Optical field distribution in close-confined laser structures

An experimental and theoretical study has been made of the radiation patterns from GaAs lasers with a "close-confined" structure. The lasers were grown by liquid-phase epitaxy and consisted of a p+ - p-n structure with Al in the p+ region. Photometric measurements were made of the intensity distribution at the emitting facet (microscope observations) and the radiation pattern in a plane perpendicular to the junction. The electromagnetic field distribution in the vicinity of the p-n junction and the radiation pattern were calculated by solving the wave equation for a three-layer structure with complex dielectric constants in each layer. The theory predicts enhanced confinement of the radiation by the increased dielectric discontinuity due to the heterojunction, in agreement with the low lasing threshold and high efficiencies of the close-confined diodes. Another consequence of the theory is that as the thicknessdof thepregion of the cavity is increased, higher order modes can propagate with efficiences much greater than in ordinary lasers without the heterojunction. The third mode, corresponding to three intensity maxima along a line perpendicular to the junction, was observed ford = 5 mu. The good agreement found between the observed and calculated radiation patterns indicates that confinement of the radiation by dielectric discontinuities is an important factor in explaining the low-threshold currents found in close-confined lasers.     

Germanium laser with a hybrid surface plasmon mode

The possibility of creating an n⁺⁺-Ge laser with a hybrid surface plasmon TM mode is theoretically studied. The distribution of electromagnetic fields and the absorbance in the mode under study, the optical confinement factor, the gain, and the threshold current density in the laser under consideration are calculated. It is shown that the threshold current density at optimal layer thicknesses of an n⁺⁺-Ge laser with a hybrid surface plasmon TM mode can be 2–3 times lower than the experimentally observed threshold current density in an n⁺⁺-Ge laser with a conventional dielectric waveguide.     

A rigorous boundary value solution for the lateral modes of stripe geometry injection lasers

A new mathematical model useful for analyzing lateral modes of stripe geometry lasers is presented. The oxide stripe laser is modeled as a three-layer waveguide in which the dielectric constant of the active layer varies only along the lateral direction; the dielectric constant of the surrounding passive layers is assumed to be position independent. The solution technique affords a rigorous matching of the fields of the active layer with those of the surrounding passive layers. To illustrate the model, the modes of a waveguide with parabolic dielectric variation along the lateral direction are investigated. The fields are written as a linear combination of Hermite-Gaussian (H-G) functions; heretofore, fields have been described with a single H-G function. Fundamental mode spread (spot size at halfpower) is calculated and related to the gain distribution. (Previous estimates of the lateral field spread of the fundamental mode using a single H-G function not rigorously matched at the boundaries can yield spot sizes as much as 30 percent different from results calculated from linear combinations of H-G functions.) In addition, the peak gain fields are determined at threshold for various waveguide geometries.     

Finite element analysis of MMIC structures and electronic packagesusing absorbing boundary conditions

In this paper, a three-dimensional finite element method (FEM) is employed in conjunction with first and second-order absorbing boundary conditions (ABC's) to analyze waveguide discontinuities and to derive their scattering parameters. While the application of FEM for the analysis of MMIC structures is not new, to the best of the knowledge of the authors the technique for mesh truncation for microstrip lines using the first and higher-order ABC's, described in this paper, has not been reported elsewhere. The scattering parameters of a microstrip discontinuity are computed in two steps. As a first step, the field distribution of the fundamental mode in a uniform microstrip is obtained by exciting the uniform line with the quasi-static transverse electric field, letting it propagate, and then extracting the dominant mode pattern after the higher order modes have decayed. In step two, the discontinuity problem is solved by exciting the structure by using the fundamental mode obtained in step one. The scattering parameters based on the voltage definition are calculated by using the line integral of electric fields underneath the strip. Numerical solutions for several waveguide discontinuities and electronic packages are obtained and compared with the published data     

Analysis of Radiation Phenomena in a Wedge Ended Dielectric Slab Waveguide

Radiation phenomena observed in a wedge shape ended dielectric slab waveguide are analyzed using mode matching technique. The case of transverse electric polarization (TE) being parallel to dielectric slab waveguide is assumed. In order to describe the fields in the wedge region, a stack of dielectric plates is assumed and in each layer the fields are expanded in terms of the mixed spectrum of guided and radiated modes. A similar expansion is used in the constant thickness slab waveguide while in free space medium a continuous-radiation mode expansion is used. Then a mode matching approach is applied, incorporating the orthogonality properties of mixed spectrum modes, in order to compute the wave fields inside the dielectric slab waveguide and wedge medium. Mode matching is achieved by discretizing the continuous radiation mode spectrum leading into a numerically stable solution provided a sufficient large number of points are used to convert integrals into finite summations. Numerical computations are carried out for various wedge geometries and shapes including linear and exponential profiles.     

