Workshop on Numerical Methods for Optical Nano Structures

Monday, July 10, 2006, 8:20-17:50, ETZ E6

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 break (free sandviches, snaks, drinks): Please send an email to christian.hafner@ifh.ee.ethz.ch before June 26.

Workshop 2005

Last update 12.6.2006

Preliminary Schedule

08:20-08:30 Opening remarks (R. Vahldieck)

08:30-10:20 Session A: Optical Antennas and Scanning Nearfield Optical Microscopy (Chair: V. Sandoghdar)

  1. 08:30-09:00 Lukas Novotny, Neil Anderson, Achim Hartschuh, Pascal Anger: Nanoscale Spectroscopy with Optical Antennas

  2. 09:00-09:20 Roman Kappeler, Daniel Erni, Lukas Novotny: Modeling of Nano-Antennas for SNOM Applications

  3. 09:20-09:40 R.Esteban, R.Vogelgesang and K.Kern: Towards realistic simulations in Apertureless Scanning Near Field Optical Microscopy

  4. 09:40-10:00 W. Nakagawa, L. Vaccaro, H. P. Herzig, Ch. Hafner: Analysis of metal-layer defects in microfabricated apertureless SNOM probes

  5. 10:00-10:20 F. Kaminski, M. Agio, V. Sandoghdar: Finite-Difference Time-Domain analysis of the radiative properties of single emitters coupled to metallic nanostructures

10:20:10:40: Coffee break

10:40-12:40 Session B: Boundary Methods and Surface Plasmons (Chair: Ch. Hafner)

  1. 10:40-11:20 D.Karkashadze, D. Kakulia, G. Ghvedashvili, K. Tavzarashvili, Ch. Hafner: MAS-based Computer Simulation of 3D Frequency-Selective Surfaces

  2. 11:20-12:00 J. Renger, S. Grafström, L. M. Eng: Surface plasmon polariton excitation at grooves in metals and metallic thin-film waveguides and propagation on nanopatterned interfaces

  3. 12:00-12:10 R. Kullock, J. Renger,  L.M. Eng: Near and far-field calculations of surface plasmon modes in single and arranged gold nanorods

  4. 12:10-12:20 Tino Göhler, Jan Renger, Jan Seidel, Lukas M. Eng: MMP Calculation of Surface Plasmon Propagation in Structured Metal-Insulator-Semiconductor Tunnelling Junctions

  5. 12:20-12:40 A. Mohammadi, M. Agio, V. Sandoghdar: Finite-Difference Time-Domain modelling of surface plasmons

12:40-13:30: Lunch break

13:30-15:20 Session C: Photonic Crystals and Metamaterials (Chair: D. Erni)

  1. 13:30-14:00 Jasmin Smajic, Cui Xudong, Christian Hafner, Rüdiger Vahldieck: Numerical Optimization of Photonic Crystal Structures

  2. 14:00-14:20 Friedhard Roemer, Bernd Witzigmann, Laurent Balet, Andrea Fiore: Modelling the Purcell Effect in Photonic Crystal Microcavities with a 3D FE Maxwell Solver

  3. 14:20-14:40 Nikolaj Moll, Asma Jebali , Stephan Gulde: Optimization of Resonators for All-Optical Switching

  4. 14:40-15:00 Glen Stark, Franck Robin, Daniel Erni, Robert Wüest, Andreas Christ, Heinz Jäckel, Niels Kuster: Finite-Difference Time-Domain Applications for Photonic Crystal Devices

  5. 15:00-15:20 Ping Ma, Franck Robin , Patric Strasser , Yuriy Fedoryshyn , Peter Cristea, Heinz Jäckel: Investigation of Realistic Photonic Bandgaps for TM-Polarized Light for All-Optical Switching

15:20-15:50 Coffee break

15:50-17:40 Session D: Numerical Techniques and Special Applications (Chair: J. Smajic)

  1. 15:50-16:20 Kurt Busch, Jens Niegemann, Martin Pototschnig, Lasha Tkeshelashvili: Higher-Order Time-Domain simulations of Maxwell's equations using Krylov-subspace methods 

  2. 16:20-16:40 Damir Pasalic, Rüdiger Vahldieck: Numerical modeling of traveling wave photodetectors operating under high power illumination

  3. 16:40-17:00 Arya Fallahi, Kiarash Zamani Aghaie, Amin Enayati, Mahmoud Shahabadi: Diffraction Analysis of Periodic Structures Using a Transmission Line Formulation: Principles and Applications

