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Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗

Stratified Diffractive Optic Approach for Creating High Efficiency Gratings

Gratings with high efficiency in a single diffracted order can be realized with both volume holographic and diffractive optical elements. However, each method has limitations that restrict the applications in which they can be used. For example, high efficiency volume holographic gratings require an appropriate combination of thickness and permittivity modulation throughout the bulk of the material. Possible combinations of those two characteristics are limited by properties of currently available materials, thus restricting the range of applications for volume holographic gratings. Efficiency of a diffractive optic grating is dependent on its approximation of an ideal analog profile using discrete features. The size of constituent features and, consequently, the number that can be used within a required grating period restricts the applications in which diffractive optic gratings can be used. These limitations imply that there are applications which cannot be addressed by either technology. In this paper we propose to address a number of applications in this category with a new method of creating high efficiency gratings which we call stratified diffractive optic gratings. In this approach diffractive optic techniques are used to create an optical structure that emulates volume grating behavior. To illustrate the stratified diffractive optic grating concept we consider a specific application, a scanner for a space-based coherent wind lidar, with requirements that would be difficult to meet by either volume holographic or diffractive optic methods. The lidar instrument design specifies a transmissive scanner element with the input beam normally incident and the exiting beam deflected at a fixed angle from the optical axis. The element will be rotated about the optical axis to produce a conical scan pattern. The wavelength of the incident beam is 2.06 microns and the required deflection angle is 30 degrees, implying a grating period of approximately 4 microns. Creating a high efficiency volume grating with these parameters would require a grating thickness that cannot be attained with current photosensitive materials. For a diffractive optic grating, the number of binary steps necessary to produce high efficiency combined with the grating period requires feature sizes and alignment tolerances that are also unattainable with current techniques. Rotation of the grating and integration into a space-based lidar system impose the additional requirements that it be insensitive to polarization orientation, that its mass be minimized and that it be able to withstand launch and space environments.

Chambers, Diana M.↗

Diffractive optics fabricated by direct write methods with an electron beam

State-of-the-art diffractive optics are fabricated using e-beam lithography and dry etching techniques to achieve multilevel phase elements with very high diffraction efficiencies. One of the major challenges encountered in fabricating diffractive optics is the small feature size (e.g. for diffractive lenses with small f-number). It is not only the e-beam system which dictates the feature size limitations, but also the alignment systems (mask aligner) and the materials (e-beam and photo resists). In order to allow diffractive optics to be used in new optoelectronic systems, it is necessary not only to fabricate elements with small feature sizes but also to do so in an economical fashion. Since price of a multilevel diffractive optical element is closely related to the e-beam writing time and the number of etching steps, we need to decrease the writing time and etching steps without affecting the quality of the element. To do this one has to utilize the full potentials of the e-beam writing system. In this paper, we will present three diffractive optics fabrication techniques which will reduce the number of process steps, the writing time, and the overall fabrication time for multilevel phase diffractive optics.

Kress, Bernard↗

Diffractive Optical Elements for Spectral Imaging

Diffractive optical elements fabricated on flat and non-flat substrates frequently act as dispersive elements in imaging spectrometers. We describe the design and electron-beam fabrication of blazed and computer-generated-hologram gratings for slit and tomographic imaging spectrometers.

diffractive optics gratings spectral imaging imagi↗

Diffractive Optical Elements for Spectral Imaging

Diffractive optical elements fabricated on flat and non-flat substrates frequently act as dispersive elements in imaging spectrometers. We describe the design and electron-beam fabrication of blazed and computer-generated-hologram gratings for slit and tomographic imaging spectrometer.

