Fundamental Mode Propagation Research Articles

Highly unbalanced GaAlAs–GaAs integrated Mach–Zehnder interferometer for coherence modulation at 1.3 μm

A novel integrated III–V semiconductor waveguide modulator specially designed to generate an optical delay of 100 μm is presented. This is achieved by simultaneous propagation of the TE fundamental mode in both of the arms of a highly unbalanced Mach–Zehnder interferometer with a 29 μm length difference between both arms. In order to minimize the losses in this complex curved structure, trenches were etched on the outsides of curved sections. The modulator has a contrast of 34%, a switching voltage of 6 V with a 10 mm long electrode and is suitable for the transmission and multiplexing of signals by coherence modulation of light in an optical fiber network powered by a short coherence source, such as a 1.3 μm superluminescent diode.

Fundamental leaking mode (PL) propagation along the Tonga--Kermadec--Hikurangi--Macquarie margin

High-quality digital data from the temporary Leeds Tararua broad-band array, North Island, New Zealand and the station SNZO at Wellington often record long-period oscillations within the body wave train from large, shallow events in the Tonga–Kermadec and Macquarie seismic zones at regional distances (8°–25°) along the Australasian/Pacific plate boundary. These arrivals are dispersed typically from 40 s period to 25 s and exhibit prograde elliptical polarization, which is diagnostic of the regional leaking mode PL. Theoretical dispersion curves are generated with the simplest structure of a slow layer overlying a faster half-space. We have analysed the group velocity dispersion characteristics of the recorded waveforms and successfully modelled it as purely fundamental mode propagation in a low-velocity waveguide. Our best-fitting structure north of New Zealand consists of a low-velocity layer within the mantle (β=4.1–4.3 km s-1) with a thickness of 32–34 km overlying a typical mantle structure. A seismicity study for the period 1976–1992 at SNZO shows that those events generating PL are shallow (10–60 km), with the highest concentration along the Kermadec arc, suggesting that the low-velocity layer is connected with this feature. We suggest that a small degree of partial melt within the uppermost mantle is responsible for creating a low-velocity channel within the region of backarc spreading in the Havre Trough. Dispersion curves derived from waveforms travelling northwards from events on the Macquarie Ridge give a similar structure with a slow layer 31 km thick with β=3.8 km s-1. This is consistent with the continental crust of South Island, which lies along most of the event–station paths.

Metal-insulator-semiconductor transmission lines

This paper investigates the one-dimensional metal-insulator-semiconductor transmission line. It develops closed-form expressions for equivalent-circuit parameters, compares them to exact calculations, and explores their limitations. It also investigates the usual assumption of single-mode propagation and shows that, in certain fairly common circumstances, the fundamental mode of propagation becomes so lossy that it can no longer be considered to be the dominant propagating mode.

Electrical performances of self-shielded uniplanar guided-wave structures

This paper presents electrical performance and propagation characteristics of self-shielded uniplanar guided-wave structures including circular, elliptic, diamond, and trapezoidal enclosures. Enhanced spectral domain approach is extended to characterize guided-wave property of these self-shielded lines. Particular attention is focused on fundamental mode propagation constant and characteristic impedance of coupled uniplanar line having a practical shield profile. Influence of various parameters of the structure on cutoff frequency of the slotline mode is investigated. Interesting features of the self-shielded uniplanar structures are discussed for design consideration. Results are verified with some data available and presented in support of the technical discussion. ©1999 John Wiley & Sons, Inc. Int J RF and Microwave CAE 9: 22–31, 1999.

Behavior of detonation waves at low pressures

With respect to stability of gaseous detonations, unsteady behavior of galloping detonations and re-initiation process of hydrogen-oxygen mixtures are studied using a detonation tube of 14 m in length and 45 mm i.d. The arrival of the shock wave and the reaction front is detected individually by a double probe combining of a pressure and an ion probe. The experimental results show that there are two different types of the re-initiation mechanism. One is essentially the same as that of deflagration to detonation transition in the sense that a shock wave generated by flame acceleration causes a local explosion. From calculated values of ignition delay behind the shock wave decoupled from the reaction front, the other is found to be closely related with spontaneous ignition. In this case, the fundamental propagation mode shows a spinning detonation.

Analysis of edge coupled strip inset dielectric guide

The edge coupled strip inset dielectric guide is analyzed using the extended spectral domain approach. This structure, as compared to microstrip line, has several interesting features and can be very useful for microwave and millimeter wave applications. Validity of the approach is established by comparing numerical results with measured data. As many structural and material parameters can be chosen, a wide fundamental mode bandwidth and a broad range of characteristic impedances can be achieved, leading to great flexibility. The dispersion in fundamental mode propagation constants and impedances is found to be very low. With suitable choice of different permittivities for two dielectric layers, the same propagation constants for two fundamental modes can be obtained. This property is desirable for directional coupler applications.

