Standard Transfer Matrix Method Research Articles

Specific Heat of the Mixed Spin-1/2 and Spin-S Ising Model with a Rope Ladder Structure

The mixed spin-1/2 and spin-S (S>1/2) Ising model on a rope ladder is examined by combining two exact analytical methods. By the decoration-iteration mapping transformation, this mixed-spin system is firstly transformed to a simple spin-1/2 Ising model on the two-leg ladder, which is then exactly solved by the standard transfer-matrix method. The thermal variations of the zero-field specific heat are discussed in particular.

Exact solution of a one-dimensional model of strained epitaxy on a periodically modulated substrate

We consider a one-dimensional lattice gas model of strained epitaxy with the elastic strain accounted for through a finite number of cluster interactions comprising contiguous atomic chains. Interactions of this type arise in the models of strained epitaxy based on the Frenkel-Kontorova model. Furthermore, the deposited atoms interact with the substrate via an arbitrary periodic potential of period L. This model is solved exactly with the use of an appropriately adopted technique developed recently in the theory of protein folding. The advantage of the proposed approach over the standard transfer-matrix method is that it reduces the problem to finding the largest eigenvalue of a matrix of size L instead of 2(L-1), which is vital in the case of nanostructures where L may measure in hundreds of interatomic distances. Our major conclusion is that the substrate modulation always facilitates the size calibration of self-assembled nanoparticles in one- and two-dimensional systems.

Defect Modes in Multiple-Constituent One-Dimensional PhotonicCrystals Examined by an Analytic Bloch-Mode Approach

Defect modes in one-dimensional photonic crystals (PCs) can bereadily detected from the solution of the transmission spectra viathe standard transfer-matrix method. We adopt an analytic Bloch-modeapproach to examine this problem in terms of eigenmode solutions andinvestigate the dispersion behaviour of localized defect modes supportedby a defect layer sandwiched within two symmetric semi-infinite PCs thatare made from multiple constituents. The results show that the numberof defect modes grows when the dielectric constant and width of thedefect layer increase.

One-dimensional photonic crystal: The Kronig-Penney model

We formulate the photonic band-structure problem for a one-dimensional photonic crystal in terms of the reflection and transmission coefficients, obtaining a transcendental photonic band equation. The reflection and the transmission coefficients may be evaluated by using the standard transfer-matrix method. The structure of the equation reveals the existence of gaps, analogous to the Kronig-Penney model in the electronic band-structure problem. As an example, the photonic band equation is solved for the simple case of the ``Kronig-Penney'' dielectric structure, consisting of alternating slabs of refractive indices ${n}_{1}$ and ${n}_{2}.$

Optical transmission and reflection of perfect lenses by left handed materials

We consider questions about the much discussed ``perfect lenses'' made by left handed materials. The transmission and reflection from a slab of left handed materials are investigated and the coefficients are obtained by the standard transfer-matrix method. Possible limitations on such superlenses are explored. It is shown that the quality of the lenses can be significantly affected by the absorption that is necessarily present in the materials.

Response to “Comment on ‘Study on the quantum efficiency of resonant cavity enhanced GaAs far-infrared detectors”’ [J. Appl. Phys. 93, 786 (2003)

In this response, we present reasons showing that our method is usually reasonable in device application due to its good approximation. A standard transfer matrix method has also been suggested to solve the issue concerning the interface reflection.

Stable recursive algorithm for elastic wave propagation in layered anisotropic media: stiffness matrix method.

An efficient recursive algorithm, the stiffness matrix method, has been developed for wave propagation in multilayered generally anisotropic media. This algorithm has the computational efficiency and simplicity of the standard transfer matrix method and is unconditionally computationally stable for high frequency and layer thickness. In this algorithm, the stiffness (compliance) matrix is calculated for each layer and recursively applied to generate a stiffness (compliance) matrix for a layered system. Next, reflection and transmission coefficients are calculated for layered media bounded by liquid or solid semispaces. The results show that the method is stable for arbitrary number and thickness of layers and the computation time is proportional to the number of layers. It is shown both numerically and analytically that for a thick structure the solution approaches the solution for a semispace. This algorithm is easily adaptable to laminates with periodicity, such as multiangle lay-up composites. The repetition and symmetry of the unit cell are naturally incorporated in the recursive scheme. As an example the angle beam time domain pulse reflections from fluid-loaded multilayered composites have been computed and compared with experiment. Based on this method, characteristic equations for Lamb waves and Floquet waves in periodic media have also been determined.

Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media

The numerical instability problem in the standard transfer matrix method has been resolved by introducing the layer stiffness matrix and using an efficient recursive algorithm to calculate the global stiffness matrix for an arbitrary anisotropic layered structure. For general anisotropy the computational algorithm is formulated in matrix form. In the plane of symmetry of an orthotropic layer the layer stiffness matrix is represented analytically. It is shown that the elements of the stiffness matrix are as simple as those of the transfer matrix and only six of them are independent. Reflection and transmission coefficients for layered media bounded by liquid or solid semi-spaces are formulated as functions of the total stiffness matrix elements. It has been demonstrated that this algorithm is unconditionally stable and more efficient than the standard transfer matrix method. The stiffness matrix formulation is convenient in satisfying boundary conditions for different layered media cases and in obtaining modal solutions. Based on this method characteristic equations for Lamb and surface waves in multilayered orthotropic media have been obtained. Due to the stability of the stiffness matrix method, the solutions of the characteristic equations are numerically stable and efficient. Numerical examples are given.

Localization effect of ordered and disordered orbital polarization in a simplified double-exchange model

Taking into account the orbital degree of freedom in the double-exchange model, we study the localization of conduction electrons by using a standard transfer matrix method combined with the finite-scaling ansatz. It is found that the orbital polarizations, regardless of being ordered or disordered, are always in favor of the localization of electrons. The orbital disorder plus the randomness of local spins is sufficient to localize electrons below the Curie temperature, resulting in a metal-insulator transition (MIT); while the orbital ordering gives rise to anisotropy and so has an even stronger localization effect. The relation between MIT induced by the spin and orbital configurations and the recent experimental observations in ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{MnO}}_{3}$ is discussed.

A combined finite element-Riccati transfer matrix method for free vibration of structures

A combination of Riccati transfer matrix method and finite element method is proposed for obtaining vibration frequencies of structures. This method reduces the propagation of round-off errors produced in the standard transfer matrix method and finds out the values of the frequency by Newton-Raphson method, By this technique, the number of nodes required in the regular finite element method is reduced and therefore a microcomputer may be used. Besides, no plotting of the value of the determinant versus assumed frequency is necessary, As the application of this method, some numerical examples are presented to demonstrate the accuracy as well as the capability of the proposed method for the vibration of structures.

Excitonic binding energies in diffused-intermixed GaAs/AlAs/AlGaAs double barrier quantum wells

We report a detailed study of the exciton properties in thermally diffused GaAs/AlAs/AlxGa1−xAs double barrier quantum wells (DBQW). The interband transition energies have been calculated with a standard transfer matrix method, while the exciton binding energy is obtained by a variational approach with an elliptic exciton envelope function. It is found that the inserted thin AlAs layer between the GaAs well and the AlGaAs barriers has a substantial effect on the exciton confinement and the intermixing properties. For thin enough AlAs barriers, the exciton binding energy increases for increasing diffusion lengths, reaches a maximum and then decreases gradually. The results show that a DBQW mixes faster than a single QW, due to the additional AlAs layers. Thick AlAs barriers enable the formation of an indirect AlGaAs intermixed well region, and the effects which stem from the indirect band line up are discussed.

Impedance boundary method of moments with extended boundary conditions

An improved impedance boundary method of moments is proposed to accurately and efficiently determine the propagation characteristics of multilayer planar optical waveguides whose refractive index profiles contain large step index changes or a graded-index region combined with step index changes. Extended impedance boundary conditions are used in the impedance boundary method of moments to replace regions in the waveguide structure which have refractive index discontinuities. Two methods for determining the extended boundary conditions include the standard transfer matrix method and a procedure utilizing a cascaded transmission line representation with successive calculation of input impedances. Simulation results show significantly improved convergence rates in the determination of propagation constants.

Bifurcation of resonant tunnelling current due to the accumulated electrons in a well

The effect of electron space charges in a potential well on the transmission coefficient of resonant tunnelling of electrons through a one-dimensional double barrier is investigated using the standard transfer-matrix method. It is shown that the bistable states in the transmission coefficient appear due to the positive feedback loop to incident electron space charges in the well. The growth rate of the small perturbation in the unstable region between the bistable states is also investigated numerically.

Modal propagation within ARROW waveguides

The standard transfer matrix method is applied to the antiresonant reflecting optical waveguides in SiO 2-Si structures. The results provide the first accurate picture of dispersion and attenuation of several TE-type ARROW modes at the wavelength of 1.3 μm.