Showing papers on "Brillouin zone published in 2006"

Screened hybrid density functionals applied to solids

Abstract: Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.

Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation

Abstract: The intrinsic anomalous Hall conductivity in ferromagnets depends on subtle spin-orbit-induced effects in the electronic structure, and recent ab initio studies found that it was necessary to sample the Brillouin zone at millions of $k$-points to converge the calculation. We present an efficient first-principles approach for computing this quantity. We start out by performing a conventional electronic-structure calculation including spin-orbit coupling on a uniform and relatively coarse $k$-point mesh. From the resulting Bloch states, maximally localized Wannier functions are constructed which reproduce the ab initio states up to the Fermi level. The Hamiltonian and position-operator matrix elements, needed to represent the energy bands and Berry curvatures, are then set up between the Wannier orbitals. This completes the first stage of the calculation, whereby the low-energy ab initio problem is transformed into an effective tight-binding form. The second stage only involves Fourier transforms and unitary transformations of the small matrices setup in the first stage. With these inexpensive operations, the quantities of interest are interpolated onto a dense $k$-point mesh and used to evaluate the anomalous Hall conductivity as a Brillouin zone integral. The present scheme, which also avoids the cumbersome summation over all unoccupied states in the Kubo formula, is applied to bcc Fe, giving excellent agreement with conventional, less efficient first-principles calculations. Remarkably, we find that about 99% of the effect can be recovered by keeping a set of terms depending only on the Hamiltonian matrix elements, not on matrix elements of the position operator.

Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres

Abstract: Wavelength-scale periodic microstructuring dramatically alters the optical properties of materials. An example is glass photonic crystal fibre1 (PCF), which guides light by means of a lattice of hollow micro/nanochannels running axially along its length. In this letter, we explore stimulated Brillouin scattering in PCFs with subwavelength-scale solid silica glass cores. The large refractive-index difference between air and glass allows much tighter confinement of light than is possible in all-solid single-mode glass optical fibres made using conventional techniques. When the silica-air PCF has a core diameter of around 70% of the vacuum wavelength of the launched laser light, we find that the spontaneous Brillouin signal develops a highly unusual multi-peaked spectrum with Stokes frequency shifts in the 10-GHz range. We attribute these peaks to several families of guided acoustic modes each with different proportions of longitudinal and shear strain, strongly localized to the core2,3. At the same time, the threshold power for stimulated Brillouin scattering4 increases fivefold. The results show that Brillouin scattering is strongly affected by nanoscale microstructuring, opening new opportunities for controlling light—sound interactions in optical fibres.

Distributed strain measurement with millimeter-order spatial resolution based on Brillouin optical correlation domain analysis

Abstract: Distributed strain sensing with millimeter-order spatial resolution is demonstrated in optical fibers based on Brillouin optical correlation domain analysis. A novel beat lock-in detection scheme is introduced to suppress background noises coming from the reflection of Brillouin pump waves. The Brillouin frequency shifts of 3 mm fiber sections are successfully measured with a theoretical spatial resolution of 1.6 mm.

Wave and defect dynamics in nonlinear photonic quasicrystals

Abstract: A photonic equivalent of a quasicrystal is created in which wave and defect dynamics can be made visible — for example, it is shown that a dislocation introduced in the photonic quasicrystal is healed by re-arrangements of the lattice. Quasicrystals are unique structures with long-range order but no periodicity. Their properties have intrigued scientists ever since their discovery1 and initial theoretical analysis2,3. The lack of periodicity excludes the possibility of describing quasicrystal structures with well-established analytical tools, including common notions like Brillouin zones and Bloch's theorem. New and unique features such as fractal-like band structures4,5,6,7 and ‘phason’ degrees of freedom8 are introduced. In general, it is very difficult to directly observe the evolution of electronic waves in solid-state atomic quasicrystals, or the dynamics of the structure itself. Here we use optical induction9,10,11 to create two-dimensional photonic quasicrystals, whose macroscopic nature allows us to explore wave transport phenomena. We demonstrate that light launched at different quasicrystal sites travels through the lattice in a way equivalent to quantum tunnelling of electrons in a quasiperiodic potential. At high intensity, lattice solitons are formed. Finally, we directly observe dislocation dynamics when crystal sites are allowed to interact with each other. Our experimental results apply not only to photonics, but also to other quasiperiodic systems such as matter waves in quasiperiodic traps12, generic pattern-forming systems as in parametrically excited surface waves13, liquid quasicrystals14, and the more familiar atomic quasicrystals.

