waveguide bragg gratings and resonators · 2016-07-04 · account for multiple-reflection events...
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Waveguide Bragg Gratings and Resonators
JUNE 2016
© LUMERICAL SOLUTIONS INC1
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OutlineIntroduction
Waveguide Bragg gratings Background Simulation challenges and solutions Photolithography simulation
Initial design with FDTD Band structure calculation and effect of geometric parameters
Simulation of the full device using EME Waveguide Bragg grating Phase shifted Bragg grating
Circuit simulations with INTERCONNECT Compact model for WBG Hybrid laser
Summary and Q/A
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Lumerical Products
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Component Design System Design
FDTD SolutionsNANOPHOTONIC SOLVER (2D/3D)
MODE SolutionsWAVEGUIDE DESIGN ENVIRONMENT
Optical Simulation Electrical Simulation
DEVICECHARGE TRANSPORT SOLVER (2D/3D)
Thermal Simulation
DEVICEHEAT TRANSPORT SOLVER (2D/3D)
Circuit Simulation
INTERCONNECTPHOTONIC INTEGRATED CIRCUIT SIMULATOR
InteroperabilityCadence VirtuosoMentor Graphics PyxisPhoeniX OptoDesigner
Model LibrariesCompact ModelGeneration and Management
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Optical Solvers for Different Length ScalesEigenmode analysis MODE Solutions Eigenmode solver (FDE)
Propagation methods INTERCONNECT 1D traveling wave
MODE Solutions 2.5D variational FDTD (varFDTD)
Bidirectional eigenmode expansion (EME)
FDTD Solutions 2D/3D finite difference time domain (FDTD)
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Increasing accuracyIncreasing computational cost
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Finite Difference Time Domain (FDTD) SolverRigorous time domain method for solving Maxwell’s equations in complex geometries: Few inherent approximations
General technique: many types of problems and geometries
Broadband results from one simulation
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Eigenmode Expansion (EME) SolverRigorous frequency domain solver for Maxwell’s equations Account for multiple-reflection events Only one simulation for all input/output modes and polarizations Ideal for long passive components: computational cost scales well with
propagation distance
Scattering matrix formulation Define interfaces and calculate modes Boundary conditions applied at each interface
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Waveguide Bragg Gratings
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What is a Waveguide Bragg Grating?1D photonic bandgap structure Straight waveguide with a periodic perturbation
Wavelength specific dielectric mirror ~100% reflection over a range of frequencies
~100% transmission otherwise
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Basic design of a waveguide mirrorFind condition for constructive interference of reflections Wavelenght in the waveguide: l=l0/neff
Reflected waves will be in phase if 2*a = m*l
Bragg condition for first-order grating (m=1): l0=2*a*neff
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a
N x a
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Basic design of a waveguide mirrorIt is also possible to scatter light out of the structure Another constructive interference condition
Used to design grating couplers
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a
q
cladding
oeff
n
am
nl
q
)sin(
ncladding
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Band structure analysisBelow the light line, the Bragg grating can selectively transmit or reflect light along the waveguide
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b (2p/a)
f(c
/a)
bandgap
Lightline
mirrorlow loss waveguide
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Band structure analysisBelow the light line, the Bragg grating can selectively transmit or reflect light along the waveguide
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b (2p/a)
f(c
/a)
bandgap
Lightline
mirrorlow loss waveguide
|E| at 1550nm
|E| at 1500nm
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Band structure analysisAbove the light line, we can scatter light out of the structure: grating coupler
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b (2p/a)
f(c
/a)
bandgap
lightlinef=b/nsub
mirrorlow loss waveguide
grating coupler
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Simulation Challenges and Solutions
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Challenges FDTD Simulation size: full device is usually many
periods long
EME Modes can be very discontinuous Many wavelengths required to resolve
spectrum: one simulation per wavelength in frequency-domain solvers
Geometry effects Lithography effects Corrugation depth and misalignment
Initial design with FDTD Simulate unit cell with Bloch-periodic boundary
conditions Calculate center wavelength and bandwidth
Full simulation with EME Quickly simulate many periods Check convergence by increasing number of modes To resolve the spectrum scan grating period length
instead of wavelength
Lithography corrected structure
Sweeps over corrugation depth and misalignment
Circuit simulations with INTERCONNECT
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Photolithography Effects
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Waveguide Bragg grating designed with 40 nm square corrugations
FDTD simulations of photolithography simulated design matches experimental Bragg bandwidth Lithography simulation with Mentor
Graphics’ Calibre
Original
Xu Wang, et al., "Lithography Simulation for the Fabrication of Silicon Photonic Devices with Deep-Ultraviolet Lithography", IEEE GFP, 2012
Litho simulated
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Photolithography simulationFraunhoffer diffraction at mask Infinitely thin metal (ignored plasmonic or polarization effects)
Simple resist model (defined by a threshold level)
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(a) (b) (c)
J. Pond, et al., "Design and optimization of photolithography friendly photonic components", Proc. SPIE, vol. 9751, 3/2016.