Radiation of an aperture antenna covered by a spherical-shellchiral radome and fed by a circular waveguide

This paper presents a full-wave analysis of the radiation characteristics of an aperture antenna that is flush-mounted on a ground plane and fed by a circular waveguide supporting the dominant TE₁₁ mode. The antenna is covered by a dielectric hemispherical chiral radome. Huygen's equivalence principle and the image theory are utilized to simplify the problem. The magnetic dyadic Green's function for the three-layered geometry is formulated and applied to analyze the radiated electromagnetic fields outside the chiral radome. Both the exact and approximate expressions of electric fields valid for the Fresnel and Fraunhofer zones are obtained using the spherical vector wave functions and their approximations in the far zone. Various chiral materials are assumed and computations of antenna parameters are carried out. The effects of the dielectric chiral radome on the radiation power patterns, sidelobe levels, and 3-dB beamwidths are also discussed numerically     

A Unified Approach to the Analysis of a Category of H-Plane Discontinuities

Based on the mode matching method, the generalized scattering parameters including the fundamental and higher order modes (multi-modes) are obtained for the discontinuity interface of a category of waveguide H-plane discontinuities. Then by using a general port-connection order-decrease method raised by the author, the whole discontinuity including the two interfaces and the intermediate part of finite length or zero length (as is the case for very thin inductive windows or irises) can be combined into one network, and the generalized scattering parameters of this network can be obtained from which the scattering parameters of the fundamental mode can be extracted. If needed, the equivalent circuit parameters can be calculated directly from the scattering parameters. Examples are given to show the validity and versatility of this new method for dielectric filled waveguide, inductive iris and/or window, E-plane metal and/or finline insert, and even the offset E-plane finline insert, etc.. Multiple inserts, windows and irises can also be analysed.     

Transverse mode controlled in inGaAsP inP lasers at 1.5 µm range with buffer-layer loaded piano-convex waveguide (BL-PCW) structures

A modified plano-convex waveguide structure is studied analytically and successfully applied to InGaAsP/InP lasers in the1.5- 1.6 mum wavelength region to realize stable transverse mode operation. The structure of these lasers is characterized by a standard buffer layer between an active layer and an upper cladding layer and a waveguide layer of varying thickness between the active layer and the substrate. A theoretical analysis of this structure showed that, for a given channel depth, increases in buffer-layer thickness give rise to larger maximum channel widths of the substrate for fundamental transverse mode operation. It was also shown that the optical confinement factor in the active layer decreases little as the buffer-layer thickness is increased from 0.1 to 0.3 μm. Buffer-layer loaded plano-convex waveguide lasers in the 1.5 μm range were prepared by liquid phase epitaxy and fundamental transverse mode operation up untilI = 2I_{th}was obtained. The dc threshold current was 100-300 mA and the differential quantum efficiency per facet was 10-15 percent. Continuous CW operation for over 2000 h at 25°C has been achieved.     

Investigation on propagation properties of terahertz waveguide hollow plastic fiber

The propagation properties of terahertz (THz) waveguide plastic hollow fiber have been investigated in this paper. The effects of radiation frequency, bore diameters and dielectric coating layers on the waveguide property have been shown and discussed. The results show that the attenuation loss of TM mode increases and that of TE mode decreases as radiation frequency increases. The attenuation loss decreases with the increasing of fiber bore diameter. The attenuation loss decreases as the refractive index of dielectric coating layer and the ratio of the refractive index of outer dielectric layer to that of inner dielectric layer increase.     

