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Parallel 3D FDTD Simulator for Photonic Crystals

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Parallel 3D FDTD Simulator for Photonic Crystals

  1. 1. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  2. 2. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. http://www.iqol.uwaterloo.ca http://oxfordplasma.de Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  3. 3. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. Si •  Crystal – periodic arrangement of atoms/molecules •  Propagating electrons “see” periodic potential due to atoms/molecules. •  Conduction properties dictated by crystal geometry. •  Crystal lattice introduces energy bandgap (Eg) freq [c/a] •  Optical analogy is photonic crystal •  Periodic potential due to lattice of dielectric material. •  Propagation of photons controlled by dielectric contrast and (r/a) ratio. Band Gap •  Can engineer a photonic bandgap Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  4. 4. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. •  Photonic crystals/PBM shown great deal of promise for true integrated optics. •  Waveguides with small bends possible making compact integrated photonic circuits (IPCs) achievable. •  Design/fabrication is challenging •  Efficient simulation tools needed to realize very low loss IPCs rods http://www/photonics.tfp.uni-karlsruhe.de/research.html http://pages.ief.u-psud.fr bend splitter resonator cavity Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  5. 5. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. y x 2D slice εr = 12.0 z •  Specific PC geometry requires many grid cells (~107 cells) to resolve even a limited number of periods. •  Memory intensive computations. •  Modeling of 3D PCB structures dictates vital need for parallel HPC architectures with optimized domain decomposition. εr = 1.0 a Simple example: 370 x 520 x 50 (~107 grid points) 4.5Gb RAM needed (Target SPAWAR 3D structure) Realistic grids > 109 points Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  6. 6. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. In isotropic medium, Maxwell’s curl equations are:   ∂H ∇ × E = −µ ∂t   ∂E  ∇× H = ε +J ∂t K.S. Yee, IEEE Trans. Antennas Propagat., 14(302) 1966 ∂H x ∂Ez ∂E y ∂Ex ∂H z ∂H y −µ = − ε = − − Jx, ∂t ∂y ∂z ∂t ∂y ∂z   
Direct explicit solution of Maxwell’s equations ∂H y ∂Ex ∂Ez ∂E y ∂H x ∂H z (i.e. no matrix inversion required). −µ = − ε = − − Jy, ∂t ∂z ∂x ∂t ∂z ∂x   2nd order accurate. ∂H z ∂Ex ∂E y ∂Ez ∂H y ∂H x   Complete “full-wave” method without −µ = − ε = − − Jz. ∂t ∂y ∂x ∂t ∂x ∂y approximation (i.e. no pre-selection of output modes or solution form necessary.)   Easy to parallelize. Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  7. 7. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. • 
Introduces “artificial” anisotropic electric/magnetic* conductivities within domain boundaries allowing for absorption/attenuation waves. •  Employs a numerical “split-field” approach allowing perfect (theoretical) transmission into absorbing layer (regardless of frequency, polarization, or angle of incidence). •  Perfect electric conductor (PEC) surrounds PML ABC •  Technique “simulates” effect of J. P. Bérenger, IEEE Trans. Antennas Propagat., 44(110) 1996. outward propagation of EM waves to infinity. Ex = Exy + Exz ∂Exy ∂ ( H zx + H zy ) ∂Ex ∂H z ∂H y H y = H yz + H yx ε + σ y Exy = ε = − − Jx, H = H + H ∂t ∂y ∂t ∂y ∂z z zx zy ∂Exz ∂ ( H yz + H yx ) ε + σ z Exz = − Nanostructures Research Group ∂t ∂z CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  8. 8. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. •  Stability limit, called the CFL 1 Δt FDTD ≤ 2 2 2 criterion limits maximum timestep ⎛ 1 ⎞ ⎛ 1 ⎞ ⎛ 1 ⎞ for solution of PDEs on a finite υ max ⎜ ⎟ +⎜ ⎜ Δy ⎟ + ⎜ Δz ⎟ ⎟ ⎝ Δx ⎠ ⎝ ⎠ ⎝ ⎠ grid. R. Courant, et al. , IBM Journal , 215(1967). •  For example, a uniform grid of 1nm in Si (εr=12) results in: Alternate-Direction Implicit Approach •  Timestep split into (2) sub-iterations 12 •  E-fields updated implicitly along Δt FDTD ≤ 2 specific directions. ⎛ 1 ⎞ (3 × 108 m ) 3 ⎜ ⎟ •  H-fields updated explicitly throughout. s −9 ⎝ 1× 10 m ⎠ y z RELAXES Δt FDTD ≤ 6.7 × 10−17 s ⇒ 0.067 fs CFL LIMIT Long simulation times ! T. Namiki, IEEE MTT 47(10), 2003 (1999). F. Zheng, et. al, Microwave Guided Nanostructures Research Group x Wave Lett., 9(11), 441 (1999). CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  9. 9. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. z PML y Air PC Slab Air PML 370 x 520 x 50 grid x ~107 grid points Si slab (εr =12.0) (PML completely surrounds simulated structure) cylinders (εr =6.0) 50 Si cylinders Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  10. 10. 370 x 520 x 50 grid Source plane DISTRIBUTION STATEMENT A: Cleared for public releases; Gaussian pulse ~107 grid points tw = 15 ps Si slab (εr =12.0) distribution is unlimited. 50 cylinders (εr =6.0) Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  11. 11. Source plane 370 x 520 x 50 grid Bipolar pulse ~107 grid points DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. Si slab (εr =12.0) 44 cylinders (εr =6.0) Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  12. 12. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. •  When cylinders are built in domain, each grid cell is divided into 9 subcells •  The dielectric contribution of each 1/9 of a grid cell is computed for those subcells completely within the cylinder radius. •  Results in smoothing around the stair -cased edges of cylinders y x z Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  13. 13. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. Task 0 Setup Parallel Region Initial Scatter Task 1 Task N BC's BC's BC's calc H field calc H field calc H field calc E field calc E field calc E field Communication – plane exchange Output & Finish Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  14. 14. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. •  Both 1D and 3D decompositions have been implemented within the MPI framework of the simulator •  In order to reduce the computation steps, redundant calculations at boundary regions were employed [Hanawa et al., IEEE Trans. on Mag, 43(4), 1545 (2007)] Speedup of SPAWAR vs. ASU code •  Initial 1D decomposition resulted in good scaling for long crystal geometry Interprocessor boundary Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  15. 15. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. •  Speedup for increasingly larger domains. Interprocessor boundary Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  16. 16. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited. •  3D decomposition worked best for more general geometries and particularly for large problem domains •  This is the default decomposition in the code delivered to DoD user community. Nanostructures Research Group CENTER FOR SOLID STATE ELECTRONICS RESEARCH
  17. 17. DISTRIBUTION STATEMENT A: Cleared for public releases; distribution is unlimited.   Benchmarking of parallel ADI-FDTD code. (reduced simulation times)   Demonstration of 3-layer 3D PCG structures and circuits. J. S. Rodgers, “Quasi-3D photonic crystals for nanophotonics,” Proceedings of SPIE, vol. 5732, Quantum Sensing and Nanophotonic Devices II, Manijeh Razeghi, Gail J. Brown, Editors, March 2005, pp. Nanostructures Research Group 511-519. CENTER FOR SOLID STATE ELECTRONICS RESEARCH

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