Lorentzian Type Research Articles

THz Hilbert-Transform Spectrum Analyzer Based on High- $T_{c}$ Josephson Junction in Stirling Cryocooler

A demonstrator of a terahertz (THz) Hilbert-transform spectrum analyzer with subsecond scanning times and accuracy of the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> has been developed. The spectrum analyzer is based on a high- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> Josephson junction in a compact Stirling cryocooler. Operation of the spectrum analyzer has been critically considered in the THz range and sources of errors have been studied. The voltage and frequency scales of the analyzer have been calibrated with accuracy of 7 ·10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> by Shapiro steps, induced on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> ) curve of the junction by intensive monochromatic radiation. Dynamic errors of the analyzer have been minimized with scanning rates up to 4 THz/s. An instrumental function of the spectrum analyzer is of a Lorentz type with a spectral width of 1.5 GHz and free from any harmonic and subharmonic contributions with accuracy of around 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Rapid and detailed characterization of the THz sources, based on frequency multiplication of microwave radiation, has been demonstrated with the developed spectrum analyzer. The developed spectrum analyzer will be effective in new demanding THz applications, where a combination of high speed and accuracy is required.

Analysis of nonuniform field emission from a sharp tip emitter of Lorentzian or hyperboloid shape

For a sharp tip emitter, due to the non-uniform emission feature and the electron beam expansion in the vacuum, it is difficult to precisely determine the average field enhancement factor βc as well as the effective emission area Seff for a single field emitter. In this paper, we conduct a numerical experiment to simulate the electron field emission from a sharp tip emitter (Lorentzian or hyperboloid shape). By collecting the emission current Itot at the finite anode area Stot, we establish the criteria in using Fowler-Nordheim plot to estimate both βc and Seff, which agree well with our initial emission condition. It is found that the values of βc and Seff depend on the emitter's properties as well as the size of the anode area Stot. In order to determine the precise value of βc, Stot must be large enough to collect all the emitted electrons from the sharp tip (e.g., Itot reaches maximum). As an example, a Lorentzian type emitter with an aspect ratio of 10 (height over width), the effective enhancement factor is about βc=33 as compared to the maximal enhancement of 35 at the apex. At similar maximal enhancement factor at the apex (=360), both types of emitters will give different average field enhancement dependent on the collecting area. The extension of this simple model to a statistical more complicated model to simulate field emission from a cathode consisting of many field emitters is also briefly discussed. This paper should be useful to analyze and characterize field emission data together with experimental measurement.

Characterization and suppression of low-frequency noise in Si/SiGe quantum point contacts and quantum dots

We report on the effects of a global top gate on low-frequency noise in Schottky gate-defined quantum point contacts (QPCs) and quantum dots (QDs) in a modulation-doped Si/SiGe heterostructure. For a relatively large top gate voltage, the QPC current shows frequent switching with 1/f2 Lorentzian type charge noise. As the top gate voltage is decreased, the QPC pinch-off voltage becomes less negative, and the 1/f2 noise becomes rapidly suppressed in a homogeneous background 1/f noise. We apply this top-gating technique to double QDs to stabilize the charge state for the electron number down to zero.

Identifying the roles of the excited states on the magnetoconductance in tris-(8-hydroxyquinolinato) aluminum

Magnetoconductance response (MC) in illuminated tris-(8-hydroxyquinolinato) aluminum (Alq3) single layer has been studied to clarify the role of excitons and electron-hole (e-h) pairs on the MC generation. By fitting the MC curves at different bias conditions, the contribution of e-h pairs and excitons to the MC can be differentiated in the same material. The fitting results indicated that hyperfine mixing between the singlet and triplet e-h pairs results in a Lorentzian type MC within hyperfine field and charge reaction of triplet excitons induces a high-field MC following a non-Lorentzian shape, respectively. Moreover, the characteristic field width for the high-field MC is very different at forward and reverse bias regime, implying that the rate strength for the hole/electron-exciton reactions in Alq3 should be treated separately.

