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.     

Generating function approach for creation of coherent multimode beams by diffractive optics

Tailored compositions of transverse modes provided by mathematical generating functions are exploited for the synthesis of multimode laser beams in free space. We show that analytical equations which are available for the generating functions provide physical insight into modal phase and power balance in multimode coherent light beams. Multimode coherent beams were created by methods of diffractive optics implementing the generating functions. Experimental and computer simulated results demonstrate a good match.     

Laser beam relaying with phase-conjugate diffractive optical elements

A diffractive optical element is used to relay complex laser beam profiles by phase conjugation. It has the advantage over a conventional afocal system of avoiding light concentration at the intermediate focal point. Theoretical and experimental results show that the image quality is a function of alignment errors and mode-size changes. When the optical system is within the calculated tolerances, the diffractive optic reproduces images of high quality.     

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.     

Three-dimensional laser trapping on the base of binary radial diffractive optical element

A radially symmetric binary diffractive optical element to generate an optical bottle beam is designed, fabricated, and characterized. Analysis of the numerical simulation and experimental research results shows that the fabricated element is well suited for solving three-dimensional (3D) laser trapping problems.     

Design concept for diffractive elements shaping partially coherent laser beams.

A new two-step design algorithm for the calculation of a diffractive phase element (DPE) for use with partially coherent laser beams is presented. The optical reconstruction of the DPE is modeled by the convolution of a coherent diffraction pattern and the far-field intensity distribution of a partially coherent laser beam. Numerical deconvolution is applied to derive a suitable amplitude pattern as signal input to a standard iterative Fourier transform algorithm (IFTA). Theory and numerical results are presented. Compared with a single-step IFTA design, this new approach yields nearly equal diffraction efficiencies and a relative improvement of 15% in signal reconstruction error.     

Holographically recorded photopolymer diffractive optical element for holographic and electronic speckle-pattern interferometry

A diffractive optical element is described that can be used to implement a very simple self-aligning electronic speckle-pattern interferometer and holographic interferometer that requires only a laser source and a camera in the optical setup.     

Algorithm based on rigorous coupled-wave analysis for diffractive optical element design

Diffractive optical element design is an important problem for many applications and is usually achieved by the Gerchberg-Saxton or the Yang-Gu algorithm. These algorithms are formulated on the basis of monochromatic wave propagation and the far-field assumption, because the Fourier transform is used to model the wave propagation. We propose an iterative algorithm (based on rigorous coupled-wave analysis) for the design of a diffractive optical element. Since rigorous coupled-wave analysis (instead of Fourier transformation) is used to calculate the light-field distribution behind the optical element, the diffractive optical element can thus be better designed. Simulation results are provided to verify the proposed algorithm for designing a converging lens. Compared with the well-known Gerchberg-Saxton and Yang-Gu algorithms, our method provides 7.8% and 10.8%, respectively, improvement in converging the light amplitude when a microlens is desired. In addition, the proposed algorithm provides a solution that is very close to the solution obtained by the simulated annealing method (within 1.89% error).     

Functional integrated optical elements for beam shaping with coherence scrambling property, realized by interference lithography

Many applications, such as semiconductor lithography and material processing, require the shaping of laser beams to provide a homogenous field illumination. We present the conception, implementation, and experimental verification of a combined single-element homogenizer. Additionally, for excimer laser applications, the concept is associated with a coherence scrambling capability. We used the technique of holographic interference lithography to integrate the multifunctional properties in a diffractive optical element. The wavelength difference between the recording process (457.9 nm) and the application (193 nm) results in a change of the imaging properties and requires a geometrical adaptation of the optical setup. The coherence scrambling effect of the setup is based on an off-axis design, including the beam shaping diffractive structure.     

Effect of phase imperfections on high-order mode selection with intracavity phase elements

To obtain a laser beam containing only one pure high-order transverse mode, one can insert a binary phase element (BPE) into a laser resonator. I investigate the effect of deviations in the discontinuous height of the BPE on the selection of high-order Hermite-Gaussian (HG) modes. Both matrix-diagonalization and numerical Fox-Li calculations to obtain the loss per pass and beam propagation factor of the output beam obtained with a deviated BPE are performed. Experimental results obtained with a Nd:YAG laser operated with HG (1,0) and HG (1,1) transverse modes are presented and compared with theoretical modes.     

Focusing of Novosibirsk Free Electron Laser (NovoFEL) radiation into paraxial segment

Abstract

We demonstrate results of studies of a silicon binary diffractive optical element (DOE) focusing a terahertz laser Gaussian beam into a paraxial segment. The characteristics of the DOE were examined on a Novosibirsk Free Electron Laser beam of 141-μm wavelength.     

Application of the direct search in solving a problem of forming longitudinal distribution of intensity

This paper is devoted to the application of a well-known genetic algorithm for optimization of diffractive optical element forming pre-given axial intensity distribution. Computer simulation results and experimental research are presented.     

