Showing papers on "Brillouin zone published in 2008"

Confocal Brillouin microscopy for three-dimensional mechanical imaging

Abstract: Acoustically induced inelastic light scattering, first reported in 1922 by Brillouin1, allows non-contact, direct readout of the viscoelastic properties of a material and has widely been investigated for material characterization2, structural monitoring3 and environmental sensing4. Extending the Brillouin technique from point sampling spectroscopy to imaging modality5 would open up new possibilities for mechanical imaging, but has been challenging because rapid spectrum acquisition is required. Here, we demonstrate a confocal Brillouin microscope based on a fully parallel spectrometer—a virtually imaged phased array—that improves the detection efficiency by nearly 100-fold over previous approaches. Using the system, we show the first cross-sectional Brillouin imaging based on elastic properties as the contrast mechanism and monitor fast dynamic changes in elastic modulus during polymer crosslinking. Furthermore, we report the first in situ biomechanical measurement of the crystalline lens in a mouse eye. These results suggest multiple applications of Brillouin microscopy in biomedical and biomaterial science.

Differential pulse-width pair BOTDA for high spatial resolution sensing

Abstract: A differential pulse-width pair Brillouin optical time domain analysis (DPP-BOTDA) for centimeter spatial resolution sensing using meter equivalent pulses is proposed. This scheme uses the time domain waveform subtraction at the same scanned Brillouin frequency obtained from pulse lights with different pulse-widths (e.g. 50ns and 49ns) to form the differential Brillouin gain spectrum (BGS) at each fiber location. The spatial resolution is defined by the average of the rise and fall time equivalent fiber length for a small stress section rather than the pulse-width difference equivalent length. The spatial resolution of 0.18m for the 50/49ns pulse pair and 0.15m for 20/19ns pulse pair over 1km sensing length with Brillouin frequency shift accuracy of 2.6MHz are demonstrated.

Minimal two-band model of the superconducting iron oxypnictides

Abstract: Following the discovery of the Fe-pnictide superconductors, local-density approximation (LDA) band structure calculations showed that the dominant contributions to the spectral weight near the Fermi energy came from the $\text{Fe}\text{ }3d$ orbitals. The Fermi surface is characterized by two hole surfaces around the $\ensuremath{\Gamma}$ point and two electron surfaces around the $M$ point of the two Fe/cell Brillouin zone. Here, we describe a two-band model that reproduces the topology of the LDA Fermi surface and exhibits both ferromagnetic and $q=(\ensuremath{\pi},0)$ spin-density wave fluctuations. We argue that this minimal model contains the essential low energy physics of these materials.

New generation of massless Dirac fermions in graphene under external periodic potentials.

Abstract: We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wave vector (measured from the new Dirac point), the generalized pseudospin vector, and the group velocity are not collinear. We further show that with an appropriate periodic potential of triangular symmetry, there exists an energy window over which the only available states are these quasiparticles, thus providing a good system to probe experimentally the new massless Dirac fermions. The required parameters of external potentials are within the realm of laboratory conditions.

Proposal of Brillouin optical correlation-domain reflectometry (BOCDR)

Abstract: We propose a Brillouin optical correlation-domain reflectometry (BOCDR), which can measure the distribution of strain and/or temperature along an optical fiber from a single end, by detecting spontaneous Brillouin scattering with controlling the interference of continuous lightwaves. In a pulse-based conventional Brillouin optical time-domain reflectometry (BOTDR), it is difficult in principle to achieve a spatial resolution less than 1 m, and the measurement time is as long as 5-10 minutes. On the contrary, the continuous-wave-based BOCDR can exceed the limit of 1-m resolution, and realize much faster measurement and random access to measuring positions. Spatial resolution of 40 cm was experimentally demonstrated with sampling rate of 50 Hz.

