Semi-infinite Rectangular Waveguides Research Articles

Method of Volume Singular Equations for Solving a Nonlinear Problem of Diffraction in a Semi-Infinite Rectangular Waveguide

Method of Volume Singular Equations for Solving a Nonlinear Problem of Diffraction in a Semi-Infinite Rectangular Waveguide

Non-Markovianity of an atom in a semi-infinite rectangular waveguide

We investigate the non-Markovianity (NM) of a waveguide QED with a two-level atom as the system and a semi-infinite rectangular waveguide as the environment, where the transverse magnetic (TM mn ) modes define the quantum channels of guided photons. The perfect mirror imposed by the finite end exerts a retarded feedback mechanism to allow for information backflow, which leads to NM dynamics. For the energy separation of the atom far away from the cutoff frequencies of transverse modes, the delay differential equations are obtained with single-excitation initial in the atom. Our attention is focused on the effects of multiple quantum channels involved in guiding photons on the degree of non-Markovian behavior. An asymptotic value of the non-Markovianity can be found as the atom–mirror distance is large enough, however, the asymptotic value of of the atom interacting with the effective double-modes is lower than that of the atom interacting with the effective single-mode. We also show that is a constant, and the analytical expression for is related to the parameters associated with the modes, which is related to the interference of the two modes.

Numerical Method for Recovering Permittivity of an Inhomogeneous Dielectric Body Placed in a Semi-Infinite Rectangular Waveguide

Numerical Method for Recovering Permittivity of an Inhomogeneous Dielectric Body Placed in a Semi-Infinite Rectangular Waveguide

The flexibility in choosing distinct Green’s functions for the boundary wall method: waveguides and billiards

The boundary wall method (BWM) is a general purpose protocol to treat boundary value problems for wave equations, specially Helmholtz’s (the case addressed here). Similarly to most approaches, the BWM may be computationally demanding for large borders , at which the wave function must satisfy specified boundary conditions. Also, despite the fact the BWM is an exact procedure, usually it is not amenable to closed form solutions. The BWM relies on the Green’s function G 0 of the embedding domain V of . However, in many instances—like for modeling a billiard—the specific V is not really fundamental and thus one has a certain freedom to choose distinct domains and so G 0’s. Here we consider this characteristic of the BWM and show how to obtain some analytical results and solve numerically semi-infinite waveguides by exploring proper Green’s functions. As examples, we discuss rectangular, triangular and trapezoidal structures with both Dirichlet and leaking boundaries as well as scattering states within semi-infinite rectangular waveguides.

Numerical Method for Reconstruction of Inhomogeneity Parameters of a Body Placed in a Semi-Infinite Rectangular Waveguide

The article is devoted to an inverse problem of reconstruction of inhomogeneity parameters of a body in semi-infinite rectangular waveguide. We suggest a new numerical method for solving this one. The inverse problem is reduced to the solving of volume singular integral equation of first kind and additional procedure of calculation the parameters of inhomogeneity. The numerical results are presented.

Spatial Dependent Spontaneous Emission of an Atom in a Semi-Infinite Waveguide of Rectangular Cross Section**Supported by National Natural Science Foundation of China under Grant Nos. 11374095, 11422540, 11434011, and 11575058, National Fundamental Research Program of China (the 973 Program) under Grant No. 2012CB922103, and Hunan Provincial Natural Science Foundation of China under Grant No. 11JJ7001

We study a quantum electrodynamics (QED) system made of a two-level atom and a semi-infinite rectangular waveguide, which behaves as a perfect mirror in one end. The spatial dependence of the atomic spontaneous emission has been included in the coupling strength relevant to the eigenmodes of the waveguide. The role of retardation is studied for the atomic transition frequency far away from the cutoff frequencies. The atom-mirror distance introduces different phases and retardation times into the dynamics of the atom interacting resonantly with the corresponding transverse modes. It is found that the upper state population decreases from its initial as long as the atom-mirror distance does not vanish, and is lowered and lowered when more and more transverse modes are resonant with the atom. The atomic spontaneous emission can be either suppressed or enhanced by adjusting the atomic location for short retardation time. There are partial revivals and collapses due to the photon reabsorbed and re-emitted by the atom for long retardation time.

