Transmission Matrix Approach Research Articles

Comprehensive modeling of the stationary and dynamic behaviour of imaginary Bragg gratings around threshold

This paper presents a dynamical study of an imaginary Bragg grating. It shows that when the lasing threshold is reached, the standard transmission matrix approach is no longer valid and a more comprehensive model taking in account gain saturation is required. The grating has then been studied using a direct numerical solution of the time-dependant coupled-mode equations including gain saturation effects. This description is valid for analyzing imaginary Bragg gratings operating both below and above the lasing threshold, and it has demonstrated to provide a physically consistent solution, avoiding the group delay divergences and abnormalities which are predicted by the transfer-matrix model.

Vibrational power-flow analysis of a MIMO system using the transmission matrix approach

The transmission matrix approach is employed in this paper for the vibrational power-flow analysis of a multiple-input/multiple-output (MIMO) system. The substructures in each subsystem are modelled as a group of general MIMO transmission elements, which are described in terms of discrete or distributed properties. The global transmission matrix of the system is formed by assembling the transmission matrices together. Using the proposed approach, the output variables of any subsystem can be expressed in terms of the input state variables of that subsystem. Hence, the proposed approach is very systematic in analysing the dynamic behaviour of a complex system with a group of elements. In the numerical example, the power flow of a multi-mount system is modelled analytically. The transmission of vibratory power flow from the vibrating rigid body into a simply supported plate through elastic mounts is studied in detail. The effects on the power flows of various factors, such as the plate thickness, loading type, mounting locations, and mass and damping properties of the mounts, are addressed.

Modeling of nonideal volume Bragg reflection gratings in photosensitive glass using a perturbed transmission matrix approach

Reflection spectra of volume Bragg gratings written in bulk photosensitive silicate glass for wavelength division multiplexing applications are modeled using a transmission matrix approach. This allows for the examination of the effects of spatial perturbations along the grating due to chirp, apodization, compositional inhomogeneities, and index contrast saturation leading to reflection spectra that are asymmetric about the Bragg peak. Effects of the nonlinear relationship between index contrast in the glass and exposure flux on the reflection spectrum is also studied. Volume Bragg gratings are fabricated in UV exposure-sensitive silicate glasses containing alkali-halide nano-crystalline domains, and their reflection spectra are compared with calculation. The magnitude and uniformity of the index changes observed in our glass gratings make them useful in a wide range of wavelength multiplexing applications.

Analysis of Inclined I-Slots in the Narrow Wall of Standard X-Band Rectangular Waveguide

Different types of slot configurations in one of the walls of rectangular waveguides are analyzed by different researchers. In this paper different configurations of inclined I-slot radiators have been investigated and analysed. The analysis consists of evaluation of admittance characteristics of the slot as a function of slot parameters and frequency. Slot admittance characteristics are obtained from the concepts of self-reaction and discontinuity in modal current. On the other hand, coupling and VSWR are evaluated from the shunt equivalent network parameter making use of transmission matrix approach. The variations of normalized conductance, susceptance, coupling and VSWR as a function of frequency are presented. The advantage of such types of slots is that the entire slot geometry is confined only to narrow wall.

MAGNETIC POTENTIAL GREEN'S DYADICS OF MULTILAYERED WAVEGUIDE FOR SPATIAL POWER COMBINING APPLICATIONS - Abstract

Integral equation formulation and magnetic potential Green's dyadics for multilayered rectangular waveguide are presented for modeling interacting printed antenna arrays used in waveguide-based spatial power combiners. Dyadic Green's functions are obtained as a partial eigenfunction expansion in the form of a double series over the complete system of eigenfunctions of transverse Laplacian operator. In this expansion, one-dimensional characteristic Green's functions along a multilayered waveguide are derived in closed form as the solution of a Sturm-Liouville boundary value problem with appropriate boundary and continuity conditions. A method introduced here is based on the transmission matrix approach, wherein the amplitude coefficients of forward and backward traveling waves in the scattered Green's function in different dielectric layers are obtained as a product of transmission matrices of corresponding layers. Convergence of Green's function components in the source region is illustrated for a specific example of a two-layered, terminated rectangular waveguide.

Analysis of a bilateral distributed amplifier using scattering parameters

AbstractA formulation for the bilateral distributed amplifier network using a normalized transmission matrix approach is proposed in this letter. The analysis takes into consideration the effect of Cgd in the active device. Our approach is compared to the theoretical predictions for the unilateral case and measured results. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 120–122, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10693

Note on formulation of the enhanced scattering- (transmittance-) matrix approach

The enhanced transmittance matrix approach developed by Moharam et al. [J. Opt. Soc. Am. A 12, 1077 (1995)] is reformulated in a concise and illuminating form in terms of scattering (reflection and transmission) matrices directly. Two equivalent recursive formulations, corresponding to their full- and partial-solution approaches, are presented and extended to allow simultaneous determination of both reflected and transmitted amplitudes. The relationships between these formulations and the S-matrix algorithm, together with their relative efficiencies and usefulness, are ascertained and compared by means of compact formulas featuring parallel algebraic structures. It is made evident that given the eigenmode solutions, the enhanced approach is the most direct and efficient way for deducing global scattering matrices.

