I was wondering if surface electromagnetic waves can propagate at interface between two dielectrics, both isotropic and homogeneous, but having different relative permittivities.
The literature shows that their characteristics must be different.
You are probably right - these seem to be any number of differences between properties that can support a surface wave. See the presentation below.
http://emlab.utep.edu/ee5390em21/Lecture%2021%20--%20Surface%20waves.pdf
There are no longer any controversies regarding trapped electromagnetic surface waves along the boundaries in layered materials (as in the case of the Zenneck surface wave, dating from 1907). A detailed overview of the historical and recent developments in the field can be found in [1].
[1] K Li, Electromagnetic Fields in Stratified Media (Springer, Berlin, 2009). https://www.springer.com/us/book/9783540959649
The surface wave is pressed against the dielectric. There will be two surface waves.
The solution depends on the boundary conditions of the problem.
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