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The relationship between waveguide separation and coupling coefficient is characterized with a test chip containing varying spaced waveguides. This relationship follows an exponential decay κ = aebd, where a = 115 cm−1 and b = 0.36 μm−1 are experimentally measured constants and d is the separation between the waveguides. We can invert this function to find the waveguide separation necessary to achieve the desired coupling coefficients in Eq. 2. These κn(z) coupling coefficients control the transfer of the topological boundary state from the sides of the array to the center.

We numerically optimized the coupling coefficient c in Eq. 1 such that the boundary states couple with 50% probability. This implements a 50:50 beamsplitter operation. Finally, the waveguide separations were adjusted to transfer the boundary states back to the sides of the array.

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