A synthesizing method is presented to design and implement digital dual-band filters in the microwave frequency range. A dual-band filter consists of a bandstop filter and a wide-band bandpass filter in a cascade connection, wherein the transfer functions of both the bandpass filter and bandstop filter are expressed in the Z domain. The bandstop filter is implemented by using a coupled-serial-shunted line structure, while the wide-band bandpass filter is constructed by using a serial-shunted line configuration. In particular, the bandwidth of each passband of the dual-band filter is controllable by adjusting the characteristics of both the bandpass filter and bandstop filter. By neglecting the dispersion effect between microstrip lines of different widths over a wide bandwidth, a dual-band filter is realized in the form of microstrip lines and its frequency responses are measured to validate this method.

Dual-band bandpass filters using equal-length coupled-serial-shunted lines and Z-transform technique

Fiber-optic communication systems are nowadays facing serious challenges due to the fast growing demand on capacity from various new applications and services. It is now well recognized that nonlinear effects limit the spectral efficiency and transmission reach of modern fiber-optic communications. Nonlinearity compensation is therefore widely believed to be of paramount importance for increasing the capacity of future optical networks. Recently, there has been steadily growing interest in the application of a powerful mathematical tool—the nonlinear Fourier transform (NFT)—in the development of fundamentally novel nonlinearity mitigation tools for fiber-optic channels. It has been recognized that, within this paradigm, the nonlinear crosstalk due to the Kerr effect is effectively absent, and fiber nonlinearity due to the Kerr effect can enter as a constructive element rather than a degrading factor. The novelty and the mathematical complexity of the NFT, the versatility of the proposed system designs, and the lack of a unified vision of an optimal NFT-type communication system, however, constitute significant difficulties for communication researchers. In this paper, we therefore survey the existing approaches in a common framework and review the progress in this area with a focus on practical implementation aspects. First, an overview of existing key algorithms for the efficacious computation of the direct and inverse NFT is given, and the issues of accuracy and numerical complexity are elucidated. We then describe different approaches for the utilization of the NFT in practical transmission schemes. After that we discuss the differences, advantages, and challenges of various recently emerged system designs employing the NFT, as well as the spectral efficiency estimates available up-to-date. With many practical implementation aspects still being open, our mini-review is aimed at helping researchers assess the perspectives, understand the bottlenecks, and envision the development paths in the upcoming NFT-based transmission technologies.

Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives

A rectangular silver strip and two strips separated by a narrow gap are considered as optical resonators. A surface integral equation method is used to study theoretically their scattering cross section and local enhancement of the electric field relative to the incident wave. Peaks in the scattering spectra are shown to be related to the excitation of standing waves caused by forward and backward travelling slow plasmon polaritons (PPs) in the silver strip or in the gap between two strips. This is shown via analysis of the electric near-field inside and outside the strips, and by showing that an increase of the length of strips equal to half the slow PP wavelength re- sults in a scattering resonance at app. the same wavelength. We study the broadening of resonances with strip thickness or gap size, respectively, for the two types of resonators. For field enhancement purposes we consider taking advantage of the fact that the electric field component of slow PPs along the axis of PP propagation is dominating inside the metal strips. Due to this fact and the electromagnetics boundary conditions forcing the surface normal electric field component to jump across the silver-air interface a small (5 nm) gap introduced in one of the strips leads to a factor ∼25 enhancement of the field magnitude. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Strip and gap plasmon polariton optical resonators

Plane wave scattering from lossy, periodic surfaces with periodicity in one direction is considered for arbitrary polarization and incidence angles The material is assumed to be homogeneous and characterized by complex values of permittivity and permeability Muller-type coupled integral equations are derived for the surface electric and magnetic currents The power reflection coefficient is defined in terms of the scattered far fields The integral equations are solved by the boundary element method (BEM) with constant elements Arbitrary surfaces are accommodated by approximating the actual profile by means of linear segments Other speed-up techniques are utilized to generate a numerically efficient solution Substantial comparison is made for special cases to verify the formulation The reflection coefficient is calculated for a variety of surface shapes A new profile shape is presented that results in a lower reflection coefficient than the commonly used triangular shape >

Oblique scattering from lossy periodic surfaces with applications to anechoic chamber absorbers

