A two-dimensional photonic crystal slab mirror with silicon on insulator for wavelength 1.3 mu m

A concrete two-dimensional photonic crystal slab with triangular lattice used as a mirror for the light at wavelength 1.3 mu m with a silicon-on-insulator (Sol) substrate is designed by the three-dimensional plane wave expansion method. For TE-like modes, the bandgap in the F-K direction is from 1087nm to 1559nm. The central wavelength in the bandgap is about 1.3 mu m, hence the incident light at wavelength 1.3 mu m will be strongly reflected. Experimentally, such a photonic crystal slab is fabricated on an SOI substrate by the combination of EBL and ICP etching. The measurement of its transmission characteristics shows the bandgap edge in a longer wavelength is about 1540mn. The little discrepancy between the experimental data and the theoretical values is mainly due to the size discrepancy of the fabricated air holes.

Light-propagation characteristics of photonic crystal waveguide based on SOI materials at different polarized states

Straight single-line defect optical waveguides in photonic crystal slabs are designed by the plane wave expansion method and fabricated into silicon-on-insulator (SOI) wafer by 248-nm deep UV lithography. We present an efficient way to measure the light transmission spectrum of the photonic crystal waveguide (PhC WG) at given polarization states. By employing the Mueller/Stokes method, we measure and analyse the light propagation properties of the PhC WG at different polarized states. It is shown that experimental results are in agreement with the simulation results of the three-dimensional finite-difference-time-domain method.

Dipole mode photonic crystal point defect laser on InGaAsP/InP

In this paper, we focus on the dipole mode of the two-dimensional (2D) photonic crystal (PC) single point defect cavity (SPDC) lasers and we report the fabrication and characterization of 2D PC SPDC lasers with the structure of adjusted innermost air holes. The photonic band and cavity Q factors are simulated by means of plane wave expansion (PWE) and finite-difference time-domain (FDTD), respectively. In order to improve the optical confinement of the SPDC, the diameter of the innermost holes was adjusted. Different lasing performances are observed experimentally. The experimental results agree with the theoretical prediction very well. (c) 2006 Elsevier B.V. All rights reserved.

Electronic structures of GaAs/AlAs lateral superlattices

The electronic energy subbands and minigaps in lateral superlattices (LSLs) have been calculated by the plane-wave expansion method. The effect of the lateral modulation on the critical well width at which an indirect-direct (X-Gamma) optical transition occurs in the LSLs is investigated. Our theoretical results are in agreement with the available experimental data. Totally at variance with the previous variation calculational results, the minigaps between the first two subbands in LSLs, as functions of the modulation period, exhibit a maximum value at a specific length and disappear on decreasing the modulation period further. The modulations of several types of lateral potential are also evaluated; the indication is that the out-of-phase modulation on either side of the wells is the strongest while the in-phase modulation is the weakest. Our calculations also show that the effect of the difference between the effective masses of the electrons in the different materials on the subband structures is significant.

Experimental investigation of slow light phenomenon in photonic crystal waveguide line defect laser

The guide mode whose frequency locates in the band edge in photonic crystal single line defect waveguide has very low group velocity. So the confinement and gain of electromagnetic field in the band edge are strongly enhanced. Photonic crystal waveguide laser is fabricated and the slow light phenomenon is investigated. The laser is pumped by pulsed pumping light at 980nm whose duty ratio is 0.05%. The active layer in photonic crystal slab is InGaAsP multiple quantum well. Light is transimited by a photonic crystal chirp waveguide in one facet of the laser. Then the output light is coupled to a fiber and the character of laser is analysis by an optical spectrometer. It is found that single mode and multimode happens with different power of pumping light. Meanwhile the plane wave expansion and finite-difference time-domain methods are used to simulate the phenomenon of slow light. And the result of the experiment is compared with the theory which proves the slow light results in lasing oscillation.

