The authors give a brief historic perspective of the coupled mode theory. The development and applications of the theory in microwaves in early years and in optoelectronics and fiber optics in recent years are described. They then consider lossless coupling of two modes in time. Two coupled resonance circuits, or two coupled microwave or optical resonators, are the physical examples. The start-up of a parametric oscillator is another example. Then they look at the formal derivation of coupled mode theory and consider the more general case when the modes are not energy-orthogonal and the energies are not necessarily positive. A more detailed account of the nonorthogonal coupled mode theory developed in the last five years for optical waveguides is given. >

Coupled-mode theory

The coupled-mode theory (CMT) for optical waveguides is reviewed, with emphasis on the analysis of coupled optical waveguides. A brief account of the recent development of the CMT for coupled optical waveguides is given. Issues raised in the debates of the 1980’s on the merits and shortcomings of the conventional as well as the improved coupled-mode formulations are discussed. The conventional coupled-mode formulations are set up in a simple, intuitive way. The rigorous CMT is established on the basis of a linear superposition of the modes for individual waveguides. The cross-power terms appear logically as a result of modal nonorthogonality. The cross power is necessary for the self-consistency of the CMT for dissimilar waveguides. The nonorthogonal CMT, though more complicated, yields more-accurate results than the conventional orthogonal CMT for most practical applications. It also leads to the prediction of cross talk in directional couplers. The conventional orthogonal CMT is, however, reliably accurate for describing the power coupling between two weakly coupled, nearly identical waveguides. For dissimilar waveguides, a self-consistent orthogonal CMT can be derived by a redefinition of the coupling coefficients, and it predicts the coupling length and therefore the power exchange between the waveguides accurately if the two waveguides are far apart. Three typical coupler configurations—the uniform, the grating-assisted, and the tapered—are examined in detail. The accuracy, scope of validity, limitations, and extensions of the coupled-mode formulations are discussed in conjunction with each configuration. To verify the arguments in the discussions, comparisons with the exact analytical solutions and the rigorous numerical simulations are made.

Coupled-mode theory for optical waveguides: an overview

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Traditionally, inertia in power systems has been determined by considering all the rotating masses directly connected to the grid. During the last decade, the integration of renewable energy sources, mainly photovoltaic installations and wind power plants, has led to a significant dynamic characteristic change in power systems. This change is mainly due to the fact that most renewables have power electronics at the grid interface. The overall impact on stability and reliability analysis of power systems is very significant. The power systems become more dynamic and require a new set of strategies modifying traditional generation control algorithms. Indeed, renewable generation units are decoupled from the grid by electronic converters, decreasing the overall inertia of the grid. ‘Hidden inertia’, ‘synthetic inertia’ or ‘virtual inertia’ are terms currently used to represent artificial inertia created by converter control of the renewable sources. Alternative spinning reserves are then needed in the new power system with high penetration renewables, where the lack of rotating masses directly connected to the grid must be emulated to maintain an acceptable power system reliability. This paper reviews the inertia concept in terms of values and their evolution in the last decades, as well as the damping factor values. A comparison of the rotational grid inertia for traditional and current averaged generation mix scenarios is also carried out. In addition, an extensive discussion on wind and photovoltaic power plants and their contributions to inertia in terms of frequency control strategies is included in the paper.

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Power systems with high renewable energy sources: A review of inertia and frequency control strategies over time

A formulation based on the high frequency asymptotic principles of physical optics is developed for analyzing the scattering by relatively arbitrary open-ended waveguide cavities containing complex interior terminations. A magnetic field integral equation (MFIE) is obtained for the equivalent currents on the interior cavity walls and is solved using an iterative physical optics (IPO) algorithm which iteratively applies physical optics to account for multiple reflections inside the cavity. The number of iterations required for convergence is related to the expected number of important reflections. The IPO method is more approximate than a matrix solution of the MFIE, but it is quite accurate for electrically large cavities and is much more efficient. Numerical results are presented which demonstrate the convergence and accuracy of the method by comparison with modal reference solutions. >

