Abstract: A window construction and method are presented for electromagnetic signal transmission having broad bandwidth capability plus excellent resistance to ablation, rain erosion and thermal shock. The window is constructed of an odd number of three or more (i.e., 3, 5, 7, etc.) layers of reinforced PTFE material, with the dielectric constant of each layer (other than the core layer which is selected) being equal to the square root of the product of the dielectric constants of the two bordering layers. In a three layer version, the outer layers each have a dielectric constant which is the square root of the dielectric constant of the center layer; or, stated conversely, the center layer has a dielectric constant which is the square of the dielectric constant of each of the outer layers.