Multiple Bragg Diffraction Research Articles

Bragg reflection spectroscopy of opal-like photonic crystals

We have studied Bragg reflection spectra of photonic crystals based on synthetic opals. The samples under study represented opal-semiconductor composites, in which the opal pores were filled with GaN and GaP, and GaN-inverted structures with the opal matrix removed from the composite. Bragg reflection spectroscopy is found to possess new capabilities for characterization of opal-like structures. A theoretical approach to the reflectance spectrum analysis has been developed on the assumption of a planar spatially periodic medium, accounting for the effects of sintering of $\mathrm{Si}{\mathrm{O}}_{2}$ opal spheres and their uniaxial strain. For an additional characterization of the samples, we considered a structural invariant relating to each other the photonic crystal lattice parameters and the spectral positions of features in multiple Bragg diffraction spectra.

Fabrication and optical properties of photonic crystals based on opal-GaP and opal-GaPN composites

Nanocrystalline GaP and amorphous GaPN solid solution have been synthesized in voids of artificial opal. The opal-GaP and opal-GaPN composites obtained clearly demonstrate properties of photonic crystals. The reflection spectra of the opal-GaPN composite exhibit specific features related to multiple Bragg diffraction on two systems of {111} planes, parallel and nonparallel to the surface of the photonic crystal. The study of photoluminescence spectra revealed a considerable modification of the emission band of the opal-GaPN composite, which was attributed to the influence of the photonic band gap.

Angle-resolved reflectivity of single-domain photonic crystals: effects of disorder.

Angle-resolved reflectivity has been measured from single-domain photonic crystals consisting of air spheres in a TiO2 backbone. Monochromatic beams are focused to a 10 microm spot, and kept on the rotation axis with a precision better than 10 microm. We report high reflectivity up to 94% and surface domains as large as 200 microm, with a mosaic spread of +/-3 degrees. The maximum reflectivity at normal incidence agrees well with theoretical calculations in the scalar-wave approximation, extended to include an extinction length due to diffuse scattering, that is obtained from independent experiments. The angle-resolved stop bands compare favorably with previous measurements using coarse beams as well as with prior theoretical calculations. Inhomogeneous broadening introduced by coarse beams in previous measurements is found to be small. Our results can only be understood if we assume multiple Bragg diffraction from more than one family of planes simultaneously to take place.

Multiple Bragg diffraction in quasicrystals: The issue of centrosymmetry in Al-Pd-Mn.

When a crystal is rotated around the scattering vector for a Bragg reflection {bold P}, another reflection {bold H} may be simultaneously excited for a particular value {psi} of the azimuthal angle. The plot of the intensity {ital I}{sub {bold P}} vs {psi} (called the {open_quote}{open_quote}azimuthal plot{close_quote}{close_quote}) shows peaks with asymmetric features from which phases of structure factors can be obtained. Multibeam diffraction data have been obtained with a high-quality Al-Pd-Mn quasicrystal using synchrotron x rays. Rocking widths of 36 arcsec have been obtained, which made it possible to obtain data that could be interpreted using dynamical theory without any need of smearing functions to take into account the mosaic spread or other instrumental resolution effects. The asymmetric features and the peak intensity of all azimuthal plots could be fitted with phases consistent with a noncentrosymmetric structure. This conclusion was reinforced by the results of a multibeam experiment with circularly polarized x rays. This is in contrast with several other diffraction experiments based on intensity measurements in the two-beam case. Possible reasons for this discrepancy are discussed. {copyright} {ital 1996 The American Physical Society.}

A new algorithm for computation of X-ray multiple Bragg diffraction

A new method for computation of X-ray multiple Bragg diffraction in perfect crystals is presented. The method is based on the extended dynamical diffraction theory and implies the reduction of the diffraction equations to a generalized eigenvalue problem. The advantage of the proposed approach is the possibility of decreasing the scattering-matrix size and simplifying the solution when some X-ray beams are not grazing. The boundary conditions are also simplified by the analysis of Bloch-wave structure inside the crystal and the proper selection of their polarization states.

Computation of parametric X-ray production by relativistic particles in crystals under multiple Bragg diffraction

An algorithm for computing spectral-angular and angular distributions of parametric X-ray radiation (PXR) produced by ultrarelativistic particles in crystals under multiple Bragg diffraction is developed. The algorithm is based on the methods applied in the dynamical theory of X-ray multiple diffraction. The angular distribution of three-wave PXR angular distribution into the simulated forbidden reflex (222) in the Ge crystal is computed. It is shown that using multiple PXR generation it is possible to generate X-ray beams with double angular collimation approximately=1 angular s2 and spectral width approximately=10-3.

