Generalized reaction and unrestricted variational formulation of cavity resonators. II. Nonorthogonal and free-boundary mode-matching method

For pt. I see ibid., vol. 50, no. 11, p. 2480-90 (2002). This paper addresses a systematic method whereby the conventional mode-matching method is generalized to the cases where the set of modes used for the field expansion within a cavity resonator are relaxed to be orthogonal or satisfy any specific boundary conditions. It is shown that this approach is based on the unrestricted variational formulation of a cavity resonator. Reciprocity theorem and generalized reaction are the mathematical foundations of this new formulation. We have shown that the conventional mode-matching method is a special case of this generalized formulation and indeed is variational in nature. More precisely, we have proven that, if the field distribution obtained based on the conventional mode-matching method is used as a trial one in some variational formulas, the resonant frequency will be the same as the one obtained by the mode-matching method.     

A theory of complex open resonators in the form of cavity chain

Journal of Infrared, Millimeter, and Terahertz Waves - The previous theory ((2,6)) of microwave open resonators has been improved, which can be applicable not only to simple cavities, but also to...     

Design and testing of SMA temperature-compensated cavity resonators

In this paper, we present a method for designing temperature-compensated cavity resonators using shape memory alloys (SMAs). This paper gives an expression for the temperature drift of resonant frequency, which is valid for any conductor-loaded cavity regardless of its shape. This formula, combined with a field perturbation model, is used to derive the resonant frequency of an SMA-compensated resonator subject to temperature fluctuation. Experimental results are given that confirm the feasibility of the proposed design approach. A design method is proposed for specifying SMA alloys to build the actuator. An expression is derived to accurately predict the performance of an actuator design.     

Generalized sampling: a variational approach .II. Applications

For pt.I see ibid., vol.50, no.8, p.1965-76 (2000). The variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion. It is suitable for treating vector and multidimensional signals. Here, we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling. We provide ready-made formulas, which should permit application of the technique directly to problems at hand. We comment on the practical aspects of the method, such as numerical stability and speed. We show the reconstruction formula and apply it to several practical examples, including new variational formulation of derivative sampling, landmark warping, and tomographic reconstruction     

Coupled-mode theory of unstable resonators

Although there has been a sustained interest in unstable open resonators for high-power laser applications, no satisfactory theory has previously been developed to explain the intricate behavior of the complex eigenvalues obtained by numerical solution of the resonator integral equation. The present study proposes a remarkably simple model that predicts the basic features of the published results. In this model, a two-dimensional resonator with finite convex mirrors is regarded as an open-ended waveguide with hyperbolic boundaries. Through use of the modal fields in the waveguide region and modal reflection and coupling coefficients due to the open end, one may construct a resonance equation for the eigenvalues of the free resonant fields (eigenmodes) in the unstable resonator. From a study of the resonance equation as a function of mirror size, it may be concluded that a single waveguide mode is primarily responsible for the eigenmode behavior near a loss minimum, and that two selectively coupled waveguide modes provide the behavior in the intervals between loss minima. The selection of the appropriate waveguide modes is accomplished with the aid of a resonance chart for the simpler problem wherein mode coupling at the open waveguide end is omitted. Results are presented and compared with the earlier literature.     

General theory and design of microwave open resonators

Based on the analysis of wave propagation in a waveguide with slowly varying cross-section, a general theory is developed for microwave open resonators with rotational-symmetric waveguides; this geometry has been extensively used in the gyrotrons. The theoretical analysis is carried through under the most general conditions, that is the cross-section radius r(z) of the resonator is a slowly varying arbitrary function of z and the resonator is open. The general expressions for the resonant frequencies and the Q have been derived. A design method for this kind of open resonator has been proposed. Calculation results for two practical resonators are presented.     

Warm cavity modes of free-electron laser resonators with on-axisholes

The optical mode structure and gain of a free-electron laser (FEL) resonator with holes on axis in the small optical signal regime is examined using a matrix formulation. A gain matrix, describing optical mode mixing and amplitude gain in the wiggler, is derived from the FEL evolution equations. A loss matrix, describing the effect on the transverse optical mode structure of the resonator end mirrors, is derived using the method of A.G. Fox and T. Li (1960). The laser matrix is the product of the gain and loss matrices. The eigenvectors and eigenvalues of the laser matrix give the transverse optical mode profile and gain of the resonator. The resonator of the Mark III infrared FEL at Duke University and a confocal resonator, for two holes sizes are examined. The results demonstrate the possibility of output coupling through the holes of the Mark III resonator, and the possibility of using the holes of the confocal resonator for gain control     

An improved theory of microwave open resonators

The analytic theory of microwave open resonators is improved here by means of solving the complex Airy equation, that the Q-value as well as the argument of field profile may be given accurately. The resonance conditions for open cavities with high and moderate Q-values are derived analytically. Theoreticl Q-values are well agreed with the measured ones from experiments.     

