Diploma thesis

and 3.10).
Figure 3.9: 0-0 waveguide mode Figure 3.10: 0-1 waveguide mode
In geometrical optics, the light rays are not travelling straight through the waveguide,
but are reflected up and down from left to right inside the guiding structure
(see Figure 3.11). Therefore, we cannot assume a linear propagation of the waves
through the crystal like in our derivation in Equation 3.23. In a 2-dimensional
waveguide, with perfect conducting edges and width and height b, it is possible to
consider these effects by introducing an effective refractive index [19].
neff ≈
�
nbulk − 2
� �2 λ
2b
(3.32)
However, this model is rather crude. It neither considers evanescent waves nor wave
propagation in the bulk crystal nor higher order spatial modes (Figure 3.12).
Figure 3.11: Light propagation Figure 3.12: Different spatial modes
For a consideration of these effects, we have a more advanced model [19] available,
that has already been implemented [20]. It accounts for evanescences in the
surrounding material and transversal modes. The differences, in refractive indices
between bulk crystal and slab waveguide and a waveguide with evanescences are not
negligible (Figure 3.13).
This model predicts different refractive indices for different spatial modes (Figure
3.14). That way multiple spatial modes in the waveguide introduce several slightly
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