Quantum oscillations in an overdoped high-Tc superconductor

Abstract: As well as their elevated superconducting transition temperatures (Tcs), the copper-oxide superconductors display a variety of novel physical properties that have inspired many theories to explain their electronic ground state. One topic of note is the nature of the metallic phase in these compounds, in particular, how coherent electronic states or quasiparticles emerge from the antiferromagnetic insulator with doping — the addition of trace amounts of impurities. Vignolle et al. report the observation of quantum oscillations, that is, oscillations in the electrical and magnetic response as a function of magnetic field, in the overdoped superconductor Tl2Ba2CuO6+δ. These oscillations point to the existence of a large Fermi surface of well-defined quasiparticles covering two-thirds of the Brillouin zone. The measurements confirm the applicability of a generalized Fermi-liquid picture to the overdoped side of the superconducting dome and mean that the important charge carriers involved in superconductivity are essentially similar to those found in normal metals. This paper reports the observation of quantum oscillations in the overdoped superconductor Tl2Ba2CuO6+δ that show the existence of a large Fermi surface of well-defined quasiparticles covering two-thirds of the Brillouin zone. These measurements firmly establish the applicability of a generalized Fermi-liquid picture on the overdoped side of the superconducting dome. The nature of the metallic phase in the high-transition-temperature (high-Tc) copper oxide superconductors, and its evolution with carrier concentration, has been a long-standing mystery1. A central question is how coherent electronic states, or quasiparticles, emerge from the antiferromagnetic insulator with doping. Recent quantum oscillation experiments on lightly doped copper oxides have shown evidence for small pockets of Fermi surface2,3,4,5, the formation of which has been associated with the opening of the pseudogap—an anisotropic gap in the normal state excitation spectrum of unknown origin1. As the doping is increased, experiments suggest that the full Fermi surface is restored6,7, although the doping level at which the pseudogap closes and the nature of the electronic ground state beyond this point have yet to be determined. Here we report the observation of quantum oscillations in the overdoped superconductor Tl2Ba2CuO6+δ that show the existence of a large Fermi surface of well-defined quasiparticles covering two-thirds of the Brillouin zone. These measurements confirm that, in overdoped superconducting copper oxides, coherence is established at all Fermi wavevectors, even near the zone boundary where the pseudogap is maximal and electronic interactions are strongest; they also firmly establish the applicability of a generalized Fermi-liquid picture on the overdoped side of the superconducting phase diagram.

Electron and Phonon Properties of Graphene: Their Relationship with Carbon Nanotubes

Abstract: The discovery of Novoselov et al. (2004) of a simple method to transfer a singleatomic layer of carbon from the c-face of graphite to a substrate suitable for themeasurement of its electrical and optical properties has led to a renewed interest inwhat was considered to be before that time a prototypical, yet theoretical,two-dimensional system. Indeed, recent theoretical studies of graphene reveal that thelinear electronic band dispersion near the Brillouin zone corners gives rise to electronsand holes that propagate as if they were massless fermions and anomalous quantumtransport was experimentally observed. Recent calculations and experimentaldetermination of the optical phonons of graphene reveal Kohn anomaliesat high-symmetry points in the Brillouin zone. They also show that theBorn–Oppenheimer principle breaks down for doped graphene. Since a carbonnanotube can be viewed as a rolled-up sheet of graphene, these recent theoretical andexperimental results on graphene should be important to researchers working oncarbon nanotubes. The goal of this contribution is to review the exciting newsabout the electronic and phonon states of graphene and to suggest howthese discoveries help understand the properties of carbon nanotubes.