Highly stable low-noise Brillouin fiber laser with ultranarrow spectral linewidth

Abstract: We demonstrate an all-fiber high-power single-frequency Brillouin fiber ring laser with maximum power of 100 mW at 1.55 mum, which is actively stabilized by using the Pound-Drever-Hall frequency-locking scheme. Significant reduction (~20dB) of both relative intensity noise and frequency noise was observed in the Brillouin Stokes radiation as compared with those noises of its pump source, a narrow-linewidth Er-doped fiber laser. Ultranarrow spectral linewidth of the Brillouin fiber lasers was investigated by both delayed self-heterodyne technique and heterodyne beat technique between two independent Brillouin fiber lasers

The peculiar electronic structure of PbSe quantum dots.

Abstract: PbSe is a pseudo-II-VI material distinguished from ordinary II-VI's (e.g., CdSe, ZnSe) by having both its valence band maximum (VBM) and its conduction band minimum (CBM) located at the fourfold-degenerate L-point in the Brillouin zone. It turns out that this feature dramatically affects the properties of the nanosystem. We have calculated the electronic and optical properties of PbSe quantum dots using an atomistic pseudopotential method, finding that the electronic structure is different from that of ordinary II-VI's and, at the same time, is more subtle than what k·p or tight-binding calculations have suggested previously for PbSe. We find the following in PbSe dots: (i) The intraband (valence-to-valence and conduction-to-conduction) as well as interband (valence-to-conduction) excitations involve the massively split L-manifold states. (ii) In contrast to previous suggestions that the spacings between valence band levels will equal those between conduction band levels (because the corresponding effect...

Quantum spin Hall effect in three dimensional materials: Lattice computation of Z$_2$ topological invariants and its application to Bi and Sb

Abstract: We derive an efficient formula for Z$_2$ topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model.

Nodal structure of unconventional superconductors probed by angle resolved thermal transport measurements

Abstract: Over the past two decades, unconventional superconductivity with gap symmetry other than s wave has been found in several classes of materials, including heavy fermion, high Tc, and organic superconductors. Unconventional superconductivity is characterized by anisotropic superconducting gap functions, which may have zeros (nodes) along certain directions in the Brillouin zone. The nodal structure is closely related to the pairing interaction, and it is widely believed that the presence of nodes is a signature of magnetic or some other exotic, rather than conventional phonon mediated, pairing mechanism. Therefore experimental determination of the gap function is of fundamental importance. However, the detailed gap structure, especially the direction of the nodes, is an unresolved issue for most unconventional superconductors. Recently it has been demonstrated that thermal conductivity and specific heat measurements under a magnetic field rotated relative to the crystal axes provide a powerful method for determining the shape of the gap and the nodal directions in the bulk. Here we review the theoretical underpinnings of the method and the results for the nodal structure of several unconventional superconductors, including borocarbide YNi2B2C, heavy fermions UPd2Al3, CeCoIn5 ,a nd PrOs 4Sb12, organic superconductor κ-(BEDT-TTF)2Cu(NCS)2, and ruthenate Sr2RuO4, determined through angular variation of the thermal conductivity and heat capacity.

