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Stress induced-Optical Effects in a
Photonic Waveguide
• Waveguide layers are grown
at high temperatures
The materials have different
thermal expansion
coefficients, i
T = 1000 C
T = 20 C
• Thermally induced stresses
remain at the operating
temperature resulting in a
weakly birefringent material
• Variations in the z-direction
are neglected thus reducing
the problem to 2D
Air
Cladding (SiO2)
Buffer (SiO2)
• The optical core and planar
waveguide layers are made
of Silica (SiO2) which is
deposited unto a Silicon (Si)
wafer
Core (doped SiO2)
Silicon Wafer (Si)
• The 2D plane strain
approximation with thermal
loads is used for the structural
part of the model
• An exact perpendicular hybridmode wave formulation is used
for the optical mode analysis
Optical computational domain
with PEC boundary conditions,
nE  0
Displacement
constrained in x,
and y -directions
Displacement
constrained in the
y-direction
Relation between the refractive index and
stress tensors
Stress tensor
nij = -Bijklkl
Refractive index
tensor, nij-n0Iij

Stress-optical tensor
nx = n0 – B1 σx – B2 [σy + σz]
ny = n0 – B1 σy – B2 [σz + σx]
nz = n0 – B1 σz – B2 [σx + σy]
Stress analysis
• The extension of the
layers in the x-direction
is chosen to minimize
the horizontal stresses
Refractive index
Vertical
birefringence
Horizontal
birefringence
• A constant horizontal birefringence
means that the influence of the edges
is reduced to a minimum
Mode analysis
• We will study optical
modes for a freespace wavelength of
1.55 m
• Visualization of the
power flow, also called
the optical intensity or
the Poynting vector, in
the z-direction (out of
plane direction)
The two lowest modes
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
Mode analysis, higher eigenmodes
Larger energy
leakage compared
to lower modes