Diffractive optical elements (DOEs) have demonstrated applicability to a wide range of optical problems which cannot be solved with conventional optical elements. DOEs are increasingly becoming solutions for numerous nonconventional imaging tasks such as fan-out gratings and extended imagers. Applications include product marking, machining, robotics, medical diagnostic instruments, alignment instruments, optical computers, and fiber optic switches, to list only a few. However, the phase functions provided by most commercial lens design codes for DOE design lack the generality needed for these nonconventional imaging tasks. The solution taken in the past, of pixelating the aperture and independently varying the phase of every pixel, requires writing a specialized wavefront propagator code since such a phase function is unsuitable for ray tracing codes. We show here new phase functions which are more general than those currently provided in commercial lens design codes but which remain easily adaptable to these codes. Example designs, demonstrating the increased flexibility of these new phase functions, are also shown.

In this paper, cascaded diffractive optical elements are investigated using a design strategy combining genetic algorithms with beam propagation methods. Results are presented for a two element cascaded system for multiple wavelength performance.

This paper describes techniques developed for the design of diffractive beam shaping elements for use with lasers. These techniques have been applied to systems containing both single and multiple cascaded DOEs. Past work by the authors and others described the use of genetic algorithms (GAs) for optimization of diffractive gratings. By appropriate choice of variable encoding and evaluation kernel, we were able to develop a modified genetic algorithm to optimize single diffractive optics for laser beam shaping. Genetic algorithms are a subset of a large class of evolution-based optimization and search algorithms. By developing specific software modules, we are able to apply a variety of evolutionary programming optimization algorithms to a number of design problems.

A paraxial diffractive element is defined by a signal wave which is specified in a window of finite extent. The iterative Fourier transform algorithm is a well-known method to iteratively encode paraxial diffractive elements by making use of parameters of freedom. However, the algorithm suffers from a slow convergence if the parameters of freedom are limited. Thus, there is a demand for more efficient encoding strategies. Fienup considered to use descent methods for solving phase-retrieval problems which turned out to be very efficient. In this paper, we modify his theory that it can be applied for the design of diffractive phase elements. Computer simulations document that descent methods have a clearly better performance than the iterative Fourier transform algorithm.

User-friendly computer-aided design tools for the implementation of diffractive optical elements may on the one hand influence the acceptance of diffractive optics in industry and on the other help to simplify research work in this area. In the present paper we describe the software system DIGIOPT which was designed to fulfill our demands on the design of paraxial diffractive elements for optical information processing applications.

The paper is a description of a dedicated software for performing the mask layout of diffractive optical elements (DOE). This computer-aided design (CAD) tool is a high productivity tool developed to speed-up the layout process of DOE masks. This utility designs the mask layout, starting from the phase diffraction pattern of DOE expressed as re-usable objects, which are generated by different computing methods and optimization algorithms. The diffraction phase pattern of some frequently used diffraction structures (gratings, lenses), can be computed from the optical parameters entered as input data. The mask layout design can be made for any number of phase levels between 2 and 64, resulting in a set of binary encoding masks. Many DOE functions with the same number of levels can be combined on the same substrate. The mask layout, containing not only the diffractive pattern, but also all the process control patterns needed for manufacturing, is generated in GDS format. The capabilities of this design software are illustrated in an example containing many 4-phase level elements on the same substrate. This CAD mask design software was designed to run on PCs and on SUN Sparc workstations.

Diffraction characteristics of high-spatial-frequency gratings (HSF) are evaluated for application to polarization-selective computer generated holograms using two different approaches, second order effective-medium theory (EMT) and rigorous coupled-wave analysis (RCWA). The reflectivities and the phase differences for TE and TM polarized waves are investigated in terms of various input parameters, and results obtained with second order EMT and RCWA are compared. It is shown that while the reflection characteristics can be accurately modeled using the second order EMT, the phase difference created by form birefringence for TE and TM polarized waves requires the use of a more rigorous, RCWA approach. Design of HSF gratings in terms of their form birefringence and reflectivity properties is discussed in conjunction with polarization-selective computer generated holograms. A specific design optimization example furnishes a grating profile that provides a trade-off between largest form birefringence and lowest reflectivities.

