Symmetric Slab Research Articles

Analysis of symmetric and asymmetric nanoscale slab slot waveguides

Nanoscale slab slot waveguides provide for high optical confinement and have found abundant applications in silicon photonics. After developing an analytical mode solver for general asymmetric slot waveguides, the confinement performance of symmetric as well as asymmetric geometries was systematically analyzed and compared. For symmetric structures, 2D confinement optimization by varying both low-index slot and high-index slab width revealed a detailed saturation trend of the confinement factor with the increase of the studied width. Furthermore, simple design rules on how to choose the slot and slab width for achieving optimal confinement was obtained. For asymmetric structures, we demonstrated that the confinement performance was always lower than the 2D optimized confinement of the symmetric structures providing the two high-index slab layers and the two cladding layers have same refractive indices, respectively. In addition, the sensitivity of the confinement to the degree of asymmetry was studied, and we found that the fabrication tolerance on the material and structural parameters may be reasonably large for symmetric structures designed at optimal confinement.

High Emittance Electron Beam Source Coupled to Slab Loaded Accelerating Structure

High power line source emitter assembly was coupled to a twin symmetric H-plane slab loaded accelerating structure for beam acceleration. Closed form field analysis of the accelerating structure that includes guideline information regarding modal hierarchy, mode nomenclature, propagation plane, cut-off plane and dispersion relations is presented. Furthermore it was confirmed that by using symmetrically loaded dielectric accelerating structures with one rotated through 90° results in exerting a uniform acceleration impact on a travelling beam passing through the structure.

Positively and negatively large Goos–Hänchen lateral displacements from a symmetric gyrotropic slab

A detailed study on the lateral displacements of a transverse magnetic (TM) wave transmitted and reflected from a symmetric gyrotropic slab is presented. We give the analytic formulas for the transmission coefficient and the reflection coefficient, as well as the corresponding lateral displacements. It is found that due to the external magnetic field the displacement of a transmitted beam is different from that of reflected one, even for a lossless symmetric configuration. Furthermore, within the chosen frequency band, when the incident angle is near the Brewster angle, the shift of a reflected wave can be large with nonzero reflectance, and can be positive or negative depending on the direction of the applied magnetic field and the incident wave.

Propagation properties for five-layer symmetric slab waveguides including left-handed materials

In this paper, we discussed a slab wave-guide of five layers, The core is a left-handed material, but the claddings are right-handed materials. A dispersion equation of TE modes is obtained by using Maxwell’s equations, and some new dispersion characteristics are obtained based on the equation.

The mode characteristics of a symmetrical slab waveguide with single-negative-material cladding

The propagating characteristics of a symmetrical three-layer slab waveguide with mu-negative (MNG) media are studied in detail. It is found the MNG waveguide can propagate not only quick waves but also slow waves of TE0 and TE1 modes. The properties of this guided mode are different from those of the left-handed waveguide and the conventional waveguide. In MNG slab waveguide, the region of effective refractive index of the guided mode is wider than those of the other two. In addition, the TE0 fundamental guided mode does not exist at all, while the higher-order TE guided modes and all TM guided modes do exist. However the surface wave of TE0 and TE1 modes can emerge under a certain condition. The propagation constant of higher-order TE mode is greater than that of the TM mode of the same order. Two TE modes of the same order can coexist in the MNG, which is closely related to the structural parameters. The energy fluxes of two TE modes are oppositely directed inside and outside the inner layer, therefore the total energy flux can be negative.

INFLUENCE OF EXTERNAL MAGNETIC FIELD ON A SYMMETRICAL GYROTROPIC SLAB IN TERMS OF GOOS-HÄNCHEN SHIFTS

A detailed study on the influence of an external magnetic field on a symmetrical gyrotropic slab in terms of Goos-Hanchen (GH) phase shifts is presented. The GH phase shifts at both boundaries of the slab are calculated, and the guidance condition is explained by means of them. It is found that the external magnetic field destroys the spatial symmetry of the field distribution, and we use the concepts of ‘penetration’ distance as well as effective thickness to illustrate the phenomenon. In term of the GH phase shifts, the spatial distribution of the time-average Poynting power is also derived. We find that influenced by the external magnetic field, the positive and negative time-average Poynting power along the waveguide direction can exist simultaneously in the gyrotropic medium, depending on the transverse position. † Also with Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA02139, USA

Resistive stability of a plasma with runaway electrons

In tokamak disruptions the Ohmic current is often replaced by a current of runaway electrons, which is likely to be more peaked in the center of the discharge than the predisruption current. This raises the question of the resistive stability of the postdisruption plasma, where the equilibrium current is entirely carried by the runaway electrons while the cold (∼10eV) background plasma is relatively resistive. It is found that the linear properties of the classical tearing mode are essentially determined by the cold bulk plasma, and the growth rate is approximately the same as in a plasma without runaways but with the same current profile. The nonlinear saturation amplitude is different, however. In a symmetric plasma slab, the saturated island size is larger when the current is carried by runaway electrons than in the Ohmic case, and undergoes a nonlinear bifurcation when the stability index Δ′ exceeds a critical value.

