RF MODULE

includes only two independent parameters, B 1 and B 2 . The stress-optical relation
simplifies to
where n x = n 11, n y = n 22, n z = n 33, σ x = σ 11, σ y = σ 22, and σ z = σ 33.
This translates to
∆n x
∆n y
∆n z
Using the two parameters B 1 and B 2, the model assumes that the nondiagonal parts
of n ij and σ kl are negligible. This means that the shear stress corresponding to
σ 12 = τ xy is neglected. In addition, the shear stresses corresponding to σ 13 = τ xz and
σ 23 = τ yz are neglected by using the plane strain approximation. The plane strain
approximation holds in a situation where the structure is free in the x and y directions
but where the z strain is assumed to be zero. Note that this deformation state is not
correct if the structure is free also in the z direction. In such a case a modified
deformation state equation, which handles the x and z directions equivalently, is
needed.
The first part of this model utilizes the Plane Strain application mode of the Structural
Mechanics Module. The resulting birefringent refractive index is computed using
expression variables and can be considered a postprocessing step of the plane strain
model. The refractive index tensor is used as material data for the second part of the
model, the mode analysis.
The model “Stress-Optical Effects with Generalized Plane Strain” on page 277
demonstrates a computation where the structure is free also in the z direction, using a
formulation called generalized plane strain.
Perpendicular Hybrid-Mode Waves
=
–
nx = n0 B2σx ny = n0 B2σy nz =
n0 B2σz B 2 B 1 B 1
B 1 B 2 B 1
B 1 B 1 B 2
For a given frequency ν, or equivalently, free-space wavelength λ 0 = c 0 /ν, the RF
Module’s Perpendicular Hybrid-Mode Waves application mode can be used for the
mode analysis. In this model the free-space wavelength is 1.55 µm. The simulation is
σ x
σ y
σ z
– – B1( σy + σz) – – B1( σz + σx) – – B1( σx + σy) STRESS-OPTICAL EFFECTS IN A SILICA-ON-SILICON WAVEGUIDE | 261