Workshop on Numerical Methods for Optical Nano Structures

Thursday, January 20, 2005, 11:00-17:30, ETF E1

Sponsored by OptETH and Fred Tischer Lecture Series

Organizer: Ch. Hafner, Computational Optics Group, IFH, ETH

No registration required for attending the workshop

Registration for the lunch: Please send an email to christian.hafner@ifh.ee.ethz.ch

Last update 21.1.2005

Schedule and Downloadable PDFs

11:00-11:20 M. Agio (mario.agio@phys.chem.ethz.ch), A.F. Koenderink, and V. Sandoghdar (ETH-NOG): The Finite-Difference Time-Domain codes at the Nano-Optics Group (PDF not available, please contact the first author for more information)

11:20-11:40 N. Moll (nim@zurich.ibm.com), A. Jebali, R. Harbers, S. Gulde, R. F. Mahrt (IBM, ETH-IFH): Photonic engineering of nonlinear-optical properties of hybrid materials for efficient ultra-fast optical switching (PDF not available, please contact the first author for more information)

11:40-12:00 A.F. Koenderink (femius.koenderink@phys.chem.ethz.ch), B. C. Buchler, and V. Sandoghdar (ETH-NOG): Controlled near-field coupling to optical resonances in photonic crystal membranes (PDF not available, please contact the first author for more information)

12:00-12:20 Wataru Nakagawa (wataru.nakagawa@unine.ch) (University of Neuchatel): Accurate Electromagnetic Modeling of Metal-Coated Scanning Near-field Optical Microscopy (SNOM) Probes (PDF not available, please contact the first author for more information)

12:20-12:40 Damir Pasalic (dpasalic@ifh.ee.ethz.ch) (ETH-IFH): A Rigorous Analysis of Traveling Wave Photodetectors

12:40-13:20 Lunch (offered by OptETH, Fred Tischer), Discussions

13:20-13:40 Bernd Witzigmann (bernd@iis.ee.ethz.ch), Matthias Streiff (ETH-IIS): Optical Modes in Microcavities PDF of full presentation

13:40-14:00 Jasmin Smajic (jasmin.smajic@ch.abb.com) (ABB): 3D simulation of photonic crystal structures using FEM PDF of full presentation

14:00-14:20 Christian Hafner (ETH-IFH) MMP Simulation of Optical Nanostructures PDF of full presentation

14:20-14:40 Kakhaber Tavzarashvili (kakhaber@ifh.ee.ethz.ch) (ETH-IFH): Photonic Crystal Simulations using the Method of Auxiliary Sources PDF of full presentation

14:40-15:00 Rik Harbers (rharbers@ifh.ee.ethz.ch), Niko Moll, Rainer Mahrt, Daniel Erni, Werner Bächtold (ETH-IFH, IBM): Enhancement of the Mode Coupling in Photonic Crystal-Based Organic Lasers (PDF will be available after publication of the results)

15:00-15:20 Break, Discussions

15:20-15:40 Lyudmyla Raguin-Illyashenko (mila.raguin@inf.ethz.ch), P. Arbenz (ETH-ICS): Boundary Integral Equation Method for the Numerical Modeling of Particles with Arbitrary Shape (PDF not available, please contact the first author for more information)

15:40-16:00 Bogdan Cranganu-Cretu (bogdan.cranganu-cretu@ch.abb.com) (ABB): Direct Boundary Integral Equation Method for Electromagnetic Scattering at Partly Coated Dielectric Objects PDF of full presentation

16:00-16:20 Lavinia Rogobete (lavinia.rogobete@phys.chem.ethz.ch), Vahid Sandoghdar, Carsten Henkel (ETH-NOG, University Potsdam): Radiative properties in a sub-wavelength environment characterized with boundary integral equations (PDF not available, please contact the first author for more information)

16:20-16:40 Nicolas Guérin (nguerin@ifh.ee.ethz.ch) (ETH-IFH): Optimization of metallic bi-periodic photonic crystals - Application to compact directive antennas PDF of full presentation

16:40-17:00 R. Hiptmair (hiptmair@sam.math.ethz.ch), P. Ledger (ETH-SAM): The Curse of Dispersion PDF of full presentation

17:00-17:30 Final Discussions


Abstracts:


