Cutoff Condition Research Articles

Multipactor Breakdown Prediction in a Rectangular Waveguide: Statistical Theory and Simulation Results

AbstractStatistical theory of the initial study of the multipactor discharge in a rectangular waveguide is constructed. The recurrent relation between the emission phase and position distributions is derived taking into account the velocity spread of secondary electrons. A general integral equation allowing prediction of the threshold value of the secondary yield (above which electron multipaction occurs) is formulated. It has been found that the presence of directional anisotropy can significantly alter the multipacting discharge cutoff conditions in comparison with isotropic emission. It has been established that the combined action of tangential velocity components and magnetic field leads to an increase of the threshold of multipactor growth. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Semianalytical Method to Determine Parasitic Elements of Quantum-Well Laser

A parameter-extraction approach for the quantum- well laser, which combines the analytical approach and the empirical optimization procedure, is developed in this paper. The initial values of the parasitic pad capacitance and the feedline inductance are extracted by using a set of closed-form expressions derived from above-threshold mode input reflection coefficient on wafer measurement, and the extrinsic contact resistance and capacitance determined by using the analytical method are described as functions of the parasitic pad capacitance and the feedline inductance. Advanced Design System (Agilent commercial software) is then used to optimize only the parasitic pad capacitance and the feedline inductance with very small dispersions of initial values. An excellent fit between measured and simulated input reflection coefficients under cutoff and above-threshold biased conditions in the frequency range of 50 MHz-40 GHz is obtained.

On the non-existence of the micro-causal sector of Lorentz non-invariant quantum field theory on a continuum

We study a model for a Lorentz non-invariant quantum field theory. In this model Lorentz violation is due to a non-linear dispersion relation admitting signals in form of wave packets propagating with super-luminal (faster than the low-energy speed of light) group velocities. We characterize the causal sector of the theory by a cutoff condition protecting the theory against such signals and study the question as to whether the causal sector exhibits micro-causality (locality in all frames), in which case we call the causal sector the micro-causal sector. It is argued that in the causal sector the canonical commutation relation are changed in such a way that the imposition of locality postulate becomes incompatible with the continuity of space. The conclusion therefore is that there is no micro-causal sector of the theory on the continuum space underlying the model and in this respect it suggests the sensitivity of an effective Lorentz non-invariant quantum field theory to a short-distance cutoff.

Guided modes of one-dimensional photonic bandgap waveguides

Using a ray-optics model, we analyze the guided modes of a slab waveguide that consists of a low-index layer sandwiched between two photonic bandgap structures. Normalized band diagrams and dispersion curves for the TE and TM waves are investigated in detail, and a nomenclature system for the guided modes based on the mode-field patterns in the waveguide is proposed. The cutoff conditions and the confinement factors of the modes are discussed. The effects of varying the physical parameters of the waveguide on the dispersion characteristics of the modes are also analyzed.

Approximate solution in a doubly clad optical fiber including left-handed material

A doubly clad fiber with a right-handed-material core and outer cladding but a left-handed-material inner cladding has been analyzed in weakly guiding approximation. The characteristic equations for four kinds of guided modes (HE, EH, TE, and TM) are derived and further simplified under far from cutoff condition. Dispersion curves for the lowest-order mode of each of the four modes have been calculated for different inner-cladding refractive index and thickness. Compared with corresponding curves for a common right-handed doubly clad fiber, these curves all behave with abnormal dispersion. Near cutoff, double degeneracy occurs for HE11 and EH11 modes.

Unruh’s detector in the presence of Lorentz symmetry breaking

We investigate the quantum field theory of a Lorentz non-invariant model with a massive nonlinear dispersion relation in Minkowski space. The model involves some non-causal signals in the form of wave packets propagating with super-luminal group velocities. To avoid the problems with causality we characterize the causal sector of the theory by a cutoff condition excluding all super-luminal group velocities. It is argued that in the causal theory satisfying the energy positivity condition an Unruh’s detector moving with a constant velocity with respect to the preferred frame does not detect any particle. But in a causal theory violating energy positivity, detection of a field quanta occurs. We comment on the origin of this particle creation.

