Stress induced-Optical Effects in a Photonic Waveguide

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

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

• 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

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

Stress analysis• The extension of the

layers in the x-direction is chosen to minimize the horizontal stresses

Refractive index

Vertical birefringence

Horizontalbirefringence

• A constant horizontal birefringence means that the influence of the edges is reduced to a minimum

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

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

Mode analysis, higher eigenmodes

Larger energy leakage compared to lower modes