Enhancing the radiative decay rate of fluorescent organic molecules using micropillar microcavities and optical nanocavities

We discuss the enhancement of spontaneous emission of fluorescent organic dyes when placed in micropillar microcavities and also in an optical nanocavity. We show experimentally that an enhancement in the spontaneous-emission rate of 1.78 ± 0.04 times can be realized by placing a thin-film of the molecular dye Lumogen Red dispersed in a polymer matrix into a 3 μm diameter micropillar having a Q-factor of 680. We then model the optical properties of Noda nanocavities in vertically symmetric and asymmetric slab waveguides using TiO 2 as a high-index dielectric, with the cavity mode wavelength tuned to 713 nm. We estimate that such cavities will have a maximum Q-factor of 4455 and a Purcell Factor (maximum enhancement in the spontaneous-emission rate) of 340.

Metal iris influence on guided-mode diffraction

The effects of the presence of metal irises on guided-mode propagation through a symmetrical three-layer slab waveguide are examined by using the integral equation method. The aperture electric field distribution is expressed in terms of a finite series of Chebyshev polynomials. The modal reflection and transmission coefficients, the near-field structure, and the far-field radiation pattern are calculated, while numerical results are presented for several iris apertures.

Leaky mode directional coupler for prism coupling interconnection

A leaky mode directional coupler was fabricated with its beam shaped into a Gaussian-like profile and was experimentally demonstrated for suppressing the diffraction of an out-coupled beam. The demonstrated coupler consists of a multilayered waveguide with six layers that are embedded in a symmetric slab waveguide. The out-coupled beam profile was measured to be shaped into a Gaussian function by using the prism coupling method. There was an excellent agreement between the measured and theoretically predicted coupling angles, and it was also confirmed that the diffraction was suppressed.

Reflectivity of buried slab waveguides

The scattering properties of an abruptly ended buried slab waveguide for both TE and TM modes are examined by an improved iteration technique that is based on the integral equation method with "accelerating" parameters. The waveguide is considered a symmetrical slab, for which the weakly guiding conditions are invalid, and it is embedded in a different dielectric material. The tangential electric field distribution on the terminal plane, the reflection coefficient of the first TE and TM guided modes, and the far-field radiation pattern are computed. Numerical results are presented for several ended waveguides, while special attention is given to the far-field radiation pattern rotation and the terminal field distributions.

Numerical study of polarisation-selective side-illuminated pin photodetectors grown on InP substrate for hybridisation on silicon platform

A monolithic polarisation-selective side-illuminated pin photodetector is described using the coupling properties of symmetric and asymmetric slab optical waveguides. First, a basic structure is proposed, analysed and optimised by modal analysis, leading to a computed polarisation ratio of 15.7 dB. Then the symmetric waveguide is replaced by a multimode diluted waveguide optimised by a genetic algorithm coupled to a beam propagation method. This significantly improves the performance of the device and particularly the computed polarisation ratio, which reaches 21 dB. This InP-based photodetector is suitable for hybridisation on a silicon platform and is compatible with 10 Gbit/s operation.

Accurate analysis of power coupling between two arbitrarily ended dielectric slab waveguides by the boundary-element method.

The boundary integral equations that are called guided-mode extracted integral equations are applied to the investigation of the power-coupling-properties between two arbitrarily ended dielectric slab waveguides. The integral equations derived in this paper can be solved by the conventional boundary-element method. The reflection and coupling coefficients of the guided wave, as well as the scattering power, are calculated numerically for the case of incident TE guided-mode waves. The results presented are checked by the energy conservation law and the reciprocity theorem. Numerical results are presented for several geometries of coupling, including systems with three-layered symmetrical and asymmetrical slab waveguides.

Propagating modes in gain-guided optical fibers.

Optical fibers in which gain-guiding effects are significant or even dominant compared with conventional index guiding may become of practical interest for future high-power single-mode fiber lasers. I derive the propagation characteristics of symmetrical slab waveguides and cylindrical optical fibers having arbitrary amounts of mixed gain and index guiding, assuming a single uniform transverse profile for both the gain and the refractive-index steps. Optical fibers of this type are best characterized by using a complex-valued v-squared parameter in place of the real-valued v parameter commonly used to describe conventional index-guided optical fibers.