Scattering of the TE/sub 01/ and TM/sub 01/ Modes on Transverse Discontinuities in a Rod Dielectric Waveguide-Application to the Dielectric Resonators

Our purpose is to determine the resonance frequency together with the radiation quality factor of dielectric resonators. To do that, the reflection and the scattering properties of the TE/sub 01/ and TM/sub 01/ modes, incident on an abruptly ended dielectric rod, are analyzed. After the building of the complete mode spectrum on each side of the discontinuity, the continuity relations in the discontinuity plane associated with the orthogonality properties lead to a coupled integral equation system. That one is solved by means of an iterative procedure, providing all the characteristics of the discontinuity (reflection or coupling coefficients, radiation losses). Then, these solutions are used to determine the resonant frequency and the radiation quality factor of cylindrical resonators which are considered as waveguide lengths between two interacting discontinuities.     

Equivalent circuit formulation for an array of phased waveguide apertures

An expression for the radiation admittance of an infinite planar array of rectangular waveguide apertures is formulated and a technique for finding the complete equivalent circuit of the waveguide to space junction is given. The formulation includes multiple layers of dielectric above the array ground plane and waveguide elements which are center loaded with dielectric. Experimental verification of the radiation admittance formulation and the equivalent circuit concepts is given.     

Modal analysis of step discontinuities in graded-index dielectricslab waveguides

The modal solutions of the TE- and TM-modes of an arbitrary graded-index dielectric slab waveguide have been derived by applying the generalized telegraphist's equations to the equivalent inhomogeneous parallel-plate waveguide model with electric or magnetic walls. These modal solutions have been employed in a mode-matching procedure to calculate the transmission properties of step discontinuities in arbitrarily graded-index dielectric slab waveguides such as diffused optical waveguides having exponential, Gaussian and complementary error-function index profiles. For slab waveguides containing an abrupt offset, the radiated power is found to increase smoothly with increasing displacement. Power loss calculations for an abrupt change in diffusion depth for which the dominant mode is in the vicinity of cutoff, exhibit a sharp transition from almost zero loss to nearly total radiation loss     

Optical theorems for electromagnetic scattering by inhomogeneitiesin layered dielectric media

The optical theorem, which relates the forward scattering amplitude to the total cross section of a scatterer in free-space, is extended to problems of scattering of an incident transverse electric plane wave or guided mode by inhomogeneities in lossless, waveguiding, dielectric interfaces or layers. The cases of a compact irregularity on either the interface between two unbounded dielectric media or in the waveguiding layer of a dielectric-slab waveguide are considered. Simple formulas that connect the scattered amplitudes of the different types of waves excited by the incident energy are derived. They can be used as an independent check of numerical codes when benchmark solutions are not available or are hard to obtain. In addition, a relationship between the scattered amplitudes and the spectral power of each excited wave is derived using the method of stationary phase     

Full-wave modeling of coplanar waveguide discontinuities withfinite conductor thickness

An extended version of the spectral domain approach (SDA) is developed to analyze discontinuities in open coplanar waveguide with finite metallization thickness. By making use of the exact Green's function in the spectral domain, the effects of surface wave and radiation phenomena are accurately accounted for. Both longitudinal and transverse components of the aperture electric fields are used in the analysis to allow modelling of structures with large transverse dimensions at high frequencies. The procedure also includes mode conversion near the discontinuities. As an illustration of the method, analytical steps and computed scattering parameters of the coplanar waveguide short-circuits and transitions are provided and compared against measured data     

Scattering of Surface Waves on Transverse Discontinuities in Symmetrical Three-Layer Dielectric Waveguides

This paper presents a rigorous Wiener-Hopf solution to the problem of transverse discontinuities in a symmetrical three-layer dielectric waveguide excited by the dominant TE mode. Fourier transformation and the proper boundary conditions provide the Wiener-Hopf equation for the Fourier components of the scattered fields at the interface between the free space and the dielectric waveguide. A formal solution to this equation is derived by conventional factorization methods, and an iterative method is proposed to calculate the reflected, transmitted, and radiated fields numerically.     

Scattering by Abrupt Discontinuities on Planar Dielectric Waveguides

Two unifying aspects of the problem of scattering by an abrupt discontinuity on a planar dielectric waveguide are considered. The first aspect is concerned with the numerical solution of the scattering problem through consideration of a corresponding bounded waveguide problem in which perfect electric or magnetic conductor bounds with variable locations are introduced. It is shown that the solutions to the bounded problem, when numerically integrated over a range of bound locations defined within half a wavelength, allow the complete mode spectra of the unbounded waveguide to be accurately accounted for. Scattering solutions for both TE- and TM-modes are presented for a wide range of discontinuities and, in the TE-mode case, are in agreement with results obtained using the method due to Rozzi [5]. The second aspect is concerned with the relationship between scattering and "inter-waveguide mode orthogonality." Based on a simple iterative scheme, a meaningful physical interpretation of the scattering process is developed. This allows the scattering to be classified as being of first or higher order, to be explained in terms of the physical characteristics of the mode fields.     

