Propagation of soliton waves in nonlinear dielectric slab waveguides of parabolic index of refraction

The pulse propagation in a non-linear slab waveguide of parabolic index of refraction is treated by using differential equation techniques. A graded index dielectric slab waveguide free of material dispersion with a cubic order non-linearity is considered. The electromagnetic wave inside the waveguide is described in terms of a non-linear equation. Slowly varying envelope function representation is employed to develop a non-linear partial differential equation for the unknown envelope function of the electric field. An averaging method over the transverse direction is applied to reduce the unknown envelope function non-linear differential equation into a form resembling the well known non-linear Schrödinger differential equation. This equation is solved by applying the Inverse Scattering Method. The N-soliton solution is developed and presented explicitly for the practical case of the single mode dielectric slab waveguide. Numerical results presenting single and double soliton propagation are also given.     

Propagation properties of TE-mode soliton in rectangular waveguides with nonlinear dielectrics

The problem of rectangular waveguide with nonlinear dielectrics is discussed. The components of electromagnetic fields in the waveguide satisfy nonlinear partial differential equations. Using slowly varying envelope approximation, they can become well known nonlinear Schrodinger equation and soliton solution is got from the equation.     

Scattering and mode conversion by a screen-like inhomogeneityinside a dielectric slab waveguide

In this paper, the interaction of surface guided waves with a perfectly conducting scatterer shaped as a part of a circular screen and placed into a dielectric slab waveguide is investigated in mathematically correct manner. Due to the geometry of screen the original boundary value problem is reduced to dual series equations treated further by means of the Riemann-Hilbert Problem technique. Based on this approach, the numerical solution can be obtained, theoretically, with any desired accuracy. The reflection, transmission, and radiated-field quantities are computed for both single-mode and multimode slab guides containing cavity-shaped and strip-shaped scatterers     

A computation of the reflection and transmission coefficients for dielectric coated waveguides

A previously developed variational technique for finding the approximate solution to the electromagnetic field inside waveguides of varying shapes and containing non-uniform dielectric and magnetic materials is applied to the specific case of an axisymmetric waveguide containing three layers of different dielectric materials. The magnetic permeability is taken equal to unity. The method enables the problem to be reduced to a two point boundary value problem for a pair of second order, linear, ordinary differential equations. The values of the reflection and transmission coefficients obtained by this method are in good agreement with those derived from solving the partial differential equations for the field.     

Discontinuities in a Rectangular Waveguide Partially Filled with Dielectric

The modal spectrum for a rectangular waveguide with a dielectric slab at the bottom of the guide is obtained following the Characteristic Green's Function method developed by Marcuvitz. Then a four-terminal network is found as equivalent to the junction of the partially filled waveguide and an empty rectangular waveguide. An integral equation is written for the electric field at the plane of the junction and variational expressions are derived for the parameters of the four-terminal network connecting the transmission line equivalent to the partially filled waveguide to the transmission line equivalent to the empty guide. A reasonable guess for the electric field at the discontinuity gives approximate values for the parameters of the four-terminal network. These values agree with experiment. The parameters of the network are plotted vs frequency and thickness of the slab.     

An Efficient and Simple Analytical Model for Analysis of Propagation Properties in Impedance Waveguides

In this paper, propagation properties of a parallel-plate waveguide with tunable artificial impedance surfaces as sidewalls are studied both analytically and numerically. The impedance surfaces comprise an array of patches over a dielectric slab with embedded metallic vias. The tunability of surfaces is achieved with varactors. Simple design equations for tunable artificial impedance surfaces, as well as dispersion equations for the TE and TM modes are presented. The propagation properties are studied in three different regimes: multimode waveguide, single-mode waveguide, and below-cutoff waveguide. The analytical results are verified with numerical simulations.      

Field analysis of dielectric-loaded lens applicator for microwavehyperthermia

A dielectric-loaded waveguide applicator for microwave hyperthermia is analyzed. The phase constant in the waveguide is determined from the numerical solution of the characteristic equation. The field pattern in human muscle which is produced by the applicator is determined by using the Kirchhoff-Huygens principle. The field focusing effect is dependent on the properties of the low permittivity dielectric slab centered in the water-filled waveguide. The greatest field enhancement is found to occur when the slab is 75-mm wide for a 150-mm×100 mm waveguide at 430 MHz     

Variational analysis of the dielectric rib waveguide using theconcept of `transition function' and including edge singularities

