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. References: 13
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