Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries

The influence of imperfect boundaries on the mode quality factor is investigated for equilateral-triangle-resonator (ETR) semiconductor microlasers by the finite difference time domain technique and the Pade approximation with Baker's algorithm. For 2-D ETR with a refractive index of 3.2 and side length of 5 mum, the confined modes can still have a quality factor of about 1000 as small triangles with side length of 1 mum are cut from the vertices of the ETR. For a deformed 5 mum ETR with round vertices and curve sides, the simulated mode quality factors are comparable to the measured results.

Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Pade approximation

The mode wavelength and quality factor (Q-factor) for resonant modes in optical equilateral triangle resonators (ETR's) are calculated by the finite-difference time-domain (FDTD) technique and the Pade approximation, For an ETR with the side length of 3 mu m and the refractive index of 3.2, we get the mode wavelength interval of about 70 nm and the Q-factor of the fundamental mode over 10(3), The results show that the ETR is suitable to realize single-mode operation, and that the radiation loss in the corner regions of ETR is rather low, In addition, the numerical results of the mode wavelength agree very well with our analytical formula.

Mode characteristics for equilateral triangle optical resonators

Mode characteristics of equilateral triangle resonators (ETRs) are analyzed based on the symmetry operation of the point group C-3v. The results show that doubly degenerate eigenstates can be reduced to the A(1) and A(2) representations of C-3v, if the longitudinal mode number is a multiple of 6; otherwise, they form the E irreducible representation Of C-3v. And the one-period length for the mode light ray is half of the perimeter of the ETR. Mode Q-factors are calculated by the finite-difference time-domain (FDTD) technique and compared with those calculated from far-field emission based on the analytical near-field pattern for TE and TM modes. The results show that the far-field emission based on the analytical field distribution can be used to estimate the mode Q-factor, especially for TM modes. FDTD numerical results also show that Q-factor of TE modes reaches maximum value as the longitudinal mode number is a multiple of 7. In addition, photoluminescence spectra and measured Q-factors are presented for fabricated ETR with side lengths of 20 and 30 mu m, and the mode wavelength intervals are compared with the analytical results.

Investigation on multiple-port microcylinder lasers based on coupled modes

Microcylinder resonators with multiple ports connected to waveguides are investigated by 2D finite-difference time-domain (FDTD) simulation for realizing microlasers with multiple outputs. For a 10 mu m radius microcylinder with a refractive index of 3.2 and three 2 mu m wide waveguides, confined mode at the wavelength of 1542.3 nm can have a mode Q factor of 6.7 x 10(4) and an output coupling efficiency of 0.76. AlGaInAs/InP microcylinder lasers with a radius of 10 mu m and a 2 mu m wide output waveguide are fabricated by planar processing techniques. Continuous-wave electrically injected operation is realized with a threshold current of 4 mA at room temperature, and the jumps of output power are observed accompanying a lasing mode transformation.

Mode characteristics of semiconductor equilateral triangle microcavities with side length of 5-20 mu m

Semiconductor equilateral triangle microresonators (ETRs) with side length of 5, 10, and 20 mum are fabricated by the two-step inductively coupled plasma (ICP) etching technique. The mode properties of fabricated InGaAsP ETRs are investigated experimentally by photoluminescence (PL) with the pumping source of a 980-nm semiconductor laser and distinct peaks are observed in the measured PL spectra. The wavelength spacings of the distinct peaks agree very well with the theoretical longitudinal mode intervals of the fundamental transverse modes in the ETRs, which verifies that the distinct peaks are corresponding to the enhancement of resonant modes. The mode quality factors are calculated from the width of the resonant peaks of the PL spectra, which are about 100 for the ETR with side length of 20 mum.

Analysis of equilateral triangle semiconductor microlasers with rough sidewalls

The mode frequencies and quality factors are calculated for the equilateral triangle semiconductor microlasers with sinusoidal and random Gaussian sidewalls. The results show that the modes can still have high Q-factors.

Nodal domains of the equilateral triangle billiard

We characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula. We believe that the results belong generically to non-separable systems, thus extending the previous works which are concentrated on separable and chaotic systems.

Fixed-orientation equilateral triangle matching of point sets

Given a point set P and a class C of geometric objects, G(C)(P) is a geometric graph with vertex set P such that any two vertices p and q are adjacent if and only if there is some C is an element of C containing both p and q but no other points from P. We study G(del)(P) graphs where del is the class of downward equilateral triangles (i.e., equilateral triangles with one of their sides parallel to the x-axis and the corner opposite to this side below that side). For point sets in general position, these graphs have been shown to be equivalent to half-Theta(6) graphs and TD-Delaunay graphs. The main result in our paper is that for point sets P in general position, G(del)(P) always contains a matching of size at least vertical bar P vertical bar-1/3] and this bound is tight. We also give some structural properties of G(star)(P) graphs, where is the class which contains both upward and downward equilateral triangles. We show that for point sets in general position, the block cut point graph of G(star)(P) is simply a path. Through the equivalence of G(star)(P) graphs with Theta(6) graphs, we also derive that any Theta(6) graph can have at most 5n-11 edges, for point sets in general position. (C) 2013 Elsevier B.V. All rights reserved.

