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NASA NTRS1992

On the convergence of the coupled-wave approach for lamellar diffraction gratings

Among the many existing rigorous methods for analyzing diffraction of electromagnetic waves by diffraction gratings, the coupled-wave approach stands out because of its versatility and simplicity. It can be applied to volume gratings and surface relief gratings, and its numerical implementation is much simpler than others. In addition, its predictions were experimentally validated in several cases. These facts explain the popularity of the coupled-wave approach among many optical engineers in the field of diffractive optics. However, a comprehensive analysis of the convergence of the model predictions has never been presented, although several authors have recently reported convergence difficulties with the model when it is used for metallic gratings in TM polarization. Herein, three points are made: (1) in the TM case, the coupled-wave approach converges much slower than the modal approach of Botten et al; (2) the slow convergence is caused by the use of Fourier expansions for the permittivity and the fields in the grating region; and (3) is manifested by the slow convergence of the eigenvalues and the associated modal fields. The reader is assumed to be familiar with the mathematical formulations of the coupled-wave approach and the modal approach.

Li, Lifeng↗

NASA NTRS1993

Fabrication techniques for very fast diffractive lenses

Aspheric lenses with arbitrary phase functions can be fabricated on thin light weight substrates via the binary optics fabrication technique. However, it is difficult and costly to fabricate a fast lens (f/number less than 1) for use as the shorter wavelengths. The pitch of the masks and the alignment accuracy must be very fine. For a large lens, the space-bandwidth product of the element can also become impractically large. In this paper, two alternate approaches for the fabrication of fast aspheric diffractive lenses are described. The first approach fabricates the diffractive lens interferometrically, utilizing a spherical wavefront to provide the optical power of the lens and a computer generated hologram to create the aspheric components. The second approach fabricates the aspheric diffractive lens in the form if a higher order kinoform which trades groove profile fidelity for coarser feature size. The design and implementation issues for these two fabrication techniques are discussed.

Tai, Anthony M.↗

NASA NTRS1993

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.↗

NASA NTRS1993

Rotary encoding device using polygonal mirror with diffraction gratings on each facet

A device for position encoding of a rotating shaft in which a polygonal mirror having a number of facets is mounted to the shaft and a monochromatic light beam is directed towards the facets. The facets of the polygonal mirror each have a low line density diffraction grating to diffract the monochromatic light beam into a number of diffracted light beams such that a number of light spots are created on a linear array detector. An analog-to-digital converter is connected to the linear array detector for reading the position of the spots on the linear array detector means. A microprocessor with memory is connected to the analog-to-digital converter to hold and manipulate the data provided by the analog-to-digital converter on the position of the spots and to compute the position of the shaft based upon the data from the analog-to-digital converter.

Leviton, Douglas B.↗

NASA NTRS1996

Two-Photon Ghost Image and Interference-Diffraction

One of the most surprising consequences of quantum mechanics is entanglement of two or more distance particles. The two-particle entangled state was mathematically formulated by Schrodinger. Based on this unusual quantum behavior, EPR defined their 'physical reality' and then asked the question: 'Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?' One may not appreciate EPR's criterion of physical reality and insist that 'no elementary quantum phenomenon is a phenomenon until it is a recorded phenomenon'. Optical spontaneous parametric down conversion (SPDC) is the most effective mechanism to generate an EPR type entangled two-photon state. In SPDC, an optical beam, called the pump, is incident on a birefringent crystal. The pump is intense enough so that nonlinear effects lead to the conversion of pump photons into pairs of photons, historically called signal and idler. Technically, the SPDC is said to be type-1 or type-2, depending on whether the signal and idler beams have parallel or orthogonal polarization. The SPDC conversion efficiency is typically on the order of 10(exp -9) to 10(exp -11), depending on the SPDC nonlinear material. The signal and idler intensities are extremely low, only single photon detection devices can register them. The quantum entanglement nature of SPDC has been demonstrated in EPR-Bohm experiments and Bell's inequality measurements. The following two experiments were recently performed in our laboratory, which are more closely related to the original 1935 EPR gedankenezperiment. The first experiment is a two-photon optical imaging type experiment, which has been named 'ghost image' by the physics community. The signal and idler beams of SPDC are sent in different directions, so that the detection of the signal and idler photons can be performed by two distant photon counting detectors. An aperture object (mask) is placed in front of the signal photon detector and illuminated by the signal beam through a convex lens. Surprisingly, an image of this aperture is observed in the idler beam, by scanning the idler photon detector in the transverse plane of the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal, which can be easily performed by a coincidence measurement. This effect is even more striking when we found that the object-lens-image relationship satisfies the Gaussian thin lens equation. The second experiment demonstrates two-photon 'ghost' interference-diffraction. The experimental set up is similar to the image experiment, except that rather than a lens and an aperture it is a Young's double-slit (or a single-slit) inserted into the path of the signal beam. We could not find any interference (or diffraction) pattern behind the slit. Surprisingly, an interference (or diffraction) pattern is observed when scanning the detector in the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal.