  4. 17:00-17:20 R. Vogelgesang: Linear plane waves in arbitrary tensorial media

  5. 17:20-17:40 Nicolas Guérin, Christian Hafner, Rüdiger Vahldieck: On the role of losses in Left-Handed Media

17:40-17:50 Closing remarks


Abstracts:

Session A: Optical Antennas and Scanning Nearfield Optical Microscopy 

08:30-09:00

Lukas Novotny, Neil Anderson, Achim Hartschuh, Pascal Anger

The Institute of Optics, University of Rochester, Rochester, NY 14627

Nanoscale Spectroscopy with Optical Antennas

Abstract download: Novotny.pdf
In optics, lenses and mirrors are used to redirect the wavefronts of propagating optical radiation. But because of diffraction, propagating radiation cannot be localized to dimensions much smaller than the optical wavelength. Borrowing concepts developed in the radiowave and microwave regime, we use antennas to localize optical radiation to length-scales much smaller than the wavelength of light.
We place a laser-irradiated optical antenna, such as a bare metal tip, a few nanometers above a sample surface in order to establish a localized optical interaction and a spectroscopic response (fluorescence, absorption, Raman scattering, .. ). A high-resolution, hyperspectral image of the sample surface is recorded by raster-scanning the antenna pixel-by-pixel over the sample surface and acquiring a spectrum for each image pixel.  This type of near-field optical spectroscopy has been applied to map out phonons and excitons in individual single-walled carbon nanotubes (SWNT) with a resolution of 10nm. The method is able to resolve defects in the tube structure as well as interactions with the local environment.
The proximity of the antenna influences the local light-matter interaction and affects the selection rules, the quantum yield, and momentum conservation. Using the fluorescence from a single molecule we are investigating these effects and we characterized the trade-off between fluorescence enhancement and fluorescence quenching as a function of the separation between the antenna and the molecule.

09:00-09:20

Roman Kappeler1,2, Daniel Erni1, Lukas Novotny2

1Laboratory for electromagnetic fields and microwave electronics, ETH Zurich, 8092 Zurich, Switzerland

2The Institute of Optics, University of Rochester, Rochester, NY 14627

Modeling of Nano-Antennas for SNOM Applications

Abstract download: Kappeler.pdf

09:20-09:40

R.Esteban, R.Vogelgesang and K.Kern

Max Planck Institute für Festkörperforschung, Heisenbergstrasse 1, 70569  Stuttgart, Germany

Towards realistic simulations in Apertureless Scanning Near Field Optical Microscopy

Apertureless Scanning Near Field Microscopy (SNOM) is a powerful technique to go beyond the optical resolution limit. By illuminating a sharp tip, for example from a non contact AFM, with a focused laser source, strong and very localized fields usually appear around the apex, which can be used to raster scan a sample and gain local information. To be able to differentiate between the near field components and the background, the obtained signal is often demodulated at the higher harmonics of the tip oscillation frequency. Lateral resolution in the order of 10 nm can be achieved. The interpretation of experimental results is however often complicated, and numerical simulations can help to better understand the measurements.
To approach the experimental conditions, realistic tips and substrates must be considered. Moreover, the actual scattered far field must be obtained and the demodulation scheme must be included. We find a multiple multipole boundary method (MAX-I) appropriate for our purposes. Using both spherical and long tips, we discuss the imaging process including demodulation for a realistic scenario consisting of a gold sphere inserted into a glass substrate. We discuss the effect of the tip length, inclusion depth and different experimental conditions, i.e. oscillation amplitude or tip-substrate distance.
The numerical convergence of the simulations is also discussed. In particular, the need to include the demodulation process considerably increases the required precision. In first approximation, demodulating at the nth harmonic can be approximated as obtaining the nth derivative of the fields with respect to the tip-substrate distance, i.e. it is very sensitive to fast field variations. Even small numerical errors at two closely situated simulated points can results in highly inaccurate predictions. We show that we are able to obtain a satisfying convergence.

09:40-10:00

W. Nakagawa*, L. Vaccaro*, H. P. Herzig*, Ch. Hafner**

* IMT, University of Neuchatel, 2007 Neuchatel, Switzerland

** Laboratory for electromagnetic fields and microwave electronics, ETH Zurich, 8092 Zurich, Switzerland

Analysis of metal-layer defects in microfabricated apertureless SNOM probes

The impact of structured and quasi-random defects in the metal coating of apertureless microfabricated SNOM probes on mode conversion in the probe and on the emitted optical fields is analyzed using numerical simulation.