Aspects of magnetotunnelling drawn fromab-initio-type calculations

Tunnelling between two semi-in®nite ferromagnetic electrodes separated by vacuum is studied theoretically on an ab-initio level by using the fully relativistic spin-polarized screened Korringa±Kohn±Rostoker and the spin-polarized nonrelativistic tight-binding linear muA n-tin orbital method. The Kubo± Greenwood equation is employed to calculate the non-local conductivity and layer-resolved sheet resistances; the transmission matrix formulation in turn is used to evaluate the conductance. We show that the dependence of sheet resistance on the imaginary part of the Fermi energy allows us to distinguish between the tunnelling and conductive regimes of electron transport. Our numerical studies of the system bcc Fe(100)/vacuum/bcc Fe(100) show quite dramatic variations in the electrostatic potential in the vacuum region and a gradual development of the tunnelling barrier with increasing thickness of the vacuum barrier. Varying the Madelung potential in the interior of the vacuum barrier allowed us to simulate spacers made of semiconducting or insulating material and to discuss the conditions for the presence of a magnetoresistance in such multilayers. As far as the thickness of the vacuum barrier is concerned the results obtained with the transmission matrix approach for fcc Co(001)/vacuum/ fcc Co(001) show a similar tendency to those obtained within the Kubo± Greenwood equation for bcc Fe(100)/vacuum/bcc Fe(100); asymptotically, that is with increasing thickness of the vacuum barrier, the magnetoresistance tends to zero.

Magnetic Potential Green's Dyadics of Multilayered Waveguide for Spatial Power Combining Applications

Integral equation formulation and magnetic potential Green's dyadics for multilayered rectangular waveguide are presented for modeling interacting printed antenna arrays used in waveguide- based spatial power combiners. Dyadic Green's functions are obtained as a partial eigenfunction expansion in the form of a double series over the complete system of eigenfunctions of transverse Laplacian operator. In this expansion, one-dimensional characteristic Green's functions along a multilayered waveguide are derived in closed form as the solution of a Sturm-Liouville boundary value problem with appropriate boundary and continuity conditions. A method introduced here is based on the transmission matrix approach, wherein the amplitude coefficients of forward and backward traveling waves in the scattered Green's function in different dielectric layers are obtained as a product of transmission matrices of corresponding layers. Convergence of Green's function components in the source region is illustrated for a specific example of a two-layered, terminated rectangular waveguide.

Evaluation of Impedance Matching Schemes for Pulse-Echo Ultrasonic Piezoelectric Transducers

In order to optimize the broadband response of a piezoelectric transducer, different impedance matching procedures are used, looking for a compromise between efficiency and bandwidth. In this paper a general methodology for the evaluation of acoustic and electrical matching schemes is presented. Broadband acoustic impedance matching schemes are evaluated in the frequency domain using the transmission line analogy. Electrical matching networks at the reception stage are evaluated using the transmission matrix approach. In practical cases of ultrasonic imaging and NDE, electronic "spike" generators based on capacitive discharges are used. The special topology of such generators (including semiconductor devices) conditions the electrical driving pulse at the transducer terminals. This driving waveform (determined by the interactions among the spike generator, the electrical matching network and the transducer) is approximately evaluated in the frequency domain for the low Megahertz range. Several examples in emission and reception illustrate the methodology, including a comparative study of criteria proposed for the optimum design of quarter-wave transmission line matching layers.

The influence of defects on electrical transport in magnetic multilayers

The transmission matrix approach was used to evaluate the perpendicular magnetotransport in metallic multilayers on an abinitio level. The spin-polarized, surface Green function technique was employed within the framework of the tight-binding, linear muffin-tin orbital method. The effect of impurities was included in terms of lateral supercells with random arrangements of two types of atoms. This approach treats both the ballistic and the diffusive regimes of magnetotransport on equal footing. The method was also applied to face-centered-cubic-based Co/Cu/Co(001) trilayers.

The CPP transport in metallic magnetic multilayers

The transmission matrix approach is used to evaluate perpendicular magnetotransport in metallic multilayers that consist of two magnetic slabs separated by a non-magnetic spacer. We employ the spin-polarized surface Green function technique within the framework of the tight-binding linear muffin-tin orbital method. Our approach allows both the ballistic and the diffusive regime of magnetotransport to be treated on equal footing. The effect of disorder is included in terms of lateral supercells confined to individual atomic layers. In this paper, we apply the method to fcc-based Co/Cu/Co(001) trilayers.

Dynamic Behavior of Complex Fluid-Filled Tubing Systems—Part 1: Tubing Analysis

A general transmission-matrix approach is given for finding the frequency response of linearized long-wavelength models for the vibration in systems with straight and curved fluid-filled tubes. Couplings between the fluid and wall motions include the Bourdon effect, frequency-dependent wall shear, the Poisson coupling and the effect of discontinuities. The introduction of a global transmission matrix allows nonplanar tubing systems of virtually any complexity to be analyzed, overcoming the round-off error problem that plagues the basic transmission-matrix approach for this and analogous system models. Corroborating experiments focus on the Poisson and Bourdon effects.