The Peculiar electronic structure of PbSe quantum dots

Abstract: PbSe is a pseudo-II-VI material distinguished from ordinary II-VI's (e.g., CdSe, ZnSe) by having both its valence band maximum (VBM) and its conduction band minimum (CBM) located at the fourfold-degenerate L-point in the Brillouin zone. It turns out that this feature dramatically affects the properties of the nanosystem. We have calculated the electronic and optical properties of PbSe quantum dots using an atomistic pseudopotential method, finding that the electronic structure is different from that of ordinary II-VI's and, at the same time, is more subtle than what k·p or tight-binding calculations have suggested previously for PbSe. We find the following in PbSe dots: (i) The intraband (valence-to-valence and conduction-to-conduction) as well as interband (valence-to-conduction) excitations involve the massively split L-manifold states. (ii) In contrast to previous suggestions that the spacings between valence band levels will equal those between conduction band levels (because the corresponding effect...

Ultrafast relaxation and exciton–exciton annihilation in PTCDA thin films at high excitation densities

Abstract: Femtosecond pump–probe spectroscopy is applied to thin films of the quasi-one-dimensional organic semiconductor 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA). We present transient absorption spectra over a broad spectral range. Ultrafast intraband relaxation in the S1 manifold towards the border of the Brillouin zone is shown to depend on temperature and excitation density. The intraband relaxation time is of the order of 100 fs. At high excitation densities (>1019 cm−3), the major de-excitation mechanism for the relaxed excitons is exciton–exciton annihilation. The experimental decay dynamics can be explained very well by two alternative annihilation models: one-dimensional diffusion limited bimolecular recombination or single-step long range Forster-type annihilation. In contrast, a three-dimensional diffusion limited annihilation model is significantly inferior. For all three models, we extract annihilation rates, diffusion constants, diffusion lengths, and Forster radii for room and liquid Helium temperature.

Excitation spectra of the spin- 1 2 triangular-lattice Heisenberg antiferromagnet

Abstract: We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-(1)/(2) triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find rotonlike minima at special wave vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [Phys. Rev. B74, 180403(R) (2006)]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a nonlinear sigma model description of the finite-temperature properties is only applicable at temperatures < 0.1J. Finally, we review recent NMR measurements on the organic compound kappa-(BEDT-TTF)(2)Cu-2(CN)(3). We argue that these are inconsistent with long-range order and a description of the low-energy excitations in terms of interacting magnons, and that therefore a Heisenberg model with only nearest-neighbor exchange does not offer an adequate description of this material.

Short light pulse amplification and compression by stimulated Brillouin scattering in plasmas in the strong coupling regime

Abstract: Short light pulse amplification using the stimulated Brillouin backscattering mechanism is considered. The novel feature is that the interaction process takes place in the strongly coupled regime and therefore the pulse compression is not limited by the ion-acoustic wave period. The mechanism is very efficient due to the large ratio of light frequency to the characteristic ion-acoustic wave frequency. Although large-amplitude ion-acoustic waves are generated and subsequent wave breaking takes place, the fluid and kinetic nonlinearities do not intervene with the amplification itself.

Two-dimensional electrons occupying multiple valleys in AlAs

Abstract: Two-dimensional electrons in AlAs quantum wells occupy multiple conduction-band minima at the X-points of the Brillouin zone. These valleys have large effective mass and g -factor compared to the standard GaAs electrons, and are also highly anisotropic. With proper choice of well width and by applying symmetry-breaking strain in the plane, one can control the occupation of different valleys thus rendering a system with tuneable effective mass, g -factor, Fermi contour anisotropy, and valley degeneracy. Here we review some of the rich physics that this system has allowed us to explore. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Nodal Structure of Unconventional Superconductors Probed by the Angle Resolved Thermal Transport Measurements

Abstract: Over the past two decades, unconventional superconductivity with gap symmetry other than s-wave has been found in several classes of materials, including heavy fermion (HF), high-T_c, and organic superconductors. Unconventional superconductivity is characterized by anisotropic superconducting gap functions, which may have zeros (nodes) along certain directions in the Brillouin zone. The nodal structure is closely related to the pairing interaction, and it is widely believed that the presence of nodes is a signature of magnetic or some other exotic, rather than conventional phonon-mediated, pairing mechanism. Therefore experimental determination of the gap function is of fundamental importance. However, the detailed gap structure, especially the direction of the nodes, is an unresolved issue in most unconventional superconductors. Recently it has been demonstrated that the thermal conductivity and specific heat measurements under magnetic field rotated relative to the crystal axes are a powerful method for determining the shape of the gap and the nodal directions in the bulk. Here we review the theoretical underpinnings of the method and the results for the nodal structure of several unconventional superconductors, including borocarbide YNi$_2$B$_2$C, heavy fermions UPd$_2$Al$_3$, CeCoIn$_5$, and PrOs$_4$Sb$_{12}$, organic superconductor, $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$, and ruthenate Sr$_2$RuO$_4$, determined by angular variation of the thermal conductivity and heat capacity.