Fast‐fourier transform beam‐propagation method using Fadé approximant operators

AbstractThe (1, 1) Fadé approximant operator is applied to the fast Fourier transform beam‐propagation method (FFT‐BPM). The Fadé operator for FFT‐BPM is derived, and its relation to the wide‐angle and paraxial operators is investigated. Next, the propagation error of the fundamental mode of a straight step‐index waveguide is evaluated by the mode mismatch loss. It is proved that, in contrast to the wide‐angle operator, Fadé operator does cot exhibit loss, even at small transverse grid‐widths. Finally, as an example of when transverse propagating waves cannot be neglected, the problem of fundamental mode propagation in a tilt waveguide is investigated. It is clarified that the Paé operator preserves an accuracy comparable to that of the wide‐angle operator, even if the tilt angle is widened up to 25 degrees.

High impedance anisotropic composites manufactured from ferromagnetic thin films for microwave applications

We have manufactured anisotropic composite materials from ferromagnetic thin films with high permeability and low permittivity for one polarization. The geometry of the composite was also adapted so that the large impedance was obtained for the fundamental propagation mode in a coaxial line. We report measurements of the complex permittivities and permeabilities on several composites in the 0.1 GHz to 18 GHz range. While permittivity levels remained small (typically less than 5) high permeability levels mere obtained, with the product of initial permeability-by-resonance-frequency as high as 260 GHz.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Propagating beam analysis by alternating-direction implicit finite-difference method

The three-dimensional beam propagation problem expressed by the Fresnel equation is analyzed by the beam-propagation method using an alternating-direction implicit finite-difference method (ADI-BPM). First, following the formulation of the finite-difference method, the equations to be analyzed are rearranged. The fundamental and higher-order mode propagation problems in a step index fiber are treated, and the accuracy and advantages of the ADI-BPM are investigated. It is found that the computing time is shorter and the step length in the propagation direction can be made larger in the ADI-BPM than in the beam-propagation method based on the fast Fourier transform (FFT-BPM). As another advantage in the ADI-BPM, the usefulness of the transparent boundary condition is described. It is shown that the spreading problem of a Gaussian beam can be analyzed without setting up the absorbing functions needed in the FFT-BPM. Further, as an example to prove the effectiveness of the ADI-BPM for the analysis of the problem in which the guided mode and the radiation mode are mixed, the transmission efficiency is evaluated in the case where an axial offset exists in the fiber junctions. The effect of the coherent coupling is studied.

Space-charge wave considerations in MIS waveguide analysis

A transport-based small-signal analysis of the fundamental mode of propagation in a metal-insulator-semiconductor (MIS) waveguide is presented. The formulation incorporates the full set of Maxwell's equations and the equations of motion of the carriers based on a drift-diffusion model, providing a quantitative description of the space-charge wave induced of the surface of the semiconductor. Effects of an external DC bias on the propagation characteristics are also accounted for. Numerical solutions to the system of equations for a waveguide with typical material parameters and dimensions are obtained using an iterative algorithm. Results indicate that the transverse component of the electric field in the semiconductor is strongly influenced by the screening effect of the charge carriers, whereas the longitudinal component is governed mainly by energy dissipation arising from the conduction current. >

Analysis of polarization characteristics of cylindrical waveguide containing anisotropic dielectric using spatial network method

AbstractRecently, various anisotropic materials have been used in the applications to the microwave and millimeter wave circuits. In such a structure, it is indispensable to analyze systematically the medium conditions, boundary conditions and resultant propagation characteristics of complicated electromagnetic fields. Of the electromagnetic characteristics associated with the anisotropic materials, the polarization characteristic is particularly important. Especially, the circular polarization recently has been used extensively as the fundamental propagation mode in satellite communication due to the stability of its propagation characteristics. The polarization characteristics are expected to be applied to the modulation/demodulation in the optical region and to the erasable optical disk memory.The present analysis considers the generating mechanism of these polarizations and carries out a numerical simulation of the fundamental mechanism by means of the spatial network method as applied to a structure made of an anisotropic dielectric disk or plate inserted in a circular waveguide. By taking advantage of the method, studies in the time domain are carried out so that the variations of the amplitude and phase of the electric field components at each spatial point are presented. From their mutual relationship, as the variation of the electric vector, the analysis determines the process in which the polarization plane characteristics are caused, including the rotation of the polarization plane from the linear polarization through elliptic polarizations and, finally, to the circular polarization depending on the rotation of the principal axis of the anisotropy.

Monte Carlo simulation of the propagation properties of single-mode dielectric waveguide structures

We have used Monte Carlo simulation to obtain the propagation constants of the fundamental and first-order modes of a number of realistic dielectric waveguide structures. We find that Monte Carlo simulation requires a comparatively modest increase in computer time to treat a channel waveguide to the same degree of accuracy as a slab waveguide. Excellent agreement has been found in 1-D and 2-D with the fundamental mode propagation constants of the analytically soluble refractive-index profiles involving 1/cosh(2). For realistic air/ Ti:LiNbO(3) diffused waveguides, excellent predictions are obtained for the propagation constant of the fundamental mode. The Monte Carlo simulation evaluation of the first-order mode requires more time and predictions are obtained with a fair degree of accuracy.