PROPAGATION PROPERTIES OF THE SPP MODES IN NANOSCALE NARROW METALLIC GAP, CHANNEL, AND HOLE GEOMETRIES

The propagation properties of surface plasmon polaritons (SPP) modes in nanoscale narrow metallic structures: gap, channel, and rectangular-hole waveguides, are analyzed by the complex effective dielectric constant approximation. The results show that all the SPP modes exist below the critical frequency where the real part of metal permittivity is negative unity. It is found that both cutoff frequency and cutoff height exist in channel waveguide and rectangularhole waveguide. The channel and rectangular-hole waveguides have different propagation properties at cutoffs due to their different cutoff conditions. Compared with the gap waveguide, the channel waveguide has shorter propagation length and better confinement when the operation frequency is near the critical frequency, but has longer propagation length and worse confinement when the operation frequency is far from the critical frequency. Among the three waveguides, the rectangular-hole waveguide has the best confinement factor and the shortest propagation length. The comprehensive analysis for the gap, channel, and rectangular-hole waveguides can provide some guidelines in the design of subwavelength optical devices.

Optical fibers with high-index-contrast dielectric thin films

The authors analyze electromagnetic wave propagation through optical fibers consisting of a glass core surrounded by a high-refractive-index dielectric thin film, in turn surrounded by a glass cladding. The asymmetry of the structure due to different core and cladding refractive indices results in two types of guided modes: they propagate either in the core and film or only in the film. The dispersion equations are derived, and mode classifications are established for transverse and hybrid modes. The cutoff conditions of transverse modes are given. Numerical simulations are performed to obtain the effects of film index and thickness on the cutoff frequencies and dispersion curves. It is shown that a high-index film causes the modes to become evanescent in the core and guided only in the film. These modes form two types of linearly polarized modes, according as they follow the TE or the TM mode propagation curves of asymmetric slab waveguide. Investigation of power flow along the propagation direction shows that the higher the refractive index of the film, the higher the power density in the film.

Short-wavelength fluctuation effect on the c-axis paraconductivity within the Ginzburg–Landau theory

Effects of short-wavelength cutoffs on the fluctuation conductivity σc′ above Tc in the out-of-plane direction are studied in a layered superconductor. Equations with spectral cutoffs are derived in the context of the Ginzburg–Landau theory under two kinds of the cutoff condition, a momentum-cutoff and a total-energy cutoff. From numerical results for our formulae, it is found that, in the vicinity of Tc, both cutoff effects on σc′ are less important than those on the in-plane paraconductivity σab′ while a total-energy cutoff becomes as effective as in the case of σab′ at a temperature range far away from Tc. The present results are discussed in comparison to experiments.

Tunneling-Current-Induced Light Emission from Copper Phthalocyanine Thin Films

Molecular fluorescence induced by tunneling electrons from a scanning tunneling microscope was investigated for copper phthalocyanine thin films deposited on the highly ordered pyrolytic graphite and the Au(111) substrates. No light emission was observed from the copper phthalocyanine thin films on the highly ordered pyrolytic graphite substrate, on the other hand, the fluorescence of copper phthalocyanine on the Au(111) substrate was observed with plasmon-mediated light emission related to the Au(111) substrate. These results are due to the differences in the charge injection efficiency and surface plasmon resonance mode of two substrates. The obtained fluorescence did not satisfy the quantum cutoff condition, that is, observed photon energy was higher than the energy of injected electrons. [DOI: 10.1380/ejssnt.2006.559]

Modal Analysis and Waveguide Dispersion of an Optical Waveguide Having a cross-section of the Shape of a Cardioid

In this paper, we choose a simple and practical analytical method based on scalar wave approximation to study the modal behaviour, cutoff condition of an unconventional optical waveguide having a cross section of the shape of a cardioid. We take the appropriate orthogonal coordinates for the proposed structure and impose the boundary conditions under the weak guidance approximation to get the modal eigen value equation. Using this equation we obtain numerical results in the form of dispersion curves and cutoff frequencies. Also the dependence, d(Vb′)/dV on V has been obtained and shown graphically, where V stands for normalized frequency parameter and b′ stands for normalized propagation constant. An attempt has been made to estimate how the modal behaviour and waveguide dispersion change as circular shape is changed to the shape of a cardioid.