Topological analysis of the quantum Hall effect in graphene: Dirac-Fermi transition across van Hove singularities and the edge vs bulk quantum numbers

Abstract: Inspired by a recent discovery of a peculiar integer quantum Hall effect (QHE) in graphene, we study QHE on a honeycomb lattice in terms of the topological quantum number, with two-fold interests: First, how the zero-mass Dirac QHE around the center of the tight-binding band crosses over to the ordinary finite-mass fermion QHE around the band edges. Second, how the bulk QHE is related with the edge QHE for the entire spectrum including Dirac and ordinary behaviors. We find the following: (i) The zero-mass Dirac QHE persists up to the van Hove singularities, at which the ordinary fermion behavior abruptly takes over. Here a technique developed in the lattice gauge theory enabled us to calculate the behavior of the topological number over the entire spectrum. This result indicates a robustness of the topological quantum number, and should be observable if the chemical potential can be varied over a wide range in graphene. (ii) To see if the honeycomb lattice is singular in producing the anomalous QHE, we have systematically surveyed over square-honeycomb-$\pi$-flux lattices, which is scanned by introducing a diagonal transfer $t'$. We find that the massless Dirac QHE forms a critical line, that is, the presence of Dirac cones in the Brillouin zone is preserved by the inclusion of $t'$ and the Dirac region sits side by side with ordinary one persists all through the transformation. (iii) We have compared the bulk QHE number obtained by an adiabatic continuity of the Chern number across transformation and numerically obtained edge QHE numbers calculated from the whole energy spectra for sample with edges, which shows that the bulk QHE number coincides, as in ordinary lattices, with the edge QHE number throughout the lattice transformation.

Band-contact lines in the electron energy spectrum of graphite

Abstract: We discuss the known experimental data on the phase of the de Haas--van Alphen oscillations in graphite. These data can be understood if one takes into account that four band-contact lines exist near the HKH edge of the Brillouin zone of graphite.

First-principles scattering matrices for spin transport

Abstract: Details are presented of an efficient formalism for calculating transmission and reflection matrices from first principles in layered materials. Within the framework of spin density functional theory and using tight-binding muffin-tin orbitals, scattering matrices are determined by matching the wave functions at the boundaries between leads which support well-defined scattering states, and the scattering region. The calculation scales linearly with the number of principal layers N in the scattering region and as the cube of the number of atoms H in the lateral supercell. For metallic systems for which the required Brillouin zone sampling decreases as H increases, the final scaling goes as H2N. In practice, the efficient basis set allows scattering regions for which H2N -10 6 to be handled. The method is illustrated for Co/Cu multilayers and single interfaces using large lateral supercells (up to 20 x 20) to model interface disorder. Because the scattering states are explicitly found, "channel decomposition" of the interface scattering for clean and disordered interfaces can be performed.