diffractive optics gratings spectral imaging imagi↗

Optical system storage design with diffractive optical elements

Optical data storage systems are gaining widespread acceptance due to their high areal density and the ability to remove the high capacity hard disk from the system. In magneto-optical read-write systems, a small rotation of the polarization state in the return signal from the MO media is the signal which must be sensed. A typical arrangement used for detecting these signals and correcting for errors in tracking and focusing on the disk is illustrated. The components required to achieve these functions are listed. The assembly and alignment of this complex system has a direct impact on cost, and also affects the size, weight, and corresponding data access rates. As a result, integrating these optical components and improving packaging techniques is an active area of research and development. Most designs of binary optic elements have been concerned with optimizing grating efficiency. However, rigorous coupled wave models for vector field diffraction from grating surfaces can be extended to determine the phase and polarization state of the diffracted field, and the design of polarization components. A typical grating geometry and the phase and polarization angles associated with the incident and diffracted fields are shown. In our current stage of work, we are examining system configurations which cascade several polarization functions on a single substrate. In this design, the beam returning from the MO disk illuminates a cascaded grating element which first couples light into the substrate, then introduces a quarter wave retardation, then a polarization rotation, and finally separates s- and p-polarized fields through a polarization beam splitter. The input coupler and polarization beam splitter are formed in volume gratings, and the two intermediate elements are zero-order elements.

Kostuk, Raymond K.↗

Linearization of an annular image by using a diffractive optic

The goal for this project is to develop the algorithms for fracturing the zones defined by the mapping transformation, and to actually produce the binary optic in an appropriate setup. In 1984 a side-viewing panoramic viewing system was patented, consisting of a single piece of glass with spherical surfaces which produces a 360 degree view of the region surrounding the lens which extends about 25 degrees in front of and 20 degrees behind the lens. The system not only produces images of good quality, it is also afocal, i.e., images stay in focus for objects located right next to the lens as well as those located far from the lens. The lens produced a panoramic view in an annular shaped image, and so the lens was called a PAL (panoramic annular lens). When applying traditional measurements to PAL images, it is found advantageous to linearize the annular image. This can easily be done with a computer and such a linearized image can be produced within about 40 seconds on current microcomputers. However, this process requires a frame-grabber and a computer, and is not real-time. Therefore, it was decided to try to perform this linearization optically by using a diffractive optic.

Matthys, Donald R.↗

Three-Dimensional Displacement Measurement Using Diffractive Optic Interferometry

This paper introduces a powerful new optical method which utilizes diffractive optic interferometry (DOI) to measure both in-plane and out-of-plane displacement with variable sensitivity using the same optical system. Sensitivity is varied by utilizing various combinations of the different wavefronts produced by a conjugate pair of binary Optical elements; a transmission grating is used to produce several illumination beams while a reflective grating replicated on the surface of a specimen, provides the reference for the undeformed state. A derivation of the equations which govern the method is included along with a discussion Of the experimental tests conducted to verify the theory. Overall, the results are excellent, with experimental data agreeing to within a few percent of the theoretical predictions.

Gilbert, John A.↗

Technology Development of Stratified Volume Diffractive Optics for Waveguide Coupling

Stratified Volume Diffractive Optical Elements (SVDOE) appear to be viable as high-efficiency waveguide couplers. Preliminary design studies were conducted under this task to provide initial device parameters for evaluation. However, these designs should be revisited prior to fabrication of a device for testing. The emphasis of this task has been development and implementation of fabrication procedures necessary for SVDOE'S, namely alignment of grating layers, Including offsets, to within required tolerances. Progress in this area Indicates that the alignment technique chosen is viable and tolerances have been reached that allow reasonable performance ranges. Approaches have been identified to improve alignment tolerances even further.

Chambers, Diana M.↗

Diffractive optics for particle velocimetry and sizing

Beam-shaping diffractive optical elements are used to create structured light patterns in fluid flows. Particle scattering results in detected signals that can be used to determine the particle size and velocity.

diffractive optics laser velocimetry↗

SURPHEX (tm): New dry photopolymers for replication of surface relief diffractive optics