Waveguide T-junctions with resonant coupling between sections of different dimensions

Electromagnetic characteristics of the E-plane T-junction for two rectangular waveguides using resonant coupling between the waveguide sections were studied by mathematical modeling. The problem of coupling between infinite and semi-infinite rectangular waveguides through a resonant slot in the end-wall of the semi-infinite waveguide in the presence of resonant monopole is solved in a strict electrodynamic formulation. The monopole with variable surface impedance is placed parallel to the narrow walls at an arbitrary position inside the infinite waveguide. The problem is solved analytically by the generalized method of induced electro-magneto-motive forces. Impedance vibrator inclusions with variable electro-physical parameters have been analyzed as control elements for waveguide junctions. To this purpose energy characteristics of the junction in the single-mode regime of the both waveguides, and also in multi-mode regime of the semi-infinite waveguide is investigated. The results may be useful for development of variety antennas and waveguide devices, which involves waveguide junctions.

The method of induced magnetomotive forces for many-element cavity-backed slot radiators

The method of induced magnetomotive forces is used for solving the problem of distribution of equivalent magnetic currents in an antenna-waveguide structure of the “two-slot resonant diaphragm—rectangular resonator—radiating slot” type on the end face of a semi-infinite rectangular waveguide. The numerical and experimental investigations of this system are performed and the plotted electrodynamic characteristics are presented.

ANALYTICAL METHODS IN THEORY OF SLOT-HOLE COUPLING OF ELECTRODYNAMIC VOLUMES

The approximate analytical solution of the integral equation concerning the equivalent magnetic current in the narrow slot, coupling two electrodynamic volumes, has been obtained by the averaging method. The formulas and the plots for currents and the coupling coefficients of longitudinal and transverse slots in the common walls of rectangular waveguides are represented. By means of the induced magnetomotive forces method using basis functions of current distribution, obtained by the averaging method, the following electrodynamic structures have been considered: the electrically long longitudinal slot in the common broad wall of rectangular waveguides; two symmetrical transverse slots in the common broad wall of rectangular waveguides; the transverse slots system in the common broad wall of rectangular waveguides. The problem about the resonant iris with the arbitrary oriented slot in the plane of cross-section of a rectangular waveguide has been solved by the averaging method. The problem about stepped junction of two semi-infinite rectangular waveguides with the impedance slotted iris has been solved by the induced magnetomotive forces method. The analytical formulas for the distributed surface impedance of homogeneous and inhomogeneous magnetodielectric coatings of iris surface have been obtained. For a greater number of the considered electrodynamic structures the calculated values are compared with the results, obtained by numerical methods (also using commercial programs) and the experimental data.

Diffraction Radiation from a Slot in the Impedance End of a Semi-Infinite Rectangular Waveguide

Using the induced magnetomotive force method, we obtain an approximate analytical solution of the problem of diffraction of the H10 mode by a narrow slot which is cut in the impedance finite-thickness wall on the end of a semi-infinite rectangular waveguide and radiates into free half-space over an infinite, perfectly conducting screen. The scattering-matrix coefficients of a slotted waveguide radiator are studied numerically for the values of the complex surface impedance which correspond to some particular types of a thin-film coating of the waveguide end wall.

The method of induced magnetomotive forces for cavity-backed slot radiators and coupling slots

The method of induced magnetomotive forces is used for solving the problem of magnetic current distribution in an antenna-waveguide structure of the “coupling slot in waveguide wall — rectangular resonator — radiating slot” type for the cases of infinite and semi-infinite rectangular waveguides. The numerical and experimental investigations of such systems are performed and the plotted electrodynamic characteristics are presented.

