Jasmin Smajic 1, Christian Hafner 2, Dirk Baumann 2, Christophe Fumeaux 3, July 5, 2010 Simulations of Optical Plasmonic Nano-Antennas

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1 Jasmin Smajic 1, Christian Hafner 2, Dirk Baumann 2, Christophe Fumeaux 3, July 5, 2010 Simulations of Optical Plasmonic Nano-Antennas 1 ABB Switzerland Ltd. Corporate Research Dättwil Segelhofstrasse 1K, CH-5405 Baden-Dättwil, Switzerland jasmin.smajic@ch.abb.com 2 Swiss Federal Institute of Technology (ETH) Laboratory for EM Fields and Microwave Electronics Gloriastrasse 35, CH-8092 Zürich, Switzerland christian.hafner@ifh.ee.ethz.ch dbaumann@ifh.ee.ethz.ch 3 School of Electrical & Electronic Engineering The University of Adelaide 5005 Australia cfumeaux@eleceng.adelaide.edu.au January 12, 2011 Slide 1

2 Outline Introduction Geometric arrangement of the optical antenna Dispersive material description Numerical methods Multiple Multipole Program (MMP) Finite-Volume Time-Domain (FVTD) Finite Element Method (FEM) Resonance search Modes of the optical antenna Accuracy analysis Results comparison Conclusions January 12, 2011 Slide 2

3 Introduction Geometric Arrangement 70nm Plane wave excitation: E 60nm 2nm y z x Au H k Au January 12, 2011 Slide 3

4 Introduction Geometric Arrangement ABC ABC Plane wave excitation: E y z Au x Au January 12, 2011 Slide 4 ABC H k 500nm Air ABC

5 Introduction Dispersive Material Description Gold at optical and infrared wavelength range (300nm -1600nm) (Drude - Lorentz): Fitted (solid lines) versus measured (dashed lines) bulk gold permittivity. January 12, 2011 Slide 5

6 Numerical Methods Overview Domain Methods Boundary Methods Multiple Multipole Program (MMP) Finite Element Method (FEM) Finite-Volume Time-Domain (FVTD) January 12, 2011 Slide 6 Frequency Domain Time Domain

7 Numerical Methods Multiple Multipole Program (MMP) Silver: 3D ring expansion Air: 3D ring expansion Excitation: plane wave January 12, 2011 Slide 7

8 Numerical Methods Finite-Volume Time-Domain (FVTD) Tetrahedral volume mesh Excitation: Gaussian pulse plane wave (600nm 1600nm) 7 levels of adaptive time stepping: (dt i =2 i-1 dt 1 ), dt 1 = s. Simulation time: s ABC: PML Air gap element size ~1nm The CPU time of the entire simulation: ~180hours (Intel Core i7 CPU, 2.67 GHz), required RAM: GB The estimated CPU time with optimized code: ~90hours January 12, 2011 Slide 8 Very fine mesh of the 2nm air gap between the golden disks Gaussian pulse (a) and system response (b)

9 Numerical Methods Finite Element Method (FEM) Excitation: Plane wave (wavelength sweep: 600nm 1600nm) CPU time (single run) ~16 min. (4 CPU cores, Intel Xeon 2.5GHz, 32GB RAM) Number of tetrahedrons: Number of DOFs: Required RAM: 17.3GB (linear elements) Matrix solver: PARDISO ABC: Silver-Müller (1 st order) Air gap element size ~1nm Software: COMSOL Multiphysics January 12, 2011 Slide 9 5nm 3nm 1.5nm Mesh study: the air gap element size is a parameter. The element size of the air box (30nm) and gold (10nm) was kept constant.

10 Resonance Search Modes of the Optical Antenna Plane wave excitation: E P 4 H k P 4 P 3 P 2 P 1 P 3 P 1 The sensor points P 1, P 2, P 3, and P 4 are placed on the plane in the gap s middle and 5nm, 30nm, 50nm, and 65nm away from the disks axis, respectively. P 2 January 12, 2011 Slide 10

11 Resonance Search Modes of the Optical Antenna P 4 E, 1337nm E, 830.5nm January 12, 2011 Slide 11 E, 938nm

12 Resonance Search Accuracy Analysis =1337nm 5nm 3nm 1.5nm January 12, 2011 Slide 12 Mesh study: the air gap element size is a parameter. The element size of the air box (30nm) and gold disks (10nm) was kept constant.

13 Results Comparison FEM vs. FVTD P 4 FVTD: P 3 Air gap element size ~1nm 1 CPU core:.. CPU time ~ 90 hours P 2 P 1 FEM: Air gap element size ~1.5nm January 12, 2011 Slide 13 4 CPU cores: Intel Xeon 2.5GHz CPU time ~ 53 hours

14 Results Comparison FEM vs. MMP Model Based Parameter Estimation (MBPE) was used. E, 830.5nm January 12, 2011 Slide 14 In the MMP model the permittivity of gold is represented by measured data and not by our Drude-Lorentz model. This is the main reason for the difference between the results.

15 Conclusions The antenna under consideration is an example of very simple geometry that requires enormous computational effort for an accurate analysis The domain methods FVTD and FEM yielded the results of similar accuracy within similarly long CPU time (several days) The boundary method MMP does not require an air box and ABCs The resonance search within MMP was accelerated by using the Model Based Parameter Estimation (MBPE) January 12, 2011 Slide 15

16 January 12, 2011 Slide 16