The problem of determining the electromagnetic field scattered by two-dimensional structures consisting of both dielectric and conducting cylinders of arbitrary cross section is considered. The conductors may be in the form of strips and the dielectrics may be in the form of shells. The conductors may be partially or fully covered by dielectric layers, while the dielectrics may be partially covered by conductors. Only homogeneous dielectrics are studied. Both the transverse electric (TE) and the transverse magnetic (TM) cases are considered. The problem is formulated in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents radiating in unbounded media. The method of moments is used to solve the integral equations. Simple expansion and testing procedures are used. Numerical results for scattering cross sections are given for various structures. >

RCS of two-dimensional structures consisting of both dielectrics and conductors of arbitrary cross section

The computation of low frequency scattering of electromagnetic fields by solid/hollow dielectric or conducting cylinders using the boundary element method (BEM) is considered. A general computer program has been developed for both transverse electric and magnetic cases. Numerical examples are given for conducting circular cylinders, and solid and hollow dielectric cylinders. The computational accuracy is checked by comparing the results with the analytic solution or computing an error defined from the optical theorem. In addition some problems at an interior resonance of the scatterer are discussed. The method can be directly applied to more complicated geometries.

Boundary element method for electromagnetic scattering from cylinders

An effective method is presented in this paper to design nonuniformly coupled transmission-line filters. This kind of filter can be used to realize almost an arbitrary filter characteristics as nonuniform transmission-line filters do. They can be cascaded directly, and no directional coupler is needed. This method begins with calculating characteristic impedance of a nonuniform transmission line by those techniques already established for designing nonuniform transmission-line filters, then determining the even- and odd-mode impedances of a nonuniformly coupled transmission line by a simple transformation. A first-order solution to the related nonlinear equations is especially proposed to calculate effective dielectric constants and line dimensions from the obtained characteristic impedances simultaneously. A device was built and tested, and the measured results verify that the proposed method is of practical use.

An effective method for designing nonuniformly coupled transmission-line filters

A three-port equivalent circuit model of microstrip transducers used for the generation and detection of magnetostatic forward volume waves (MSFVW) is derived from fundamental physical considerations. In this circuit model, each microstrip MSFVW transducer is modeled as a three-port circuit incorporating a frequency-dependent series reactance, a frequency-dependent lossless transformer, and a lossy transmission line. Circuit parameters are determined in closed form by the use of solutions of pertinent boundary-value problems. The effects of parasitics, for example, capacities of bonding pads, are easily taken into account. Some typical transducer configurations are analyzed numerically. The three-port model developed is in excellent agreement with experiments. The model can be applied directly to nonuniform arrays of microstrips weighted by varying the separation between strip centers and the widths of successive strips or reversing the current direction of some groups of strips. >

A new development of an equivalent circuit model for magnetostatic forward volume wave transducers

The Daubechies orthogonal wavelet (DOW) is compared with the nonorthogonal cardinal spline wavelet (NCSW) in the wavelet transform approach and it is shown that the DOW is better than the NCSW in view of the computation cost. First, the computation cost required for the wavelet transform based on the DOW is less than that based on the NCSW because the DOW has smaller support provided the same number of vanishing moments of wavelets is used. Second, in contrast with the fact that the wavelet transform based on the DOW does not affect the condition number of the impedance matrix, that, based on the NCSW, has an effect to make it very large. As a result, even though the NCSW results in a sparser impedance matrix, it requires more computation cost for solving the resultant matrix equation in comparison with the DOW because the cost depends not only on the sparsity, but also on the condition number of the matrix.

On a choice of wavelet bases in the wavelet transform approach

We present a method to solve a kind of integral equations (we call it the integral kernel expansion method), and apply it to an analysis of excitation of magnetostatic surface-wave/magnetostatic backward-volume-wave modes in a magnetized yttrium-iron-garnet film. The Fourier integral of a normal component of magnetic flux density is derived in terms of an unknown current density flowing in a microstrip transducer. The integral kernel is expanded into a series of the Legendre polynomials and expansion of the unknown current density in terms of appropriate functions reduces the Fourier integral to a system of linear equations with unknown coefficients. Determination of the unknown coefficients allows us to estimate the power of magnetostatic waves, which characterizes the excitation. It is found that our numerical method is superior to the previous conventional method based on an assumed current density. In order to verify the validity of our method, we compare our results with the corresponding experiments, and we have found good agreement between the two.

An analysis of excitation of magnetostatic surface waves in an in-plane magnetized YIG film by the integral kernel expansion method

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