11:00-11:20 M. Agio, A.F. Koenderink, and V. Sandoghdar (ETH-NOG)

The Finite-Difference Time-Domain codes at the Nano-Optics Group

The Finite-Difference Time-Domain (FD-TD) method is among the most widely used numerical techniques that solve Maxwell's equations. Its major feature is the ability to treat complex structures with a simple algorithm, but at the price of  large CPU and memory usage. Nevertheless, the continuous improvement of computers makes this method more and more affordable and of practical use. After reviewing the basics of the FD-TD approach, I will briefly present the two- and three-dimensional implementations available at the Nano-Optics Group, showing what kind of modeling we can do. Emphasis will be given on solutions for integrated optics, specifically photonic crystals and microcavities, and near-field optics.


11:20-11:40 N. Moll , A. Jebali, R. Harbers, S. Gulde, R. F. Mahrt (IBM, ETH-IFH)

Photonic engineering of nonlinear-optical properties of hybrid materials for efficient ultra-fast optical switching

All-optical switching is becoming a key point with the steady increase of bandwidth demand. Switching elements in hybrid organic/inorganic photonic nanostructures could lead to higher channel rates and the base for more space-, power- and cost-efficient routing devices. Combing organic films with high Kerr-nonlinearities and highly optimized resonant structures is a promising way to allow fast switching with low switching energies. Therefore, the design of resonator structures is optimized and solid knowledge about the deposition of organic films on structured inorganic substrates is necessary. Hybrid structures consisting of an inorganic micro-cavity with an organic material are investigated experimentally and theoretically.


11:40-12:00 A.F. Koenderink, B. C. Buchler, and V. Sandoghdar (ETH-NOG)

Controlled near-field coupling to optical resonances in photonic crystal membranes

Solid state optical resonators that confine light in ultrasmall volumes currently enjoy wide interest, partly rooted in cavity quantum electrodynamics and partly motivated by applications, including spontaneous emission control, low threshold lasers, optical switching and sensors. A particular advantage of photonic crystal microcavities is that one can achieve subwavelength cavity dimensions while keeping high quality factors of up to 10^5. In our group we use scanning probe techniques to realize controlled coupling between such optical resonances and nano-objects in the near-field. By performing Finite Difference Time Domain (FDTD) as well as perturbative analytic calculations, we demonstrate that near-field probes can be used to tune the resonance of a microcavity over a large range while maintaining a high quality factor. Furthermore, we have used FDTD simulations to assess the prospects for control of spontaneous emission rates by positioning emitters in the near field of photonic crystal membranes. Sizeable enhancement and inhibition of emission is possible, in qualitative agreement with two-dimensional plane-wave models.


12:00-12:20 Wataru Nakagawa (University of Neuchatel)

Accurate Electromagnetic Modeling of Metal-Coated Scanning Near-field Optical Microscopy (SNOM) Probes

We apply commercially available FITD electromagnetic modeling software to analyze optical propagation in microfabricated metal-coated SNOM probes. Specifically, we investigate the influence of the input optical polarization, the probe shape, and nanoscale defects in the metal layer on the emitted near field of the probe. Finally, we also consider the limitations imposed by computational workload on this type of analysis.


12:20-12:40 Damir Pasalic (ETH-IFH)

A Rigorous Analysis of Traveling Wave Photodetectors PDF of full presentation

Traveling wave photodetectors (TWPDs) are opto-electrical transducers, specially suitable for modern ultra-wide-band optical communication systems. The TWPDs’ ability to maintain high efficiency and broad bandwidth even under high-power optical illumination is important in microwave fiber optic links, especially since optical pre-amplification is utilized more widely. The analyses of traveling wave photodetectors, performed in the literature so far are mostly based on the equivalent circuit or transmission line models. However, these models are linked to the specific geometries of the photodetectors and often, do not compare well with the measurements. In this project, we have developed an efficient, hybrid method for rigorous analysis of TWPDs. The analysis is performed in two stages: a semiconductor and an electromagnetic (EM) stage. The semiconductor analysis is based on 2D drift diffusion (DD) method. It takes into account effects like bias voltage, carrier lifetime and drift velocity, and intensity of the applied optical power. As a result of the semiconductor simulation, we obtain current density at the cross-section of the photodetector. The obtained current density is than applied to the input of the full-wave EM simulator to obtain microwave characteristics of interest: bandwidth, RF velocity, fields, etc. The EM simulations are performed using the time-domain TLM method. The obtained results are compared with the available experimental data and a good agreement was observed.