A coupled mode formulation by reciprocity and a variational principle

A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions(E^{(1)}, H^{(1)})and(E^{(2)}, H^{(2)})satisfying Maxwell's equation and the boundary conditions in two different mediaepsilon^{(1)}(x,y)andepsilon^{(2)}(x,y), respectively, is derived. Based on the generalized reciprocity theorem, we then formulate the coupled mode equations. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the "conventional" and the new coupling coefficients are derived. It is shown analytically that our formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the Hardy-Streifer theory by 0.033 percent, for example.     

Application of variational principle for calculation of resonant frequencies of cylindrical dielectric resonators

In the letter we present a new method for the calculations of resonant frequencies of cylindrical dielectric resonators using the variational principle. This method is applicable for determining the resonant frequencies of cylindrical isolated and shielded dielectric resonators. Computations for all modes (TE, TM and HEM) are given.     

Superconducting resonators and charge qubits: Spectroscopy and quantum operations. Part I

For the past few years, considerable progress has been made in the fabrication of quantum devices using mesoscopic semiconductor elements. These devices can represent the elemental base for a wide class of high-tech devices from supersensitive detectors of an electromagnetic field to reliable sources of single photons and quantum computers. The article reviews the main experimental results obtained to date with the participation of superconducting quantum devices.     

Analytic theory of coupling from tapered fibers and half-blocksinto microsphere resonators

Coupling from tapered fibers and polished half-block couplers into the high-Q whispering gallery modes of microsphere resonators is investigated analytically. Numerous formulas are derived to predict the external coupling Q values, and intrinsic whispering gallery loss, for arbitrary structures, and for any sphere mode. Phase-mismatch due to the differences in propagation constants between input and sphere modes is taken into account. These formulas are strictly mechanical once a simple characteristic equation is solved which relates the spherical mode orders to the resonant wave vector. Results are in very good agreement with values that are calculated by different numerical methods     

Application of asymptotic methods in the theory of open resonators

The problem of the eigenmodes of a 2D open resonator is solved. Two polarizations are considered. Eigenmodes in resonators with various mirror shapes are investigated. The results of a rigorous approach are compared to the results obtained with the help of various approximate asymptotic techniques.     

Control of smart exercise machines. I. Problem formulation andnonadaptive control

Concerns the design of intelligent controllers for a class of exercise machines. The control objective is to cause the user to exercise in a manner which optimizes a criterion related to the user's mechanical power. The optimal exercise strategy is determined by a biomechanical behavior of the individual user, which is assumed to satisfy an affine force-velocity relationship dependent on the body geometric configuration. Consequently, the control scheme must simultaneously: 1) identify the user's biomechanical behavior; 2) optimize the controller; and 3) stabilize the system to the estimated optimal states. Moreover, to ensure that the exercise machine is safe to operate, the control system guarantees that the interaction between the exercise machine and the user is passive. We formulate the control problem and propose a controller structure which satisfies the safety requirement and is capable of causing the user to execute an arbitrary exercise strategy if the user's biomechanical behavior is known. The controller is of the form of a dynamic damper and can be implemented using only passive mechanical components     

Interference-free assignment grids. I. Basic theory

A mathematical method using linear algebra is developed for generating interference-free simplex channel assignment grids for base stations in the VHF land mobile band for large urban areas. The frequency assignment model checks for interference from adjacent channels, desensitization, transmitter intermodulation, and receiver intermodulation. The basic philosophy of the model is presented, and the required electromagnetic compatibility computations are reviewed. Both single-frequency and multiple-frequency (sharing) assignment strategies are described     

The inverse problem in electroneurography. I. Conceptual basis andmathematical formulation

A mathematical technique for the analysis of the compound action potential (CAP) of a peripheral nerve is presented. The procedure deals with the estimation of the number of active fibers contributing to the CAP and the distribution of their conduction velocities. The CAP is described as a filtered Poisson process, the (time-varying) filter representing the single-fiber action potential waveshapes. The estimation procedure consists of two parts. The first part, related to the fast conducting fibers contributing to the CAP main complex, uses least-squares optimization techniques for the reconstruction of the CAP waveshape. The second part, applying to the small late components of the CAP due to slowly conducting fibres, explicitly uses the Poisson process formulism and is based on reconstructing the energy for variance in the CAP     

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