Soliton refraction and Goos–Hänchen shifts at diffusion step nonlocal interfaces

Diffusive Kerr-type interfaces separating media that differ only in the diffusion strength are studied within the Helmholtz framework. We obtain an analytical expression for a soliton effective nonlinear refractive index that takes into account diffusion. A discontinuity in this coefficient makes a soliton undergo external refraction after entering a second medium with a higher diffusion strength. Our theory also predicts total internal reflection and giant Goos H\"anchen shifts when the diffusion is higher in the first medium. Numerical simulations are used to test the validity of the model showing an excellent agreement with theoretical predictions.