Optical properties of bcc transition metals in the range 0 – 40 eV

Abstract: We present a systematic analysis of the optical properties of bcc transition metals in the groups VB: V, Nb, and Ta, and VIB: paramagnetic Cr, Mo, and W. For this we use our formulation of time-dependent currentdensity-functional theory for the linear response of metals. The calculated dielectric and electron energy-loss functions are compared with our ellipsometry measurements and with data reported in literature, showing an overall good agreement. The experimental data of the dielectric functions presented by Nestell and Christy and by Weaver et al. differ mostly in the low-frequency region. However, we found that their reflectivity data are in very good agreement up to about 3 eV. We attribute this apparent discrepancy to the Drude-like extrapolation model used by Weaver et al. in the Kramers-Kronig procedure to extract the optical constants from their reflectivity data. Our experiments are in good agreement with Nestell and Christy’s data. The calculated absorption spectra show some deviations from the experiments, in particular in the 3d metals. We assign the spectra in terms of transitions between pairs of bands and we analyze which parts of the Brillouin zone are mainly involved in the absorption. Our results suggest that the blueshift of some spectral features in our calculations can be attributed mainly to the incorrect description of the virtual d bands by the approximations used for the ground state exchange-correlation functional. These virtual bands are too weakly bound by the local density and generalized gradient approximations, in particular in the 3d metals. We calculate separately the inter- and intraband contributions to the absorption and we show using a k·p analysis that, within the scalar-relativistic approximation, interband transitions contribute to the absorption already at frequencies well below 0.5 eV. This finding makes questionable the Drude-like behavior normally assumed in the experimental analysis of the linear response. We find that the combination of the Drude model in which we use the calculated plasma frequency and an optimized relaxation time, and the calculated interband response can well describe the experimental spectra. The electron energy-loss spectra are very well reproduced by our calculations showing in each metal a dominant plasmon peak at about 22‐24 eV, well above the corresponding Drude-like freeelectron plasma frequency, and additional features in the range 10‐15 eV. We show that the renormalization of the plasma frequency is due to the interplay between inter- and intraband processes, and that the additional features arise from the rich structure in the dielectric function caused by interband transitions.

Ideal strength of silicon: An ab initio study

Abstract: The ideal strength of silicon is predicted along various loading paths using density functional theory. Stress-strain curves are calculated under uniaxial tension, relaxed shear, and uniaxial deformation conditions. In order to check the stability of the deformation paths, the phonon spectra and the stiffness tensors are computed within density-functional perturbation theory. A second-order phase transition is found to occur before the elastic instability when applying a {111} relaxed shear. In all the other deformation conditions, the first predicted instabilities are located at the center of the Brillouin zone. Finally, the crystallographic nature of the instabilities is investigated by the calculation of the phonon eigendisplacements and by the decomposition of the stiffness tensors.

Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes.

Abstract: We demonstrate resonant guiding in a chalcogenide glass photonic crystal membrane. We observe strong resonances in the optical transmission spectra at normal incidence, associated with Fano coupling between free space and guided modes. We obtain good agreement with modeling results based on three-dimensional finite-difference time-domain simulations, and identify the guided modes near the centre of the first Brillouin zone responsible for the main spectral features.

Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions

Abstract: A metallic electron system near an orientational symmetry breaking Pomeranchuk instability is characterized by a ``soft'' Fermi surface with enhanced collective fluctuations. We analyze fluctuation effects in a two-dimensional electron system on a square lattice in the vicinity of a Pomeranchuk instability with $d$-wave symmetry, using a phenomenological model which includes interactions with a small momentum transfer only. We compute the dynamical density correlations with a $d$-wave form factor for small momenta and frequencies, the dynamical effective interaction due to a fluctuation exchange, and the electron self-energy. At the quantum critical point the density correlations and the dynamical forward scattering interaction diverge with a dynamical exponent $z=3$. The singular forward scattering leads to large self-energy corrections, which destroy Fermi liquid behavior over the whole Fermi surface except near the Brillouin zone diagonal. The decay rate of single-particle excitations, which is related to the width of the peaks in the spectral function, exceeds the excitation energy in the low-energy limit. The dispersion of maxima in the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The contribution from classical fluctuations to the self-energy spoils $(\ensuremath{\omega}∕T)$ scaling in the quantum critical regime.

Flat spin-wave dispersion in a triangular antiferromagnet

Abstract: The excitation spectrum of an $S=1∕2$ two-dimensional triangular quantum antiferromagnet is studied using $1∕S$ expansion. Due to the noncollinearity of the classical ground state significant and nontrivial corrections to the spin-wave spectrum appear already in the first order in $1∕S$ in contrast to the square lattice antiferromagnet. The resulting magnon dispersion is almost flat in a substantial portion of the Brillouin zone. Our results are in quantitative agreement with recent series expansion studies by Zheng et al. [Phys. Rev. Lett. 96, 057201 (2006); cond-mat/0608008 (unpublished)].

