Generalized Finite-Difference Time-Domain Method Utilizing Auxiliary Differential Equations for the Full-Vectorial Analysis of Photonic Crystal Fibers

We present the generalized finite-difference time-domain full-vectorial method by reformulating the time-dependent Maxwell's curl equations with electric flux density and magnetic field intensity, with auxiliary differential equations using complex-conjugate pole-residue pairs. The model is generic and robust to treat general frequency-dependent material and nonlinear material. The Sellmeier equation is implicitly incorporated as a special case of the general formulation to account for material dispersion of fused silica. The results are in good agreement with the results from the multipole method. Kerr nonlinearity is also incorporated in the model and demonstrated. Nonlinear solutions are provided for a one ring photonic crystal fiber as an example.     

Self-consistent analysis of side-mode suppression in gain-coupledDFB semiconductor lasers

Based on a set of spatially dependent multimode rate equations derived from Maxwell's equations, a self-consistent analysis of gain-coupled distributed feedback (DFB) lasers is developed. By introducing the modal net gain into the coupled wave equations, we also obtain a closed form formula of the side-mode suppression ratio (SMSR) for DFB lasers. It is shown that, associated with the distributed feedback, the longitudinal spatial hole burning, and the nonlinear gain compression effects, gain coupling produces significant effects on the SMSR of DFB lasers     

Generalized material models in TLM .I. Materials withfrequency-dependent properties

This paper presents the fundamentals of a unified approach for the treatment of general material properties in time-domain simulation based on transmission-line modeling (TLM). Linear frequency-dependent isotropic materials are dealt with in the first instance. The iteration schemes for one-dimensional (1-D) and three-dimensional (3-D) models are developed from Maxwell's curl equations and the constitutive relations. Results are presented showing the accuracy of this approach     

Detailed study of AlAs-oxidized apertures in VCSEL cavities foroptimized modal performance

We present a numerical optical model for calculating threshold material gain in vertical-cavity surface-emitting lasers. It is based on a vectorial solution of Maxwell's equations and therefore gives exact results where other approaches fail, e.g., in the case of oxide-confined devices, which have high lateral index contrasts. Results are given concerning the influence of oxide window thickness and position on threshold gain and modal stability. We also propose an intuitive plane-wave model to enhance the physical understanding of these effects     

Multidimensional Electro-Opto-Thermal Modeling of Broad-Band Optical Devices

This paper investigates the self-consistent modeling of broad-band optical devices such as super-luminescent light-emitting diodes (SLEDs) and semiconductor optical amplifiers. A multidimensional electro-opto-thermal approach using many-body gain theory, and temperature-dependent microscopic transport equations is presented. In addition, a Green's function based model for amplified spontaneous emission is derived from Maxwell's equations in a consistent way. To illustrate the model's validity it is implemented into an existing simulation tool and benchmarked with two InP-based edge-emitting SLEDs operating around 1310 nm, featuring nonidentical quantum wells as active region. A comparison between simulated and measured characteristics (both electro-thermal and spectral) proves the applicability of the novel model.     

Coupling characteristics between five-layer slab wave-guides including left-handed materials

To obtain the coupling characteristics between slab wave-guides including left-handed material, we modify the coupled wave equations by using Maxwell＇s equations. First, we obtain new-coupled wave equations and new-coupling coefficient. Second, the coupling between two identical five-layer slab wave-guides where their cores are left-handed material, but their claddings are right-handed materials is studied. The coupling coefficient for even TE mode which is more complex than that of the riglt-handed material slab wave guides, is obtained.     

A general method for FDTD modeling of wave propagation in arbitraryfrequency-dispersive media

A general formulation is presented for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media. Two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations. The first employs a frequency-dependent complex permittivity (denoted Form-1), and the second employs a frequency-dependent complex conductivity (denoted Form-2). A Pade representation is used in Z-transform space to represent the frequency-dependent permittivity (Form-1) or conductivity (Form-2). This is a generalization over several previous methods employing either Debye, Lorentz, or Drude models. The coefficients of the Pade model may be obtained through an optimization process, leading directly to a finite-difference representation of the dispersion relation, without introducing discretization error. Stability criteria for the dispersive FDTD algorithms are given. We show that several previously developed dispersive FDTD algorithms can be cast as special cases of our more general framework. Simulation results are presented for a one-dimensional (1-D) air/muscle example considered previously in the literature and a three-dimensional (3-D) radiation problem in dispersive, lossy soil using measured soil data     