ACOUSTIC ABSORPTION OF MACRO-PERFORATED POROUS MATERIALS

The paper discusses the absorption of non-homogeneous thin macro-porous materials. In particular, the acoustic absorption performance of three-dimensional (3-D) porous media made up from thin porous patches, with different acoustic properties, is investigated using a numerical model. The presented model considers the configuration wherein the material is bonded onto the hard-walled termination of a semi-infinite rectangular waveguide. It couples a finite element description for the porous material to a modal description in the waveguide and uses a power balance approach to accurately quantify the absorption performance of the material. Experimental results are presented to validate the model in the special case of a macro-perforated porous material. Using this model a parameter study is presented. It is shown that absorption may be increased at low frequency by using non-homogeneous patch-works.

Input impedance of a probe-excited semi-infinite rectangular waveguide with arbitrary multilayered loads: part II-a full-wave analysis

For pt.I see ibid., vol.43, pt.A, pp.1559-66 (July 1995). Utilizing the dyadic Green's functions (DGF's) derived in Part I of this paper, the input impedance of a coaxial probe located inside a semi-infinite rectangular waveguide has been generally formulated. The electromagnetic DGF's for a rectangular cavity with a dielectric load are also obtained from the general expressions given in Part I. Using the full-wave analysis, a dielectric-loaded rectangular cavity is further considered and the input impedance is specified. To improve the computational accuracy, an alternative form of electric DGF's of the second kind is developed and expressed in terms of the guided-wave eigenvalues for the rectangular loaded cavity. The probe-input reactance and the phase of the reflection coefficients are computed using the conventional form of electric DGF and the alternative form of magnetic DGF. Data are obtained from experiments performed on a dielectric-loaded cavity and compared with the numerical results. Agreement of the theoretical and experimental results confirms the applicability of the theoretical analysis given in this paper.

Input impedance of a probe-excited semi-infinite rectangular waveguide with arbitrary multilayered loads. I. Dyadic Green's functions

This paper presents both the electric and the magnetic types of dyadic Green's functions defined for electromagnetic fields due to electric and magnetic current sources in a semi-infinite rectangular waveguide filled with arbitrary multilayered media. Applying the principle of scattering superposition, the dyadic Green's functions in each of the multiple loads are constructed in general for such EM current sources located in an arbitrary layer of the waveguide. Analytical expressions of the scattering dyadic Green's functions' coefficients are obtained in terms of transmission matrices. To demonstrate how the method presented is used and how the results are obtained for some special cases, a semi-infinite rectangular waveguide with one load is considered. The dyadic Green's functions and their coefficients in such a case are derived in closed form by reducing the general formulae of the dyadic Green's functions for the arbitrary multiple case to those for the special case concerned. Further comparison of the dyadic Green's functions obtained here with previous publications shows good agreement, demonstrating the applicability of the results presented here.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the eigenfunction expansion of electromagnetic dyadic Green's functions in rectangular cavities and waveguides

The electric dyadic Green's functions of both the first and the second kinds due to the presence of electric and equivalent magnetic sources in rectangular cavities are obtained. A method for directly reducing the dyadic Green's functions for a rectangular cavity to those for a semi-infinite and an infinite rectangular waveguides is presented. The Green dyads of the second kind for an infinite and a semi-infinite rectangular waveguides, and a rectangular cavity are obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Broadwall slot coupling into butt‐ended waveguide

AbstractWe present an analysis of a slot cut in a broadwall of a rectangular waveguide, coupling into a semiinfinite rectangular waveguide capped by a conducting transverse plate containing the slot. Slots coupling into butt‐ended waveguides are employed in test fixtures in slot array applications. Pertinent integral equations for the slot‐aperture electric field are solved by the method of moments, and scattering characteristics of slot couplers for butt‐ended guides are deduced. Numerical results indicate limitations of these couplers for applications involving reduced‐height guides. © 1994 John Wiley &amp; Sons, Inc.