound velocity gradient in the bottom sediment layer results in the formation of additional zones of diffraction focusing of the acoustic field generated by a vertical line array in the water layer. It is also established that, depending on the sound velocity step at the upper boundary of the sediment layer, the diffraction focusing of the acoustic field in the main focusing zones can be enhanced or reduced.

Diffractive Multifocal Focusing of Gaussian Beams

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the quasi-optical approximation. It is shown that when a Gaussian beam illuminates a bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The proposed diffractive method allows the focusing of the wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensive and high-power radiation.

Diffractive Focusing of a Gaussian Beam

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the framework of the quasi-optical approximation. It is shown theoretically and experimentally that when a Gaussian beam illuminates such a type of bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The diffractive method proposed allows the focusing of wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensity and high-power radiation.

A Compact Pulsed HF Laser Based on an Auto-Wave Photon-Branched Chain Reaction

Huge energy gain is detected theoretically in a pulsed chemical laser-amplifier based on a photon-branched chain reaction initiating in a gaseous disperse medium composed of H2–F2–O2–He and Al particles by focused external infrared radiation. It is shown that this effect is observed due to the other optical effect of diffractive multifocal focusing of the input radiation on a certain type of bicomponent optical system coupled structurally with the input mirror of an unstable telescopic laser cavity. Such a relatively simple bicomponent diffraction system, consisting of two plane screens with circular apertures on a given optical axis, enables one to focus the input beam without using classical refraction elements such as lenses and prisms. The focusing of the input signal ensures the minimization of the initially excited volume of the laser active medium and the appropriate sharp lowering of the necessary energy of the input pulse up to ∼ 10-6 J. This enables the laser system to reach a high value of the energy gain of 109. The huge laser energy gain allows us to use a master oscillator in the form of a small microjoule laser powered by an accumulator, and consequently makes it possible to construct a completely self-contained compact pulsed chemical HF-laser.