Properties of an algebraic spin liquid on the kagome lattice

Abstract: In recent work, we argued that a particular algebraic spin liquid (ASL) may be the ground state of the $S=1/2$ kagome lattice Heisenberg antiferromagnet. Furthermore, this state, which lacks a spin gap, is appealing in light of recent experiments on herbertsmithite $[{\text{ZnCu}}_{3}{(\text{OH})}_{6}{\text{Cl}}_{2}]$. Here, we study the properties of this ASL in more detail using both the low-energy effective field theory and Gutzwiller-projected wave functions of fermionic spinons. We identify the competing orders of the ASL, which are observables having slowly decaying power-law correlations---among them we find a set of magnetic orders lying at the $M$ points of the Brillouin zone, the familiar $\mathbit{q}=0$ magnetic ordered state, the ``Hastings'' valence-bond solid (VBS) state, and a pattern of vector spin-chirality ordering corresponding to one of the Dzyaloshinskii--Moriya (DM) interaction terms present in herbertsmithite. Identification of some of these orders requires an understanding of the quantum numbers of magnetic monopole operators in the ASL. We discuss the detection of the magnetic and VBS competing orders in experiments. While we primarily focus on a clean system without DM interaction, we consider the effects of small DM interaction and argue that, surprisingly, it leads to spontaneously broken time-reversal symmetry (for DM interaction that preserves $XY$ spin rotation symmetry, there is also $XY$ magnetic order). Our analysis of the projected wave function provides an estimate of the ``Fermi velocity'' ${v}_{F}$ that characterizes all low-energy excitations of the ASL---this allows us to estimate the specific heat, which compares favorably with experiments. We also study the spin and bond correlations of the projected wave function and compare these results with those of the effective field theory. While the spin correlations in the effective field theory and wave function seem to match rather well (although not completely), the bond correlations are more puzzling. We conclude with a discussion of experiments in herbertsmithite and make several predictions.

Geometrical approach for the study of G band in the Raman spectrum of monolayer graphene, bilayer graphene, and bulk graphite

Abstract: In this paper, a geometrical approach is presented for the study of the double-resonance process, giving rise to the ${G}^{\ensuremath{'}}$ band in monolayer graphene, bilayer graphene, and bulk graphite. It is shown that there are four discrete peaks present in the ${G}^{\ensuremath{'}}$ band spectrum obtained from the stacking of two graphene layers, and these discrete peaks arise from the quantization of the first Brillouin zone caused by its finite size along the $c$ axis. Our analysis includes the study of the selection rules imposed on the electron-radiation and electron-phonon Hamiltonian interactions involving $\ensuremath{\pi}$ electrons near the $K$ point. We show that the anisotropy in the optical absorption (emission) near the $K$ point in the first Brillouin zone of graphite should be taken into account in order to gain an understanding of the selection rules for optical transitions in bilayer graphene. The validity of considering a linear dispersion for $\ensuremath{\pi}$ electrons along the $K\text{\ensuremath{-}}\ensuremath{\Gamma}$ direction is taken into consideration. We present four numerical equations, giving the dependencies of the frequencies of the four peaks composing the ${G}^{\ensuremath{'}}$ feature in the Raman spectrum of bilayer graphene on the laser excitation energy in the visible range. We also show that the two-peak shape of the ${G}^{\ensuremath{'}}$ band in the Raman spectrum of bulk graphite is in fact caused by the convolution of an infinite number of peaks.

Theoretical prediction of perfect spin filtering at interfaces between close-packed surfaces of Ni or Co and graphite or graphene

Abstract: The in-plane lattice constants of close-packed planes of fcc and hcp Ni and Co match that of graphite almost perfectly so that they share a common two-dimensional reciprocal space. Their electronic structures are such that they overlap in this reciprocal space for one spin direction only allowing us to predict perfect spin filtering for interfaces between graphite and (111) fcc or (0001) hcp Ni or Co. First-principles calculations of the scattering matrix show that the spin filtering is quite insensitive to amounts of interface roughness and disorder which drastically influence the spin-filtering properties of conventional magnetic tunnel junctions or interfaces between transition metals and semiconductors. When a single graphene sheet is adsorbed on these open d-shell transition-metal surfaces, its characteristic electronic structure, with topological singularities at the K points in the two-dimensional Brillouin zone, is destroyed by the chemical bonding. Because graphene bonds only weakly to Cu which has no states at the Fermi energy at the K point for either spin, the electronic structure of graphene can be restored by dusting Ni or Co with one or a few monolayers of Cu while still preserving the ideal spin-injection property.