Efficient Absorbing Layers for the Guided-mode Analysis Using the Imaginary-Distance BPM

The imaginary-distance beam-propagation method (ID-BPM) with the conventional perfectly matched layer (PML) often yields unstable results for the guided-mode analysis of an optical waveguide. To address this issue, two efficient absorbing layers are discussed on the basis of suitable modifications to the stretching coordinate variables of the conventional PML. Theoretical descriptions of these layers are presented using the plane wave solutions. The performance of these layers is investigated for several two- and three-dimensional problems. It is found for the analysis of a light-guiding metal line near the cutoff condition that the calculation time is reduced to one sixth of that using a zero boundary.

Experimental and theoretical investigations of birefringent holey fibers with a triple defect

We have manufactured and characterized a birefringent holey fiber of a new construction. The birefringence in this fiber is induced by the highly elliptical shape of the core, which consists of a triple defect in a hexagonal structure. Using a hybrid edge-nodal finite-element method, we calculated the spectral dependence of phase and group modal birefringence for spatial modes E11 and E21 in idealized and in real fiber, whose geometry we determined by using a scanning-electron microscope. Results of our calculations show that technological imperfections significantly affect the fiber's birefringence. Normalized cutoff wavelengths for higher-order modes relative to the filling factor were also determined for the idealized structure. We observed a significant disagreement between theoretical and experimental values of cutoff wavelengths, which was attributed to high confinement losses near the cutoff condition. We also measured the spectral dependence of the phase and the group modal birefringence for spatial modes E11 and E21. The measured parameters showed good agreement with the results of modeling.

Comparison between a graded and step-index optical cavity in InGaN MQW laser diodes

In this paper we theoretically analysed the influence of the number of QWs in the active region and the cladding layer width on the confinement factor, near field patterns and far field patterns. A comparison between the conventional step separate confinement heterostructure (SCH) and a graded-index separate structure (GRIN-SCH) is done regarding these parameters. We found that in the case of single quantum well structure the step cavity gives the highest values of the confinement factor. As the number of wells (N) in the active region is increased the superiority of one structure or the other depends on the cladding layer width and the value of N, but for values of N higher than six, the confinement factor is always higher in the structure with a GRIN cavity, independent of the cladding layer width. In general the far field patterns in GRIN structure have lower values of the full width half-maximum (FWHM). The cutoff condition for a mono mode optical cavity is also calculated in both structures.

Propagation properties of Bragg fiber analyzed by a Hankel function formalism

This article describes the propagation characteristics of a Bragg fiber whose guiding principle is based on Bragg diffraction due to the periodic cladding. An asymptotic expansion for Hankel function at large arguments is used to express cladding fields with a simple form. A division in matrix calculation enables us to understand the cladding field physically. Condition for getting an asymptotically decaying wave in the cladding is revealed on the basis of property of Bloch wavenumber. It is shown that cutoff effective index giving the cutoff condition determines the lower limit for the cladding index difference.

