Mechanism of apparent gain observed in focused beam measurements of a planar FSS

Apparent gain in focused beam measurements (tenths of a dB above 0 dB for calibrated VNA transmission) has been observed on many occasions for low loss resonant structures that include photonic/electromagnetic band-gap (PBG/EBG) structures [1] or frequency selective surface (FSS) stacks [2]. The authors are unaware of any previously published explanations perhaps due to the small magnitude of deviation. However, for a device with tight specifications, tenths of a dB deviation without explanation may be unacceptable, and transmission coefficient data greater than 0 dB can create controversy. This paper will demonstrate that the apparent gain seen in focused beam measurements occur due to radiation via mutual coupling from FSS elements not directly illuminated. Radiation from these elements increases the directivity of the stack resulting in an effective gain as measured by a VNA.