Dynamic magnetic properties of Fe70Co30(100) single-crystal thin films deposited at various substrate temperatures

Crystallographic orientation dependence of Gilbert damping constant, α , has been measured under different static magnetic fields for Fe70 Co30 (100) single-crystal thin film samples prepared at various substrate temperatures. Lorentz type resonance peaks are observed for the samples prepared below 200 oC. For a sample deposited at 400 oC, broadening of the resonance peak is observed, which is related with an increased surface roughness. α value decreases monotonically with increasing the static field when the field is applied parallel to the easy magnetization axis, whereas it increases when the field is applied along the hard magnetization axis up to around the anisotropy field and then decreases. The minimum value of α is determined to be 0.012 for the hard axis under static fields greater than 650 Oe. The value is twice larger compared with that of Fe(100) single-crystal film. The static magnetization curves measured for Fe70 Co30 films show large deviations from the curves expected by coherent rotation mode. Such deviation seems to be a possible reason for a larger α value of Fe70 Co30 thin film.

Extraordinary resonance transmission of two-dimensional terahertz metallic photonic crystals without defect

In this paper, we have demonstrated a kind of extraordinary transmission in the photonic first pass band of two-dimensional terahertz metallic photonic crystals: in the regime of low-middle metal filling radio, resonances among the metallic cylinders lead to sharp and high resonance peaks of Lorentz type, layer dependency of the peak numbers. The effect of positional disorders of metallic cylinders has been investigated as well. Based on a simple model proposed in this paper, we can intuitively understand the extraordinary transmission and roughly estimate resonance frequencies. Our results agree qualitatively with the experimental data reported in Appl. Phys. Lett. 65, 645.

Tunneling modes in a multilayer system of single-negative heterostructures with Lorentz model

Abstract We construct a one-dimensional multilayer system with heterostructures containing dispersive ENG and MNG metamaterials which are defined by Lorentz type model. Although no defect layer is introduced into the system, there are still tunneling modes and a “W” shape transmittance is observed, which is different from the properties in a multilayer system with heterostructures containing metamaterials of Drude type model.

Maximum entropy and stability of a random process with a [formula omitted] power spectrum under deterministic action

Abstract The principle of maximum entropy has been used to analyze the stability of the resulting process observed during the interaction of a random process with a 1 / f spectrum and a deterministic action in lumped and distributed systems of nonlinear stochastic differential equations describing the coupled nonequilibrium phase transitions. Under the action of a harmonic force the stable resulting process is divided into two branches depending on the amplitude of the harmonic force. Under the action of exponential relaxation in a lumped system with an increase in the dumping coefficient the power spectrum of the resulting process becomes a spectrum of the Lorentz type.

Boundedness of solutions to the Schrödinger equation under Neumann boundary conditions

We deal with Neumann problems for Schrödinger type equations, with non-necessarily bounded potentials, in possibly irregular domains in R n . Sharp balance conditions between the regularity of the domain and the integrability of the potential for any solution to be bounded are established. The regularity of the domain is described either through its isoperimetric function or its isocapacitary function. The integrability of the sole negative part of the potential plays a role, and is prescribed via its distribution function. The relevant conditions amount to the membership of the negative part of the potential to a Lorentz type space defined either in terms of the isoperimetric function, or of the isocapacitary function of the domain. On considère des problèmes de Neumann pour des équations de type Schrödinger, avec des potentiels non nécessairement bornés, dans des domaines éventuellement irréguliers de R n . Des estimations optimales qui tiennent compte de la régularité du domaine et de lʼintégrabilité du potentiel sont établies afin dʼassurer que toute solution soit bornée. La régularité du domaine est décrite soit grâce à sa fonction isoperimétrique, soit grâce à sa fonction isocapacitaire. Seulement lʼintégrabilité de la partie négative du potentiel joue un rôle et elle est décrite grâce à sa fonction de distribution. La condition optimale est liée à lʼappartenance de la partie négative du potentiel à un espace de type Lorentz défini soit en termes de la fonction isopérimétrique, soit en termes de la foncion isocapacitaire du domaine.

The Lagrangian and Hamiltonian Aspects of the Electrodynamic Vacuum-Field Theory Models

