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Multilevel diffractive elements for generalized wavefront shaping
Abstract
A new approach to designing computer-generated multilevel diffractive elements, in which the phase and the amplitude of the output wavefront can be controlled independently, is presented. In this approach the diffraction efficiency of the elements can be arbitrarily controlled to reach 100 percent efficiency over the entire element. The approach is based on varying the local diffraction efficiency by changing the width and the number of levels in every period. To reduce complexity, an algorithm for designing the element with the least number of levels and masks is developed. This design algorithm determines the needed mask parameters in which compensation for distortions introduced by the lithographic recording of the element are taken into account. Calculated and experimental investigations that confirm the new design approach are presented.
... Many years of collaborations with Adolf Lohmann [1][2][3][4][5][6][7][8][9][10] have indirectly led to our investigations on incorporating optical processing techniques into laser cavities, and particularly on phase locking many coupled lasers. Phase locking of lasers has attracted considerable interest because it leads to high stable output power with good output beam quality [11][12][13] that can be useful for medical, communications, and industrial applications. ...
Talbot diffraction, together with Fourier filtering, are incorporated into a degenerate laser cavity to demonstrate efficient and controlled phase locking of hundreds of coupled lasers formed in different geometries and having different phase distributions. Such a combined approach leads to higher efficiency, better control, and greater variety of output phase distributions than would be possible with either separately. Simulated and experimental results for square, triangular, and honeycomb laser array geometries are presented.
... Many years of collaborations with Adolf Lohmann [1][2][3][4][5][6][7][8][9][10][11] have indirectly led to our current investigations on incorporating optical processing techniques into laser cavities. These include the exploitation of optical processing inside a degenerate cavity laser in order to obtain efficient control of the spatial coherence with little variation of output power [12][13], unique phase locking of many coupled lasers formed in different geometries [14][15][16], and rapid wavefront shaping and controlling of light propagating through dynamically varying heterogeneous media [17]. ...
Optical processing inside a degenerate cavity laser is exploited for efficient control of the spatial coherence, unique phase locking of many coupled lasers, and rapid wavefront shaping. Supporting experimental and calculated results are presented.
... Wavefront shaping has become not only the subject of a great research interest, but has also found applications in commercial devices, such as semiconductor lasers and LEDs 1,2 . Typically, beam shapers are based on diffractive optical elements with a relatively large size, 1 mm or more, and require a sophisticated computerassisted design 3 . The rapid development of nanoand bio-sciences along with the corresponding applications has stimulated interest in micro-and nano-scaled, high efficient optical components. ...
Using finite element method (FEM) implemented in Comsol Multiphysics simulation package, we present a model of beam shaper that converts spherical waves into one or two plane waves as a function of wavelength. Thus, the device can realize both wavefront shaping and beam splitting in only one structure. Comparing with different methods already presented, we introduce a solution for a smaller, simpler, and easier to manufacture device. We demonstrate a wavefront shaper using a microstructure of 8 x 8 µm size with commercially available material. We also discuss fabrication methods suitable for implementing the SU-8 polymer in the device.
... As an example, an 8-10 m telescope 25 using compensating adaptive optics for wavefront shaping increases its resolution power by a factor between 20 and 30. In micro-sized effects and operations, such wavefront correction is usually referred as beam shaping 26,27 since the interest lies mostly in the power distribution along the propagation axis. Indeed the shape of a laser beam has a Gaussian profile whereas some applications require a flat-top over a certain width in order to function properly or to increase efficiency. ...
Currently, an intense research takes place in the field of optical design, both on indusrial as well as academic plarforms. With my Ph.D. dissertation I wish to contribute to this activity, through the improvement of commercial optical design programmes. My research work encompasses the following branches of modern optical design: integrated optics, beam shaping and hybrid diffractive/conventional optics. For the modelling of the above devices I developed new techniques to make their design process (analysis and synthesis) more powerful (i.e. accurate, fast, convenient, providing additional degrees of freedom, allowing easy integration into complex systems) in comparison with former methods. Making a model in my case partly implies the creation of a new physical approach to describe some optical phenomenon, as well as the efficient implementation (usually on the basis of exact ray-tracing) of one that already existed. This way I could enrich the selection of "engineering tools" (i.e. models), by which modern optical devices can be more easily incorporated in the process of optical design...
The design, fabrication, and potential performance of micro- actuated mirrors for beam steering are considered. Micro- actuators are by definition small devices that implement small displacements; they typically function using either electrostatic attraction or thermal expansion and are much smaller and less expensive than voice coil, piezoelectric stack, and related macro-actuators. Mirrors for use with micro-actuators may consist of rigid optically flat plates, continuous deformable membranes of facesheets, or arrays of elements with many possible element shapes, spacings, and displacement patterns. In general, the number of potentially practical micro-actuated mirror designs for beam steering increases as angular range, aperture size, steering speed, optical quality, and optical power requirements decrease.
This paper presents methods for designing and recording optimal computer-generated diffractive optical elements. The design method is based on an analytic ray-tracing procedure for minimizing aberrations. The recording involves computer-generated masks and multiple lithographic processes in order to form reflective and transmissive multilevel, surface relief-phase, diffractive elements. As a result, the elements can have high diffraction efficiencies over a broad range of incidence angles. Even generalized diffractive elements that operate with highly uniform diffraction efficiency and polychromatic radiation can be designed and recorded by optimizing the shape and height of the relief gratings. To illustrate the effectiveness of the diffractive optical elements, they have been incorporated into a number of applications, involving visible as well as infra-red radiation. Some that deal with coordinate transformation, beam shaping, and polarization control are briefly reviewed.