A radial, modulo-m2(pi) diffractive lens and a modulo-2(pi) diffractive lens are superposed in a single integrated optical element. The resulting compound lens both introduces optical power and cancels material dispersion. The lens is a microthin, planar achromat suitable for broadband imaging applications. An f/5, 100 mm focal length lens is fabricated by precision diamond-turning. A master mold is generated from the diamond turned copper; the master is then used to form a second-generation replica in an optical quality, uv-cured photopolymer. The measured effective V-number of the replicated lens is 213. Measured narrowband (2 nm) resolution is 120 lp/mm with a contrast of 10%.

The implementation of paraxial diffractive elements with complex transfer functions is a difficult problem since current technologies impose restrictions to certain modulation domains. In optical information processing, addressable spatial light modulators are already used to implement diffractive elements. The spatial resolution of such modulators is strongly limited. Moreover, they are restricted to a certain modulation domain. In this paper, we examine how to make optimal use of the available space-bandwidth product of an SLM to realize optical functions on the basis of encoding methods in diffractive optics. Theoretical considerations are documented by an example, where a classical matched filter is encoded into a diffractive phase element.

Holographic memory devices (HMD) are considered from the point of view of the possibility to minimize the light power spent for unit of the recorded and sampled information. The range of this power value is evaluated. The difference in specific power expenses for different HMD versions is noticed and the conditions under which these expenses may be minimal are analyzed.

We have fabricated sub-wavelength diffractive optical elements with binary phase profiles for operation at 975 nm. Blazed transmission gratings with minimum features 63 nm wide were designed by using rigorous coupled-wave analysis and fabricated by direct-write e-beam lithography and reactive ion beam etching in gallium arsenide. Transmission measurements show 85% diffraction efficiency into the first order. Anti-reflection surfaces, with features 42 nm wide were also designed and fabricated.

Diffractive optics is becoming a standard part of the optical designer's toolkit. The transition from design to manufacturing, especially for elements larger than a few millimeters in diameter, has been impeded by the relatively high cost of producing diffractive elements by standard photolithographic means. Replications techniques, such as injection molding, have the potential to significantly lower the cost for such elements. We report on results of the application of injection molding techniques to the replication of diffractive elements. Several examples of diffractives fabricated by these techniques, as well as present process capability, are discussed.

Switchable holograms open up the possibility of real-time electro-optical control of diffractive optic components. We have developed a novel photopolymer-liquid crystal material system which allows fast, single-step recording of holograms with diffraction efficiency controllable by conveniently applied electric fields. With the addition of a surfactant to our standard material recipe, we have achieved complete switching of a first-order Bragg diffracted beam into the zero-order with an applied field of approximately 5 V/micrometers and microsecond response time. We have also demonstrated image storage and electro-optical readout with these materials. Low voltage, high resolution scanning electron microscopy studies have confirmed that gratings formed in this material system consist of periodic polymer-dispersed liquid crystal planes. The critical fields for switching and the response times agree very well with a simple liquid crystal shaped-droplet model which we have applied to these gratings.

Binary optical generated interference patterns are used to produce close-packed microchannel azo dye images within optical resins for use as new types of optical elements. These optical elements may be used to control the angular components of optical wavefront dynamics in new ways. Low density azo dye micro-honeycomb images with high aspect ratios resulting in extended ray pathways filter out skew rays and allow transmission of meridional rays while suppressing diffractive effects. Whereas an aperture stop may be used in a conventional optical system to block the wider angle light rays which are a prime source of optical system aberrations, these directional light filters achieve a similar effect at any integral point across the transverse of the wavefront. The projector system also affords a production method of writing highly corrected peripheral-field as well as center-field micro-mesh patterns in photoresist on non-planar surfaces such as domes.

We have used a coupled wave analysis and solved numerically the coupled wave equations to model the performance of the diffraction gratings produced by the metal photo-dissolution effect in As - S thin films. This analysis is based on the material properties of arsenic sulphide silver doped films. We have analyzed both a sinusoidal and a square wave profile to consider both the holographic gratings and gratings produced by a mask exposure technique. Our model computes the diffraction efficiency versus two parameters (Omega) and (xi) where (Omega) is a thickness parameter and (xi) is a modulation parameter which is related to the change in the refractive index of the films. For the case of the sinusoidal profile the result of our model for very small values of (Omega) fits very well with the Bessel functions of the first kind which is the expected analytic results. As we change (Omega) from a small value of on the order of 0.01 to a value of on the order of 10, fewer diffraction orders become important in the replay of the grating with a red wavelength. For (Omega) on the order of 10 only one significant order is seen in the replay. The same results are generally obtained for the square grating. The angular response of the efficiency for a typical grating shows that the efficiency is a maximum near the Bragg angle. This result is in good agreement with the experimental results of the diffraction efficiency measurements obtained on a grating with the same parameters.