High efficiency, deep groove, surface relief Diffractive Optical Elements (DOE) with various optical functions can be recorded in a photoresist using conventional interferometric holographic and computer generated photolithographic recording techniques. While photoresist recording media are satisfactory for recording individual surface relief DOE, a reliable and precise method is needed to replicate these diffractive microstructures to maintain the high aspect ratio in each replicated DOE. The term 'high aspect ratio' means that the depth of a groove is substantially greater, i.e. 2, 3, or more times greater, than the width of the groove. A new family of dry photopolymers SURPHEX was developed recently at Du Pont to replicate such highly efficient, deep groove DOE's. SURPHEX photopolymers are being utilized in Du Pont's proprietary Dry Photopolymer Embossing (DPE) technology to replicate with very high degree of precision almost any type of surface relief DOE. Surfaces relief microstructures with width/depth aspect ratio of 1:20 (0.1 micron/2.0 micron) were faithfully replicated by DPE technology. Several types of plastic and glass/quartz optical substrates can be used for economical replication of DOE.

Shvartsman, Felix P.↗

Multiple-Zone Diffractive Optic Element for Laser Ranging Applications

A diffractive optic element (DOE) can be used as a beam splitter to generate multiple laser beams from a single input laser beam. This technology has been recently used in LRO s Lunar Orbiter Laser Altimeter (LOLA) instrument to generate five laser beams that measure the lunar topography from a 50-km nominal mapping orbit (see figure). An extension of this approach is to use a multiple-zone DOE to allow a laser altimeter instrument to operate over a wider range of distances. In particular, a multiple-zone DOE could be used for applications that require both mapping and landing on a planetary body. In this case, the laser altimeter operating range would need to extend from several hundred kilometers down to a few meters. The innovator was recently involved in an investigation how to modify the LOLA instrument for the OSIRIS asteroid mapping and sample return mission. One approach is to replace the DOE in the LOLA laser beam expander assembly with a multiple-zone DOE that would allow for the simultaneous illumination of the asteroid with mapping and landing laser beams. The proposed OSIRIS multiple-zone DOE would generate the same LOLA five-beam output pattern for high-altitude topographic mapping, but would simultaneously generate a wide divergence angle beam using a small portion of the total laser energy for the approach and landing portion of the mission. Only a few percent of the total laser energy is required for approach and landing operations as the return signal increases as the inverse square of the ranging height. A wide divergence beam could be implemented by making the center of the DOE a diffractive or refractive negative lens. The beam energy and beam divergence characteristics of a multiple-zone DOE could be easily tailored to meet the requirements of other missions that require laser ranging data. Current single-zone DOE lithographic manufacturing techniques could also be used to fabricate a multiple-zone DOE by masking the different DOE zones during the manufacturing process, and the same space-compatible DOE substrates (fused silica, sapphire) that are used on standard DOE s could be used for multiple- zone DOE s. DOEs are an elegant and cost-effective optical design option for spacebased laser altimeters that require multiple output laser beams. The use of multiple-zone DOEs would allow for the design and optimization of a laser altimeter instrument required to operate over a large range of target distances, such as those designed to both map and land on a planetary body. In addition to space-based laser altimeters, this technology could find applications in military or commercial unmanned aerial vehicles (UAVs) that fly at an altitude of several kilometers and need to land. It is also conceivable that variations of this approach could be used in land-based applications such as collision avoidance and robotic control of cars, trains, and ships.

Ramos-Izquierdo, Luis A.↗

Measuring In-Plane Displacements with Variable Sensitivity Using Diffractive Optic Interferometry

This paper introduces a method called diffractive optic interferometry (DOI) which allows in-plane displacement components to be measured with variable sensitivity. DOI relies on binary optical elements fabricated as phase-type Dammann gratings which produce multiple diffraction orders of nearly equal intensity. Sensitivity is varied by combining the different wavefronts produced by a conjugate pair of these binary optical elements; a transmission element is used to produce several illumination beams while a reflective element, replicated on the surface of a specimen, provides the reference for the undeformed state. The steps taken to design and fabricate these binary optical elements are described. The specimen grating is characterized, and tested on a disk subjected to diametrical compression. Overall, the results are excellent, with experimental data agreeing to within a few percent of the theoretical predictions.

