The altering permittivity tensor of a hyperbolic medium from diagonal to off-diagonal by the constructive manipulation of the optical axis (also called tilted hyperbolic medium) has attracted much interest recently. Here, the electromagnetic field solutions of waves interacting with a tilted hyperbolic medium are established. Detailed calculations reveal that when a transverse magnetic (TM) polarized wave is incident from a tilted hyperbolic medium to a dielectric medium, tangential components of electric fields are expected to be discontinuous at the interface. Extraordinary surface voltages are induced at the inner boundary of the tilted hyperbolic medium, which prevents the reflection of electromagnetic waves. This alternative behavior of induced extraordinary surface voltages enriches the understanding of continuity across the boundary and provides a novel perspective for their realizations among multiple experimental platforms.
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