Analysis and design of electromagnetic crystals in microstrip technology using a fibre grating model

Electromagnetic crystals (EC) in microstrip technology have been recently proposed as efficient Bragg reflectors. They are implemented by etching the ground plane or by drilling the substrate following a periodic pattern. In this paper we propose a simple and fast fibre Bragg grating (FBG)-based model for the synthesis and analysis of these microstrip ECs with sinusoidal patterns. The method rests on the analogy found between the frequency responses of a microstrip EC and a FBG. Based on this analogy, an equivalence relationship between the physical parameters of a microstrip EC and those of an equivalent FBG has been established. The equivalence assures that the frequency response of the microstrip EC is a down-shifted replica of the one corresponding to its equivalent FBG. This model avoids the use of the time-consuming electromagnetic calculations involved in the analysis of the microstrip ECs as well as the trial method employed until now in the synthesis, since a FBG response arises immediately from coupled-mode theory. At the same time the theoretical difficulties encountered in the formal derivation of coupled-mode theory for microstrip ECs are also avoided by the equivalence relationship found.