Propagation Properties of a Modified Slot Surface Plasmonic Waveguide

In this paper, we present a modified slot surface plasmonic waveguide formed by metallic rod, core dielectric layer, and metallic film on the substrate. Using the finite-difference frequency-domain method, modal field distribution are analyzed firstly. Results show that the fundamental mode could be well confined in the space between the metal rod and the metal film. The dependence of modal field distribution, effective index, and propagation length of the fundamental plasmonic mode without gain on dielectric constant of the core layer, geometrical parameters, and working wavelengths are analyzed and discussed. A kind of available gain dielectric medium was used for the core dielectric layer to extend the propagation length. Results show that the propagation length can be extended observably with the help of the gain dielectric medium. Finally, effect of the thickness of the core dielectric layer on modal field distribution, effective index, and propagation length are analyzed and discussed. Since the modal field distribution, effective index, and propagation length can be controlled by adjusting the geometrical parameters, dielectric constant and gain of the core layer and working wavelengths of the waveguide, this kind of surface plasmonic waveguide can be applied to the field of photonic device integration and sensors.      

Numerical analysis of arbitrarily shaped discontinuities betweenplanar dielectric waveguides with different thicknesses

An approach that combines the finite-element and boundary-element methods is applied to the analysis of arbitrarily shaped discontinuities between planar dielectric waveguides with different thicknesses. The fields interior and exterior to the region enclosing the discontinuities are treated by the finite-element method and the boundary-element method, respectively. The waveguide regions connected to the discontinuities are handled by analytical solutions. In this approach, scattering characteristics of the discontinuities can be accurately evaluated, and far-field radiation patterns can be easily calculated. To show the validity and usefulness of this approach, the scattering characteristics of a step, a staircase transformer, and a tapered transformer are analyzed. Also, a simple equivalent network approach is introduced for estimating the reflection and transmission characteristics of planar dielectric waveguide discontinuities, and the effectiveness of this simple approach is confirmed by comparing the numerical results with those of the approach that combines the finite-element and boundary-element methods     

Slot antenna impedance for plasma layers

The rectangular cavity or waveguide backed slot is covered by a plasma layer of finite thickness. The longitudinal variation of the voltage across the slot is obtained from the variational solution of an integral equation. The solution for plasma layer of finite thickness is obtained from the free space Green's function by the method of images. The fields outside the slot depend on the surface integral of the fields over the slot plane and over the surface of the plasma layer. If the thickness of the plasma layer is large compared with the wavelength, the fields on the surface of the plasma may be related to the voltage distribution along the slot by plane wave reflection coefficients. This leads to an integral equation that is reduced to a form suitable for machine computations. These calculations show the slot admittance to remain almost constant for plasma layers of various thicknessesh. The slot conductance tends to increase forh/ lambda <0.5. The presence of a plasma layer affects the voltage distribution along the slot for a center excited slot. The field distribution along the waveguide excited slot differs only slightly from the principal mode field distribution in the guide.     

Nonuniform Layer Model of a Millimeter-Wave Phase Shifter

The electromagnetic wave propagation of millimeter waves in dielectric waveguides with thin surface plasma layers is characterized. The phase and attenuation of a 94-GHz wave are computed for various surface plasma layer thicknesses as a function of earner density levels. The electron/hole pairs generated in the vicinity of the dielectric waveguide surface by photo excitation are assumed to have an exponential profile due to either carrier diffusion or the exponential absorption of the optical field. Field computations made for a uniform plasma layer are compared with those of the nonuniform plasma to illustrate the effects of the exponential tails of the carrier profiles on both the phase and attenuation of the millimeter wave. The thin plasma layers slightly affect the field profile of the transverse electric modes (fields polarized parallel to the plasma layer). The transverse magnetic fields are highly distorted at plasma densities greater than 10/sup 16/ cm/sup -3/.