The use of the frequency-dependent finite-difference time-domainmethod for induced current and SAR calculations for a heterogeneousmodel of the human body

This paper describes the use of the previously formulated frequency-dependent finite-difference time-domain ((FD)²TD) method for analysis of an anatomically based heterogeneous man model exposed to ultra-wide-band electromagnetic pulse sources. The human tissues' electrical permittivities, ϵ_i*(ω) are described by Debye equations with two relaxation constants, and the equation D(t)=ϵ*(ω))E(t) is converted to a finite-difference equation along with the Maxwell's equations used by the standard FDTD method. Using a single run with a broad-band pulse excitation, the (FD) ²TD method is used to calculate mass normalized rates of energy deposition (specific absorption rates or SARs) and induced currents in the man model over a broad band of frequencies. Time-domain coupling of a representative ultrashort pulse of subnanosecond rise time and nanosecond pulse duration to the human body is also examined     

Maxwell 方程组的多辛算法

Maxwell方程在线性、各向同性、均匀、无源的介质中具有自然的多辛结构,可以表示为多辛Hamilton系统。Maxwell方程的多辛算法即对Maxwell方程在时间、空间同时进行保辛离散得到相应的差分格式。文中给出了5种麦克斯韦方程的多辛算法,分析并比较了这5种方法的数值色散特性。数值计算结果表明这些算法能很好地保持Maxwell方程的离散全局能量守恒特性。     

The Maxwell's equations in the sense of distributions

It is well known that there is no direct one-to-one correspondence between the electromagnetic theory based on the physical laws and that based on the Maxwell's differential equations. For example, in order to derive the boundary conditions from the Maxwell's differential equations, one assumes that some integral identities derived from them are valid even when the field components (or material parameters) are discontinuous. This assumption violates, in a sense, the completeness of the theory of electromagnetism based on the Maxwell's differential equations. We will prove that if one postulates that the Maxwell's equations are valid in the sense of distributions, then this incompleteness will be removed and the boundary conditions will appear implicitly in the basic differential equations.     

The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers

We discuss the effect of uniaxial planar stress on polarization switching in vertical-cavity surface-emitting lasers (VCSELs). The approach is based on an explicit form of a frequency-dependent complex susceptibility of the uniaxially stressed quantum-well semiconductor material. In this mesoscopic framework, we have taken cavity anisotropies, spin carrier dynamics, and thermal shift of the gain curve into account. In this way, we present a model that provides a global overview of the polarization switching phenomenon. The results are compared with experiments on an air-post VCSEL operating at 980 nm.     

Electromagnetic and transport considerations in subpicosecondphotoconductive switch modeling

The authors discuss a combination of direct finite-difference time-domain solutions of Maxwell's equations and Monte Carlo models of photocarrier transport used to avoid assumptions commonly made in developing equivalent circuit models for transmission lines and in other simplifications commonly made in modeling conductivity. Problems that complicate the development of an accurate model for subpicosecond optoelectronic switching and the measurement of electrical waveforms on microstrip lines are discussed     

General Solution for Excitation by Slotted Aperture Source in Conducting Cylinder with Concentric Layering

We present a general matrix analysis for the electromagnetic fields produced by an aperture source on the inner metallic snrface of a concentrically layered structure. Each layer is homogeneous and characterized by arbitrary permittivity, conductivity and magnetic permeability. The structure itself is assumed to be of infinite length so Maxwell's equations yield separable solutions. An explicit result is given for the electric current density on the inner metallic cylindrical surface which could model the mandrel in a borehole logging tool.     

Electromagnetic wave effects on microwave transistors using afull-wave time-domain model

A detailed full-wave time-domain simulation model for the analysis of electromagnetic effects on the behavior of the submicrometer-gate field-effect transistor (FET's) is presented. The full wave simulation model couples a three-dimensional (3-D) time-domain solution of Maxwell's equations to the active device model. The active device model is based on the moments of the Boltzmann's transport equation obtained by integration over the momentum space. The coupling between the two models is established by using fields obtained from the solution of Maxwell's equations in the active device model to calculate the current densities inside the device. These current densities are used to update the electric and magnetic fields. Numerical results are generated using the coupled model to investigate the effects of electron-wave interaction on the behavior of microwave FET's. The results show that the voltage gain increases along the device width. While the amplitude of the input-voltage wave decays along the device width, due to the electromagnetic energy loss to the conducting electrons, the amplitude of the output-voltage wave increases as more and more energy is transferred from the electrons to the propagating wave along the device width. The simulation confirms that there is an optimum device width for highest voltage gain for a given device structure. Fourier analysis is performed on the device output characteristics to obtain the gain-frequency and phase-frequency dependencies. The analysis shows a nonlinear energy build-up and wave dispersion at higher frequencies     