Two-dimensional photonic crystals with a large photonic band gap designed by a rapid genetic algorithm

We used Plane Wave Expansion Method and a Rapid Genetic Algorithm to design two-dimensional photonic crystals with a large absolute band gap. A filling fraction controlling operator and Fourier transform data storage mechanism had been integrated into the genetic operators to get desired photonic crystals effectively and efficiently. Starting from randomly generated photonic crystals, the proposed RGA evolved toward the best objectives and yielded a square lattice photonic crystal with the band gap (defined as the gap to mid-gap ratio) as large as 13.25%. Furthermore, the evolutionary objective was modified and resulted in a satisfactory PC for better application to slab system.

Dipole mode photonic crystal point defect laser on InGaAsP/InP

In this paper, we focus on the dipole mode of the two-dimensional (2D) photonic crystal (PC) single point defect cavity (SPDC) lasers and we report the fabrication and characterization of 2D PC SPDC lasers with the structure of adjusted innermost air holes. The photonic band and cavity Q factors are simulated by means of plane wave expansion (PWE) and finite-difference time-domain (FDTD), respectively. In order to improve the optical confinement of the SPDC, the diameter of the innermost holes was adjusted. Different lasing performances are observed experimentally. The experimental results agree with the theoretical prediction very well. (c) 2006 Elsevier B.V. All rights reserved.

Theoretical design or single-polarization single-mode microstructured polymer optical fibres

Using the full-vector plane-wave expansion method, a kind of PMMA-based polarization-maintaining microstructured optical fibre (PM-mPOF) is theoretically studied. Dependence of the cutoff wavelengths of the two orthogonal polarization states (polarized along the two principal axes of PM-mPOF) on the structure parameters of the fibre is investigated in detail. A single-polarization single-mode (SPSM) PM-mPOF working in the visible region is designed and optimized with the result of the maximum SPSM bandwidth of 140 nm.

Spontaneous spin polarization and electron localization in constrained geometries: The Wigner transition in nanowires

The Wigner transition in a jellium model of cylindrical nanowires has been investigated by density-functional computations using the local spin-density approximation. A wide range of background densities rho(b) has been explored from the nearly ideal metallic regime (r(s)=[3/4 pi rho(b)](1/3)=1) to the high correlation limit (r(s)=100). Computations have been performed using an unconstrained plane wave expansion for the Kohn-Sham orbitals and a large simulation cell with up to 480 electrons. The electron and spin distributions retain the cylindrical symmetry of the Hamiltonian at high density, while electron localization and spin polarization arise nearly simultaneously in low-density wires (r(s)similar to 30). At sufficiently low density (r(s)>= 40), the ground-state electron distribution is the superposition of well defined and nearly disjoint droplets, whose charge and spin densities integrate almost exactly to one electron and 1/2 mu(B), respectively. Droplets are arranged on radial shells and define a distorted lattice whose structure is intermediate between bcc and fcc. Dislocations and grain boundaries are apparent in the droplets' configuration found by our simulations. Our computations aim at modeling the behavior of experimental low-carried density systems made of lightly doped semiconductor nanostructures or conducting polymers.

Transmission loss analysis of rectangular expansion chamber with arbitrary location of inlet/outlet by means of Green's functions

Transmission loss of a rectangular expansion chamber, the inlet and outlet of which are situated at arbitrary locations of the chamber, i.e., the side wall or the face of the chamber, are analyzed here based on the Green's function of a rectangular cavity with homogeneous boundary conditions. The rectangular chamber Green's function is expressed in terms of a finite number of rigid rectangular cavity mode shapes. The inlet and outlet ports are modeled as uniform velocity pistons. If the size of the piston is small compared to wavelength, then the plane wave excitation is a valid assumption. The velocity potential inside the chamber is expressed by superimposing the velocity potentials of two different configurations. The first configuration is a piston source at the inlet port and a rigid termination at the outlet, and the second one is a piston at the outlet with a rigid termination at the inlet. Pressure inside the chamber is derived from velocity potentials using linear momentum equation. The average pressure acting on the pistons at the inlet and outlet locations is estimated by integrating the acoustic pressure over the piston area in the two constituent configurations. The transfer matrix is derived from the average pressure values and thence the transmission loss is calculated. The results are verified against those in the literature where use has been made of modal expansions and also numerical models (FEM fluid). The transfer matrix formulation for yielding wall rectangular chambers has been derived incorporating the structural–acoustic coupling. Parametric studies are conducted for different inlet and outlet configurations, and the various phenomena occurring in the TL curves that cannot be explained by the classical plane wave theory, are discussed.

