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Multiphysics Modeling of Electro-Optic Devices
James E. Toney
SRICO, inc.
October 13, 2011
Presented at the 2011 COMSOL Conference
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Outline
• Combined RF-Optical mode analysis
– RF waveguide mode
– Optical waveguide modes
– Electro-optic interaction
• Combined wave propagation
– Paraxial optical propagation
– DC modulation
– Time-dependent RF modulation
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The Workhorse Electro-Optic Device: Mach-Zehnder Interferometer
Df=p Df=0
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Coplanar Waveguide Structure
Optical waveguides
Electrodes
Buffer Layer
Substrate
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Geometry for RF and Optical Mode Solving in Comsol
air
LiNbO3
Au electrodes
SiO2
buffer
layer Initial dopant regions
w= 8 mm, g=28 mm, tm = 30 mm, tb = 1 mm, eb = 3.8, esub =[28,44,44] Optical waveguide profile is defined by diffusion equation
PEC boundary
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Electric Displacement Field (Dx) of RF Mode
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RF Mode Effective Index and Loss vs. Frequency
a= -2pf Im(neff)/c
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Characteristic Impedance vs. Frequency
Z0 = 2 P / |I|2
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Optical Waveguide Mode Splitting with Applied E-Field
Dno/e= -½ no/e3ri3 Ex
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Velocity Matching Bandwidth and Half-Wave Voltage vs. Device Length
fc = c / (2 nm L d) d = 1 - (no/nm) Vp = l / [2 (Dn/V) L] [does not incorporate electrode losses]
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Simplified 2D MZI Model with DC Electrodes
V=0
V=24 V
• Scalar Paraxial Wave Equation for Optics •Electrostatics •Stationary Solution
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Transmission of 2D MZI Model vs. DC Voltage
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Simplified 2D MZI Model with RF Electrodes
• Time-Dependent EM Wave Propagation for RF •Scalar Paraxial Wave for Optics (stationary solution at each time step)
Input/Output Waveforms @fin = 1 GHz
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Conclusions
• Comsol Multiphysics provides complete capabilities for modeling of electro-optic devices
• With adequate computational resources, 3D EO propagation models are possible