The important classical Ampere’s and Lorentz laws derivations are revisited and their relationships with the modern vacuum field theory approach to modern relativistic electrodynamics are demonstrated. The relativistic models of the vacuum field medium and charged point particle dynamics as well as related classical electrodynamics problems jointly with the fundamental principles, characterizing the electrodynamical vacuum-field structure, based on the developed field theory concepts are reviewed and analyzed detail. There is also described a new approach to the classical Maxwell theory based on the derived and newly interpreted basic equations making use of the vacuum field theory approach. There are obtained the main classical special relativity theory relationships and their new explanations. The well known Feynman approach to Maxwell electromagnetic equations and the Lorentz type force derivation is also. A related charged point particle dynamics and a hadronic string model analysis is also presented. We also revisited and reanalyzed the classical Lorentz force expression in arbitrary non-inertial reference frames and present some new interpretations of the relations between special relativity theory and its quantum mechanical aspects. Some results related with the charge particle radiation problem and the magnetic potential topological aspects are discussed. The electromagnetic Dirac-Fock-Podolsky problem of the Maxwell and Yang-Mills type dynamical systems is analyzed within the classical Dirac-Marsden-Weinstein symplectic reduction theory. Based on the Gelfand-Vilenkin representation theory of infinite dimensional groups and the Goldin-Menikoff-Sharp theory of generating Bogolubov type functionals the problem of constructing Fock type representations and retrieving their creation-annihilation operator structure is analyzed. An application of the suitable current algebra representation to describing the non-relativistic Aharonov-Bohm paradox is demonstrated. The current algebra coherent functional representations are constructed and their importance subject to the linearization problem of nonlinear dynamical systems in Hilbert spaces is also presented.

Potential estimates and gradient boundedness for nonlinear parabolic systems

We consider a class of parabolic systems and equations in divergence form modeled by the evolutionary p -Laplacean system u_t - \operatorname{div} (|Du|^{p-2}Du)=V(x,t) , and provide L^\infty -bounds for the spatial gradient of solutions Du via nonlinear potentials of the right hand side datum V . Such estimates are related to those obtained by Kilpeläinen and Malý [22] in the elliptic case. In turn, the potential estimates found imply optimal conditions for the boundedness of Du in terms of borderline rearrangement invariant function spaces of Lorentz type. In particular, we prove that if V\in L(n+2,1) then Du \in L^\infty_{\mathrm{loc}} , where n is the space dimension, and this gives the borderline case of a result of DiBenedetto [5]; a significant point is that the condition V \in L(n+2,1) is independent of p . Moreover, we find explicit forms of local a priori estimates extending those from [5] valid for the homogeneous case V \equiv 0 .

Nonlinear response in a multilayer system of Lorentz type single-negative metamaterial

Abstract We explore the nonlinear response in a multilayer system of Lorentz type single negative metamaterials by inserting a nonlinear layer into a symmetric periodic structure with alternating epsilon-negative (ENG) and mu-negative (MNG) materials. A pass band with flat-top is observed and concentrated at a fixed central frequency regardless of the change of other parameters of the multilayer system. Meanwhile the electric field distribution and bistability at the central frequency are also studied.

Structural and optical investigation of nonpolar a-plane GaN grown by metal—organic chemical vapour deposition on r-plane sapphire by neutron irradiation

Nonpolar (112̄0) a-plane GaN films are grown by metal—organic chemical vapour deposition (MOCVD) on r-plane (11̄02) sapphire. The samples are irradiated with neutrons under a dose of 1 × 1015 cm−2. The surface morphology, the crystal defects and the optical properties of the samples before and after irradiation are analysed using atomic force microscopy (AFM), high resolution X-ray diffraction (HRXRD) and photoluminescence (PL). The AFM result shows deteriorated sample surface after the irradiation. Careful fitting of the XRD rocking curve is carried out to obtain the Lorentzian weight fraction. Broadening due to Lorentzian type is more obvious in the as-grown sample compared with that of the irradiated sample, indicating that more point defects appear in the irradiated sample. The variations of line width and intensity of the PL band edge emission peak are consistent with the XRD results. The activation energy decreases from 82.5 meV to 29.9 meV after irradiation by neutron.

Stochastic resonance in a gain-noise model of single-mode laser under the first-order approximation

By adding periodic signal into single-mode laser, and taking the first-order approximation to the multiplication noise of the laser gain-noise model,we find that the output signal is of the Lorentz type when we obtain power spectrum by calculating the correlated function. The signal-to-noise ratio shows the stochastic resonance occurs with the variations of intensities of the pump noise and quantum noise, and the noise intensity of resonant peak is smaller than that under the zeroth approximation.

