**Figure 2.**

*Effective indices of guided modes in the structure. (Red) Index of the laser mode as a function of guide width. (Orange) Indices of guided modes in the buried waveguide, assuming a planar waveguide of Al0.1Ga0.9As (left) or GaAs (right) surrounded by Al0.3Ga0.7As on one side and Al0.8Ga0.2As on the other.*

The waveguide core should hold as little aluminum as possible in order to increase its nonlinear susceptibility. We set the exact Al fraction by comparing the effective index of guided modes in the upper waveguide to the effective index of the lower waveguide as taper width is reduced (**Figure 2**). For 10% Al composition, the laser mode index crosses the index of TE1 in the buried waveguide. We can thus expect the mode to couple to TE1. Using pure GaAs, the laser mode crosses only the TE2 index, which is the desired configuration. Absorption in GaAs at 1 μm is expected to be negligible [14]. Setting a pure GaAs waveguide has another advantage: it eliminates the uncertainty on the Al fraction.