13:20-13:40 Bernd Witzigmann, Matthias Streiff (ETH-IIS)

Optical Modes in Microcavities PDF of full presentation

Optical microcavities, which are wavelength-sized resonators, are used in semiconductor lasers, optical sensors and novel generation light-emitting diodes. Using a finite-element method, the modes in microcavities are determined by solving Maxwell's vectorial wave equation with open boundaries. The method takes into account diffraction and radiation of electromagnetic waves. In consequence, realistic microcavities without any restrictions regarding structure and size may be investigated.


13:40-14:00 Jasmin Smajic (ABB)

3D simulation of photonic crystal structures using FEM PDF of full presentation

A 3D approach for the electromagnetic simulation of photonic crystal structures using the vector finite element method (FEM) in frequency domain is presented. A short introduction to the numerical difficulties concerning the 3D simulation of photonic crystal structures using FEM is given, such as the problem of 3D PhC waveguide excitation and the selection of the type of the absorbing boundary condition. The limitations and basic problems of available commercial simulation tools using FEM (FEMLAB 3.0) are also mentioned. Matrix conditioning - mesh quality, memory requirements, direct and iterative linear solvers, preconditioning, and other important topics will be discussed and illustrated with various calculation examples including the very recent results of the analysis of 3D PhC waveguides, sharp bends and power dividers.


14:00-14:20 Christian Hafner (ETH-IFH)

MMP Simulation of Optical Nanostructures PDF of full presentation

The Multiple Multipole Program (MMP) is a semi-analytic boundary method that provides highly accurate and reliable results based on relatively small matrix equations. Additional techniques for solving eigenvalue problems, periodic symmetry problems, embedding solutions of simplified problems, and for speeding up sequences of computations are available. These techniques make MMP attractive for the detailed analysis of  many optical nano structures such as photonic crystals, gratings, waveguides, resonators, SNOM, etc. including strongly frequency-dependent, lossy materials that can be described by a complex permittivity and a complex permeability. Because of the high accuracy, MMP is also well suited to model optimizations performed with either deterministic or stochastic optimizers. After a short introduction to MMP, typical examples are presented.


14:20-14:40 Kakhaber Tavzarashvili (ETH-IFH)

Photonic Crystal Simulations using the Method of Auxiliary Sources PDF of full presentation

The Method of Auxiliary Sources (MAS) is used for the comprehensive study of doped Finite Photonic Crystals (FPC) made of biisotropic, chiral and other complex materials. The primitive cells of the FPC are supposed to have a given crystallographic structure with certain defects, such as extrinsic inclusions, vacancies, dislocations and so on. In this work, an efficient solution of wave propagation and scattering problems in such crystals is presented, including the treatment of eigenvalue and eigenfield problems and the FPC band structure calculation. A new program package to analyze and visualize the processes in the FPC is described and its possibilities for the design of FPC devices with desired properties are demonstrated.


14:40-15:00 Rik Harbers, Niko Moll, Rainer Mahrt, Daniel Erni, Werner Bächtold (ETH-IFH, IBM)

Enhancement of the Mode Coupling in Photonic Crystal-Based Organic Lasers

The mode coupling of organic photonic crystal lasers is enhanced by using a photonic crystal that consists of a thin layer of a high-index material. The high-index material increases the index contrast, the confinement in the waveguide and thus the mode coupling. Using such a photonic crystal gives rise to new design criteria. We investigate these criteria, and employ them in the design of an organic photonic crystal laser. Calculations of the coupling constant of the organic laser show that using high-index materials results in much higher coupling constants and thus smaller devices.