Hilbert Spectral Analysis of THz Radiation Sources by High-Tc Josephson Detectors

Abstract A Hilbert spectrum analyzer was developed and characterized with monochromatic radiation sources at the frequency range from 30 GHz to 1 THz. The analyzer was based on a high- Tc frequency-selective Josephson detector and cooled to temperatures of 60-80K by a Stirling cryocooler. The instrumental function of the spectrum analyzer was shown to be of Lorentz type and within accuracy up to 0.1% without any harmonic and subharmonic contributions. Spectral characterization of THz sources, based on frequency multiplication of input microwave radiation by Schottky diodes, was demonstrated for input frequencies from 10 to 20 GHz with a total scanning time as low as 50 ms per scan. The developed Hilbert spectrum analyzer might be considered as a compact and high-speed substitute of conventional Fourier spectrometers, which are used for characterization of THz radiation sources in combination with liquid-helium-cooled silicon bolometers.

Covariant jump conditions in electromagnetism

A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic phenomena described by two tensor fields, which satisfy Maxwell's equations. A generic tensorial constitutive relation between these fields is an independent ingredient of the theory. By use of different constitutive relations (local and non-local, linear and non-linear, etc.), a wide area of applications can be covered. In the current paper, we present the jump conditions for the fields and for the energy-momentum tensor on an arbitrarily moving surface between two media. From the differential and integral Maxwell equations, we derive the covariant boundary conditions, which are independent of any metric and connection. These conditions include the covariantly defined surface current and are applicable to an arbitrarily moving smooth curved boundary surface. As an application of the presented jump formulas, we derive a Lorentzian type metric as a condition for existence the wave front in isotropic media. This result holds for the ordinary materials as well as for the metamaterials with the negative material constants.

Iterated rearrangements and Gagliardo–Sobolev type inequalities

In this paper we consider Lorentz type spaces L σ p , r defined in terms of iterated rearrangements of functions of several variables ( σ is a permutation of { 1 , … , n } ). Further, we study Fournier–Gagliardo mixed norm spaces V ( R n ) closely related to Sobolev spaces W 1 1 ( R n ) . We prove estimate of ‖ f ‖ L σ n ′ , 1 via ‖ f ‖ V with the sharp constant. In particular, this gives a refinement of the known Sobolev type inequalities for the space W 1 1 ( R n ) .

Permeability spectra of yttrium iron garnet and its granular composite materials under dc magnetic field

Relative complex permeability spectra (μr=μr′-iμr′′) and the dc magnetic field effect on them for a yttrium iron garnet (YIG) and its granular composite materials have been studied to evaluate the negative permeability characteristics. In the sintered YIG, two distinct peaks corresponding to the domain wall and the gyromagnetic spin resonance were observed in the imaginary part μr′′ under zero magnetic field; the real part of complex permeability μr′ shows a small negative value in a certain frequency range. The Lorentz type magnetic resonance with the negative permeability dispersion was observed under dc magnetic field. Permeability spectra were evaluated by the numerical fitting of actual measurement data to a resonance formula using six parameters (resonance frequencies, static susceptibilities, and damping factors of the domain wall motion and the gyromagnetic spin rotation). The dc magnetic field suppresses the domain wall contribution and the spin component becomes dominant. In the YIG granular composite material, the permeability dispersion frequency shifts to higher frequency region due to demagnetizing field; the spin component becomes dominant. Negative permeability spectra were also observed in the high content YIG composites under the dc field. The negative permeability spectra of YIG composite materials can also be applied to the left-handed material as well as the sintered YIG.

On Fournier-Gagliardo mixed norm spaces

We study mixed norm spaces V (R n ) that arise in connection with embeddings of Sobolev spaces W 1 1(R n ). We prove embeddings of V (R n ) into Lorentz type spaces defined in terms of iterative rearrangements. Basing on these results, we introduce the scale of mixed norm spaces V p (R n ). We prove that V ‰ V p and we discuss some questions related to this embedding.

Optical response of supported gold nanodisks

It is shown that the ellipsometric spectra of short range ordered planar arrays of gold nanodisks supported on glass substrates can be described by modeling the nanostructured arrays as uniaxial homogeneous layers with dielectric functions of the Lorentz type. However, appreciable deviations from experimental data are observed in calculated spectra of irradiance measurements. A qualitative and quantitative description of all measured spectra is obtained with a uniaxial effective medium dielectric function in which the nanodisks are modeled as oblate spheroids. Dynamic depolarization factors in the long-wavelength approximation and interaction with the substrate are considered. Similar results are obtained calculating the optical spectra using the island-film theory. Nevertheless, a small in-plane anisotropy and quadrupolar coupling effects reveal a very complex optical response of the nanostructured arrays.