Phase reciprocity of spin-wave excitation by a microstrip antenna

Abstract: Using space-, time-, and phase-resolved Brillouin light-scattering spectroscopy we investigate the difference in phase of the two counterpropagating spin waves excited by the same microwave microstrip transducer. These studies are performed both for backward volume magnetostatic waves and magnetostatic surface waves in an in-plane magnetized yttrium iron garnet film. The experiments show that for the backward volume magnetostatic spin waves which are reciprocal and excited symmetrically in amplitude there is a phase difference of associated with the excitation process and thus the phase symmetry is distorted. On the contrary, for the magnetostatic surface spin waves which are nonreciprocal and unsymmetrical in amplitude the phase symmetry is preserved there is no phase difference between the two waves associated with the excitation. Theoretical analysis confirms this effect.

The group III–V's semiconductor energy gaps predicted using the B3LYP hybrid functional

Abstract: Details of the band gaps within semiconductor materials are of paramount importance to a wide range of technological applications. We present the results of an hybrid exchange, B3LYP, approximation to density functional theory for the band gaps of zinc-blend and wurtzite structured III–V materials. Agreement with experimentally derived band gaps at characteristic points in the first Brillouin zone is at least as good as that obtained with correlated calculations, perturbation theories and screened exchange functionals.

Optical conductivity of bilayer graphene with and without an asymmetry gap

Abstract: When a bilayer of graphene is placed in a suitably configured field effect device, an asymmetry gap can be generated and the carrier concentration made different in each layer. This provides a tunable semiconducting gap, and the valence and conductance bands no longer meet at the two Dirac points of the graphene Brillouin zone. We calculate the optical conductivity of such a semiconductor with particular emphasis on the optical spectral weight redistribution brought about by changes in gap and chemical potential due to charging. We derive an algebraic formula for an arbitrary value of the chemical potential for the case of the bilayer conductivity without a gap.

Making Massless Dirac Fermions from Patterned Two-Dimensional Electron Gases

Abstract: Analysis of the electronic structure of an ordinary two-dimensional electron gas (2DEG) under an appropriate external periodic potential of hexagonal symmetry reveals that massless Dirac fermions are generated near the corners of the supercell Brillouin zone. The required potential parameters are found to be achievable under or close to laboratory conditions. Moreover, the group velocity is tunable by changing either the effective mass of the 2DEG or the lattice parameter of the external potential, and it is insensitive to the potential amplitude. The finding should provide a new class of systems other than graphene for investigating and exploiting massless Dirac fermions using 2DEGs in semiconductors.

Two magnon scattering in ultrathin ferromagnets: The case where the magnetization is out of plane

Abstract: We extend our earlier treatment of two magnon scattering in ultrathin ferromagnets to the case where the magnetization is tipped out of plane by virtue of the application of an out of plane magnetic field. The general formalism developed earlier is generalized in this regard, so when the magnetization is canted out of plane, one may extract information on the two magnon contribution to the linewidth or on the frequency shift of the ferromagnetic resonance line with origin in two magnon scattering. We provide the full set of response functions for such a film, which describe its response to driving fields of finite wave vector, so one may also explore two magnon effects on Brillouin light scattering if desired. We present explicit calculations that illustrate the behavior of the ferromagnetic resonance linewidth, for the picture employed earlier, where surface or interface defects activate two magnon scattering.

Simultaneous occurrence of structure-directed and particle-resonance-induced phononic gaps in colloidal films

Abstract: We report on the observation of two hypersonic phononic gaps of different nature in three-dimensional colloidal films of nanospheres using Brillouin light scattering One is a Bragg gap occurring at the edge of the first Brillouin zone along a high-symmetry crystal direction The other is a hybridization gap in crystalline and amorphous films, originating from the interaction of the band of quadrupole particle eigenmodes with the acoustic effective-medium band, and its frequency position compares well with the computed lowest eigenfrequency Structural disorder eliminates the Bragg gap, while the hybridization gap is robust

Effect of a single localized impurity on the local density of States in monolayer and bilayer graphene.

Abstract: We use the T-matrix approximation to analyze the effect of a localized impurity on the local density of states in monolayer and bilayer graphene. For monolayer graphene the Friedel oscillations generated by intranodal scattering obey an inverse-square law, while the internodal ones obey an inverse law. In the Fourier transform this translates into a filled circle of high intensity in the center of the Brillouin zone, and empty circular contours around its corners. For bilayer graphene both types of oscillations obey an inverse law.