15:20-15:40 Lyudmyla Raguin-Illyashenko, P. Arbenz (ETH-ICS)

Boundary Integral Equation Method for the Numerical Modeling of Particles with Arbitrary Shape

To investigate certain properties of opto-electronic device components we propose a variant of the boundary integral equation method. Our approach arises from the fact that every component of the electromagnetic field can be expressed in terms of a Green's function. One of the key points is the recently developed global parameterization formulas for representing the particle contour in terms of fast convergent functional series. This approach provides a means to study individual particles as well as particle clusters in free space and with dielectric background for both TE and TM polarizations. We developed a numerical simulation tool based on these semi-analytical techniques that provides three primary advantages. First, it requires very little time and computer resources to obtain desired characteristics. Second, the obtained solutions are highly accurate due to taking into account geometrical singularities of the particle boundary and utilization of analytical regularization schemes for the numerical treatment of the integral equation singularities. Third, the numerical simulation tool allows essential flexibility to study the particles of almost arbitrary shape. The efficiency of the method is demonstrated by solving electro-magnetic field scattering and propagation problems for planar dielectric nanoparticles. In particular, we demonstrate that the near-field distribution and the far-field directivity strongly depend on the shape, orientation and morphology of the nanoparticle.


15:40-16:00 Bogdan Cranganu-Cretu (ABB)

Direct Boundary Integral Equation Method for Electromagnetic Scattering at Partly Coated Dielectric Objects PDF of full presentation

We present a new variational direct boundary integral equation approach for solving the scattering and transmission problem for dielectric objects partially coated with a PEC (Perfect Electric Conductor) layer. The main idea is to use to use the electromagnetic Calderon projector along with transmission conditions or the electromagnetic fields. This leads to a symmetric variational formulation, which lends itself to Galerkin discretization by means of divergence-conforming discrete surface currents (edge vectorial elements). Some numerical experiments are presented to confirm the efficacy of the new method.


16:00-16:20 Lavinia Rogobete, Vahid Sandoghdar, Carsten Henkel (ETH-NOG, University Potsdam)

Radiative properties in a sub-wavelength environment characterized with boundary integral equations

Our goal is to study the fluorescence dynamics, radiation pattern and field distributions of single emitters in the vicinity of nanoscopic systems. The problem is placed in the regime of Rayleigh scattering and quasistatic fields. In our numerical approach we transform the partial differential Maxwell equations with polarization source into boundary integral equations that we solve using a moment method. We treat a two-dimensional model (infinite in the z direction) and consider p-polarized dipoles located in the xy-plane. We validate the numerics by checking them against known analytical solutions. We show that the method is an accurate and elegant tool for solving emitters in the presence of dielectric or metallic objects as well as infinite interfaces.


16:20-16:40 Nicolas Guérin (ETH-IFH)

Optimization of metallic bi-periodic photonic crystals - Application to compact directive antennas PDF of full presentation

Three-dimensional electromagnetic problems require huge computing resources. One way to go through is to consider periodic structures in order to reduce the investigation domain to one cell of the structure. We describe here a numerical study for the diffraction by bi-periodic (in two directions) metallic photonic crystals. We use an integral method based on the Harrington formalism. The development of a fast bi-periodic Green's function allows us to reduce the unknowns to the first cell. We investigate then structures made of a source surrounded by a bi-periodic metallic photonic crystal above a ground plane. The field diffracted by the source is expanding in a plane wave packet using FFT, then we solve a grating problem for each plane wave. Theses structures are employed for the design of directive antennas in the domain of microwave telecommunications, these antennas are more compact than classical solutions and use a single feeding device. Many properties can be derived from the transmission properties of the grids in transmission illuminated by a plane wave. The calculation of the reflectivity for one grid enables an efficiently optimization of the parameters in order to obtain the suitable properties. The efficiency of antennas are analyzed and compared in terms of polarization, directivity and bandwidth. The results are confirmed by experiments in an anechoic chamber.


16:40-17:00 R. Hiptmair, P. Ledger (ETH-SAM)

The Curse of Dispersion PDF of full presentation

Whenever we discretize high frequency wave propagation problems in the frequency domain on the level of partial differential equations (i.e. the Helmholtz equation or vector wave equation), the numerical dispersion will be the main source of error. This cripples standard low order finite element approaches, because for decreasing wavelengths more and more points per wavelength are required for sufficient accuracy. We are going to review a few strategies for tackling the dispersion problem
1) The use of high order finite element schemes, 2) Plane wave modulation in the context of finite element schemes, and 3) Discontinuous Galerkin approaches with plane waves