Integrated diffractive andrefractive elements for spectrum shaping

Diffractive elements can be designed for spectrum shaping in the Fourier or Fresnel plane by iterative methods. It is necessary to use a Fourier lens and the wavelength for which the diffractive elements were designed to get the required spectrum shaping at the Fourier plane. Using a different wavelength will cause chromatic aberration. We deal with the combination of refractive and diffractive elements and two or more different diffractive elements on the same element to get appropriate beam shaping of light sources with a multiple spectral output. Simulations are preformed that transform the profile of a He-Ne laser with a Nd:YAG laser source, and shape the trapezoidal beam profile of an excimer laser into a Gaussian beam is also considered.     

Diffraction characteristics of optical elements designed as phase layers with cosine-profiled periodicity in the azimuthal direction

The article concerns an investigation of the Fresnel diffraction characteristics of two types of phase optical elements under Gaussian laser beam illumination. Both elements provide an azimuthal periodicity of the phase retardation. The first element possesses azimuthal cosine-profiled phase changes deposited on a plane base. The second element is a combination of the first element and a thin phase axicon. The cosine profile of the phase retardation of both diffractive elements produces an azimuthal cosine-profiled modulation on their diffractograms. It destroys the vortex characteristics of their diffraction fields.     

High-efficiency production of propagation-invariant spot arrays

Tailoring of the transverse intensity profiles of propagation-invariant optical fields is considered. The design of diffractive elements capable of realizing such fields by Fourier synthesis is discussed. High-efficiency realization of finite-aperture approximations of the constructed fields is demonstrated in a system consisting of two multilevel diffractive elements. The first element is a diffractive toroidal lens, which focuses the incident field into a ring pattern. The second diffractive element, located at the focal plane of the first element, introduces the phase modulation necessary to realize the desired transverse intensity profile behind a separate collimating lens. The influence of the fabrication errors of the diffractive elements on the fidelity of the propagation-invariant spot array is simulated, and system-integration aspects based on substrate-mode planar-integrated optics are considered.     

Ultrashort laser pulse beam shaping

We calculated the temporal and spatial characteristics of an ultrashort laser pulse propagating through a diffractive beam-shaping system that converts a Gaussian beam into a beam with a uniform irradiance profile that was originally designed for continuous waves [Proc. SPIE 2863, 237(1996)]. The pulse front is found to be considerably curved for a 10-fs pulse, resulting in a temporal broadening of the pulse that increases with increasing radius. The spatial intensity distribution deviates significantly from a top-hat profile, whereas the fluence shows a homogeneous radial distribution.     

Regenerative ring-laser design by use of an intracavity diffractive mode-selecting element

We report what we believe to be the first application of diffractive phase elements for transverse mode selection in laser ring resonators. We show that this resonator type offers several advantages over Fabry-Pérot resonators with diffractive mirrors. The design for a regenerative ring resonator that produces an eighth-order super-Gaussian intensity profile beam is presented. Numerical simulations, including modeling of the gain saturation and experimental tests, have been carried out to demonstrate the performance of this approach for cw and pulsed operations.     

Diffractive light attenuators with variable transmission

Abstract

A new application of diffractive optical elements (DOEs) for continuous or multistage adjustment of optical radiation intensity is described. The diffractive attenuators are linear or circular gratings (amplitude or phase) with constant period and diffraction efficiency that varies across the grating. The zero order of diffraction is used as the output and transmitted through the grating without angular deviation. The diffractive attenuators, in distinction to conventional analogues, allow one to change the intensity of the light beam according to predetermined function and have no limitations for power of the regulated light beam. These elements can be used in optical systems as a beam splitter with adjusted splitting coefficient. The experimental results on a circular diffractive attenuator fabricated by direct laser writing on a chromium film are presented. The range of transmission variation was 20 times within a 340° angle of attenuator turn. The possibility to use a phase diffractive attenuator as a light radiation modulator for a powerful technological laser is discussed.     

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.     

Diffractive shaping of excimer laser beams

Abstract

We address the problem of shaping the intensity distribution of a highly directional partially coherent field, such as an excimer laser beam, by means of diffractive optics. Our theoretical analysis is based on modelling the multi-transverse-mode laser beam as a Gaussian Schell-model beam. It is shown numerically that a periodic element, which is unsuitable for the shaping of a coherent laser beam, works well with an excimer laser beam because of its partial spatial coherence. The conversion of an approximately Gaussian excimer laser beam into a flat-top beam in the Fourier plane of a lens is demonstrated with a diffractive beam shaper fabricated as a multilevel profile in SiOl by electron-beam lithography and proportional reactive-ion etching.     

