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) 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

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

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]

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 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)

The two lowest modes Effective mode index Stress No stress Difference neff1 1.450871 1.449898 9.73e-4 neff2 1.451135 12.37e-4 mode splitting

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