Shih, Y. H.↗

NASA NTRS1996

A tunable crystal diffraction telescope for the International Space Station

A focusing gamma ray telescope is proposed for use onboard the International Space Station. It consists of a tunable crystal diffraction lens which focuses gamma rays onto a small array of germanium detectors located on an extendable boom. While the weight of such an instrument is less than 500 kg, it features an angular resolution of 15 arcsec, an energy resolution of 2 keV and a 3 sigma sensitivity of the order of 10(exp -7) photons/sq cm sec for any individual narrow line at energies of between 200 and 1300 keV. The scientific potential of such a telescope is discussed. The principles of a diffraction lens and a tunable diffraction lens are described.

VonBallmoos, P.↗

NASA NTRS1993

Diffraction of a Gaussian Beam by a Spherical Obstacle

The Kirchhoff integral for diffraction in the near-forward direction is derived from the exact solution of the electromagnetic boundary value problem of a focused Gaussian laser beam incident on a spherical particle. The diffracted intensity in the vicinity of the particle is computed and the way in which the features of the diffraction pattern depend on the width of the Gaussian beam is commented on.

Lock, James A.↗

NASA NTRS1999

High Resolution Triple Axis X-Ray Diffraction Analysis of II-VI Semiconductor Crystals

The objective of this research program is to develop methods of structural analysis based on high resolution triple axis X-ray diffractometry (HRTXD) and to carry out detailed studies of defect distributions in crystals grown in both microgravity and ground-based environments. HRTXD represents a modification of the widely used double axis X-ray rocking curve method for the characterization of grown-in defects in nearly perfect crystals. In a double axis rocking curve experiment, the sample is illuminated by a monochromatic X-ray beam and the diffracted intensity is recorded by a fixed, wide-open detector. The intensity diffracted by the sample is then monitored as the sample is rotated through the Bragg reflection condition. The breadth of the peak, which is often reported as the full angular width at half the maximum intensity (FWHM), is used as an indicator of the amount of defects in the sample. This work has shown that high resolution triple axis X-ray diffraction is an effective tool for characterizing the defect structure in semiconductor crystals, particularly at high defect densities. Additionally, the technique is complimentary to X-ray topography for defect characterization in crystals.

Volz, H. M.↗

NASA NTRS1999

Efficient IR Transmission Diffraction Grating for Circularly Polarized Light

Numerical methods, using rigorous coupled wave theory, are used to design rectangular relief diffraction gratings for an infrared application which requires comparable first order efficiencies in the TE and TM polarization states. The depth, period, and fill factor of the grating are varied to identify optimal two level binary lamellar grating profiles which predict efficiencies for individual TM and TE polarizations above 75 percent, while keeping the difference between the two efficiencies within 10 percent. The application at hand is a rotating, transmissive diffractive scanner for space-based coherent lidar. The operating wavelength is 2.0 microns. A collimated, circularly polarized beam is incident on the diffractive scanner at the Bragg angle; 30 and 45 degree beam deflection angles being studied. Fused silica is the substrate material of choice. Selected designs are fabricated on 3 inch fused silica substrates using lithographic methods. The performance of the test pieces is measured and compared to theoretical predictions.