Effect of wall thickness on the end corrections of the extended inlet and outlet of a double-tuned expansion chamber

Simple expansion chambers, the simplest of the muffler configurations, have very limited practical application due to the presence of periodic troughs in the transmission loss spectrum which drastically lower the overall transmission loss of the muffler. Tuned extended inlet and outlet can be designed to nullify three-fourths of these troughs, making use of the plane wave theory. These cancellations would not occur unless one altered the geometric lengths for the extended tube in order to incorporate the effect of evanescent higher-order modes (multidimensional effect) through end corrections or lumped inertance approximation at the area discontinuities or junctions. End corrections of the extended inlet and outlet have been studied by several researchers. However the effect of wall thickness of the inlet/outlet duct on end correction has not been studied explicitly. This has significant effect on the tuning of an extended inlet/outlet expansion chamber. It is investigated here experimentally as well as numerically (through use of 3-D FEM software) for stationary medium. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

Multipole expansion of strongly focussed laser beams

Multipole expansion of an incident radiation field-that is, representation of the fields as sums of vector spherical wavefunctions-is essential for theoretical light scattering methods such as the T-matrix method and generalised Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but only approximations of radiation fields. This results from the standard laser beam representations being solutions to the paraxial scalar wave equation. We present an efficient method for determining the multipole representation of an arbitrary focussed beam. (C) 2003 Elsevier Science Ltd. All rights reserved.

A Direct Approach to the Problem of Diffraction by a Half-Plane under Mixed Boundary Conditions

A general direct technique of solving a mixed boundary value problem in the theory of diffraction by a semi-infinite plane is presented. Taking account of the correct edge-conditions, the unique solution of the problem is derived, by means of Jones' method in the theory of Wiener-Hopf technique, in the case of incident plane wave. The solution of the half-plane problem is found out in exact form. (The far-field is derived by the method of steepest descent.) It is observed that it is not the Wiener-Hopf technique which really needs any modification but a new technique is certainly required to handle the peculiar type of coupled integral equations which the Wiener-Hopf technique leads to. Eine allgemeine direkte Technik zur Lösung eines gemischten Randwertproblems in der Theorie der Beugung an einer halbunendlichen Ebene wird vorgestellt. Unter Berücksichtigung der korrekten Eckbedingungen wird mit der Methode von Jones aus der Theorie der Wiener-Hopf-Technik die eindeutige Lösung für den Fall der einfallenden ebenen Welle hergeleitet. Die Lösung des Halbebenenproblems wird in exakter Form angegeben. (Das Fernfeld wurde mit der Methode des steilsten Abstiegs bestimmt.) Es wurde bemerkt, daß es nicht die Wiener-Hopf-Technik ist, die wirklich irgend welcher Modifikationen bedurfte. Gewiß aber wird eine neue Technik zur Behandlung des besonderen Typs gekoppelter Integralgleichungen benötigt, auf die die Wiener-Hopf-Technik führt.

Diffraction of a cylindrical pulse by a half plane under mixed boundary conditions

The general time dependent source problem has been solved by the method of transforms (Laplace, Lebedev–Kontorovich in succession) and the solution is obtained in the form of an infinite series involving Legendre functions. The solutions in the case of harmonic time dependence and the incident plane wave have been derived from the above solution and are presented in the form of an infinite series. In the case of an incident plane wave, the series has been summed and the final solution involves an improper integral which behaves like a complementary error function for large values of the argument. Finally, the far field evaluation has been shown. The results are compared with those of Sommerfeld's half-plane diffraction problem with unmixed boundary conditions.