Spin-orbit interaction effect in the electronic structure of Bi2Te3 observed by angle-resolved photoemission spectroscopy

Abstract: The electronic structure of p-type doped Bi2Te3 is studied by angle-resolved photoemission spectroscopy (ARPES) to experimentally confirm the mechanism responsible for the high thermoelectric figure of merit. Our ARPES study shows that the band edges are located off the Γ-Z line in the Brillouin zone, which provides direct observation that the spin-orbit interaction is a key factor to understand the electronic structure and the corresponding thermoelectric properties of Bi2Te3. A successive time-dependent ARPES measurement also reveals that the electron-like bands crossing EF near the -point are formed in an hour after cleaving the crystals. We interpret these as surface states induced by surface band bending, possibly due to quintuple inter-layer distance change of Bi2Te3.

Pseudospin and Deformation-Induced Gauge Field in Graphene

Abstract: The electronic properties of a single layer of graphite, graphene1)–4) have attracted much attention due to the “relativistic” character of π-electrons near the Fermi level. The energy band structure of graphene exhibits a linear energy dispersion relation around the two inequivalent, hexagonal corners of the first Brillouin zone in the k-space (the K and K′ points).5),6) The wavefunction (Hamiltonian) of π-electrons has two component (a 2 × 2 matrix) form due to the fact that the unit cell of graphene consists of two carbon atoms (A and B atoms). The effective-mass Hamiltonian of π-electrons around the K point or the K′ point is given by linear momentum operator, which is relevant to the linear energy dispersion relation of graphene. The effective-mass equation is similar to the massless Dirac equation or the Weyl equation.7) The original Dirac equation for an electron has the form

FeAs systems: a new class of high-temperature superconductors

Abstract: This is the first systematic review of a new class of high-Tc superconductors which includes iron-based layered compounds such as REOFeAs (RE is a rare-earth element), AFe2As2 (A= Ba, Sr, Ca), and LiFeAs, all of which are antiferromagnetic normal metals while being stoichiometric and becoming superconducting (with the current maximum Tc given by 55 K) when doped with an element of a different valence. The common structural element of all these compounds is layers formed by FeAs4 complexes. Electron states near the Fermi level are formed by Fe 3d states. As was shown theoretically by LDA calculations and experimentally by ARPES, the electronic structure of all compounds of the FeAs class is similar; their Fermi surface is multi-sheeted, consisting of two hole pockets at the center and two electron pockets at the corners of the Brillouin zone. In this paper, the superconducting properties of such systems are reviewed in detail, including the dependence of Tc on the doping level, external pressure, superconducting critical field, and superconducting order parameter. The controversy over the order parameter symmetry determined from different measurements is discussed. The transport, magnetic, and superconducting properties of FeAs systems are analyzed in comparison with those of cuprates. Basic electronic models of FeAs compounds, with their electronic structure and the proximity of the state of doped compounds to the antiferromagnetic ordering taken into account, are described to explain the specific features of electron pairing in them. It is shown that unlike the cuprates, superconducting FeAs systems are weakly (or moderately) correlated materials that are far from the Mott – Hubbard transition. A conclusion is made that the physical properties of FeAs compounds have mainly been well understood, except for the symmetry of the superconducting order parameter.

Partial frequency band gap in one-dimensional magnonic crystals

Abstract: Collective spin wave modes propagating in an array of magnetic stripes coupled by dynamic dipole interaction are investigated by Brillouin light scattering. It is demonstrated that this structure supports propagation of discrete spin waves at any angle with respect to the stripes length. The data are interpreted using a theoretical model based on the Bloch wave approach. It is shown that, due to the one-dimensional artificial periodicity of the medium, the gaps in the spin wave spectrum are partial: the frequency passbands for propagation along the direction of periodicity overlap with the stop bands for propagation along the stripes.