The authors focus on the pure LSE/LSM cases. They derive a highly accurate transverse resonance diffraction variational solution of the problem, of order 1 (a scalar dispersion equation), by assuming at the transverse step discontinuity a single function trial field which incorporates the physical properties of the solution. This is, in fact, the surface wave mode of a slab waveguide of a height intermediate between that of the rib and that of the cladding slab, including dielectric edge singularities in the LSM case. The height of the intermediate guide is obtained by optimizing the overlapping integral with the slab mode in the rib and in the cladding. This criterion turns out to be equivalent to choosing an intermediate guide whose effective dielectric constant (EDC) is the geometric mean of those of the rib and cladding. Numerical results are in excellent agreement with those obtained by finite difference, even at cutoff, where the EDC fails and most methods tend to overestimate the value of β     

A single-mode waveguide laser

A laser has been constructed in which a neodymium-doped glass slab forms the core region of a single-mode optical dielectric waveguide. The observed laser output is in a single, spatially coherent, transverse mode, which is characteristic of the waveguide structure, and has a diffraction-limited beamwidth.     

Analysis of Electromagnetic-Wave Modes in Anisotropic Slab Waveguide

Electromagnetic-wave modes propagating in anisotropic slab waveguide are analyzed theoretically in detail. The propagation conditions are derived under which waves can propagate along the axis of the guide. A two-dimensional three-layered waveguiding structure consisting of an anisotropic dielectric slab coated on, or immersed in, isotropic surrounding substrate materials is considered as a typical configuration of the guide. Field-intensity distributions of the propagating modes and their propagation constants are obtained by numerical computations. Techniques for achieving the mode discrimination and the single-mode operation are given. Some possible applications in integrated optics are suggested.     

Full-wave analysis of a transversely magnetized ferritenonradiative dielectric waveguide

A full-wave analysis is applied to a nonradiative dielectric waveguide where the isotropic dielectric slab is replaced by a transversely magnetized ferrite. The characteristic equation is obtained and the corresponding effects are discussed. The above structure exhibits reciprocal propagation characteristics. Nonreciprocal effects are also possible with a proper dielectric loading. Several numerical results are presented in the form of dispersion curve and an operational diagram, as a function of several ferrite and guide parameters. Electronically tuned and nonreciprocal devices can be implemented using this simple structure     

Diffraction from an abruptly terminated dielectric slab waveguide in the presence of a cylindrical scatterer

The efficiency of using an adaptor lens in front of an abruptly terminated symmetric slab optical waveguide is examined analytically in this paper. The adaptor lens is assumed to be of cylindrical shape with a constant refractive index. The coupling of the modes propagating inside the slab guide into radiation waves in the presence of the lens is treated by integral equation methods. In the first step an integral equation is derived for the Green's functionG(r/r')of an abruptly terminated slab waveguide. The integral equation is solved approximately by an iterative procedure giving accurate results when the difference of the refractive indices between the slab waveguide and substrate-cover regions is small. The Green's function is then used to formulate another integral equation for the unknown field inside the adaptor lens. The latter integral equation for the cylindrical lens cross section area is solved by adopting a cylindrical partial wave expansion for the unknown interior field. After determining this field, the reflection-coupling coefficients for the guided modes propagating in the opposite direction of the incident wave, are computed by using the Green's functionG(r/r'). Radiation patterns are also derived in the far field region for an incident slab guided mode. Numerical results are computed and presented for several guide dimensions, lens radii, and refractive indices.     

An Approximate Wave Equation for an Axially Symmetric Periodic Waveguide

The field problem of wave propagation in a waveguide of periodically varying section is investigated. An orthogonal curvi-linear coordinate system is developed leading to a separable wave equation. As a result, the problem is reduced to solving Hills Equation. The discussion is limited to the case of a waveguide with slowly varying radius but there is some expectation that useful results would be obtained, particularly for axial fields, without this restriction.     

Optimization techniques and inverse problems: Reconstruction of conductivity profiles in the time domain

The iterative probing of an inhomogeneous lossy dielectric slab, whose conductivity is unknown, is discussed. The probing is done in the time domain from the measurements of the field on the interface when this slab is illuminated by a known field. An exact integral formulation is used. Minimization of a cost function, characteristic of the discrepancy between the measured field and the field which would be scattered by a known slab, is specified by the optimization theory. The notion of the adjoint state of the field is introduced. The influence of some parameters of this minimization is studied. Great importance is given to the sensitivity of the probing as function of the amplitude of errors in the data. Such an iterative probing appears fast, accurate, and efficient, even in the case of large errors.     

