Disclosed here are systems and methods which enable high-bandwidth communication between a mobile device and an accessory. The high-bandwidth communication uses electromagnetic waves in the extremely high frequency range between 30 GHz and 300 GHz inclusive, also known as millimeter waves. The millimeter waves travel through at least the chassis of the accessory and the chassis of the mobile device without significant scattering and attenuation. The properties of the materials through which the millimeter waves travel determine the attenuation of the millimeter waves. Disclosed here are various materials, and their thicknesses, which form a transmission stack through which the millimeter waves can travel unimpeded. In effect, the transmission stack acts as a dielectric member which facilitates the transmission of the millimeter waves, while attenuating transmission of waves outside of the extremely high frequency range.