Comments on a short paper by El-Shandwily on transient solutions ofMaxwell's equations

The commenter claims that M.E. El-Shandwily (see ibid., vol.30, no.4, p.577-82, Nov. 1988) made four mistakes in obtaining his results, namely the belief that Dirac's delta function integrated from zero to infinity has a defined value, the attempt to derive solutions of a system of partial differential equations interpreted for distributions without a method that is known to yield uniform convergence, to disregard for the fact that Maxwell's equations are a mathematical model of physical phenomena, and the belief that the need to modify Maxwell's equations is a topic for serious scientific discussion     

Incorporation of a frequency-dependent dielectric response for the barrier material in the Josephson junction circuit model

We extend the resistively shunted Josephson (RSJ) junction circuit model originally proposed by Stewart and McCumber to incorporate a frequency-dependent dielectric response so that the influence of free carriers in the barriers can be taken into account. The methodology that we have developed uses an iterative numerical technique to calculate the current-voltage (I-V) characteristics of a Josephson junction with a barrier exhibiting both dissipation and dispersion. We give detailed results for two barrier materials with conductivities near the metal-insulator transition: a conventional semiconductor with a relatively high mobility and a strongly scattered defect solid. We show that the incorporation of the dynamic response of free carriers in the barriers of superconductor-normal-superconductor (SNS) junctions significantly influences the dc I-V characteristics for the case of material near the metal-insulator transition with high mobility. Hysteretic anomalies occur at nonzero voltages in the I-V characteristics associated with the barrier layer's plasma frequency. The resulting features, which we call critical regions, occur when the dc junction voltage is equal to /spl planck/ / 2en/spl radic//spl omega/~/sub p//sup -2/-/spl Gamma//sup 2/, where /spl omega/~/sub p/ is the barrier's plasma frequency, /spl Gamma/ is the quasi-particle scattering rate, n is an integer, and /spl planck/ is the reduced Planck's constant. We also show that our results for SNS junctions with a low-mobility barrier material are essentially identical to the predictions of the simpler RSJ model. Since the method we develope can solve the nonlinear junction equations for a barrier with an arbitrary complex conductivity, it is also capable of including other relevant processes within the barrier, including the influence of excitation from shallow defects or very soft phonon modes, as well as boundary resistances.     

A microscopic model for the static and dynamic lineshape of semiconductor lasers

Direct frequency modulation characteristics in semiconductor lasers are described theoretically in a physics-based multidimensional framework. A microscopic formulation of a phase equation without the need of linewidth enhancement factors is derived directly from Maxwell's equations. This novel model uses a local material phase coefficient instead of the linewidth enhancement factor. Hence, the impact of local phase changes on the optical mode can be described via a spatial integration in analogy to mode gain. The model is applied to the modulation-induced fine structure of the laser power spectrum. It is found that the asymmetry in the modulation-induced fine structure observed in measurements can be explained by the proposed model taking temperature, carrier, and photon effects on the material phase coefficient into account. Furthermore, the implementation of the photon phase into a multidimensional device simulator is described.     

广义柱形坐标系各向异性完善匹配吸收媒质

Ｂｅｒｅｎｇｅｒ提出的完善匹配层只能用于直角坐标系。本文将完善匹配各向异性吸收媒质推广到广义柱形坐标系。推导是在广义柱形坐标系均匀媒质的Ｍａｘｗｅｌｌ方程与直角坐标系各向异性媒质的Ｍａｘｗｅｌｌ方程之间等效基础上进行的。得出了广义柱形坐标系完善匹配层电导率计算公式。     

Propagation properties for five-layer symmetric slab waveguides including left-handed materials

In this paper, we discussed a slab wave-guide of five layers, The core is a left-handed material, but the claddings are right-handed materials. A dispersion equation of TE modes is obtained by using Maxwell＇s equations, and some new dispersion characteristics are obtained based on the equation.