Diffractive variable beam splitter: optimal design

The analytical expression of the phase profile of the optimum diffractive beam splitter with an arbitrary power ratio between the two output beams is derived. The phase function is obtained by an analytical optimization procedure such that the diffraction efficiency of the resulting optical element is the highest for an actual device. Comparisons are presented with the efficiency of a diffractive beam splitter specified by a sawtooth phase function and with the pertinent theoretical upper bound for this type of element.     

A method of designing diffractive optical elements focusing into plane areas

Abstract

We propose a numerical method for designing phase function of diffractive optical elements (DOE_s) aimed at focusing into a plane area of complex shape. The method is applied to factorable intensity distribution in the domain of focusing and factorable illuminating beam of arbitrary cross-section. The diffraction analysis of a direct problem of focusing into the plane region is carried out. Based on a specially developed software, the numerical experiment was carried out, which allowed us to find that the theoretical power efficiency of typical DOE_s is no less than 85%.     

Laser weld pool management through diffractive holographic optics

Abstract

Conduction laser welding involves initiating a melt pool by exposure to high power laser induced light and controlled thermal conduction. Existing welding techniques generally provide enough energy to join the component but have no real control over the melt pool. This process can invariably lead to overheating in adjacent areas or even the melt pool itself, often causing unavoidable effects, such as ‘burn through’. The present work presents a procedure in which a desired melt pool shape is conceived, and a bespoke beam irradiance distribution is designed to match. The beam is shaped not by conventional lenses but by a diffractive holographic optical element (DHOE). The DHOE utilises holography to wholly create highly complex three-dimensional energy distributions through constructive and destructive interference. This technique allows novel beam irradiance distributions to be applied to conduction mode laser welding, with the melt pool transverse profile being shaped to a specific design. Holographic conduction laser welding has been shown to be successful and represents a significant step forward in the industry, as demonstrated in this case in both mild and stainless steels. The fusion zone is shown to be particularly influenced by the shape of the illuminating laser beam profile, and many of the welds demonstrate a highly novel weld profile because of this. The use of a bespoke beam irradiance distribution allows control of the heat flow to the workpiece, and this allows greater control over material migration due to surface tension effects. Many of the welds demonstrate unique surface solidification patterns directly linked to the beam profile used. The DHOE also presents a number of additional advantages, such as an increased usable depth of field, allowing for less stringent set-up tolerances. Comprehensive metallography has been performed on samples of these welds through the use of optical microscopy, electron microscopy, electron backscatter diffraction and energy dispersive (X-ray) spectroscopy. These techniques offer in depth analysis of crystal size, shape, orientation and phase. By incorporating DHOEs into a laser welding process, not only does the melt pool shape become controllable, but also the crystal growth is highly influenced. Many of the undesirable attributes of a conventional laser weld are reduced by using a beam distribution created by a DHOE, bringing the microstructure of the weld pool closer to that of the parent material.     

Design of diffractive phase elements that produce focal annuli: a new method

A new optimization method based on the general theory of amplitude-phase retrieval is proposed for designing the diffractive phase elements (DPE's) that produce focal annular patterns. A set of equations for determining the phase distribution of the DPE is given. The profile of a surface-relief DPE can be designed with an iterative algorithm. Numerical calculations are carried out for several examples. A comparison of the performance of the DPE's designed with the Gerchberg-Saxton algorithm and the new algorithm is presented. The effect of quantization of the phase distribution of the DPE's on the results is also investigated. The results show that the new algorithm can successfully achieve the design of the DPE's that convert the uniform incident beam into the focal annular patterns.     

Diffractive optical elements with modulated zone sizes

Abstract

The standard design for phase-only diffractive optical elements comprises a transformation of the continuous phase function into a surface relief by means of wrapping the phase into regular intervals of M2π. This results in a structure with diffractive zones aligned in a horizontal plane. We present an alternative design concept with modulated zone sizes leading to non-periodic boundary positions and non-aligned surface structures. The diffractive properties are compared to those of conventional diffractive optical elements. It can be shown that they are fully equivalent for the design wavelength, but exhibit a different spectral behaviour for deviating wavelengths. These properties are exploited for the improvement of the optical performance of blazed gratings and diffractive lenses under conditions of deviating wavelengths. Special emphasis is put on the optimization of the ratio between diffractive efficiencies of the design order and other orders for blazed gratings and focusing diffractive lenses, as well as the suppression of interference effects within Gaussian beams collimated with diffractive lenses.     