Phonon-Mediated Tunneling into Graphene

Abstract: Recent scanning tunneling spectroscopy experiments on graphene reported an unexpected gap of about $\ifmmode\pm\else\textpm\fi{}60\text{ }\text{ }\mathrm{meV}$ around the Fermi level [V. W. Brar et al., Appl. Phys. Lett. 91, 122102 (2007); Y. Zhang et al., Nature Phys. 4, 627 (2008)]. Here we give a theoretical investigation explaining the experimentally observed spectra and confirming the phonon-mediated tunneling as the reason for the gap: We study the real space properties of the wave functions involved in the tunneling process by means of ab initio theory and present a model for the electron-phonon interaction, which couples the graphene's Dirac electrons with quasifree-electron states at the Brillouin zone center. The self-energy associated with this electron-phonon interaction is calculated, and its effects on tunneling into graphene are discussed. Good agreement of the tunneling density of states within our model and the experimental $dI/dU$ spectra is found.

Unique characteristic features of stimulated Brillouin scattering in small-core photonic crystal fibers

Abstract: We present extensive stimulated Brillouin scattering (SBS) results from experiments and modeling for four different photonic crystal fibers (PCFs) with core diameters ranging from 8 to 1.7 μm. These results reveal several SBS characteristic features of small-core PCFs, high thresholds, and acoustic peaks, which are due to their antiguiding nature and highly multimode acoustic character. The nature of what we believe to be new acoustic modes is examined in the light of the large variations observed in the Brillouin gain, Brillouin threshold, and Brillouin shift with decreasing core diameter and optical wavelength.

Light-mass Bragg cavity polaritons in planar quantum dot lattices

Abstract: The exciton-polariton modes of a quantum dot lattice embedded in a planar optical cavity are theoretically investigated. Umklapp terms, in which an exciton interacts with many cavity modes differing by reciprocal lattice vectors, appear in the Hamiltonian due to the periodicity of the dot lattice. We focus on Bragg polariton modes obtained by tuning the exciton and the cavity modes into resonance at high symmetry points of the Brillouin zone. Depending on the microcavity design, these polariton modes at finite in-plane momentum can be guided and can have long lifetimes. Moreover, their effective mass can be extremely small, of the order of ${10}^{\ensuremath{-}8}{m}_{0}$ (${m}_{0}$ is the bare electron mass), and they constitute the lightest excitonlike quasiparticles in solids.

Optical Investigation of Quantum Confinement in PbSe Nanocrystals at Different Points in the Brillouin Zone

Abstract: We present detailed investigations on the optical properties of PbSe nanocrystals. The absorption spectra of monodisperse, quasispherical nanocrystals exhibit sharp features as a result of distinct optical transitions. To study the size dependence, absorption spectra of nanocrystals ranging from 3.4 to 10.9 nm in diameter are analysed and a total of 11 distinct optical transitions are identified. The assignment of the various optical transitions is discussed and compared to theoretically calculated transition energies. By plotting all transitions as a function of nanocrystal size (D) we find that the energy (E) changes with the following relationship ED-1.5 for the lowest energy transitions. The transition energy extrapolates to approximately 0.3 eV for infinite crystal size, in agreement with the bandgap of bulk PbSe at the L-point in the Brillouin zone. In addition, high-energy transitions are observed, which extrapolate to 1.6 eV for infinite crystal size, which is in good agreement with the bulk bandgap of PbSe at the -point in the Brillouin zone. Tight-binding calculations confirm that the high-energy transitions originate from the -point in the Brillouin zone. The -character of the high-energy transitions may be of importance to explain the mechanism behind multiple exciton generation in PbSe nanocrystals.

Spin-orbit interaction effect in the electronic structure of \BiTe \ observed by angle-resolved photoemission spectroscopy

Abstract: The electronic structure of $p$-type doped \BiTe is studied by angle resolved photoemission spectroscopy (ARPES) to experimentally confirm the mechanism responsible for the high thermoelectric figure of merit. Our ARPES study shows that the band edges are located off the $\Gamma$-Z line in the Brillouin zone, which provides direct observation that the spin-orbit interaction is a key factor to understand the electronic structure and the corresponding thermoelectric properties of \BiTe. Successive time dependent ARPES measurement also reveals that the electron-like bands crossing E$_F$ near the $\underline{\Gamma}$ point are formed in an hour after cleaving the crystals. We interpret these as surface states induced by surface band bending, possibly due to quintuple inter-layer distance change of \BiTe.