Simple bounds on modal propagation constant for arbitrarily shaped optical fibres

We show that, when a fibre core cross-section is distorted from circular, the fundamental mode propagation constant β always decreases. To complement the upper bound on β thus obtained, we give a second approximation to β giving a simple lower bound and which only requires computation of a geometric shape factor and results for circular cross-sections. The results hold for arbitrary shape and grading.

Propagation properties of single-mode dielectric waveguide structures: a path integral approach

A simple and efficient numerical method for the calculation of the fundamental and first-order mode propagation properties of single-mode waveguide structures with arbitrarily graded refractive-index profiles is presented. The method is based on a path integral treatment of the propagation equation of paraxial optics. The accuracy of the method and its potential for use in waveguide-structure design and characterization are illustrated by calculating the propagation constant for the fundamental and first-order modes of a graded-index slab waveguide, the intensity distribution of the fundamental mode of a graded-index slab waveguide, and by calculating the coupling length of a graded-index slab directional coupler as a function of fabrication-related variables.

Propagation characteristics of eccentric core fibers using point-matching method

The propagation characteristics of homogeneous single-mode optical fibers with eccentric core are analyzed by a numerical method based on the Improved Point-Matching Method (IPMM). The variation of fundamental mode propagation constant has been computed for various eccentricities with different fiber parameters.

Slab waveguides characterized by moments of the index profile

The fundamental mode of a symmetric slab waveguide is described to a high degree of accuracy using only two moments of the refractive index profile rather than its exact form. The two moments can be used to define an equivalent step index slab waveguide, and the fundamental mode propagation constant of an arbitrary profile guide is given by the step index value multiplied by a simple correction factor. The limit to single-mode operation, the second-mode cutoff point, is also given by a simple formula requiring only profile moments. Numerical confirmation of the method is given.

Equivalent optical waveguides

We develop a comparison method which identifies a waveguide with properties that are well known and are very similar to the one under investigation. It has a very simple mathematical basis which allows a trivial derivation of the moment method for circular cross-sectional fibers including W -fibers, and an extension to noncircular optical waveguides. We first use the scalar approximation, and then extend to the full vector theory which accounts for polarization. Our concern is with fundamental mode propagation constants and higher mode cutoffs.

Low-Frequency Behavior of the Propagation Constant Along a Thin Wire in an Arbitrarily Shaped Mine Tunnel

Seidel and Wait have investigated the complex propagation constant (phase and attenuation coefficients) of the fundamental mode of propagation for radio waves along a thin wire or cable, located in an elliptical mine tunnel, and found that the attenuation rate for low frequency is insensitive to the shape of the ellipse if the cable-wall distance and cross-sectional area are kept constant. We consider here tunnels of more general cross section, and obtain a characteristic equation for the propagation constant valid for sufficiently low frequency, by means of a variational formulation of an integral equation. The characteristic equation involves only the electrical parameter of the tunnel walls, the radius of the wire, and the capacitance per unit length that the wire would have if the tunnel walls were perfectly conducting. Agreement with exact calculations for several geometries is found to be excellent below about 100 kHz, and acceptable even up to 1 MHz or more, for typical tunnel parameters. Since the wire capacitance can be shown to depend most importantly on its distance from the wall and on the area of the tunnel, the conclusion of Seidel and Wait can be made more precise and extended to tunnels of arbitrary cross section.

Propagation of Gaussian beams through parabolic index optical waveguides with random dielectric constant gradient

Abstract The propagation of gaussian beams through parabolic index optical waveguides having random irregularities in the dielectric constant gradient has been studied. For fundamental mode propagation, the perturbation approach has been employed and an analytic expression for the loss of power from the fundamental mode has been obtained. For an incident gaussian beam with arbitrary width, geometrical optics approximation has been used and an exact analytical expression for the average value of the beamwidth has been derived for a particular random process, namely, the dichotomic Markov process. The fluctuations in the beamwidth have also been calculated.

Sound generation and transmission in flow ducts with axial temperature gradients

This article describes a one-dimensional, linearized, analysis of fundamental mode sound generation and propagation in rigid-walled flow ducts with axial temperature variation. An acoustic wave equation, including damping effects and volume sources, is derived and its solution (in the absence of sources) by a numerical technique and an approximate analytical method is discussed. The “forced” wave equation is then solved (the existence of an oscillating solution to the “unforced” equation being assumed) for sound generation by a side-branch volume source in an infinite duct, and the results are applied to a duct of finite length. Reasonably good agreement is obtained between measurements and predictions of the sound pressure field in a flow duct, away from the source region.