Stress inducedOptical Effects in a Photonic Waveguide Waveguide

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 2 D Air Cladding (Si. O 2) Buffer (Si. O 2) • The optical core and planar waveguide layers are made of Silica (Si. O 2) which is deposited unto a Silicon (Si) wafer Core (doped Si. O 2) Silicon Wafer (Si)

• The 2 D 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, 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-n 0 Iij Stress-optical tensor nx = n 0 – B 1 σx – B 2 [σy + σz] ny = n 0 – B 1 σy – B 2 [σz + σx] nz = n 0 – B 1 σz – B 2 [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 neff 1 1. 450871 1. 449898 9. 73 e-4 neff 2 1. 451135 1. 449898 12. 37 e-4 mode splitting

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