Cole, Helen↗

NASA NTRS1999

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.↗

NASA NTRS1998

X-Ray Diffraction Analysis of NLO Crystals: Traditional Applications and More New Opportunities

Single crystal X-ray diffraction analysis is one of the more important methods for the molecular and crystal structure determination of matter and therefore it has a great importance in material science including design and engineering of different compounds with non-linear optical (NLO) properties. It was shown in our previous publications that this method provides unique information about molecular structure of NLO compounds, their crystal symmetry and crystal packing arrays, molecular conformation and geometries and many other structural and electronic characteristics that are important for understanding the nature of NLO properties of solids. A very new application of the X-ray diffraction method is related to analysis of the electron density distribution p(r) in crystals and some of its characteristics (atomic and group charges, dipole and higher multipole moments, etc.), that may be obtained directly form the diffraction measurements. In the present work, we will discuss our preliminary low temperature high-resolution X-ray data for the m-nitroaniline (mNA) single crystal (VI). This is one of the "classical" organic NLO materials and electron density distribution analysis in this simple compound has a great scientific interest.

Antipin, Mikhail Yu.↗

NASA NTRS2000

Synchrotron X-Ray Reciprocal Space Mapping, Topography and Diffraction Resolution Studies of Macromolecular Crystal Quality

A comprehensive study of microgravity and ground grown chicken egg white lysozyme crystals is presented using synchrotron X-ray reciprocal space mapping, topography techniques and diffraction resolution. Microgravity crystals displayed, on average, reduced intrinsic mosaicities but no differences in terms of stress over their earth grown counterparts. Topographic analysis revealed that in the microgravity case the majority of the crystal was contributing to the peak of the reflection at the appropriate Bragg angle. In the earth case at the diffraction peak only a small volume of the crystal contributed to the intensity. The techniques prove to be highly complementary with the reciprocal space mapping providing a quantitative measure of the crystal mosaicity and stress (or variation in lattice spacing) and topography providing a qualitative overall assessment of the crystal in terms of its X-ray diffraction properties. Structural data collection was also carried out both at the synchrotron and in the laboratory.

Boggon, T. J.↗

NASA NTRS2000

High Resolution X-Ray Diffraction of Macromolecules with Synchrotron Radiation

We recently combined synchrotron-based monochromatic X-ray diffraction topography methods with triple axis diffractometry and rocking curve measurements: high resolution X-ray diffraction imaging techniques, to better understand the quality of protein crystals. We discuss these methods in the light of results obtained on crystals grown under different conditions. These non destructive techniques are powerful tools in the characterization of the protein crystals and ultimately will allow to improve, develop, and understand protein crystal growth. High resolution X-ray diffraction imaging methods will be discussed in detail in light of recent results obtained on Hen Egg White Lysozyme crystals and other proteins.

Stojanoff, Vivian↗

NASA NTRS2003

X-Ray Diffraction and Imaging Study of Imperfections of Crystallized Lysozyme with Coherent X-Rays

Phase-sensitive x-ray diffraction imaging and high angular-resolution diffraction combined with phase contrast radiographic imaging are employed to characterize defects and perfection of a uniformly grown tetragonal lysozyme crystal in symmetric Laue case. The fill width at half-maximum (FWHM) of a 4 4 0 rocking curve measured from the original crystal is approximately 16.7 arcseconds, and defects, which include point defects, line defects, and microscopic domains, have been clearly observed in the diffraction images of the crystal. The observed line defects carry distinct dislocation features running approximately along the <110> growth front, and they have been found to originate mostly at a central growth area and occasionally at outer growth regions. Individual point defects trapped at a crystal nucleus are resolved in the images of high sensitivity to defects. Slow dehydration has led to the broadening of the 4 4 0 rocking curve by a factor of approximately 2.4. A significant change of the defect structure and configuration with drying has been revealed, which suggests the dehydration induced migration and evolution of dislocations and lattice rearrangements to reduce overall strain energy. The sufficient details of the observed defects shed light upon perfection, nucleation and growth, and properties of protein crystals.