Field Profile In A Single-mode Curved Dielectric Waveguide Of Rectangular Cross Section

An approximate and simple method for predicting the field profile in a curved dielectric waveguide of rectangular cross section is described. For a single-mode propagation, it is shown that the transverse field can be approximated inside the dielectric guide by the Airy function of the first kind and that the radial attenuation constant is a function of the bending radius outside the guide. Experimental verification of the theoretical results is included.     

EM analysis of a conducting scatterer in optic dielectric waveguide

A method to compute the scattered field of curved mirrors and gratings in a dielectric slab waveguide is proposed. In contrast to the beam propagation method (BPM) for this kind of problems, the method of moment is adopted. By introducing the dyadic Green's function in a slab waveguide, the electric field integral equations for induced current distribution on the conducting obstacles are derived. To improve the computational efficiency, the modified Green's function is incorporated into the computation program. With this study, the effects of grooves of gratings and the finite extent of the mirrors in dielectric waveguides can be investigated in more detail     

A finite difference BPM analysis of bent dielectric waveguides

A new version of the scalar TE wave equation is introduced, one that is particularly useful in bent waveguide analysis. The slowly varying envelope equation in cylindrical coordinates for the field amplitude E is finite-differenced, with no other approximations made to it. It will be shown that this version of the equation has several advantages over other forms and gives good results for the power loss rates even at radii ⩽100 μm, as well as being useful for the study of curved structures with varying radii of curvature. Evidence is provided to show that the loss rates calculated from this equation using the two dimensional finite difference beam propagation method compare favorably with other numerical and analytical results found in the literature. Special care must be taken when applying transparent boundary conditions as the curvature increases     

Transmission Characteristics of Ridge Waveguide Loaded with Left-Handed Materials

This paper presents a numerical study of the electromagnetic wave propagation in a double ridge waveguide, loaded with left-handed materials (LHM). The LHM is defined phenomenologically by assigning to it a negative permittivity and negative permeability simultaneously. Transmission characteristics such as cutoff wavelength, single-mode bandwidth, dispersion and field patterns have been investigated by edge-based finite element method. The results are compared to those with air- and dielectric-loaded ridge waveguide. It was found that the LHM-loaded ridge waveguide can greatly increase the cutoff wavelength with the disadvantage of a dramatic reduction in the single-mode bandwidth. The behavior of the dispersion curve of LHM-loaded ridge waveguide is similar to the cases of waveguide loaded with air or dielectric, except for a significant improvement of the propagation constant. The boundary conditions at the interface between the air and the LHM have been well illustrated and the antiparallel wave vector in LHM were obtained by considering the field patterns. The unusual behaviors of the LHM-loaded ridge waveguide provides the potential opportunities to design novel microwave and millimeter devices.     

Propagation Mode and Scattering Loss of a Two-Dimensional Dielectric Waveguide with Gradual Distribution of Refractive Index

An analytical discussion of the mode property and the scattering loss of a two-dimensional dielectric waveguide with gradual refractive-index distribution in the transverse direction is presented. To describe scattering loss, a transverse correlation as well as an axial correlation of the irregular variation of the refractive index have been used. The field distribution, the group delay, and the maximum film thickness of a single-mode waveguide scarcely depends on the shape of the distribution. The maximum value of the film thickness in the single-mode transmission region optimizes the scattering loss and the energy confinement. The scattering loss of a waveguide with a gradual index distribution is smaller than that of a three-layer waveguide when the transverse correlation is small, but it is not much altered when the transverse correlation is large.     

Radiation and scattering from infinite periodic printed antennaswith inhomogeneous media

The hybrid method of moments (MoM)/Green's function method technique is applied to infinite periodic printed antenna arrays containing dielectric inhomogeneities. The solution uses an integral equation for an infinite periodic printed array on or over a homogeneous dielectric substrate, coupled with equivalent volume polarization currents for dielectric inhomogeneities on top of the homogeneous substrate. Volume pulse-basis functions were used to expand the volume polarization currents. A hybrid MoM/Green's function method solution was then obtained through the matrix form of the problem. The two-dimensional (2-D) solution of plane wave scattering from a grounded dielectric slab was used to validate the reaction impedance of the dielectric inhomogeneity. Several infinite periodic printed dipole arrays with dielectric supports and overlays were studied with this solution and good agreement was observed between the hybrid MoM/Green's function method and waveguide simulator experiments