Transmission Matrix Analysis of Cascaded Discontinuities in the Center Conductor of Microstripline

The transmission and reflection properties of the network consisting of a cascade connection of discontinuities in the center conductor of microstripline are analyzed employing transmission matrix approach. Computed and measured values of transmission and reflection coefficients are compared in the lower microwave frequency band. The cascaded discontinuities are proposed to be used in improving the skirt selectivity of the band stop filters.The taper which is used to match the low impedance line containing the discontinuities, to a normal 50 Ω line is also anlayzed. The input voltage reflection coefficient of the taper is computed by determining the polynomial approximation for logarithmic variation of impedance along the taper, by transmission matrix approach and by employing theory of small reflections. The performance of the linear taper is compared with those of standard tapers like exponential and triangular tapers. Experimental results are also presented.

Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach

An enhanced, numerically stable transmittance matrix approach is developed and is applied to the implementation of the rigorous coupled-wave analysis for surface-relief and multilevel gratings. The enhanced approach is shown to produce numerically stable results for excessively deep multilevel surface-relief dielectric gratings. The nature of the numerical instability for the classic transmission matrix approach in the presence of evanescent fields is determined. The finite precision of the numerical representation on digital computers results in insufficient accuracy in numerically representing the elements produced by inverting an ill-conditioned transmission matrix. These inaccuracies will result in numerical instability in the calculations for successive field matching between the layers. The new technique that we present anticipates and preempts these potential numerical problems. In addition to the full-solution approach whereby all the reflected and the transmitted amplitudes are calculated, a simpler, more efficient formulation is proposed for cases in which only the reflected amplitudes (or the transmitted amplitudes) are required. Incorporating this enhanced approach into the implementation of the rigorous coupled-wave analysis, we obtain numerically stable and convergent results for excessively deep (50 wavelengths), 16-level, asymmetric binary gratings. Calculated results are presented for both TE and TM polarization and for conical diffraction.

Transmission matrix approach for electron transport in inversion layers

An efficient “transmission matrix” (TM) approach is proposed for including quantization effects in the treatment of electron transport in inversion layers. For each input mode of the momentum space, the probabilities of the output modes and average times are computed and used to follow the electron motion in time. The TM approach makes it possible to treat electron transport with improved numerical efficiency while maintaining the accuracy of the Monte Carlo (MC) approach. Examples with a constant electric field are considered to demonstrate the TM approach and it is shown that the results obtained by the TM and MC techniques are in excellent agreement with each other. The TM approach reduces the computation time by a factor of 6 or more. Integration of the TM approach in device analysis is discussed.

Traversal time analysis in resonant tunnelling structures

Abstract The wave function is used to calculate the traversal time of a resonant tunnelling structure. It is established that the traversal time increases with increasing width and height of the barriers as well as the width of the well. Based on the real part of the quantum mechanical wave impedance, the traversal time is calculated using the transmission matrix approach and the results are in good agreement with other reported theoretical and experimental results. Traversal times as a function of applied voltage and Fermi energy level are calculated.

The generalized transmission matrix for electron-wave-optics through biased heterostructures: Quantum device applications

The transmission matrix approach is generalized to calculate the transmission probability of obliquely incident electrons through arbitrary shape potential profiles. Transmission probability is obtained as a function of the electron energy, the angle of incidence, and the applied voltage across the structure. Applications to electron waveguide and quantum resonant tunneling are outlined. Numerical results are presented for angle dependent resonant tunneling through biased multibarrier GaAs-AlxGa1−xAs heterostructures. As a consequence, various novel quantum devices, i.e., high speed switch, tunable electron wave filter, and electron wave beam splitter are proposed.

Transmission of an obliquely incident electron wave through GaAs-AlxGa1−xAs structures: Application to an electron wave filter

Transmission of an obliquely incident electron wave through GaAs-AlxGa1−xAs structures is analyzed using a generalized transmission matrix approach. Angle dependence is investigated quantitatively. Concepts of critical angle are discussed for step barrier structures. It is verified that the transmission probability is a function of longitudinal energy. Consequences of resonant tunneling of a non-normal incident electron wave through a double barrier heterostructure (DBHS) are discussed. It is found that the angle of incidence largely affects the probability of tunneling of electrons through DBHS. Application to an electron wave filter is discussed.

Double barrier resonant tunneling device with selectively applied field in the well

Resonant tunneling of an electron through a model Al 0.5Ga 0.5AsAl y Ga 1− y AsAl 0.5Ga 0.5As structure is investigated numerically using a transmission matrix approach. Our model considers the electric field, α in the well region only. This model is physically realized by changing Al-concentration continuously in the well region. Transmission coefficient is obtained as a function of incident electron energy for various α values. Tunneling characteristics (transmission coefficient vs voltage) are examined as a function of α. The effect of change in temperature is discussed.