Hu, Zheng-Wei↗

NASA NTRS2002

Examination of Short- and Long-Range Atomic Order Nanocrystalline SiC and Diamond by Powder Diffraction Methods

The real atomic structure of nanocrystals determines unique, key properties of the materials. Determination of the structure presents a challenge due to inherent limitations of standard powder diffraction techniques when applied to nanocrystals. Alternate methodology of the structural analysis of nanocrystals (several nanometers in size) based on Bragg-like scattering and called the "apparent lattice parameter" (alp) is proposed. Application of the alp methodology to examination of the core-shell model of nanocrystals will be presented. The results of application of the alp method to structural analysis of several nanopowders were complemented by those obtained by determination of the Atomic Pair Distribution Function, PDF. Based on synchrotron and neutron diffraction data measured in a large diffraction vector of up to Q = 25 Angstroms(exp -1), the surface stresses in nanocrystalline diamond and SiC were evaluated.

Palosz, B.↗

NASA NTRS2003

Perfection of Apoferritin Crystals: An Advanced X-Ray Imaging and Diffraction Study

Ferritin is a well-known iron-storage protein, and is a spherical shell that consists of 24 identical subunits packed in a 432 symmetry. The typically large protein size and its distinction from lysozyme as to chemical and physical characteristics make ferritin an attractive model protein for crystal growth and perfection investigation-as an alternative to the most widely studied lysozyme. In this contribution, the latest results obtained from coherence-based x-ray diffraction imaging and diffraction experiments will be presented on octahedral apoferritin (a demetalized form of ferritin) crystals grown from various growth conditions. Crystal specimens, which have the measured rocking-curve widths varying from a few arcseconds to several tens arcseconds (or more), are comparatively examined by intrinsically highly sensitive mapping of lattice perfection and defects. The richness of the observed defects and growth features offers insight into perfection and growth of protein crystals. Beautiful interference fringe patterns formed in diffraction images and fine oscillation structure of rocking curves observed will be discussed for understanding of physical origins and the underlying impact.

Hu, Z. W.↗

NASA NTRS2003

Examination of the Atomic Pair Distribution Function (PDF) of SiC Nanocrystals by In-situ High Pressure Diffraction

Key properties of nanocrystals are determined by their real atomic structure, therefore a reasonable understanding and meaningful interpretation of their properties requires a realistic model of the structure. In this paper we present an evidence of a complex response of the lattice distances to external pressure indicating a presence of a complex structure of Sic nanopowders. The experiments were performed on nanocrystalline Sic subjected to hydrostatic or isostatic pressure using synchrotron and neutron powder diffraction. Elastic properties of the samples were examined based on X-ray diffraction data using a Diamond Anvil Cell (DAC) in HASYLAB at DESY. The dependence'of the lattice parameters and of the Bragg reflections width with pressure exhibits a ha1 nature of the properties (compressibilities) of the powders and indicates a complex structure of the grains. We interpreted tws behaviour as originating from different elastic properties of the grain interior and surface. Analysis of the dependence of individual interatomic distances on pressure was based on in-situ neutron diffraction measurements done with HbD diffractometer at LANSCE in Los Alamos National Laboratory with the Paris-Edinburgh cell under pressures up to 8 GPa (Qmax = 26/A). Interatomic distances were obtained by PDF analysis using the PDFgetN program. We have found that the interatomic distances undergo a complex, non-monotonic changes. Even under substantial pressures a considerable relaxation of the lattice may take place: some interatomic distances increase with an increase in pressure. We relate this phenomenon to: (1), changes of the microstructure of the densified material, in particular breaking of its fractal chain structure and, (2), its complex structure resembling that of a material composed of two phases, each with its distinct elastic properties.

Grzanka, E.↗

NASA NTRS2005

Integrated particles sensor formed on single substrate using fringes formed by diffractive elements

Integrated sensors are described using lasers on substrates. In one embodiment, a first sensor forms a laser beam and uses a quartz substrate to sense particle motion by interference of the particles with a diffraction beam caused by a laser beam. A second sensor uses gradings to produce an interference. In another embodiment, an integrated sensor includes a laser element, producing a diverging beam, and a single substrate which includes a first diffractive optical element placed to receive the diverging beam and produce a fringe based thereon, a scattering element which scatters said fringe beam based on particles being detected, and a second diffractive element receiving scattered light.

Gharib, Morteza↗