Brillouin–Raman comb fiber laser with cooperative Rayleigh scattering in a linear cavity

Abstract: We demonstrate a multiple-wavelength Brillouin comb laser with cooperative Rayleigh scattering that uses Raman amplification in dispersion-compensating fiber. The laser resonator is a linear cavity formed by reflector at each end of the dispersion-compensating fiber to improve the reflectivity of the Brillouin Stokes comb. Multiple Brillouin Stokes generation has been improved in terms of optical signal-to-noise ratio and power-level fluctuation between neighboring channels. Furthermore, the linewidth of the Brillouin Stokes is uniform within the laser output bandwidth.

Stimulated Brillouin scattering in single-mode tellurite glass fiber.

Abstract: Stimulated Brillouin scattering properties in a single-mode tellurite glass fiber were studied using a cw laser with an operating wavelength of 1.54 µm. The Brillouin frequency shift vB and the gain linewidth ΔvB were 7.882 GHz and 23.6 MHz, respectively. A Brillouin gain coefficient gB in the range of 1.47×10-10-2.16×10-10 m/W was measured. The higher gain coefficient of the tellurite fiber, together with its relatively low loss compared with other non-silica fibers, makes it a suitable candidate for realizing efficient, all-optical, slow-light devices.

Simple metals at high pressures: the Fermi sphere – Brillouin zone interaction model

Abstract: High-pressure structural transformations are analyzed for simple sp-elements and some binary alloys. The crystal structure stability of these metals depends on the Fermi surface–Brillouin zone interaction. An increase in this interaction with pressure results in transitions to less symmetric and less closely packed structures. A structural similarity is shown to exist between the high-pressure phases for alkali and alkali-earth metals and for polyvalent group IV and V elements. The correlation between the behavior under compression of the structure and the physical properties (resistivity and superconductivity) of these metals is discussed in terms of the Fermi sphere–Brillouin zone interaction model.

Detailed analysis of the dielectric function for wurtzite InN and In‐rich InAlN alloys

Abstract: A detailed analysis of the dielectric function (DF) for wurtzite InN as well as for In-rich InAIN alloys is presented. The experimental_data, covering the energy range from 0.72 up to 9.5 eV, were obtained by ellipsometric studies of an (1120) a-plane InN film and low carrier density (0001) c-plane films. Model calculations of the imaginary part of the DF around the band gap provide direct insight how to determine the energetic position of the Fermi energy from the experimental results. Then, taking into account both, band gap renormalization and Burstein-Moss shift, the values of the gaps at zero carrier density are calculated. The dependence of the InAIN band gap on the alloy composition is described by a bowing parameter of 4.0 eV. The a-plane film exhibits a characteristic optical anisotropy below 1 eV which is attributed to the polarization dependence of transition probabilities from the three valence bands at the Γ point of the Brillouin zone into the conduction band. The splitting of 25 meV between the absorption edges for the two polarization directions can be well explained by a crystal field energy of 19 (24) meV if a calculated spin-orbit energy of 13 (5) meV is assumed. All results emphasize a band gap value of wurtzite InN of about 0.68 eV. By fitting the third derivatives of the dielectric function up to 9.5 eV we determine the compositional dependences of the transition energies for at least three critical points of the band structure.

Theoretical and experimental investigation of Brillouin scattering for the generation of millimeter waves

Abstract: We investigate and discuss stimulated Brillouin scattering in optical fibers for the generation of millimeter waves in theory and experiment. With a derivation of the responsible differential equation system we show that the phases of two independently amplified sidebands of a frequency comb will remain the same. Neither third-order nonlinear effects like self- and cross-phase modulation nor the Brillouin amplification has an influence on the phases. We verify our theoretical predictions with phase noise measurements of the generated millimeter-wave signal. The results show that the generated phase noise is in fact very low.