Double resonant Raman spectra in graphene and graphite : A two-dimensional explanation of the Raman amplitude

Abstract: We report calculated Raman spectra of the D and 2D modes in graphene and graphite. Evaluating the Raman amplitude in the two-dimensional Brillouin zone, we reproduce the splitting of the modes when going from single-layer graphene to graphite. The energy dependence of the D mode in graphene is 24%--32% smaller than in graphite. We discuss the intensity of the D line and show that the double resonant phonons originate from the low-symmetry parts of the Brillouin zone.

Spectral signatures of modulated d -wave superconducting phases

Abstract: We calculate, within a mean-field theory, the spectral signatures of various striped $d$-wave superconducting phases. We consider both in-phase and antiphase modulations of the superconducting order across a stripe boundary and the effects of coexisting inhomogeneous orders, including spin stripes, charge stripes, and modulated $d$-density wave. We find that the antiphase modulated $d$-wave superconductor exhibits zero-energy spectral weight, primarily along extended arcs in momentum space. Concomitantly, a Fermi surface appears and typically includes both open segments and closed pockets. When weak homogeneous superconductivity is also present, the Fermi surface collapses onto nodal points. Among them are the nodal points of the homogeneous $d$-wave superconductor, but others typically exist at positions that depend on the details of the modulation and the band structure. Upon increasing the amplitude of the constant component, these additional points move toward the edges of the reduced Brillouin zone where they eventually disappear. The above signatures are also manifested in the density of states of the clean, and the disordered system. While the presence of coexisting orders changes some details of the spectral function, we find that the evolution of the Fermi surface and the distribution of the low-energy spectral weight are largely unaffected by them.

Analysis of optical pulse coding in spontaneous Brillouin-based distributed temperature sensors

Abstract: A theoretical and experimental analysis of optical pulse coding techniques applied to distributed optical fiber temperature sensors based on spontaneous Brillouin scattering using the Landau-Placzek ratio (LPR) scheme is presented, quantifying in particular the impact of Simplex coding on stimulated Brillouin and Raman power thresholds. The signal-to-noise ratio (SNR) enhancement and temperature resolution improvement provided by coding are also characterized. Experimental results confirm that, differently from Raman-based sensors, pulse coding affects the stimulated Brillouin threshold, resulting in lower optimal input power levels; these features allow one to achieve high sensing performance avoiding the use of high peak power pulses.

Stimulated Brillouin Scattering in a Single-Mode Tellurite Fiber for Amplification, Lasing, and Slow Light Generation

Abstract: In this paper, Brillouin gain performances of tellurite fiber are investigated for photonics applications. We demonstrate stimulated Brillouin amplification and lasing and the simulated performance of slow light generation in a single-mode tellurite fiber. A Brillouin gain of 29 dB is achieved in a 100-m tellurite fiber with a pump power of 10 mW at 1550 nm. A peak value of Brillouin gain coefficients of 1.6989 X 10-10 m/W is measured on the base of gain characteristics. An all-fiber Brillouin laser with the maximum unsaturated power of 54.6 mW at 1550 nm and a slope efficiency of 38.2% is achieved from a 200-m tellurite fiber by employing a ring cavity. Furthermore, widely tunable (~27 nm) Brillouin comb laser with 26 lines spaced at 7.97 GHz is obtained from the ring laser cavity including an erbium-doped fiber amplifier (EDFA). A simple theoretical model based on laser threshold theory successfully explains the properties of Brillouin comb lasers. Stimulated Brillouin scattering (SBS)-induced time delay per unit power and per unit length is also calculated using the measured data of Brillouin gain coefficients. A peak value of 0.09246 ns/mW/m and a time delay slope efficiency of 1.75 ns/dB are obtained for this tellurite fiber. Potential performance of a tellurite fiber for slow light generation is clarified on the base of Brillouin gain characteristic. Our results show that tellurite fiber is a promising gain medium for Brillouin fiber amplifiers, lasers, and slow light generation due to its low background loss and large Brillouin gain coefficient.