Phase determination of X-ray reflections in a quasicrystal

Multiple Bragg diffraction effects have been observed in an Al–Cu–Fe quasicrystal. The experimental data are analyzed by means of a multibeam perturbation theory. Good fits are obtained between experimental and calculated profiles. The feasibility for phase determination of structure factors is demonstrated. It is found that there is no inversion symmetry in Al–Cu–Fe.

Integrated optic matrix-vector multiplier using multifrequency acoustooptic Bragg diffraction

An integrated optic numerical processor performing matrix-vector multiplication in an analog representation is proposed. Parallel processing of a number of numerical products is made in the same area of a substrate by means of multiple Bragg diffraction of multiwavelength optical signals due to multifrequency surface acoustic waves. The wavelength interval of multiplexed optical signals can be 0.77 nm for the optical beamwidth of 3 mm and the acoustic frequency of 1 GHz. Preliminary demonstrations of matrix-vector multiplication are presented with a waveguide type Ti:LiNbO(3) acoustooptic deflector. An alternative processor using one optical wavelength is also described.

Integrated Optic Matrix-Vector Multipliers Using Acousto-Optic Bragg Diffraction

An integrated optic numerical processor performing matrix-vector multiplication in analog representation is proposed. Parallel processing of a number of numerical products is operated in the same area of a substrate by means of multiple Bragg diffraction of multi-wavelength optical signals caused by multi-frequency surface acoustic waves. The wavelength interval of multiplexed optical signals can be 0.77 nm for the optical beam width of 3 mm and the acoustic frequency of 1 GHz.

The current status of phase determination by means of multiple Bragg diffraction

The feasibility of multibeam diffraction for determining phases of structure factors is assessed on the basis of recent contributions and experiments in progress. It is shown that the method works well in situations in which the global interaction between X-ray photons and the crystal is weak, in which case diffraction takes place by single scattering events, and crystal perfection does not play a role in interpreting the experimental results. Two successful examples of phase determinations using the notion of virtual Bragg scattering are presented. One case is of particular interest, because the crystal (V3Si) is mosaic, and the phases were a priori unknown. Some problems and limitations of the method are encountered when trying to extend this technique to organic crystals of relatively large cell size, with spherical or irregular shape. Some data and calculations are presented for benzil, C14H10O2, a crystal isomorphous with quartz. It is concluded that the resolution presently available from standard laboratory set-ups is not adequate for application of this method to a crystal like benzil, but that use of synchrotron radiation beams will probably remove these obstacles.

Simultaneous Bragg diffraction of X-rays from liquid-phase epitaxial thin films

Multiple simultaneous Bragg diffraction effects of X-rays in quaternary III-V liquid-phase epitaxial thin layers are investigated with both photographic and counter detection methods. For the photographic investigation, a divergent source is used. The geometric aspects of this type of diffraction, affected by lattice mismatch between epitaxial layers and substrates, are discussed for cases involving five-, six- and eight-beam reflections. The lattice mismatches in directions parallel and perpendicular to the interface normal of InGaAsP/ InP, determined from a single divergent-beam photograph, are obtained. For the counter detection study, a collimated incident beam and several single and double heterojunction samples, with large lattice mismatches are used. A kinematical treatment for a general n-beam diffraction, from double- and triple-layer systems, is derived to account for the measured intensities.

Three-layer 1.3 µm In<inf>1-x</inf>Ga<inf>x</inf>As<inf>y</inf>P<inf>1-y</inf>lasers with quaternary confining layers

Improvements in the surface morphology of InGaAsP DH wafers were obtained with addition of small amounts of Ga and As in the confining layers. This method was used to improve interface flatness between active and confining layers, consequently improving wafer yield and reproducibility. Three-dimensional lattice-mismatch data of the confining layers were determined in detail using simultaneous multiple Bragg diffraction of X-rays. In all wafers tested, independent of the active layer thickness, the maximum threshold current density J th was at most 60 percent higher than J th minimum. The minimum normalized threshold current density obtained by us-3.4 kA/cm2μmis to our knowledge the lowest reported to date. Low resistance contacts-differential series resistance of 1 to 2 Ω for 10 μm SiO 2 stripe-geometry contact-can consistently be directly applied to tile top confining layer, thus dispensing with file need of a cap layer. CW operation at room temperature has been achieved with these three-layer devices.