Virtual EM Prototyping: From Microwaves to Optics Dr. Frank Demming, CST AG Dr. Avri Frenkel, Anafa Electromagnetic Solutions
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
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
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
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
Discretization of Maxwell's Equations (II) Regular and curved tetrahedral meshing
Microwaves Example (I)
Microwaves Example (II) Robust import Transient FIT solver Specific Absorption Rate evaluation
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
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)
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:
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
Transmission Differential Line S 21 inaccurate for 1 st order fit, but perfect match for 10 th order fit.
Broadband Filter Excellent correlation between simulated (Transient FIT solver) and measured results by Intel
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
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
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
frequency in THz phase shift 2 PBG dispersion diagram band gap M Γ X phase shift 1 Γ X M Γ
PBG components 90 degrees bent S 21 1 at 200 THz
Plate thickness=1mm Period=0.68mm Hole radius=0.24, 0.26 mm THz Filter Example
Transmission in Oblique Incidence Filter performance deteriorates As a function of incidence angle
Filter Plate Experiment Plate has 16X16 holes, radius 0.24mm 15 Mcells using symmetry Transient FIT solver
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
Transmission Spectrum The experiment gives a narrower filter response, because the filter deteriorates beyond 15 deg incidence
THz Window Example Periodic grid of sub-resonant scatterers Dielectric constant 2.94 Total thickness 0.762 mm => 1.5 wavelength at 0.35 THz Metal via : diameter =0.11mm height=0.127mm, periodicity= 0.2mm
Transmission Dielectric vs. Metallodielectric Window
Reflection Dielectric vs. Metallodielectric Window
Transmission Oblique Incidence
Radome Plate Experiment 54X54 unit-cells plate 15.6 Mcells, Transient FIT solver
Transmission Spectrum Radome plate performs well, despite the large angles of incidence
Optics : Terminology Differences Terminologies are slightly different: Optical Engineer: Electrical Engineer: - n and k - wavelength [380 750 nm] - Transmission & Reflection coefficients - and - frequency [400 790 THz] - S-parameters
Terminology Translation However, translation is simple: / 2 ) (1 2 2 c f nk k n i n k i n n 21 2 1, 11, ) cos( ) cos( S n n t S r p s p s
Dielectric Guiding structures
Dielectric Guiding Structures Dispersion Curves
Dielectric Micro-Ring Coupler Transient Solver, memory efficient algorithm for electrical large problems
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 -30-40 resonance peaks 198 199 200 201 202 Frequency [THz]
Metals at Optical Frequencies Au Ag Negative eps & mue are supported W
Plasmon Generation
Plasmonic Grating -Periodic Dependence on grating period
Plasmonic Grating to Sheet Transition
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
Hardware Based Acceleration Techniques Multithreading GPU Computing Distributed Computing MPI Computing
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 20..70% faster than Tesla 10.
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. 2 1.5 1 Ethernet Infiniband (SDR) 1 2 3 4 Number of Nodes
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