Matthias Streiff

A comprehensive VCSEL device simulator

This paper deals with the design and implementation of a self-consistent electrothermooptical device simulator for vertical-cavity surface-emitting lasers (VCSELs). The model is based on the photon rate equation approach. For the bulk electrothermal transport, a thermodynamic model is employed in a rotationally symmetric body. Heterojunctions are modeled using a thermionic emission model and quantum wells are treated as scattering centers for carriers. The optical field is expanded into modes that are eigensolutions of the vectorial electromagnetic wave equation with an arbitrary, complex dielectric function. The open nature of the VCSEL cavity is treated by employing perfectly matched layers. The optical gain and absorption model in the quantum-well active region is based on Fermis Golden Rule. The subbands in the quantum well are determined by solving the stationary Schrodinger equation and using a parabolic band approximation for the electrons, light and heavy holes. The photon rate equation is fully integrated into the Newton-Raphson scheme used to solve the system of nonlinear device equations. An efficient numerical optical mode solver is used, that is based on a Jacobi-Davidson type iterative eigensolver. The latter combines a continuation scheme with preconditioner recycling. The practical relevance of the implementation is demonstrated with the simulation of a realistic etched-mesa VCSEL device.

Computation of optical modes in axisymmetric open cavity resonators

The computation of optical modes inside axisymmetric cavity resonators with a general spatial permittivity profile is a formidable computational task. In order to avoid spurious modes the vector Helmholtz equations are discretised by a mixed finite element approach. We formulate the method for first and second order Nedelec edge and Lagrange nodal elements. We discuss how to accurately compute the element matrices and solve the resulting large sparse complex symmetric eigenvalue problems. We validate our approach by three numerical examples that contain varying material parameters and absorbing boundary conditions (ABC).

Correction of the numerical reflection coefficient of the finite-difference time-domain method for efficient simulation of vertical-cavity surface-emitting lasers

Traditionally, one can calculate the update coefficients of the finite-difference time-domain algorithm at material interfaces by averaging the material properties of both sides, which leads to numerical inaccuracies of the reflection depending on the grid resolution. We propose a novel method to calculate the update coefficients such that the algorithm exactly fulfills the boundary conditions at a frequency of optimization, which allows a significant increase in grid spacing while limiting the numerical error. Using the proposed method, we reduced the computational expenses for the full-wave simulation of vertical-cavity surface-emitting lasers such that large structures can be treated without the need to exploit rotational symmetry. The method is demonstrated with the help of several examples.

Hardware implementation of a systolic antenna array signal processor based on CORDIC arithmetic

We present the practical hardware implementation of a systolic array for performing recursive least-squares minimisation via orthogonal matrix triangularisation. This is an extremely demanding task for high speed, real-time operation such as required in many modern adaptive antenna, radar, and sonar systems. Since the underlying Givens rotations can be efficiently computed by the CORDIC algorithm, we have implemented a dedicated CORDIC processor element (CPE) in an ASIC. All the required calculations are carried out by a network of these small and simple circuits, which are suitable for constructing a high performance systolic array, either based on MCM technology or as a macro-cell building block for a very highly integrated single chip solution. The design of an adaptive antenna signal processor is described in a top-down manner, from the proposed algorithm down to the bit-level details of the realised component.

A full three-dimensional microscopic simulation for vertical-cavity surface-emitting lasers

A three-dimensional simulation tool for vertical-cavity surface-emitting lasers is presented. The microscopic electronic equations are solved in all spatial directions, and a separation approach is used for the electromagnetic equations in frequency domain. Selected examples requiring a three-dimensional treatment are discussed, e.g. spatial hole burning for higher-order modal operation.

Analysis of the static and dynamic characteristics of 1310 nm vertical-cavity surface-emitting lasers

We present the static and dynamic simulation of a long-wavelength vertical-cavity surface-emitting laser (VCSEL) operating at around 1310 nm. The device consists of AlGaAs/GaAs distributed Bragg reflectors (DBRs) which are wafer-fused to both sides of the InP-based cavity with InAlGaAs quantum wells. A tunnel junction is used for current injection into the active region. The structure is simulated with a modified version of the commercial device simulator Synopsys Sentaurus Device. The fully-coupled two-dimensional electro-opto-thermal simulations use a microscopic physics-based model. Carrier transport is described by the continuity and Poisson equations and self-heating effects are accounted for by a thermodynamic equation. To obtain the opticalmodes, the wave equation is solved using a finite element approach. The optical gain model includes many-body effects. The equations are solved self-consistently. Calibrations of static (L-I, V-I curves) and dynamic characteristics (RIN) show good agreement with measurements at different temperatures. On this basis, the simulations reveal the critical factors that determine the modulation-current efficiency factor (MCEF) of the device.

Transfer function simulation of all-air-gap filters based on eigenmodes

The analysis of filter devices based on eigenmodes provides a facile and fast means to simulate the reflection and transmission function and shows good agreement with the measurements. The computing time is proportional to the number of eigenmodes, and the analysis yields an analytical expression for the transfer functions. The method can be easily applied on the analysis of geometries which are not rotationally symmetric. The coupling with different source fields of an arbitrary shape can be handled without recomputing the eigenmodes.

Study of substrate modes in a (Al,In)GaN/SiC semiconductor laser using finite element approach

Penetration of the waveguide mode into the substrate has some effects in Nitride-based semiconductor lasers grown on Silicon Carbide while it is usually not a problem in Arsenide-based devices. We observe oscillations in the red part of the measured gain spectrum of an (Al,In)GaN semiconductor lasers. These have been attributed to the presence of a standing wave in the substrate. We use a finite element approach to solve the Helmholtz equation and a complex notation for the dielectric function. Our intention is to estimate the effects of localized optical loss on the waveguide mode. In order to analyze measured oscillation in the Hakki-Paoli experiment we need to take into account optical loss in the P-doped region and in the substrate.

Microscopic opto-electro-thermal VCSEL device simulation

Optical modes of microcavities are determined by solving Maxwells vectorial wave equation subject to an open boundary taking radiation, diffraction effects, optical gain and absorption into account. Using a continuation scheme the optical problem is solved together with the electro-thermal device equations in a self-consistent fashion. The model is suitable for the analysis of a wide range of VCSEL device types with realistic device structures and sizes. Simulation results are compared to measurements for a multimode device. The practical use of the simulator as a computer aided design tool is demonstrated.