Virtual EM Prototyping: From Microwaves to Optics

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1 Virtual EM Prototyping: From Microwaves to Optics Dr. Frank Demming, CST AG Dr. Avri Frenkel, Anafa Electromagnetic Solutions

2 Virtual EM Prototyping Efficient Maxwell Equations solvers has been developed, that can solve complex devices and subsystems Advances in both numerical algorithms and hardware systems allow High Performance Computing with Giga unknowns Virtual prototyping is becoming an engineering tool

3 Maxwell Solvers in Time Domain Several types of Time Domain Maxwell Solvers are presently available: FDTD Finite Difference Time Domain on Hexa mesh, approximate geometry FIT Finite Integration on Hexa mesh, good geometry approximation DGTD Discontinuous Galerkin Time Domain on Tetra mesh, good geometry approximation

4 Maxwell Solvers in Frequency Domain Several types of Maxwell Solvers in Frequency are presently available: FDFD Finite Difference Frequency Domain on Hexa mesh, low geometry approximation FEM Finite Elements on Tetra mesh, good geometry approximation IEFD Integral Equation Frequency Domain on Tria surface mesh, good geometry approximation

5 Discretization of Maxwell's Equations (I) Continuous material distribution (object with curved boundaries) FIT Hexahedral mesh with PBA material approximation for metallic objects Hexahedral mesh with simple "staircase" approximation FIT Hexahedral mesh with TST material approximation for metallic objects

6 Discretization of Maxwell's Equations (II) Regular and curved tetrahedral meshing

7 Microwaves Example (I)

8 Microwaves Example (II) Robust import Transient FIT solver Specific Absorption Rate evaluation

MPI Computing and GPU Computing System: 8 compute nodes with Dual Intel Xeon

9 Microwaves Example (IV) RCS Calculation 1.1 billion mesh cells, Transient FIT solver Electric field at 900 MHz Combined MPI Computing and GPU Computing System: 8 compute nodes with Dual Intel Xeon E5530, 2.27 GHz, Ethernet interconnect GPU hardware: 2x Tesla C1060 per compute node. Simulation time (total time): 15h 9m

10 What about higher frequencies? The full-wave 3D Maxwell Solvers have no inherent limitation on frequency as long as: Passive structures are simulated Materials properties are known ( nonhomogeneous, dispersive, non-reciprocal ) Problem size can be handled by the hardware The problem is classic (non quantum)

11 The transient solver is broadband dispersive materials: fit required. nth order Debye/Lorentz fit more accurate than simple Debye or Lorentz models. Dispersive Materials 0 ' ' 1 ) ( j j N i i r i 0 ' ' 1 ) ( j r 2 ' 2 1 ' ' 1 1 ) ( 1 j j r 1 st order Debye model: 2 nd order Debye (Lorentz) model: n th order Debye/Lorentz model:

12 FR-4 Dispersion in microwaves FR-4 is a very widely used dielectric substrate with substantial losses. An nth order dielectric dispersion fit can be made to accurately represent the material properties. Djordjević et al., 2001

13 Transmission Differential Line S 21 inaccurate for 1 st order fit, but perfect match for 10 th order fit.

14 Broadband Filter Excellent correlation between simulated (Transient FIT solver) and measured results by Intel

15 Periodic Structures There are many 1D & 2D periodic structures like optical grids, frequency selective surfaces, photonic bandgap structures & metamaterials. Frequency domain solvers can solve efficiently a single unit with periodic boundary conditions, instead of a very large array

16 THz Photonic Bandgap Example Consider a 2D PBG crystal consisting of a square lattice of GaAs rods of radius r and with a periodicity a. r a a ε r = 12.94; a = 0.58 μm; r = 0.18a

For given propagation factors k_x=phasex/a k_y=phasey/a the bands frequencies are

17 phasey Periodic Boundaries We can determine the band gap for surface waves by plotting the dispersion diagram over the irreducible Brillouin zone (Γ-X-M-Γ). For given propagation factors k_x=phasex/a k_y=phasey/a the bands frequencies are determined by the Eigenmode Solver. electric boundaries at ±z let us consider TM mode M Γ X phasex

18 frequency in THz phase shift 2 PBG dispersion diagram band gap M Γ X phase shift 1 Γ X M Γ