Conductance calculation of a long tube with equilateral triangle cross section

Using the stratified gas flow model for calculating the conductance of long tubes with constant cross section, an analytical expression for calculating the conductance of along tube with equilateral triangle cross section has been derived. The formula given is applicable to the full pressure range. A minimum in the conductance in the intermediate flow state is shown. 2002 American vacuum Society.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 mu m and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 mu m. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 mu m. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor. (C) 2009 Optical Society of America

Experimental study of mode characteristics for equilateral triangle semiconductor microcavities

Equilateral triangle semiconductor microcavities with tensile-strained InGaAsP multi-quantum-well asthe active region are fabricated by the inductively coupled plasma (ICP) etching technique. The modecharacteristics of the fabricated microcavities are investigated by photoluminescence, and enhanced peaksof the photoluminescence spectra corresponding to the fundamental transverse modes are observed formicrocavities with side lengths of 5 and 10 μm. The mode wavelength spacings measured experimentallycoincide very well with those obtained by the theoretical formulae.

A semiconductor laser suitably fabricated by planar technology

The semiconductor microlasers with an equilateral triangle resonator which can be fabricated by dry etching technique from the laser wafer of the edge emitting laser, are analyzed by FDTD technique and rate equations. The results show that ETR microlaser is suitable to realize single mode operation. By connecting an output waveguide to one of the vertices of the ETR, we still can get the confined modes with high quality factors. The EM microlasers are potential light sources for photonic integrated circuits.

Mode Simulation for Midinfrared Microsquare Resonators With Sloped Sidewalls and Confined Metals

EQUILATERAL-TRIANGLE; MU-M; LASERS; MICROLASERS; MICRODISK Abstract: Mode characteristics for midinfrared microsquare resonators with sloped sidewalls and confined metal layers are investigated by finite-difference time-domain (FDTD) techniques. For a microsquare with a side length of 10 mu m, the mode quality (Q)-factors of 8329, 4772, and 2053 are obtained for TM5,7 mode at wavelength 7.1 mu m by three-dimensional FDTD simulations, as the tilting angles of the side walls are 90 degrees, 88 degrees, and 86 degrees, respectively. Furthermore, microsquare resonators laterally surrounded by SiO2 and metal layers are investigated by the two-dimensional FDTD technique for the metal layers of Au, Ti-Au, Ag-Au, and Ti-Ag-Au, respectively.

Evoluções nas modelagens de substratos artificiais (metamateriais) com práticas experimentais em antenas de microfita

Esse trabalho tem como objetivo apresentar configurações de substratos dielétricos inovadores projetados e fabricados a partir de estruturas metamateriais. Para isso, são avaliados diversos fatores que podem influenciar no seu desempenho. A princípio, foi feito um levantamento bibliográfico a respeito dos temas, que estão relacionados com as pesquisas sobre: materiais dielétricos, metamateriais e interferometria óptica. São estudados, pesquisados e desenvolvidos dois projetos experimentais propostos, que comprovam a eficiência de métodos, para se alcançar a permeabilidade magnética negativa na formação de metamateriais. O primeiro projeto é a produção de uma nova estrutura, com u anel ressoador triangular equilateral (Split Equilateral Triangle Resonator - SETR). O segundo projeto: aplica os princípios da interferometria óptica, especialmente, com o interferômetro de Fabry-Perot. Técnicas para obtenção dos dispositivos que complementam a placa metamaterial como substrato foram pesquisadas na literatura e exemplificadas principalmente por meio de simulações e medições. Foram feitas comparações, simulações e medições de estruturas convencionais e especiais. As experiências se concentram nas evoluções e modelagens de substratos metamateriais com aplicações em antenas de microfita. As melhorias de alguns parâmetros de desempenho de antenas também são relatadas. As simulações das antenas foram feitas nos programas computacionais comerciais. Os resultados medidos foram obtidos com um analisador vetorial de redes da Rhode and Schwarz modelo ZVB 14.

Evoluções nas modelagens de substratos artificiais (metamateriais) com práticas experimentais em antenas de microfita

Esse trabalho tem como objetivo apresentar configurações de substratos dielétricos inovadores projetados e fabricados a partir de estruturas metamateriais. Para isso, são avaliados diversos fatores que podem influenciar no seu desempenho. A princípio, foi feito um levantamento bibliográfico a respeito dos temas, que estão relacionados com as pesquisas sobre: materiais dielétricos, metamateriais e interferometria óptica. São estudados, pesquisados e desenvolvidos dois projetos experimentais propostos, que comprovam a eficiência de métodos, para se alcançar a permeabilidade magnética negativa na formação de metamateriais. O primeiro projeto é a produção de uma nova estrutura, com u anel ressoador triangular equilateral (Split Equilateral Triangle Resonator - SETR). O segundo projeto: aplica os princípios da interferometria óptica, especialmente, com o interferômetro de Fabry-Perot. Técnicas para obtenção dos dispositivos que complementam a placa metamaterial como substrato foram pesquisadas na literatura e exemplificadas principalmente por meio de simulações e medições. Foram feitas comparações, simulações e medições de estruturas convencionais e especiais. As experiências se concentram nas evoluções e modelagens de substratos metamateriais com aplicações em antenas de microfita. As melhorias de alguns parâmetros de desempenho de antenas também são relatadas. As simulações das antenas foram feitas nos programas computacionais comerciais. Os resultados medidos foram obtidos com um analisador vetorial de redes da Rhode and Schwarz modelo ZVB 14.