Waveguide for electromagnetic radiation

A waveguide for electromagnetic radiation, which is a substrate integrated waveguide, comprising:

• a substrate layer of dielectric material;
• a bottom layer and a top layer of an electrically conductive material provided on the respective bottom surface and top surface of the substrate layer;
• a plurality of pillars of electrically conductive material which extend through the substrate layer from the bottom surface to the top surface and which are electrically connected to the bottom layer and top layer;
• wherein at least one of the bottom layer and top layer contains at least one part that is void of electrically conductive material, which part is referred to as a slot;
• wherein
• the at least one slot is delimited, in the plane of the respective layer in which it is present, by a contour which is defined by an x and y coordinate which fulfils the following equations:
• x(ϕ)=cxR(ϕ)cos(ϕ)
• y(ϕ)=cyR(ϕ)sin(ϕ)
• wherein:
• R
• 
• (
• φ
• )
• =
• [
• 
• cos
• 
• (
• m
• 1
• 
• φ
• 4
• )
• a
• 1
• 
• n
• 1
• +
• 
• sin
• 
• (
• m
• 2
• 
• φ
• 4
• )
• a
• 2
• 
• n
• 2
• ]
• 1
• b
• 1
• wherein the values for the parameters cx, cy, m1, m2, a1, a2, n1, n2 and b1 are selected from a group of real numbers of positive value, and φ is an angular coordinate that covers a range from −π to π;
• wherein the contour is not of a rectangular shape, not of a rounded rectangular shape, and not of a cross-shape.