The application of dichromated gelatin holographic transmission gratings to spectroscopy, spectral filtering, and ultrafast lasers is discussed. Volume holographic gratings provide advantages over conventional dispersing elements including higher diffraction efficiencies, simple alignments, and greater ease of handling. This paper identifies the design parameters used to define the basic grating and then expands to describe the considerations necessary when the grating is a volume holographic grating. A general description is provided of the holographic process used to produce the volume gratings identifying key process steps and concerns.

Electrically switched holographic composites (ESHC) based on Polaroid photopolymer materials were described previously using optically generated holograms. These techniques have now been extended to include computer generated holograms. A highly accurate laser writing engine was utilized to write multi-phase level diffractive gratings in Polaroid type DMP-128 photopolymer film. After compositing with liquid crystals and applying an electric field, the diffraction efficiency of the elements could be switched or tuned continuously over approximately a 100:1 range of diffraction efficiencies, opening a new range of interconnect applications.

An optical device is presented that uses the highly wavelength dispersive nature of diffractive optics to provide a means of either removing a small waveband of incident radiation from a scene, to function as a tunable notch filter, or passing only a small waveband of incident radiation from the scene, to function as a tunable bandpass filter. Design examples are given along with system performance analysis. Experimental verification is also presented.

Planar optical configurations combine holographic elements with a substrate mode planar structure where the light is trapped inside the structure by total internal reflections. As a result, usual free space propagation can be replaced by guided propagation in the planar structures on which holographic elements are recorded on either side. These configurations can thus be very compact and readily modularized so as to eliminate the, usually needed, extreme alignment accuracies between input light sources, holographic elements, and output detectors. The principles and examples of how such elements can be incorporated into display and data processing applications are presented.

A novel design for a zero-order achromatic diffractive optical element is presented. Applications of the optical element are discussed. Tolerances on the material properties and fabrication considerations are presented. The predicted performance characteristics, including optical efficiency and effective bandwidth, are presented.

We specified 406 mm diameter off axis powered HOEs to operate at 1.06 microns and for trials at 670 nm, then looked for ways to construct them at 488 nm. We were able to write holographic surfaces directly in Zemax, then play back other wavelengths through them to display the aberrations that needed to be canceled. Zemax had easy entry and optimization routines that allowed us to do cut and try construction variations on screen rather than on the table. We designed construction set ups using only off the shelf lenses and mirrors and were able then to fabricate the HOEs with only small incremental improvements being made on the table. The computed spot sizes were less than .5 mm diameter and constructed holographic optics were on Bragg with outputs as small as .5 mm and high efficiencies.

The optical performance of a holographic projection system is analyzed by a physical optics simulation code. This holographic projector is used to produce micro-optical devices which are generated by a photolytic process involving exposure and development. These devices can be used as a new generation of directional light filters and monolithic micro-channel optical arrays. This projection system consists of a laser, a beam expander, a beam reshaping system which reshapes the Gaussian beam profile of the laser into a uniform beam profile, a holographic diffraction grating which is used to produce multiple beams, and an interferometric optical system behind the grating. This interferometric optical system creates broadly diverging cones of light which mutually overlap creating a three-dimensional standing wave interference pattern. A diazo-acid-coupler coated substrate can be placed within the overlapping cones of light so that an interference pattern may be recorded within the substrate coating to produce micro-optical devices or directional light filters.

We discuss the implementation of an optoelectronic programmable logic array using arrays of optical thyristors and Fourier plane diffractive optical elements. The effects of the spectral line-width of the optical thyristors on dispersive inter-element cross-talk are modelled and found to be tolerable. An experimental demonstration of an optical interconnection with diffractive fan-out for optical thyristor arrays is presented.

We present an optical system for the polar formatting of data in a spotlight mode SAR. This system is implemented with only one holographic optical element (HOE). Previously such a HOE could not be produced because the phase of the required transmission function of the HOE does not obey the continuity condition which is prerequisite for the conventional implementation of such optical transforms. Here we show how a HOE can be produced to perform the complete polar formatting transform by incorporating branch point phase singularities in the transmission function of the HOE. The computation of the transmission function is shown and numerically computed diffraction patterns obtained from this HOE are also shown.