10:00-10:20

F. Kaminski, M. Agio, V. Sandoghdar

Laboratory of Physical Chemistry, ETH Zurich, 8093 Zurich, Switzerland

Finite-Difference Time-Domain analysis of the radiative properties of single emitters coupled to metallic nanostructures

Abstract download: Kaminski.pdf

Session B: Boundary Methods and Surface Plasmons

10:40-11:20

D.Karkashadze*, D. Kakulia*, G. Ghvedashvili*, K. Tavzarashvili**, Ch. Hafner**

*LAE, Tbilisi State University, Georgia

** Laboratory for electromagnetic fields and microwave electronics, ETH Zurich, 8092 Zurich, Switzerland

MAS-based Computer Simulation of 3D Frequency-Selective Surfaces

The Method of Auxiliary Sources (MAS) is outlined and applied for solving  problems of electromagnetic diffraction at structures that are periodic in one or two directions. The reflection and transmission of different structures are analyzed.

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11:20-12:00

J. Renger, S. Grafström, L. M. Eng
Institute for Applied Physics / Photophysics, Technische Universität Dresden, D-01062 Dresden, Germany

Surface plasmon polariton excitation at grooves in metals and metallic thin-film waveguides and propagation on nanopatterned interfaces

Breaking the translational symmetry of surfaces by introducing a groove locally cancels the requirement of momentum conservation, thus enabling surface plasmon polaritons (SPP) excitation in metal structures by using simple plane waves. We investigate the SPP excitation efficiency for different groove geometries (width, height) as well as when using a finite number of such grooves in metal surface for plasmon coupling. Similarly, SPPs on metallic thin films can also be excited at discontinuities as inherently are manifested by grooves or slits. Our theoretical calculations using MaX-1 show that plasmon excitation and energy confinement either at the metal-air or the metal-dielectric support interface can be realized depending only on the groove width. Finally, we study the propagation of SPPs at nanopatterned metallic interfaces aiming at controlling the nanooptical properties by tailoring the metallic waveguide.

12:00-12:10

R. Kullock, J. Renger,  L.M. Eng

Institute of Applied Physics / Photophysics, Technische Universität Dresden, Dresden, Germany

Near and far-field calculations of surface plasmon modes in single and arranged gold nanorods

Metallic nanorods can show several different surface plasmon (SP) modes, depending on their material properties, size, geometry, and arrangement. Hence, they may be ideally used as nanoantennas hosting localized SP modes that can be excited with light. Recently, some near and far-field experiments with single nanorods were conducted and an analytic electrostatic modell was successfully applied to 'small' nanorods [1-4].
In this work a more fundamental understanding of SP resonaces in gold nanorods is initiated by applying the Multiple Multipole methode (MMP) to simulate the near-field optical properties and the extinction of such nanorods. We study the dependence of SP resonances on their size, aspect-ratio, and surrounding medium as well as the interaction between several nanorods.
[1] Chang, S.; Shih, C.; Chen, C.; Lai, W. & Wang, C.R.C. The Shape Transition of Gold Nanorods Langmuir, 1999, 15, 701-709
[2] Link, S.; Mohamed, M.B. & Sayed, M.A.E. Simulation of the Optical Absorption Spectra of Gold Nanorods as a Function of Their Aspect Ratio and the Effect of the Medium Dielectric Constant J. Phys. Chem. B, 1999, 103, 3073 -3077
[3] Imura, K.; Nagahara, T. & Okamoto, H. Near-field Optical Imaging of Plasmon Modes in Gold Nanorods. J Chem Phys, 2005, 122, 154701
[4] Payne, E.; Shuford, K.; Park, S.; Schatz, G. & Mirkin, C. Multipole Plasmon Resonances in Gold Nanorods. J Phys Chem B Condens Matter Mater Surf Interfaces Biophys, 2006, 110, 2150-2154

12:10-12:20

Tino Göhler, Jan Renger, Jan Seidel, Lukas M. Eng

Institute of Applied Physics / Photophysics, Technische Universität Dresden, D-01062 Dresden, Germany

MMP Calculation of Surface Plasmon Propagation in Structured Metal-Insulator-Semiconductor Tunnelling Junctions

Surface Plasmon Polaritons (SPPs) can be generated electrically both in Metal-Insulator-Metal (MIM) and in Metal-Insulator-Semiconductor (MIS) tunnel junctions through inelastic electron tunnelling [1-3]. The excitation and also the dispersion relation of such SPPs mostly depends on the insulator thickness, but on the local dielectric constant of such an area, too. Hence, it is important to understand how SPPs propagate inside such areas of different insulator thickness. We calculate the plasmon propagation in these regions using the Multiple Multipole method (MMP). As a first step we analyse the transmission and reflection of SPPs on boundaries between areas that have different optical constants. Additionally, the influence of a topographic step separating areas of different thickness is investigated.
[1]    Z. Szentirmay, Prog. Quant. Electr. 15, 175 (1991).
[2]    M.X. Wang, J. Yu, and C.X. Sun, Appl. Surf. Sci. 161, 9 (2000).
[3]    M.X. Wang, Y.W. Zhang, H.W. Cheng, C.X. Sun, Appl.
Surf. Sci. 173, 362  (2001)

