The Broadband Fixed-Angle Source Technique (BFAST) LUMERICAL SOLUTIONS INC. 1
Outline Introduction Lumerical s simulation products Simulation of periodic structures The new Broadband Fixed-Angle Source Technique (BFAST) Details on BFAST Limitations Basic example: transmission through a dielectric stack Performance considerations Application Examples Lamellar plasmonic grating (2D) Plasmonic solar cell (3D) Summary 2
Introduction 3
Our Products System/Circuit Level INTERCONNECT PHOTONIC INTEGRATED CIRCUIT SIMULATOR FDTD Solutions NANOPHOTONIC SOLVER (2D/3D) MODE Solutions WAVEGUIDE DESIGN ENVIRONMENT spatial distribution of charge carriers optical generation rate of charge carriers DEVICE CHARGE TRANSPORT SOLVER (2D/3D) Component Level: Optical Component Level: Electrical 4
Simulation of Periodic Structures with FDTD Large class of systems in photonics is periodic Gratings Photonics crystals Meta-materials CMOS sensor arrays and solar cells 5
Reduction to a unit cell Example of a basic grating, excited by a plane-wave Problem can be reduced to simulation of a single unit cell Periodic boundary conditions 6
Changing the angle of incidence Tilting the plane-wave source breaks the symmetry Bloch s theorem: E x = E x + a e i k a k Bloch boundary conditions k https://en.wikipedia.org/wiki/bloch_wave a 7
Wavelength-dependence of the angle Works well for narrow-band simulations around a given center frequency f 0 : Then k = 2πf 0 sin(θ c 0 ) is constant Length of the k-vector is frequency dependent, i.e. k = k f = 2πf For a given frequency range f min, f max k min, k max As a result, θ f = sin 1 k k = sin 1 f 0 f sin(θ 0) c In broadband simulations with Bloch boundary conditions, different frequency components are injected at different angles! k 8
Current solutions to obtain broadband results For one or a few fixed angle(s): Run separate narrow-band simulations for each wavelength/frequency 100 frequency points 100x the computational time! To compute an angle-wavelength map Sweep the angle and re-interpolate the data https://kb.lumerical.com/en/ref_sim_obj_bloch_broadband_sweep.html 9
The Broadband Fixed-Angle Source Technique (BFAST) AVAILABLE IN RELEASE 2016A 10
Details on BFAST BFAST allows to inject light at a fixed angle over a broad spectrum! BFAST is not just a new type of boundary condition. The core algorithm is different from standard FDTD! It is based on the split-field method, but was customized to ensure compatibility with most existing material models and monitors! 11
Limitations of BFAST Two fundamental limitations: 1. Nonlinear and all flexible material plugin materials will not function using BFAST. 2. Injection above the critical angles for total internal reflection (TIR) is not stable. 12
Basic Example Transmission through a dielectric stack (4 layers) n=1.0 n=1.5 n=2.5 n=1.5 Broadband source (0.8μm 1.6μm) l 1 = 2.5μm l 2 = 2.5μm Frequency domain monitor 13
Results 14
Results (20 deg) 15
Results (40 deg) 16
Results (60 deg) 17
Performance Considerations BFAST simulations take more time than identical simulations with Bloch boundary conditions. Two contributions: 1. Angle-independent overhead: 1.5x - 4x 2. Angle-dependent factor: Δt~(1 sinθ) Rule of thumb: For angles > 60, it might still be faster to use Bloch BCs instead of BFAST. Angle θ [degrees] Simulation time 0 1.0x 10 1.2x 20 1.5x 30 2.0x 40 2.8x 50 4.3x 60 7.5x 70 16.6x 80 65.8x 19
Application Examples 21
500nm Lamellar Plasmonic Grating Gold surface with narrow but deep trenches Acts as a perfect absorber around λ 3.2μm Study angular dependence of reflectance spectrum 80nm Gold Nicolas Bonod et al., "Total absorption of light by lamellar metallic gratings," Opt. Express 16, 15431-15438 (2008) F. J. Garcia-Vidal et al., "Localized Surface Plasmons in Lamellar Metallic Gratings," J. Lightwave Technol. 17, 2191-2195 (1999) 2µm 22
FDTD Setup for the Lamellar Grating Narrow spectral features require high frequency resolution Also: a longer simulation time (20ps) and lower auto-shutoff tolerance (10 7 ) Frequency domain monitor (1001 pts) Broadband source (2.2μm 4.2μm) Strong field gradients in the slot require local mesh refinement Mesh refinement region (10nm) 23
Lamellar Plasmonic Grating Reflection spectrum under normal incidence 24
Lamellar Plasmonic Grating Comparison of Bloch BCs and BFAST (10 deg) Broadband simulation with Bloch BCs fails to accurately simulate this resonance (even at only 10 degrees). 25
Lamellar Plasmonic Grating Comparison of Bloch BCs and BFAST (20 deg) 26
Lamellar Plasmonic Grating Comparison of Bloch BCs and BFAST (30 deg) 27
Lamellar Plasmonic Grating BFAST allows convenient and accurate sweeps 28
Performance For BFAST, computational time increases with angle: Angle BFAST 0 3s 10 20s 20 25s 30 31s 40 56s Comparison with Bloch-sweep difficult due to varying auto-shutoff. A broad-band Bloch simulation takes about 15s (at 10 )! Computer: Intel Core i5-4460 (4 cores @ 3.2GHz) 29
Plasmonic enhanced solar cell Broadband simulation (400nm 1100nm) Contains highly dispersive media (silver and silicon) Symmetries can be exploited to accelerate the simulations kb.lumerical.com/en/index.html?solar_cells_plasmonic_at_normal_and_oblique_incidence.html 30
Plasmonic enhanced solar cell Normal incidence, standard FDTD Symmetries Materials Wavelength Simulation time 4 x reduction Silicon, Silver 400 1100 nm (351 points) 90 seconds BFAST FDTD (θ = 30 ) Symmetries Simulation time 2 x reduction 1800s << 15 x 400s Bloch BC (θ = 30, 15 wavelengths) Symmetries Simulation time 2 x reduction approx. 400s per λ 31
Summary The new Broadband Fixed-Angle Source Technique (BFAST) will be available in the next release of FDTD Solutions (2016A) Accurate broadband results can be obtained from a single simulation Faster simulations for a fixed angle of incidence More convenient and/or accurate for angle-wavelength sweeps Significant performance gains for broad spectra and moderate angles (below 45 degrees) 32
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