Shepherd, Robert L.↗

Stratified Volume Diffractive Optical Elements as Low-Mass Coherent Lidar Scanners

Transmissive scanning elements for coherent laser radar systems are typically optical wedges, or prisms, which deflect the lidar beam at a specified angle and are then rotated about the instrument optical axis to produce a scan pattern. The wedge is placed in the lidar optical system subsequent to a beam-expanding telescope, implying that it has the largest diameter of any element in the system. The combination of the wedge diameter and asymmetric profile result in the element having very large mass and, consequently, relatively large power consumption required for scanning. These two parameters, mass and power consumption, are among the instrument requirements which need to be minimized when designing a lidar for a space-borne platform. Reducing the scanner contributions in these areas will have a significant effect on the overall instrument specifications, Replacing the optical wedge with a diffraction grating on the surface of a thin substrate is a straight forward approach with potential to reduce the mass of the scanning element significantly. For example, the optical wedge that will be used for the SPAce Readiness Coherent Lidar Experiment (SPARCLE) is approximately 25 cm in diameter and is made from silicon with a wedge angle designed for 30 degree deflection of a beam operating at approx. 2 micrometer wavelength. The mass of this element could be reduced by a factor of four by instead using a fused silica substrate, 1 cm thick, with a grating fabricated on one of the surfaces. For a grating to deflect a beam with a 2 micrometer wavelength by 30 degrees, a period of approximately 4 micrometers is required. This is small enough that fabrication of appropriate high efficiency blazed or multi-phase level diffractive optical gratings is prohibitively difficult. Moreover, bulk or stratified volume holographic approaches appear impractical due to materials limitations at 2 micrometers and the need to maintain adequate wavefront quality. In order to avoid the difficulties encountered in these approaches, we have developed a new type of high-efficiency grating which we call a Stratified Volume Diffractive Optical Element (SVDOE). The features of the gratings in this approach can be easily fabricated using standard photolithography and etching techniques and the materials used in the grating can be chosen specifically for a given application, In this paper we will briefly discuss the SVDOE technique and will present an example design of a lidar scanner using this approach. We will also discuss performance predictions for the example design.

Chambers, Diana M.↗

Scalar limitations of diffractive optical elements

In this paper, scalar limitations of diffractive optic components are investigated using coupled wave analyses. Results are presented for linear phase gratings and fanout devices. In addition, a parametric curve is given which correlates feature size with scalar performance.

Johnson, Eric G.↗

Transmissive Diffractive Optical Element Solar Concentrators

Solar-thermal-radiation concentrators in the form of transmissive diffractive optical elements (DOEs) have been proposed as alternatives to mirror-type solar concentrators now in use. In comparison with functionally equivalent mirror-type solar concentrators, the transmissive, diffractive solar concentrators would weigh and cost less, and would be subject to relaxed mechanical tolerances. A DOE concentrator would be made from a thin, flat disk or membrane of a transmissive material having a suitable index of refraction. By virtue of its thinness, the DOE concentrator would have an areal mass density significantly less than that of a functionally equivalent conventional mirror. The DOE concentrator would have a relatively wide aperture--characterized by a focal-length/aperture-diameter ratio ('f number') on the order of 1. A kinoform (a surface-relief phase hologram) of high diffractive order would be microfabricated onto one face of the disk. The kinoform (see figure) would be designed to both diffract and refract incident solar radiation onto a desired focal region, without concern for forming an image of the Sun. The high diffractive order of this kinoform (in contradistinction to the low diffractive orders of some other kinoforms) would be necessary to obtain the desired f number of 1, which, in turn, would be necessary for obtaining a desired concentration ratio of 2,500 or greater. The design process of optimizing the concentration ratio of a proposed DOE solar concentrator includes computing convolutions of the optical bandwidth of the Sun with the optical transmission of the diffractive medium. Because, as in the cases of other non-imaging, light-concentrating optics, image quality is not a design requirement, the process also includes trading image quality against concentration ratio. A baseline design for one example calls for an aperture diameter of 1 m. This baseline design would be scalable to a diameter as large as 10 m, or to a smaller diameter for a laboratory test article. Initial calculations have indicated that the characteristics of the test article would be readily scalable to a full-size unit.

Baron, Richard↗