12:20-12:40

A. Mohammadi, M. Agio, V. Sandoghdar

Laboratory of Physical Chemistry, ETH Zurich, 8093 Zurich, Switzerland

Finite-Difference Time-Domain modelling of surface plasmons

Abstract download: Mohammadi.pdf

Session C: Photonic Crystals and Metamaterials

13:30-14:00

Jasmin Smajic*, Cui Xudong**, Christian Hafner**, Rüdiger Vahldieck**

* ABB Switzerland, 5405 Baden-Dättwil, Switzerland

** Laboratory for electromagnetic fields and microwave electronics, ETH Zurich, 8092 Zurich, Switzerland

Numerical Optimization of Photonic Crystal Structures

Efficient numerical techniques for the optimization of defects and real-valued parameters in photonic crystal structures are outlined. These techniques include deterministic and stochastic algorithms working in real and binary search spaces. Since the numerical simulation of such structures may become time-consuming, highly efficient methods are required. Different strategies for speeding-up the search procedures are presented.

14:00-14:20

Friedhard Roemer, Bernd Witzigmann, Laurent Balet, Andrea Fiore

Integrated Systems Laboratory, ETH Zurich, 8092 Zurich, Switzerland

Modelling the Purcell Effect in Photonic Crystal Microcavities with a 3D FE Maxwell Solver

Abstract download: Roemer.pdf

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14:20-14:40

Nikolaj Moll, Asma Jebali , Stephan Gulde

IBM Research, Zurich Research Laboratory, Säumerstrasse 4, 8803 Rüschlikon, Switzerland

Optimization of Resonators for All-Optical Switching

General optimization arguments for resonator-based all-optical switching are discussed for several generic resonator geometries, namely Fabry-Perot resonators, circular gratings as well as micro-ring resonators. Analytical models allow a direct comparison of the different all-optical switch geometries. For the parameter range investigated, we find a clear advantage of resonators based on Bragg-type reflection over resonators based on total internal reflection (micro-ring resonators). Circular grating resonators and their in and out-coupling are studied more in detail. These resonators could lead to various photonic functionalities. Prominent examples thereof are spectral filters, light sources, lasers operated above threshold, electro-optic modulators (EOMs), and all-optical switches.

14:40-15:00

Glen Stark, Franck Robin, Daniel Erni, Robert Wüest, Andreas Christ, Heinz Jäckel, Niels Kuster
Electronics laboratory, ETH Zurich, 8092 Zurich, Switzerland

Finite-Difference Time-Domain Applications for Photonic Crystal Devices

The finite-difference time-domain (FDTD) algorithm is widely used to model the optical response of photonic crystal (PhC), plasmonic, and other nanophotonic devices. FDTD’s strength lies in its flexibility and extensibility. As PML aborbing boundary conditions and the total-field scattered-field formulation turned FDTD into a first class tool for scattering experiments, techniques are being developed to extends FDTD’s usefulness in the domain of nanophotonics. We discuss the use of FDTD for high resolution computing bandgaps of PhC structures, and introduce using the standing wave-meter to extend and improve the usefullness of 2D simulations for characterizing real devices.
 

15:00-15:20

Ping Ma, Franck Robin , Patric Strasser , Yuriy Fedoryshyn , Peter Cristea, Heinz Jäckel

Electronics laboratory, ETH Zurich, 8092 Zurich, Switzerland

Investigation of Realistic Photonic Bandgaps for TM-Polarized Light for All-Optical Switching

Nonlinear all-optical devices based on photonic crystals (PhCs) will benefit from strong light-matter interactions due to the increased light confinement, small group velocities and dispersionless pulse propagation. Intersubband (ISB) transitions in AlAsSb/InGaAs quantum wells are candidates of choice for ultra-fast relaxation time but only support TM-polarized light. Preliminary studies to envisage waveguiding in photonic crystal structures with photonic bandgaps for this polarization are presented. Novel PhC structures based on the honeycomb lattice geometry have been proposed and modeled both in two dimensions and in three dimensional slab strustures. The band diagrams show a relatively large band gap for TM-polzarized light and also the feasibility for waveguiding stuctures in all-optical switches. Our Cl2/Ar/N2 ICP etching process was applied to the etching of ISB materials and proved to be well-suited for the AlAsSb/InGaAs systems.