Electron density measurements from right-hand cutoff of ECE in the TCABR tokamak

In tokamak machines with low toroidal magnetic fields and high plasma densities, the accessibility conditions impose restrictions to the detection of the Electron Cyclotron Emission (ECE). In these machines, the righthand cutoff condition can be used as an independent method to determine the local electron density from the ECE data in thermal discharges. In this paper is shown the results obatined from the detection of ECE radiation in the TCABR tokamak, in operation at the Institute of Physics of University of São Paulo. The effect of the ECE radiation cutoff was observed for different radial positions of the plasma column. To reach the ECE cutoff condition, the electron density was increased monotonically by the use of an external gas puffing system. For sufficient high densities, the emission at some frequencies is cutoff and the first and the last frequency to be cutoff depends on the shape of the density profile. These measurements do not require the plasma to be optically thick. It was observed that, for a toroidal field B O = 1:14T, the first cutoff of ECE occurs for a radial position r <FONT FACE=Symbol>@</FONT> 5 cm. From these measurements the radial electron density was determined. For a symmetric parabolic profile n e = n eo [1 - (r/a)²]alpha , values of alpha between 0.86 and 0.97 were experimentally obtained. A good agreement of these values with those obtained from the microwave interferometer measurements (<FONT FACE=Symbol>a »</FONT>0:85) was found. Therefore, the ECE right-hand cutoff constitutes an independent method to obtain information about the electron density profile.

Large-Core Single-Mode Waveguides With Cross-Sectional Antiresonant Confinement

This paper presents a single-mode waveguide based in cross-sectional antiresonant confinement. The confinement in the vertical direction is obtained placing a Fabry-Pe/spl Sigma/rot tuned at its antiresonant condition underneath the core [defining the antiresonant reflecting optical waveguides (ARROW) structure]. Small weightings are placed on both sides of the core to achieve a local increase in the effective refractive index, obtaining the so-called lateral antiresonant structures (LASs). They assure both the cross-sectional confinement and the single-mode behavior of the global structure. Simulations predict the transition of the symmetrical mode of the LAS to a bidimensional ARROW mode below the cutoff condition of the former, while at the cutoff condition of the asymmetrical LAS mode power is directly transferred to a radiative mode. Experimental results have shown that losses decrease as the lateral core width increases, which is in agreement with a minor confinement in the structure. Near-field images from a 3-mm-thick, 16 mm-wide ARROW-two-dimensional structure have shown that when a misalignment between the input optical fiber and the waveguide is produced, no higher order modes are excited, confirming the single-mode behavior of these structures.

Explicit formulas for transmission characteristics of graded-index oval core fibers.

Transmission characteristics of graded-index oval (GIO) core fibers are theoretically analyzed, and basic equations representing the specific properties of the fiber are obtained. Formulas for the propagation constant, the field-profile function, the cutoff condition, and the total number of guided modes are derived in explicit forms. The formula for the change of the Gaussian beam radius as a function of the propagation distance is also given, and the numerical example agrees well with experimental data and agrees completely with that obtained by the beam-propagation method. These explicit expressions are useful for finding optimum structural parameters of GIO fibers to be used in practical fields.

MODAL DISPERSION CHARACTERISTICS AND WAVEGUIDE DISPERSION OF AN OPTICAL WAVEGUIDE HAVING A NEW UNCONVENTIONAL CORE CROSS-SECTION

In this article, we present a simple and practical analytical approach based on scalar wave approximation to estimate the modal dispersion characteristics and cutoff condition of an optical waveguide having an arbitrary and uniform core cross-section. This structure represents the core of a circular waveguide which is compressed at both the ends of a diameter. We choose the new and appropriate orthogonal coordinates for the proposed waveguide structure and impose the boundary conditions under the weak guidance approximation to get the modal eigen value equation. Using this equation, we achieve numerical results in the form of dispersion curves and cutoff frequencies. Further, representing the normalised frequency parameter as V and normalised propagation constant as b′, the dependence of d(Vb′)/dV on V has been obtained and shown graphically. A brief comparison of the proposed waveguide and the circular waveguide has also been made in respect of the number of sustained modes and waveguide dispersion.

Analysis of the Propagation Characteristics of a Step-Index Waveguide of Annular Circular Cross-Section with Conducting Helical Windings on the Inner and Outer Boundary Surfaces Between the Guiding and the Non Guiding Regions

We study the optical fiber of an annular cross-section with two conducting helical windings on the two interfaces between the annular guiding region and the inner and outer cladding regions. Using suitable boundary conditions, the field components are determined for different regions and thus an eighth order determinantal equation is obtained. The characteristic equation along with cutoff condition of the proposed waveguide is obtained.