Stress induced-Optical Effects in a Photonic Waveguide
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Transcript of Stress induced-Optical Effects in a Photonic Waveguide
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Stress induced-Optical Effects in a Photonic Waveguide
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The materials have different thermal expansion coefficients, i
T = 1000 T = 1000 CC
T = 20 T = 20 CC
• Waveguide layers are grown at high temperatures
• Thermally induced stresses remain at the operating temperature resulting in a weakly birefringent material
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AirCladding (SiO2)
Buffer (SiO2)
Silicon Wafer (Si)
Core (doped SiO2)
• Variations in the z-direction are neglected thus reducing the problem to 2D
• The optical core and planar waveguide layers are made of Silica (SiO2) which is deposited unto a Silicon (Si) wafer
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• The 2D plane strain approximation with thermal loads is used for the structural part of the model
• An exact perpendicular hybrid-mode wave formulation is used for the optical mode analysis
Displacement constrained in x, and y -directions
Displacement constrained in the y-direction
Optical computational domain with PEC boundary conditions,
0En
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Relation between the refractive index and stress tensors
nx = n0 – B1 σx – B2 [σy + σz] ny = n0 – B1 σy – B2 [σz + σx]
nz = n0 – B1 σz – B2 [σx + σy]
nij = -Bijklkl
Stress-optical tensor
Stress tensor
Refractive index tensor, nij-n0Iij
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Stress analysis• The extension of the
layers in the x-direction is chosen to minimize the horizontal stresses
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Refractive index
Vertical birefringence
Horizontalbirefringence
• A constant horizontal birefringence means that the influence of the edges is reduced to a minimum
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Mode analysis
• Visualization of the power flow, also called the optical intensity or the Poynting vector, in the z-direction (out of plane direction)
• We will study optical modes for a free-space wavelength of 1.55 m
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Effective mode index
Stress No stress Difference
neff1 1.450871 1.449898 9.73e-4
neff2 1.451135 1.449898 12.37e-4
mode splitting
The two lowest modes
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Mode analysis, higher eigenmodes
Larger energy leakage compared to lower modes