Theoretical analysis and experimental measurement for resonant vibration of piezoceramic circular plates

Based on the electroelastic theory for piezoelectric plates, the vibration characteristics of piezoceramic disks with free-boundary conditions are investigated in this work by theoretical analysis, numerical simulation, and experimental measurement. The resonance of thin piezoceramic disks is classified into three types of vibration modes: transverse, tangential, and radial extensional modes. All of these modes are investigated in detail. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), are used to validate the theoretical analysis. Because the clear fringe patterns are shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Good quality of the interferometric fringe patterns for both the transverse and extensional vibration mode shapes are demonstrated. The resonant frequencies of the piezoceramic disk also are measured by the conventional impedance analysis. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be measured by the impedance analysis, and only the resonant frequencies of extensional vibration modes can be obtained. Numerical calculations based on the finite element method also are performed, and the results are compared with the theoretical analysis and experimental measurements. It is shown that the finite element method (FEM) calculations and the experimental results agree fairly well for the resonant frequencies and mode shapes. The resonant frequencies and mode shapes predicted by theoretical analysis and calculated by finite element method are in good agreement, and the difference of resonant frequencies for both results with the thickness-to-diameter (h/D) ratios, ranging from 0.01 to 0.1, are presented.     

Asymptotic analysis and design of diffractive optical elements

The problem of light diffraction by a micro-optical diffractive element is investigated. The method of stationary phase is applied to obtain approximate values of the integrals in the Kirchhoff approximation. The accuracy of the asymptotic approximation is studied in detail. As an application, the obtained approximate formulas are used to solve a design problem of constructing a diffractive optical element with a desired intensity distribution.     

Iterative algorithm for determining optimal beam profiles in a three-dimensional space

A new, to our knowledge, iterative algorithm for achieving optimization of beam profiles in a three-dimensional volume is presented. The algorithm is based on examining the region of interest at discrete plane locations perpendicular to the propagation direction. At each such plane an intensity constraint is imposed within a well-defined transverse spatial region of interest, whereas the phase inside that region as well as the complex amplitude outside the region is left unchanged from the previous iteration. Once the optimal solution is found, the mask that generates the desired distribution can be readily implemented with a planar diffractive optical element such as a computer-generated hologram. Several computer simulations verified the utility of the proposed approach.     

Generating inhomogeneously polarized higher-order laser beams by use of diffractive optical elements

We propose an improved version of the earlier developed optical arrangement for generating inhomogeneously polarized laser light modes with the aid of a diffractive optical element (DOE) with carrier frequency. By eliminating lenses from the optical arrangement, we achieve the miniaturization, reduced light losses, a smaller number of parameters being matched, and a simpler system adjustment procedure. Note that all the capabilities of the previous version, namely, the universality and simple readjustment to different polarization types, are fully retained. The numerical modeling of the polarization mode combiner has made it possible to analyze its performance and capabilities. In the experiments, the quality of the resulting beams is shown to be improved. For generating higher-order cylindrical beams, a lower-order mode at the output of the polarization mode combiner is additionally transformed with a DOE that operates in the zero diffraction order, introducing radial phase changes.     

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.     

Large-area, real-time imaging system for surface acoustic wavedevices

A system for imaging the particle displacement envelope of vibrational (transverse) modes of surface acoustic wave (SAW) devices is described. The modes are being imaged using a schlieren method for visualizing the acoustic power flow with a beam-expanded helium-neon (HeNe) laser. The optical arrangement uses internal reflection from within the quartz substrate to achieve high-efficiency acousto-optic diffraction of the laser light. The use of a CCD camera coupled with a frame grabber and a computer with image calculator software establishes an imaging system for large-area, real-time visualization, recording, accurate measurement, and analysis of vibrational modes of SAW devices. These methods are part of an effort to determine the relationship between acceleration sensitivity and transverse variations in the acoustic-mode shape in SAW resonators. Use of the system in imaging a 98 MHz SAW device is presented as an example     

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.     

Achromatic fan-out diffractive system for white-light free-space optical interconnects

Abstract

A simple and versatile white-light fan-out diffractive system based on the achromatization of the fractional Talbot effect is proposed. This achromatic configuration is able to interconnect a single polychromatic point source with a 2-D array of optoelectronic microdevices with low residual chromatic aberration even for white light. The whole broadband beamsplitter system is formed by two simple diffractive optical elements, a periodic diffractive lenslet array and a diffractive lens, that are made with a direct laser writing technique giving high light efficiency. The focal amplitude distribution corresponding to the lenslet array produces, by free-space propagation, self-replicas with different density of light points. These patterns, in conjunction with the achromatization process carried out by the additional diffractive lens, are, in short, the key to achieving a set of undistorted white-light spots at the output plane with high uniformity and variable separation between them. Experimental results are also shown.