1. Stress induced-Optical Effects in a Photonic Waveguide

2. 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

3. Variations in the z-direction are neglected thus reducing the problem to 2D
Air
Cladding (SiO2)
Buffer (SiO2)
Silicon Wafer (Si)
Core (doped SiO2)
The optical core and planar waveguide layers are made of Silica (SiO2) which is deposited unto a Silicon (Si) wafer

4. 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
Optical computational domain with PEC boundary conditions,
Displacement constrained in x, and y -directions
Displacement constrained in the y-direction

5. Relation between the refractive index and stress tensors
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]

6. Stress analysis
The extension of the layers in the x-direction is chosen to minimize the horizontal stresses

7. Refractive index
Vertical birefringence
Horizontal birefringence
A constant horizontal birefringence means that the influence of the edges is reduced to a minimum

8. Mode analysis
We will study optical modes for a free-space 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)

9. The two lowest modes Effective mode index Stress No stress Difference
neff1
9.73e-4
neff2
12.37e-4
mode splitting

10. Mode analysis, higher eigenmodes
Larger energy leakage compared to lower modes