An iterative physical optics approach for analyzing the electromagnetic scattering by large open-ended cavities

A selective modal scheme is proposed to efficiently analyze the problem of high-frequency (HF) electromagnetic (EM) coupling/penetration into or radiation from open-ended waveguides. This scheme is based on the phenomenon that at sufficiently high frequencies, the modes which contribute most significantly to the fields coupled into the waveguide are those whose modal ray directions are most nearly parallel to the incident-wave direction. This concept is illustrated by calculating the EM radiation and backscattering from open-ended parallel-plate, rectangular, circular, and sectoral waveguide geometries. The calculations use the usual geometrical optics, aperture field, and Ufimtsev edge current techniques. Also included are some measured results which further verify the accuracy of the above computations. >

A selective modal scheme for the analysis of EM coupling into or radiation from large open-ended waveguides

We study the lasing eigenvalue problems for a periodic open optical resonator made of an infinite grating of circular dielectric cylinders standing in free space, in the E- and H-polarization modes. If possessing a “negative-absorption” refractive index, such cylinders model a chain of quantum wires made of the gain material under pumping. The initial-guess values for the lasing frequencies are provided by the plane-wave scattering problems. We demonstrate a new effect: the existence of specific grating eigenmodes that have a low threshold of lasing even if the wires are optically very thin.

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Low-threshold lasing eigenmodes of an infinite periodic chain of quantum wires

The radiation from circular cylindrical reflector antennas is treated in an accurate manner for both polarizations. The problem is first formulated in terms of the dual series equations and then is regularized by the Riemann-Hilbert problem technique. The resulting matrix equation is solved numerically with a guaranteed accuracy, and remarkably little CPU time is needed. The feed directivity is included in the analysis by the complex source point method. Various characteristic patterns are obtained for the front and offset-fed reflector antenna geometries with this analysis, and some comparisons are made with the high frequency techniques. The directivity and radiated power properties are also studied. >

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Accurate simulation of reflector antennas by the complex source-dual series approach

We propose and demonstrate a wireless, passive, metamaterial-based sensor that allows for remotely monitoring submicron displacements over millimeter ranges. The sensor comprises a probe made of multiple nested split ring resonators (NSRRs) in a double-comb architecture coupled to an external antenna in its near-field. In operation, the sensor detects displacement of a structure onto which the NSRR probe is attached by telemetrically tracking the shift in its local frequency peaks. Owing to the NSRR's near-field excitation response, which is highly sensitive to the displaced comb-teeth over a wide separation, the wireless sensing system exhibits a relatively high resolution ( 0.99 over 5 mm) and sensitivity (>12.7 MHz/mm in the 1-3 mm range). The sensor is also shown to be working in the linear region in a scenario where it is attached to a standard structural

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Wireless Displacement Sensing Enabled by Metamaterial Probes for Remote Structural Health Monitoring

A dual-series-based solution is obtained for the scattering of an E-polarized plane wave from a cavity-backed aperture which is formed by a slitted infinite circular cylinder coated with absorbing material. The material coating can be done on the inner or outer surface of the cylinder. For both cases, numerical results are presented for the radar cross section and comparisons are given for two different realistic absorbing materials. The radar cross-section results are also given for the aspect angle of the screen. Finally, the dependence of radar cross section on the thickness of the absorbing layer is presented. >

/pdf/radar-cross-section-study-of-cylindrical-cavity-backed-23lvzk616m.pdf

Ayhan Altintas

Papers

A selective modal scheme for the analysis of EM coupling into or radiation from large open-ended waveguides

Low-threshold lasing eigenmodes of an infinite periodic chain of quantum wires

Accurate simulation of reflector antennas by the complex source-dual series approach

Wireless Displacement Sensing Enabled by Metamaterial Probes for Remote Structural Health Monitoring

Radar cross-section study of cylindrical cavity-backed apertures with outer or inner material coating: the case of E-polarization