Nanofabrication of high refractive index contrast two-dimensional photonic crystal waveguides

We present the fabrication of high refractive index contrast two-dimensional photonic crystal (2D-PC) slab waveguides. 2D photonic crystal structures, consisting of a periodic array of holes in a GaAs matrix, are obtained by nanopatterning of epitaxially grown GaAs/AlGaAs heterostructures. Two different PC structures will be described in detail: (i) an asymmetric 2D-PC slab waveguide obtained by selective oxidation which transforms the Al-rich AlGaAs cladding layer underneath the PCs into aluminium oxide and (ii) a symmetric 2D-PC slab waveguide obtained by removing the oxide (free standing structure).

Radiation Properties of a Semi-Infinite Slab Waveguide for the Case of Odd Transverse Electric Guided Waves

We examine the radiation properties of an abruptly ended symmetric slab waveguide for the case of transverse electric (TE) guided modes with odd symmetry of the electric-field distribution by employing the integral equation method. This method converges very fast, especially in the case of small relative difference j 12 between the refractive indices of the core and cladding regions of the slab waveguide. The electric-field distribution at the terminal plane, the reflection coefficient of the first odd TE guided mode, and the far-field radiation pattern are computed. We present numerical results for several cases of abruptly ended waveguides and we examine the influence of the value of j 12 on the guided-mode reflectivity, on the electric-field distribution at the terminal plane, as well as on the angle of the maximum value (elevation angle) and on the beamwidth of the far-field radiation pattern.

Changes of dispersion relations for TE-mode in three-layer slab waveguides by the imaginary parts of refractive indices of cladding layers

We report the exact dispersion relations of TE-mode in three-layer slab waveguides whose cladding layers consist of optically amplifying or absorbing materials. It is shown from the dispersion relations that the mode cutoff manifests itself due to k even for the first mode of a symmetric slab waveguide. Additionally, for larger k, there appear two solutions of the quasi-propagation mode at the same n eff, whose region is under the refractive index of the cladding. One solution shows the more poorly confined mode and the other shows the more tightly confined mode with increasing n eff. Moreover, the former has a larger effective k than the latter, and, in this case, the mode cutoff is decided by it. On the other hand, the smaller the difference between the refractive indices of the guide layer and the cladding is, the smaller the linear region of the effective imaginary part as a function of k becomes. It shows that waveguides with more tightly confined the electric fields are more useful for the applications of the optical amplifier.

Theoretical study of the termination of the Fe 3O 4 (111) surface

Ab-initio periodic Hartree–Fock calculations for the structure of the (111) surface of Fe 3O 4 (magnetite) are presented. The slabs that are derived by an ideal bulk truncation that leaves one or two iron monolayers outside oxygen layers are found to be more stable than others since they preserve most of the coordination of the surface atoms. The stability of the slabs that represent the surface layers depends on the overall composition, specifically on the deviation from stoichiometry, and on the dipole moment perpendicular to the surface. The symmetrical slab with the layer sequence Fe 2O 4Fe 3O 4Fe 2, terminated on each side by iron bilayers, is the best compromise since symmetry insures the neutrality of the dipole moment. This slab is oxygen-deficient. The energetically preferred structure relaxes so that one of the two outermost iron layers moves toward the slab center plane, exchanging sequence with the oxygen layer. The slab with the layer sequence FeO 4Fe 3O 4Fe, which is also symmetric, is terminated by iron single monolayers, would represent an excessive oxidation of the iron atoms. This slab may be reduced by hydrogenation; it is then strongly stabilized and the vertical displacement of the oxygen atoms agrees with the structure determined by LEED (the LEED study would not have detected hydrogen).

Scheme for calculating the electronic structure of polar surfaces

A method for calculating the electronic structure at polar surfaces, based on a symmetric slab approach with column IV atoms at the center of the polar double slab, is introduced. Ab initio calculations with this method return very good results. Four different III-V (111) surfaces are compared, with corresponding results obtained by the pseudohydrogen termination method.

Free-space mode approximation for radiation modes of a slab waveguide and its application

Taking the symmetric slab waveguide as an example,we show that radiation modes of a weakly guiding planar optical waveguide can be approximated by the free space modes,their field expression and normalization constants are simple and understandable physically and can be obtained directly without any calculation.By applying this approximation,the far field and radiation loss calculations caused by random wall imperfections have been significantly simplified.