**4.1 2D approximation for the effective index**

A transverse view of the structure is shown in **Figure 8**. The two waveguides are separated by 300 nm of Al0.3Ga0.7As. **Figure 9** presents a simulation of light propagation along the structure by a beam propagation method (BPM), which has been carried out with the commercial software RSoft. To reduce calculation time and quickly converge on an intuitive model, we first make a 2D effective-index approximation, whose validity will be checked in the next section. The injected mode, visible on the right-end side of **Figure 9a**, is the eigenmode presenting the highest overlap with the active region. As is visible from **Figure 9b**, 90% of the guided power is contained in the laser core layer at Z = 0, that is, before the taper. Thus, modal gain is expected to not suffer from the presence of the underlying GaAs layer. From Z = 0 to Z = 300 μm, the two top layer widths are reduced from 4 μm to 0. From Z = 300 μm to Z = 500 μm, the separation layer (Al0.3Ga0.7As) width is reduced in the same way. Over 95% of the power is transferred to the GaAs waveguide. To estimate the robustness of the design to a limited resolution in lithography, we simulate the same transfer with widths ending at 0.4 μm instead of 0: the transfer of power to the underlying waveguide is 85%. While a more detailed set of tests would be necessary to account for fabricationinduced deviations, these results are encouraging.

In order to find out if the power in the slab is in the desired TE2 mode, we calculate the overlap of the BPM-simulated field with the GaAs waveguide eigenmodes. The result, reported in **Figure 10**, is that 97% of the power is in the TE2 mode after one transfer length.