Binary-phase optics have been used by a number of high-power laser laboratories in order to achieve relatively smooth focal spots. However, the intensity envelopes have in general been of a sinc form rather than `top-hat.' This paper presents work on the production of uniform `top-hat' intensity focal spot profiles obtained from Fresnel binary phase zone plate (PZP) arrays of various designs. Phase plates are used to generate large area smooth focal spots and both theoretical and experimental focal spots are presented. These demonstrate the flexibility of this technique which provides a simple method of generating both uniform `top-hat' intensity profiles and spatially shaped foci, for use with high-power lasers.

An optical star coupler which employs holographic optical elements as branching devices is proposed to be applied to bi-directional fiber-optic communication systems with multimode optical fibers and light emitting diodes. Variation of coupling efficiency of the coupler due to the misalignment of optical components and the shift of wavelength is analyzed. The simulated results on the coupler described here show that the efficiency is reduced by 1 dB due to lateral shift of 18 micrometers of optical fibers used for input and output ports. Experimental results of the efficiency variation are explained by the simulation.

An optical two by two exchange bypass module formed by a combination of static and dynamic Fresnel zone lenses is proposed. The basic concept of this switching element is to cascade pairs of dynamic Fresnel zone lenses and pairs of static Fresnel zone lenses, located on each side of a 1.5 mm thick quartz-glass substrate. Two types of elements were designed, to operate at wavelengths of 1.52 micrometers and 0.633 micrometers . The dynamic Fresnel zone lenses on the frontside of the substrate are off-axis lenses which are made switchable by filling them with a liquid crystal after covering the Fresnel structure with a transparent electrode. The second electrode is deposited on a face down mounted cover-glass. The static lenses on the backside of the substrate are conventional on-axis Fresnel zone lenses. The dynamic and the static Fresnel zone lenses, whose blazed profiles have been approximated by multi-levels, have been fabricated by means of micro-structuring techniques. Static and dynamic, on-axis and off-axis Fresnel zone lenses with different focal lengths and of different circular diameters ranging from 0.2 mm to 2.0 mm have been realized. The measured spot-sizes of the Fresnel zone lenses were close to eighth diffraction limited values and the diffraction efficiency of the eight-level lenses was higher than 80%. The switching times of the dynamic lenses were in the range of several milli-seconds and the switching contrast was about 1:10.

It is becoming widely recognized that there is a requirement for a head-up display (HUD) in the civil aircraft cockpit. Due to the variety of airframes used by commercial airlines there is the need for a universal HUD design which could be installed into a range of aircraft. Holographic components have been utilized to provide a display that is acceptable in terms of optical performance, and provide an optical relay that will fit the available space.

A simple hybrid diffractive-refractive optical element is developed for simultaneous display of the image and the spectrum of an object in a single plane. An optically recorded holographic lens followed by a conventional Fourier lens constitutes the building block for the double channel image processor. Preliminary results are presented.

The peculiarities of the wavefronts formation during the phase objects hologram reconstruction simultaneously by the reference and object beams are discussed. The interference patterns which appear if the reconstructed waves and those passed through the hologram without deflection are superposed, carry information on the reconstructed beams variations. Influence of the factors describing the considered system on the correspondence of the interference patterns to the variations of the reconstructed beams is evaluated.

Diffraction from a photorefractive grating in the presence of two input beams is studied both theoretically and experimentally. The results are extended to the control of the interference of diffracted beams from two photorefractive gratings, which adopts a nondegenerate pulsed wave coupling technique.

A system of fabricating and evaluating a holographic plate in DCG or photoresist emulsion with economical manufacturing equipment is described. Here we insist on a new concept of DCG and photoresist holographic plate fabricating process and define five film quality characteristics to evaluate the quality of the film of a holographic plate with digital image processing technique.

This paper describes the contact copying of amplitude transmission holographic gratings. Master gratings (MG) are written in silver halide sensitized gelatine. A smooth and flat sheet is coated with a layer of negative photoresist constituted from a combination of polyvinyl alcohol, ammonium dichromate and Arabic gum, then the MG is put in contact with the metal surface and exposed by a mercury lamp. After processing with deionized water at (35 degree(s)C), a reflection grating is obtained. For a MG with 117 l/mm of spatial frequency and 10% of diffraction efficiency (DE), we have obtained a DE of 12%.