Transversally sharply structured optical fields are discussed, which rotate upon propagation without any lateral expansion of the intensity profile. Finite-aperture approximations of such fields, realizable with phase-only and complex-amplitude recording, are demonstrated. Recording of at least some of the amplitude information (rather than neglecting it completely) is shown to improve the field quality considerably, in particular close to the element. Lohmann-coded binary-phase diffractive elements with restricted amplitude recording are fabricated by electron beam lithography and reactive ion etching. The experimental results are in good agreement with theory.
Binary diffractive axicons, designed to generate a uniform axial line focus over a specified interval, are fabricated by electron beam lithography. Continuous-path-control mode and dynamic beam expansion of a low-voltage electron beam pattern generator are employed to avoid quantization errors in the patterning of the circular zones. Apodization by local control of diffraction efficiency is shown to be an effective method to reduce axial intensity oscillations along the focal line. A novel split-groove apodization method is introduced to suppress second-order interference.
To convert a given single-mode He–Ne laser beam into a ring-shaped intensity distribution, a diffractive optical element with 16 levels was designed by YG amplitude-phase retrieval and iteration algorithm. This beam shaper is investigated experimentally and compared with the results of the computer design. The results show good conformity, and the measured diffraction efficiency is 87.2%. In addition, the diffractive effect is observed when the distance between diffractive optical element and CCD is changed.
A new approach for optimizing the groove depth of blazed holographic gratings that are illuminated by light with a wide range of wavelengths or incidence angles is presented. The approach is based on choosing the groove depth that maximizes the overall diffraction efficiency over the entire range of incidence angles and wavelengths. The scalar approximation is used for the diffraction efficiency calculations, with some results verified by rigorous vectorial calculations. Analytic solutions are given for some simple examples, together with experimental results. We present a new approach for optimizing the groove depth of blazed gratings that are illuminated by light with a wide range of wavelengths or incidence angles. The ap- proach is based on calculating the diffraction efficiency as a function of the incidence angle, the wavelength, and the groove depth and then choosing the depth that maximizes the overall diffraction efficiency over the entire range of angles and wavelengths. The diffraction efficiency is cal- culated by exploiting the scalar approximation," 7 with some results verified by rigorous vectorial calculations. 8 We present the general relations, analytic solutions for some simple examples, and experimental results.
A method is presented for designing optimal holographic optical elements. The method is based on an analytic ray-tracing procedure that uses the minimization of the mean-squared difference of the propagation vector components, between the actual output wave fronts and the desired output wave fronts. The minimization yields integral equations for the grating vector components that can be solved analytically, in some cases without any approximation. This leads to a well-behaved grating function that defines a holographic optical element.
A novel technique for designing holographic optical elements that can perform general types of coordinate transformation is presented. The design is based on analytic ray-tracing techniques for finding the grating vector of the element, from which the holographic grating function is obtained as a solution of a Poissonlike equation. The grating function can be formed either as a computer-generated or as a computer-originated hologram. The design and realization procedure are illustrated for a specific holographic element that performs a logarithmic coordinate transformation on two-dimensional patterns.
Multilevel phase holograms for monochromatic radiation at a wavelength of 10.6 microm are recorded as surface relief gratings with multilevel discrete binary steps. Our experiments show that diffraction efficiencies close to 90% can be achieved both for transmissive and reflective elements. The reduction of efficiency due to errors in the depth and the width of the step levels is considered.
This chapter describes the techniques and applications of computer-generated holograms. “Computer-generated holograms,” “synthetic holograms,” and “computer holograms” are terms used to refer to a class of holograms that are produced as graphical output from a digital computer. Given a mathematical description of a wavefront or an object represented by an array of points, the computer can calculate the amplitude transmittance of the hologram and display the result on a CRT or plot it on paper. Using photoreduced copy of the graphical output from a computer as holograms is only one of the many things that distinguish computer generated holograms from conventional ones. The computer-generated holograms have their greatest potential in the area of interferometry. They have been shown to be useful in supplementing existing methods of optical testing. Laser beam scanning is another promising area for computer-generated holograms. Holographic grating scanners are in many ways better than other mechanical mirror scanners.
A simple formula is derived that allows evaluation by a single integration the diffraction efficiencies of transmission relief gratings when they support a great number of orders. Validity of the method is demonstrated by comparison with a rigorous differential method.
We describe techniques for making a diffractive optical element that produces a subdiffraction-limited spot size. We provide experimental verification, using a diffraction optical element that is constructed on a magneto-optic spatial light modulator.
A technique for accurately figuring very thin, lightweight lenses is discussed. The phase change required to focus a plane wave into a point is calculated and photographically plotted with exposure proportional to phase (scaled from 0 to 2pi). The plot is photoreduced and the photoreduction is etched, with the depth of etch approximately proportional to the exposure. The result is a kinoform lens. Photographs taken with a kinoform lens are included.
Usually a hologram is produced by means of an interference experiment. Here, however, we let a computer- guided plotter draw the hologram. The plot, which has to be minified and recorded on film, contains no grey, only binary transmittance values. Our binary holograms yield reconstructed images of a quality equal to that of images obtained from usual holograms of comparable dimensions. When a Fourier hologram is inserted into the Fraunhofer plane of a coherent image forming system, it acts as a special type of a spatial filter, a so-called optical matched filter. Our binary matched filter is suitable for optical character recognition, the same as the usual optical matched filter introduced by Vander Lugt.