Session D: Numerical Techniques and Special Applications

15:50-16:20

Kurt Busch, Jens Niegemann, Martin Pototschnig, Lasha Tkeshelashvili

Institut für theoretische Festkörperphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany

Higher-Order Time-Domain simulations of Maxwell's equations using Krylov-subspace methods 

We present a highly efficient numerical method to solve Maxwell's equations in the time domain that employs a Krylov-subspace based opertor exponential technique. As compared to standard Finite-Difference Time-Domain (FDTD) methods, this approach allows much larger timesteps while at the same time the computations become more accurate. Owing to its generality, our approach can be extended to more complex problems such as those involving nonlinear optical material and situations where the electromagnetic fields are coupled to other physical systems.

16:20-16:40

Damir Pasalic, Rüdiger Vahldieck

Laboratory for electromagnetic fields and microwave electronics, ETH Zurich, 8092 Zurich, Switzerland

Numerical modeling of traveling wave photodetectors operating under high power illumination

The hybrid DD-TLM method is used for small and large signal analyses of the GaAs- and InGaAs-based TWPD structures. This new method combines semiconductor and full-wave EM analyses on the same computational platform. Thus, it takes into account effects of both carrier transport and EM propagation on the performance of the TWPD. A very good agreement between the theoretical results and measurements is observed. The field-screening effect, causing the saturation of the TWPD operating under high power illumination is investigated in details.

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16:40-17:00

Arya Fallahi, Kiarash Zamani Aghaie, Amin Enayati, Mahmoud Shahabadi

School of Electrical and Computer Engineering, University of Tehran, Kargar Ave. North, P.O. Box 14395-515, Tehran, Iran

Diffraction Analysis of Periodic Structures Using a Transmission Line Formulation: Principles and Applications

Using a linear combination of properly chosen spatial harmonics, we present a solution to Maxwell’s equations for the diffraction analysis of periodic structures. The proposed formulation is in a one-to-one correspondence with the well-known formulation governing the wave propagation along a multi-conductor transmission line. Like other modal methods, this approach can be applied to the modal analysis of a wide range of structures such as 2D and 3D photonic crystals, photonic crystal slabs including defects. Moreover, using this method, the incidence of a plane or Gaussian wave can also be analyzed so that one is able to predict the existence of the surface plasmons and negative refraction. In addition, one can take advantage of the transmission line formulation to analyze nonlinear periodic media.

17:00-17:20

R. Vogelgesang

Max Planck Institute für Festkörperforschung, Heisenbergstrasse 1, 70569  Stuttgart, Germany

Linear plane waves in arbitrary tensorial media

We present a complete, yet elegant algebraic analysis of the general planar wave solutions to the Maxwell equations for arbitrary tensorial media. No restrictions are made on the dielectric or permeability tensor: neither on their symmetry nor on their entries being positive, real or even complex. The dispersion relation between wavevector and frequency, the phase, group, and ray velocities, as well as the corresponding polarizations of the field vector amplitudes are derived. We discuss the occurrence of (electric as well as magnetic) longitudinal waves in the bulk.
These solutions are applied further to the case of two arbitrary linear media separated by a planar interface. For such systems we obtain the generalized Fresnel coefficients that relate the amplitudes of reflected and transmitted waves. We show how interface polariton modes occur as a special case and derive their dispersion relation in the plane.
This framework can be used for the analysis of any phenomena related to any linear media, including polarization effects, negative refraction, back propagation, surface waves, giant birefringence, etc. An extension to a generalized "Yeh formalism" for arbitrary anisotropic layered systems is straightforward. As an example for the use of the generalized Fresnel coefficients, we consider the possible magnetooptical contributions to the dielectric tensor in the various crystal classes, which can then be used as input to calculations of the reflection coefficients in magnetooptical Kerr effect measurements.

17:20-17:40

Nicolas Guérin, Christian Hafner, Rüdiger Vahldieck

Laboratory for electromagnetic fields and microwave electronics, ETH Zurich, 8092 Zurich, Switzerland

On the role of losses in Left-Handed Media

Contrarily to the right-handed materials (RHMs), the role of losses is very important for the left-handed material (LHM) behavior: as the loss-free case for LHM is not stable, a small variation of losses can drastically modify the expected properties of such a material.  Thus it is important to understand why LHMs are not stable and how it is possible to reduce this instability. First, the role of losses in LHMs will be investigated analytically and numerically, then some solutions will be explored in order to reduce efficiently the value of the losses in LHMs.