We describe a computational method for calculating the electric field, generated by a periodical set of electrodes, that are placed on the surface(s) of a 9/65/35 PLZT electro-optic ceramics layer. This method is based on the introduction of two auxiliary functions that describe the density of electric charge distribution on the electrodes with different potentials. The problem is then reduced to the solution of the two integral equations in these functions. The coordinate transforms of each of the two equations, which map electrode areas onto the whole period, modify these integral equations into two coupled infinite sets of algebraic equations for coefficients of expansion into a Fourier series of auxiliary functions. For the new sets of expansion coefficients, the sets of equations become decoupled ones. These equations were solved numerically by cutting to a finite number of equations. With the help of this method, the three schemes of electrode connections were analyzed. The dependences of the half-wave voltage and the switching energy on the electrode spatial frequency and on the relative electrode width were determined. These dependences give the possibility to obtain the optimal electrode pattern of the schemes and find out the optimal scheme of electrode connections.

A diffractive optical surface was inserted in a wide field of view ultraviolet sensor to increase the aperture and waveband of the system with no increase in size or weight. The diffractive optical surface was etched in sapphire using binary optics fabrication techniques.

The key to effective utilization and systematic design of resonance domain diffractive elements lies in understanding the way in which the input beam interacts with the structure to produce the output field. This is straightforward in the paraxial, scalar, regime as the diffracted signal can be related directly to the physical parameters of the grating but resonance domain optics provides at least two exciting advantages over conventional optics. The first is the ability to use the wavelength scale structure to produce grating response functions with phase and/or amplitude modulations that cannot be realized conventionally. The second advantage is to use the polarization sensitivity of such devices to increase the functionality of a given element. We report on two novel uses of resonance domain diffractive optics. The first element is a diffractive optic beam deflector intended for high power laser systems, where laser induced damage limits the usefulness of conventional elements. The second element is a reflection grating operating as a polarization beam splitter. In the case of the beam splitter we present a simple model to explain the essential physics behind the operation of the device. This model leads to simple formulae for the design of other polarization sensitive devices.

Diffractive optical elements (DOEs) have proven to be useful components in optical interconnection and routing systems, especially where volume, weight, and design flexibility are important. We show that it is possible to increase the functionality of DOEs by making them polarization-selective, i.e. anisotropic. Several anisotropic diffractive optical elements (ADOEs) were fabricated in calcite by means of simple wet etching technology, and characterized experimentally. Both anisotropic Fresnel lenses and gratings have been studied. First order efficiencies of more than 12% and contrast ratios of over 110:1 have been observed for off-axis elements. To demonstrate the potential of these ADOEs we have built an electrically controlled beam deflector which consists of a liquid crystal polarization modulator and an anisotropic grating. An incident beam can then be deflected to two different pairs of points by changing the voltage applied to the liquid crystal modulator. We show the high contrast ratios observed when simultaneously measuring the intensity in each point while the voltage on the liquid crystal is modulated.

Two boundary integral models of vector diffraction from diffractive optical elements (DOEs) are presented. The first is the method of moments and the second, the boundary element method. The advantages of boundary integral methods over alternate vector diffraction models are threefold. First, only the surface of the diffractive structure is sampled, not the entire solution space. Second, they can model both finite aperiodic and infinite periodic DOEs and, third, once the surface current distribution is determined for a given incident field, it can be used to determine the vector field amplitudes anywhere in space or over any region and/or regions of space. Results are presented for the diffraction of a TM-polarized plane wave from three conducting surfaces; a plate, grating, and diffractive lens.

Diffractive elements are designed to synthesize special purpose distributions of light which extend in three-dimensional domains. These distributions present unique physical properties: high directionality, diffraction limited spot-size, propagation invariance, extinction and regeneration. The diffractive elements are iteratively designed and exhibit an efficient utilization of the information capacity. Experimental results demonstrate good agreement with simulations.

A wavefront sensor is supposed to analyze the phase distribution of a wave without any external reference as used in most conventional interferometric systems. It is shown here that an efficient wavefront sensor can be implemented by an array of two-beam common path inversion interferometers. Each element of the array consists of two Fresnel lenses in a confocal configuration. The wavefront data can be extracted from a superposition of the zero- order, undiffracted wave and the twice diffracted first order wave. The result is a high sensitivity, compact and stable interferometric wavefront sensor.