Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Hybrid FEM/BEM modeling of finite-sized photonic crystals for semiconductor laser beams

by M. Durán and M. Guarini and C. Jerez-Hanckes

(Report number 2009-25)

Abstract
We propose a 2-D finite-element/boundary-element hybrid method for calculating the spatial distribution and frequency response of electromagnetic waves coming from a semiconductor laser when interacting with a finite-sized photonic crystal. We thus provide a flexible tool for the design of novel optical and microwave devices, among other applications. In opposition to current methodologies, we simultaneously take into account the laser modes, the finiteness of the crystal, and the unboundedness of the isotropic medium in which the crystal is embedded. At the laser output, instead of approximating reflected and transmitted beams by plane waves, we use the more realistic Hermite-Gauss functions. In the isotropic medium, we set an artificial boundary encircling the crystal and define exterior and interior domains. Radiating solutions for the scattered far-field over the exterior are derived analytically through a series of Hankel polynomials. The interior domain is described by a finite-element formulation coupled with Dirichlet-to-Neumann maps enforcing laser and far-field behaviors. Results and error analyses are provided in view of future improvements.

Keywords:

@Techreport{DGJ09_48,
  author = {M. Durán and M. Guarini and C. Jerez-Hanckes},
  title = {Hybrid FEM/BEM modeling of finite-sized photonic crystals for semiconductor laser beams},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-25},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-25.pdf },
  year = {2009}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).