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Photolithography simulation
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Mask
Image
Resist threshold
Polygon outline
Three key parameters:• Projection NA • Spatial coherence factor• Resist threshold
(a)
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Initial design with FDTD
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Band structure calculationSimulate unit cell of Waveguide Bragg grating in FDTD Mode source (other sources also possible)
Bloch-periodic boundary conditions Set appropriate Bloch wavevector -π/a < kx < π/a
Band gap usually at kx = π/a
Calculate spectrum from time monitors
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KB example: https://kb.lumerical.com/en/index.html?pic_passive_bragg_initial_design_with_fdtd.html
DEMO!
PML
PML
Blo
ch-p
erio
dic
Blo
ch-p
erio
dic
Antisymmetric
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Band structure analysisSweep over kx to get full band structure
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E(t)
Signal from time monitor
b (2p/a)
f(c
/a) bandgap
bandgap
(THz)
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Effect of corrugation depthSweep over grating depth
Coupling coefficient: 𝜅 =𝜋𝑛𝑔Δ𝜆
𝜆02
Δ𝜆 bandwidth
𝜆0 center wavelength
𝑛𝑔 group index at 𝜆0
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Effect of misalignment
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∆L
Xu Wang, et al., "Precise control of the coupling coefficient through destructive interference in silicon waveguide Bragg gratings", Optics Letters, vol. 39, issue 19, pp. 5519-5522, 10/2014.
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Effects of photolithography
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DW
W
DEMO!
Use script for photolithography simulation
J. Pond, et al., "Design and optimization of photolithography friendly photonic components", Proc. SPIE, vol. 9751, 3/2016.
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Effects of photolithography
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DW (nm) DW (nm)
Excellent agreement between simulation and experimental results:
J. Pond, et al., "Design and optimization of photolithography friendly photonic components", Proc. SPIE, vol. 9751, 3/2016.
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Simulation of Full Device using EME
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WBG: Simulation Setup in EMEWithout lithography effects Two cell groups (one per waveguide
thickness)
One cell per group
Start with 10 modes in every cell
Set the number of periods in EME settings
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WBG: Simulation Setup in EMEWith lithography effects One cell group for the entire unit cell
Start with 10 cells to resolve curvature
Make sure the mesh is fine enough
Start with 10 modes in every cell
Set the number of periods in EME settings
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Full Spectrum SimulationThe propagation length and number of periods can be modified without having to recalculate any modes, and the result can be calculated instantly
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10um taper 100um taper
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WBG: Full Spectrum SimulationBrute force method Run one simulation per wavelength
Efficient approach Solve device for one reference wavelength
Stretch or compress each cell to create an equivalent wavelength change and calculate results at all desired wavelengths
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𝛼 = 1 +𝑛𝑔
𝑛𝑒𝑓𝑓
𝜆𝑟𝑒𝑓
𝜆− 1Length scale factor:
DEMO!
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Phase-Shifted Bragg GratingsIntroduce a phase shift in the middle of the grating to create a sharp resonant peak within the stop band Sharp filter for integrated optical circuits
Sensor applications
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P. Prabhathan, et al., “Compact SOI nanowire refractive index sensor using phase shifted Bragg grating", Optics Express, Vol. 17, No. 17, 2009
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Full Spectrum SimulationUse same efficient approach as for WBG to get full spectrum Period = 320nm
Number of periods = 100
Cavity length = 320nm
Corrugation length = 20nm
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Full Spectrum Simulation
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Brute force approach (101 wavelength points) Fast approach (501 wavelength points)
KB example: https://kb.lumerical.com/en/index.html?pic_passive_bragg_phase_shifted.html
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Optimizing with EMEEfficiently optimize devices requiring Length scanning such as tapers
Modifying the number of periods
There are often tricks to avoid the disadvantage of EME when scanning wavelength
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Circuit Simulations with INTERCONNECT
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What do we want?A table that maps our design parameters to bandwidth and operating wavelength We can create compact models for PDKs
Large scale circuit design and simulation becomes easy
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DW
W
W DW Bandgap Operating wavelength
500 nm 40 nm 10 nm 1550 nm
500 nm 50 nm 12 nm 1550 nm
… … … …
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WBG Compact modelWBG PCell (will be available in Lumerical CML) Quickly simulate phase shifted Bragg grating
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DEMO!
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WBG in Hybrid LasersWBG selective reflectivity single-mode operation in a laser
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More info: https://www.lumerical.com/support/video/modeling_lasers.html
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SummaryWaveguide Bragg gratings can be Waveguides Frequency selective mirrors Grating couplers
Simulation with FDTD – bandstructure of infinite device EME – finite device, finite device with defect INTERCONNECT – calibrated traveling wave model
Many applications Filters Laser mirrors Sensors …
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