19 PBG components 90 degrees bent S 21 1 at 200 THz

20 Plate thickness=1mm Period=0.68mm Hole radius=0.24, 0.26 mm THz Filter Example

21 Transmission in Oblique Incidence Filter performance deteriorates As a function of incidence angle

22 Filter Plate Experiment Plate has 16X16 holes, radius 0.24mm 15 Mcells using symmetry Transient FIT solver

23 Current on the Filter Plate Considerations: a. Plate is in the near field of the horn at 5mm distance b. Effective angles of incidence are not normal

24 Transmission Spectrum The experiment gives a narrower filter response, because the filter deteriorates beyond 15 deg incidence

25 THz Window Example Periodic grid of sub-resonant scatterers Dielectric constant 2.94 Total thickness mm => 1.5 wavelength at 0.35 THz Metal via : diameter =0.11mm height=0.127mm, periodicity= 0.2mm

26 Transmission Dielectric vs. Metallodielectric Window

27 Reflection Dielectric vs. Metallodielectric Window

28 Transmission Oblique Incidence

29 Radome Plate Experiment 54X54 unit-cells plate 15.6 Mcells, Transient FIT solver

30 Transmission Spectrum Radome plate performs well, despite the large angles of incidence

31 Optics : Terminology Differences Terminologies are slightly different: Optical Engineer: Electrical Engineer: - n and k - wavelength [ nm] - Transmission & Reflection coefficients - and - frequency [ THz] - S-parameters

32 Terminology Translation However, translation is simple: / 2 ) (1 2 2 c f nk k n i n k i n n , 11, ) cos( ) cos( S n n t S r p s p s

33 Dielectric Guiding structures

34 Dielectric Guiding Structures Dispersion Curves

35 Dielectric Micro-Ring Coupler Transient Solver, memory efficient algorithm for electrical large problems

mλ -20 Energy is stored in the ring Signal is suppressed in the through port

36 Transmission [db] Transient Solver: MICRO RING RESONATOR Input r SILICON-ON-INSULATOR Output 0-10 Input Output At resonance : L eff 2π r n eff mλ -20 Energy is stored in the ring Signal is suppressed in the through port Model volume: 10 million meshcells resonance peaks Frequency [THz]

37 Metals at Optical Frequencies Au Ag Negative eps & mue are supported W

38 Plasmon Generation

39 Plasmonic Grating -Periodic Dependence on grating period

40 Plasmonic Grating to Sheet Transition

41 How do we solve big models? Technology is advancing in : Numerical algorithms Hardware speed and capacity Network communication speed Tight development of software and hardware

42 Hardware Based Acceleration Techniques Multithreading GPU Computing Distributed Computing MPI Computing

43 Amazing acceleration of the solver loop GPU Computing Benefit and Limitation Maximum problem size determined by the amount of memory on the GPU hardware and features/material models used. The features which need the largest amount of memory on the GPU are: dispersive materials lossy metal open boundaries Note: Tesla 20 hardware is about % faster than Tesla 10.

Scaled Speedup Infiniband vs GigaEthernet Cluster

Infiniband is especially important for GPU accelerated

The interconnect becomes the bottleneck if cluster nodes are

5 Scaled Speedup per Time Step (2 GPUs per Node) Without a

44 Scaled Speedup Infiniband vs GigaEthernet Cluster interconnect GPU accelerated cluster system GPU hardware Infiniband is especially important for GPU accelerated clusters! The interconnect becomes the bottleneck if cluster nodes are very fast. 2.5 Scaled Speedup per Time Step (2 GPUs per Node) Without a high performance interconnect with low latency scalability is completely lost for very fast (i.e. GPU accelerated) cluster nodes Ethernet Infiniband (SDR) Number of Nodes

45 Summary General Maxwell Solvers in Time Domain and in Frequency Domain can be applied from microwaves through the THz frequencies up to Optics, if materials properties are well known. Virtual EM prototyping of small devices as well as large subsystems is available with the growing power of High Performance Computing

CHAPTER 2 MICROSTRIP REFLECTARRAY ANTENNA AND PERFORMANCE EVALUATION

43 CHAPTER 2 MICROSTRIP REFLECTARRAY ANTENNA AND PERFORMANCE EVALUATION 2.1 INTRODUCTION This work begins with design of reflectarrays with conventional patches as unit cells for operation at Ku Band in