Diffractive element design for resonant scanner angular correction: a beam retardation approach

A new approach for designing diffractive optical corrective elements with zooming capability to convert nonlinear sinusoidal scanning into linear scanning is proposed. Such a device will be useful for linearizing the angular scan of a resonant mirror scanner. The design methodology is to create a graded index of a refraction device as the reference design with its index of refraction parameters based on beam retardation through propagation in an inhomogeneous medium. The diffractive element is designed by utilizing a binarizing algorithm of the accumulated phase from transmission through the refractive element. In contrast to a prior approach, which was introduced based on the beam propagation through inhomogeneous media, the new approach takes beam diameters into consideration. This makes both the refractive element and its associated diffractive element more robust against beam fanning.     

Superresolution laser beam shaping

The superresolution technique is well known for its ability to compress the central diffractive spot that is smaller than the Airy diffractive spot. In this paper, we extend the superresolution technique for different laser beam shaping. A complete set of superresolution diffractive elements is developed for the flat-top beam shaping, the single-circle beam shaping, and the novel circular Dammann grating. Five phase plates, corresponding to each of its applications, have been made by use of micro-optics technology. Experiments that are presented are in good agreement with the theoretical results. The superresolution technique presented in this paper should be highly interesting for the wide applications of laser beam shaping.     

Designing diffractive phase plates for beam smoothing in the fractional Fourier domain

A new modification of the output plane constraint is used in the iterative algorithm for designing diffractive phase plates (DPPs) to produce spatial beam smoothing in the fractional Fourier (FRT) domain. Compared with previously published algorithms, this algorithm can provide faster convergence, more powerful ability to overcome the local minimum problem and better smoothing quality. By computer simulation, it has shown that the DPP designed by this algorithm has the advantages of high uniformity at the main lobe, low profile error and steep edge.     

Design of non-paraxial array illuminators by step-transition perturbation approach

Abstract

We introduce an efficient Fourier-domain formulation of an approximate method to model non-paraxial diffractive elements. The method is based on evaluation of local field perturbations caused by abrupt surface-profile transitions. It facilitates fast parametric optimization of binary and four-level diffractive array illuminators in the non-paraxial domain of diffractive optics. Comparison with rigorous electromagnetic theory of gratings shows that optimization with the perturbation method gives accurate results if the smallest feature size in the surface profile is larger than one wavelength. Some binary designs are demonstrated using electron beam lithography.     

Diffractive microlenses replicated in fused silica for excimer laser-beam homogenizing

A diffractive beam homogenizer, based on an array of square, off-axis, continuous-relief diffractive microlenses, for use with an excimer laser has been studied. We originally fabricated the homogenizer by direct-write electron-beam lithography, from which we made replicas in UV-grade fused silica by hot embossing and reactive ion etching. Atomic force microscopy measurements of original and replicated elements showed the accuracy of the replication fidelity. One of the replicated homogenizers was evaluated together with a KrF excimer laser. The homogenized beam had a flat-top profile with 31% of the beam energy contained within an area where the beam intensity was above a threshold level of 90% of the maximum intensity.     

Refractive and diffractive properties of planar micro-optical elements

The refractive and the diffractive properties of planar micro-optical elements are investigated. The transition between purely refractive and purely diffractive planar microlenses is numerically simulated for the example of differently designed phase-matched Fresnel elements. Results obtained from numerical simulations and experiments show that the refractive and diffractive types exhibit a distinctly different behavior in the presence of small fabrication errors or wavelength deviations. Based on these results, design rules for various applications, including low- and high-numerical-aperture lenses and hybrid refractive-diffractive elements, are derived. For a high-numerical-aperture (? /# = 1.0) lens the experimental characterization of the irradiance distribution in the image space is presented and shown to agree well with theoretical predictions.     

Generation and selection of laser beams represented by a superposition of two angular harmonics

Abstract

The properties of fields generated by diffractive phase-only optical elements that generate combinations of two angular harmonic fields with different harmonic indices in Fraunhofer and Fresnel regions are investigated theoretically and experimentally. Camomile shaped diffraction patterns are predicted and observed. It is shown that multi-order diffractive phase elements can be used to both generate these beams and to identify the weights of different angular harmonics in a given incident laser beam.